摘要:

Contribution to the Theory of Electrochemical Phase Formation BY SARRIKHAI -f K. RANGARAJAN Electrochemistry Research Laboratories University of Newcastle upon Tyne Newcastle upon Tyne NE1 7RU Received 5th August 1977 A formalism to reflect the transient and steady state behaviour of phase formation is discussed. The "components " considered are (i) the nucleation (ii) electron transfer and (iii) mass transport. The current-potential behaviour and the role of a non-linear functional relationship between i and q are analysed with special reference to potential sweep and relaxation techniques (sinusoidal and rectification). Questions concerning multilayer growth and the three dimensional growth are considei ed. The stochastic nature of the problem is sketched.1. INTRODUCTION " Electrochemical phase formation " refers to a class of phenomena ranging from 2-dimensional condensation to the growth of anodic films on metal and semi-conductor substrates. For example this includes the so-called underpotential deposition and other manifestations of electrocrystallisation too. What motivates such a grouping is their phenomenological composition. What distinguishes these apparently un- connected observations is the role of individual constituents and the extent of coupling among them. Some fundamental constituents of electrochemical phase formation are :(a)several well studied interfacial phenomena like the (al)electron transfer (a2) adsorption (cf. adatoms impurities) and (a3) surface and bulk mass transport; (b) the "activation '' of nuclei a stochastic phenomenon and (c) the subsequent growth as controlled by the interfacial phenomena (a).Moreoever (d)the interaction qf centres the overlap effect being the most obvious determine the time dependent monolayer coverage and subsequently (e) the multilayer growth. More complex features like the presence of several interfaces (metal/film film/ solution) can be explicitly brought within this framework and even if not easy to solve certain epitaxial and morphological habits of growth. In this brief report we shall highlight some interesting (rather unique) features to be recognised by any theory of electrochemical phase formation. They are pheno- menological connectivity a highly nonlinear current-potential-time relationship and the stochastic components.More specifically we discuss the theory of potential sweep and also of linear and nonlinear relaxation techniques especially impedance and rectification methods. The sources of randomness and consequent fluctuations are discussed in passing. Ques-tions concerning the concentration polarisation are taken up too. t Permanent address Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012 India. THEORY OF ELECTROCHEMICAL PHASE FORMATION 2. PHENOMENOLOGICAL COMPOSITION Even an apparently simple model of nucleation and growth has several components coupled as illustrated in fig. 1. But the more interesting aspect is to be aware of the variables defined in this process and the phenomenological laws involvingthem.Table 1 indicates what may happen in a realisation. 7 a 1. electron transfer activation of nuclei current density X (q) density N (q,t) 03.03. massmass transporttransport monolayer coverage ;L_1 concentration c I J i flux In multilayer q FIG. 1 .-Schematic diagram showing connectivity of some phenomena constituting electrochemical phase formation. The primary variables are indicated. TABLE1.-ILLUSTRATING HOW THE VARIABLES IN THE SEVERAL PHENOMENA ARE COUPLED. REFER TO FIG 1 FOR NOTATION. phenomena variables rate law associated (4 s Stq t) = 1 -exp (-S,) (4 4 q/qm= S/(l -S) i(q,t) = dq/dt remarks K(q) refers to the peripheral growth and (q)to the values at the growth sites; con-czntration dependence implicit.2 is a non-linear operator. Diffusion to a changing boundary. m:constant = 2 for 2-D. g geometricfactor = n for a circle. A potential dependent nucleation " con-stant " cf. stochastic basis for the law. linear transformation of a random pro-cess; needs revision for a 3-D growth " pinned " to a substrate (cf. section 7). Avrami's law for overlap. cf. stochastic basis; non-linear transformation of the random process S,. cascade model for multilayer. Further non-linear (functional) transformation of Sx.4 S Laplace transforms of q S. SARRIKHAI K. RANGARAJAN 3. CURRENT-POTENTIAL RELATIONSHIP Even a cursory glance at table 1 shows that one has come a long way from the simple Tafel-like exponential laws ! Not only are there new potential dependent rates occurring " on the way " we find a somewhat complicating role introduced by the time variable too ! The well-known laws for 2-D models are 1*2* i(t) = 2q,gN,(y~K)~texp [-gN,(y~Kt)~] (1) (instantaneous) = qm-gANo(yeKt)2exp [-gAN,(y~K)~t~/3] (2) (progressive).Note that K(q) itself usually has exponential dependence on q. The functional form of A is less straightforward but is usually taken as1 A exp (-a/q). We want to emphasise that even eqn (1) is not informative if q is not a constant as for example in a potential sweep experiment. The general i-q-t behaviour has a functional form different from eqn (1). Explicitly expressed the charge q = / i dt for the phase formation at time t is 4 = qm[l -exp (-Sx)l (3) dVl2 dz- (4) where SXh t) = gNo(y.)'/O(A[r(t-z)l[\=~(~oi) 0 K and A are themselves functions of time via their dependence on q.It is usual to assume the exponential forms for K A like K = Ko[exp (anFq/RT] -exp [-(1 -u)nFq/RT] (5) A = A' exp (-a/qr) or A' exp [-a/(q + b)] (r usually assumed unity) The current at time t is i = dq/dt = qm (dSx/dt) exp (-Sx). (7) (dSJdt) is evaluated from eqn (4) remembering the occurrence of t in the integrand as well as the limits. We note in the above nonlinearities in i-q arising at various stages. Firstly in the rate K for electron transfer. This is an exponential function usually. Secondly in the expression for the lone centre area. This is a power law and a functional (i.e.this introduces a dependence on time t explicitly and also via q implicitly. Thirdly in the case of progressive nucleation by yet another way through the nucleation rate with an exponential inverse law. Lastly to crown it all an exponentiation is needed on overlap considerations (exponential law of Avrami) ! 4. POTENTIAL SWEEP Under potentiostatic conditions expressions (3) and (4) reduce to simple forms sug-gested by eqn (I) and (2). The potentialities of potential sweep for semi-quantitative analysis is well known. It will be interesting to analyse the current-potential response as a function of time in this case. This will also result in " decoupling " the compo- * This paper has a list of symbols at the end THEORY OF ELECTROCHEMICAL PHASE FORMATION site parameter AK2which occurs in the potentiostatic response.By this one may hope to get further confirmation of the forms assumed for A and K and thus a more de- tailed mechanistic interpretation becomes possible. Assume the potential profile to be y = vt and the expressions for A and K as in eqn (5) and (6),the coverage at time t is evaluated from eqn (3) and (4). The results are 2-D INSTANTANEOUS 4 = 4m-U -exp [-B Wlf (8) and i = qm * B(dF/dt) exp [-BF(t)]. (9) In eqn (8) and (9) B is a non-dimensional parameter defined by B = gNo[ycK0(ccc+ ~t,)2RT/(nFva,a,)]~ (10) = gN0NY&K0/2W/~c + 1/aa)23 V = nFv/4RT (v the sweep rate) (11) and F(t) = -z-exp (4a,Vt) + a,exp (-4aavt) -11. (12) [Mc aa ac + ua The above description is exact and is limited only by the model.One can analyse eqn (8)-(9) for the peak potential ypand also the peak current ip,as a function of the rate u or more simply as a function of B. We give below the appropriate forms for the simple case a,= a = 3. Then F(t)+Fl(t) = 4 sinh4 Vt and B +BI = gNo(y~2K'/V)~ writing the dependence of ypon the non-dimensional B is expressed by the cubic 16B1zg(l + zp)= 42 + 3. (1 5) The limiting forms as v -+0 or D -co (these limits have meanings in terms of non-dimensional parameter B) are seen as u -+0 4B1z -314; (nFr,/RT) -iW/gNo)2/(nFv/2RT~ &KO) (1 6) V+ CO 4BlZ;-1; (nFyp/RT)+2 In (nFv/RT)-In (gNo)-2 In (y&K0). (17) In other words B,zi stays nearly a constant while the entire range for v is scanned! Thus the plot of (zi/u2)is monotonic and slowly varying with u.This could prove useful in verifying the model and obtaining the parameter NoKo2. The above limits are valid in a slightly modified form even if a,# a # 3. We have then SARRIKHAI K. RANGARAJAN The peak current ipis found in a similar fashion when 01 = o( = 3. qp/qm= 1 -exp (-4B1zE). (20) As v ranges from 0 to 03 the coverage at the peak potential (there is no maximum for the charge itself) varies from 0.53 to 0.63. Thus the peak potential indicates approximately a half coverage region. Note also that the analogous result for the potentiostatic case is 0.39. The above limits are true irrespective of the parameters like No and KO. Obviously in the potentiostatic case this value of 0.39 for q is inde- pendent of the applied potential and there is no other parameter (like the sweep rate v) to monitor! since the dominant variation with v is contained in Vdl + zp/zp an approximate result is v-0 ipccdV v -+ m i,ccv An interesting mode of analysis could be to plot to obtain Blzg.A detailed analysis for ipwhen a # 3is also available from the author. 2-D PROGRESSIVE Understandably the expressions valid for this case become more involved and hence are not reproduced here except to indicate the limits. Instead of eqn (8) we have when M = M = 3 and A of the form (6) where (non-dimensional) and Fa(t)= 4 /ov‘exp (-a’/z) sinh4(Vt -z) dz. (26) In eqn (26) a’ = nFa/4RT (non-dimensional).(27) i = dq/dt and q(t) can be obtained by a straightforward numerical integration of eqn (26). By simple transformations we may write F,(t) = (l/4)[e4vtl(-4) -2e2vtI(-2) -2e-2YtI(2) + e-4YrI(4)+ 61(0)] (28) where the integrals I(n) are all functions of Vt and a’ defined through I(m) =/,” e-a’lz emz dz. THEORY OF ELECTROCHEMICAL PHASE FORMATION It may be much easier to evaluate Fa systematically with the help of eqn (28) and (29) if Vt +0 F,(t) -t exp (-a'/ Vt) and F,(t) -(l/4)e4vt~u'Kl(4~a') when vt +co K,(z) being the modified Bessel function. In this limit the analysis is similar to the corresponding limit under instantaneous nucleation conditions but the parameters B (and its variation with sweep rate v) and gpare different.We shall consider a de-tailed discussion on this aspect elsewhere. 5. LINEAR PERTURBATION ANALYSIS Linear and non-linear relaxation techniques have not been sufficiently exploited in studying phase formation. At the fundamental level the connectivity of the phe- nomena is clearly exhibited in such studies. Certain new parameters occur in the theory of these methods e.g. derivations of the potential dependent rates (cf. A and K). We are also in principle able to decouple composite parameters like AK2 occurring in the potentiostatic response. New input variables (like the frequency in the periodic case) become available for analysis and may be useful in confirming the proposed models. Such techniques imply an '' initial state " or " bias " that is perturbed.Let g* be '' the bias " potential and let us denote the quantities eyaluated at the bias potential by the superscript (*) as in A* K* etc. If the prefix 6 identifies the perturbations our results may be written as & = qm. 2gNoys(\ K* dr)\ K*$q dz exp [-gNO(y&lfK* d~)~] (30) 0 when T,I*(and hence K*) is a constant eqn (30) becomes s\~* 6"q= qm* 2gNOy&K:K*t* exp [-gN,(y~K*t)~] 8y1dz. (31) In the case of progressive nucleation 11 dz lor Sq = qm -[2gNoA*K*t* K; 8g dz + gNOA;K*' Sq(z)(t -z)~ dz]y2c2. (32) In the particular case of sinusoidal perturbations * 6~ = A~Icos cot, * we have Instantaneous -6q = qm-2gN,(y~)~K;K*texp [-gNo(yK*t)2].Ag -sin utlco (33) 8i = i*(t)(K:/K*)AV cos cot ; (34) i*(t)is the current that would have resulted at time t in the absence of perturbation.SARRIKHAI K. RANGARAJAN Progressive 8q = q,[2gNo(yeK*)2A*Aq] -[(a In K/ay)*t -cos (cot -n)/co2 + (a In A/ay)* cos (cot -3n/2)/w3] exp [-gN,A*(y~K*)~t~/3]. (35) If the second term is negligible compared with the first (note no such assumption is easy to make with “ bias ” alone) 8q z f*(t)(a In K/ay)* -Aq -cos (at -n)/o!2 (36) and si xf *(t)(a In K/aq)*Aq . sin wt/w (37) where f*(t) = 2i*(t)/t = 2q,gN,(y~)~A*K*K~texp [-gN,A”(y~K*)~t~/3]. -In general for all perturbation profiles 9d&/dt = 8y (progressive) (38) 38i = 8y (instantaenous) with (39) 9-l =f*(t) (a In K/av)* 9-l = i*(t)(a In KJay)*. In deriving the above we have tacitly assumed the frequency to be much larger than the system time constant.The analogy with inductance and resistance is obvious except that the elements are not constants but “ slowly varying ” (compared with the time constant of the pertur- bation). 6. NON-LINEAR ANALYSIS The above treatment is valid for small excursions from the initial state. A high degree of non-linearity (i v) exists in the system and this naturally raises questions of validity. Let us linearise K(q) (electrochemical step) and also the dependence of S on q but retain the non-linearities arising out of overlap (Avrami’s). We find then 1 -exp [-gN,(yeK*t)’] -(2 &,I (zn%y2e2K*AK*t) n co (-1)” * cos [n(cot -n/Z)])). (40) In(z)n = 0 1 2 are Bessel functions of argument z and order n.E = 1 n = 0; E = 2 n 3 1. The rectified component Fis = qm exp [-gN,(y~K*t)~][l -I,(2gNoK*AK*t/co)] cc t2 exp [-gNo(yeK*t)2]. (AK* K*/w)~(41) -if the argument of the Bessel function is small. It is obvious that &-0 as t --t co,as will the other harmonics. The non-linearity in K(q)appears to be more fundamental since its influence seems persistent at longer times too. An appropriate way of understanding this is given THEORY 0F E L ECTR0CHE MI C A L PHASE F0R MA T I0 N below. When (nF -Av/RT)+ 1 we may still employ the above equations provided we reinterpret k'* and AK* as follows K*-Ko "j exp (anFAq*/RT) [I ("$ and The above corrections become inconsequential if (nF. AqIRT) < 1. (44) Eqn (42) and (43) demonstrate how (Aq) controls the growth rate.In particular if y~*T= 0 K* = 0 eqn (42)suggests the possibility of a "zero frequency growth ". This is not predicted at q* = 0 in the absence of a.c. As a matter of fact one may visual- ise a threshold potential q, [Io(z),Z,(z) are modified Bessel functions] for growth under these conditions. qt may be positive or negative indicating apseudo " over " or " under-potential "! A more detailed analysis on this aspect and on the multilayer growth will be pre- sented later. 7. TWO-AND THREE-DIMENSIONAL GROWTH The Avrami relation linking S and S is independent of dimensions and hence one may be tempted to use this for 3 dimensional (3-D) let us say hemispherical or cylin- drical growth. But such a procedure is not valid because the so-called 3-Dgrowth is a misnomer.Though the growth extends to third dimension " freely ",it is still " pin-ned " to the substrate. Such a preferential position for a planar substrate is inconsist- ent with the randomness demanded by the formula in the entire space. Moreover S -P-co as t -+ co but S (volume in the 3-D case) will not -0 as predicted by S = 1 -exp (-SJ. (46) We recall that eqn (46) is obeyed in the 2-D because complete coverage is physically attainable. In the case of 3-D sustained growth in the perpendicular direction is built into the model. We shall give below expressions appropriate to this situation without details. HEMISPHERICAL GROWTH If the sphericicity is maintained and the radius changes with time as R(t),the total volume per unit substrate area formed is Model I S(q t) = R[1 -v(S,)] (2-D instantaneous) (47) SARRIKHAI K.RANGARAJAN Mudel II S = R[1 -l(Sx)](2-D progressive linear growth law) (48) S = K[1 -p(S,)](2-D progressive square root growth law) (cf. table 2). (49) In the above R(t)represents the growth law for the lone (isolated) centre appropriate to that model. S is the valid expression for the " extended area " in the two dimen- sional substrate. u(Sx),l(Sx),p(S,) are various functions defined by Mode/ (I) v(S,) = e-sx/l ey2.sx dy; S = gNoR2 (50) 0 p(Sx)= e-sxi,' e(2yz-y4)sx dy; S = gNoAil,Zt2/2;R = A,dr (52) Thc above functions can be expressed in alternative forms too. For example u(S,) is closely related to the well known Dawson's integral.As S --) co,all the above functions -+-0 albeit more slowly than the exponential form due to Avrami and S -+ R. The (instantaneous) model (I) has the same form independent of the law assumed for the variation of R with time. This is not so with the " progressive " models. What causes this difference is the convolution intrinsic to the evaluation of the two-dimensional S,. The result for the model (I) given here agrees with that of Armstrong et aL3and the latter becomes a special case of ours by assuming R = Kt. But the same cannot be said of results for model (11) (" progressive nucleation") with the linear law. The reason for this is in the method employed for evaluating S in ref. (3). There is an over-estimation-due to " the ghost centres " (centres with negative radii!) having been included and this is clearly reflected in the limiting be- haviour (Vt +00) i(t) cc dS/dt evaluated in ref.(3) +co! The case of cylindrical growth is trivial. The case of a growth mode as cones yields expressions different from the above but for the sake of brevity are not reproduced here. The current at time t is cc dS/dt and hence the asymptotic form is i cc dR/dt. (53) As a rule the curves are flatter (slowly varying) when compared with the monolayer transients. The next question is what variation in R is to be assumed? Our earlier sections assumed a law of growth proportional to the faradaic rate. The linear velocity is constant in the potentiostatic case but can assume more general forms. When the potential varies with time as for example in the potential-sweep the exponential de- pendence on time is found.A general result appropriate to such situations has also been worked out. Yet another variation results if one takes into account the con- centration polarisation. Then the rate of growth is determined by the diffusive fluxes at the sites of incorporation. We shall discuss this aspect briefly. 8. CONCENTRATION POLARISATTON MODELS Concentration polarisation models which incorporate concentration effects (equivalently mass transfer control) may arise in several ways. For example they could be due to surface diffusion of intermediates involved in the film formation or a more straightforward diffusion of metal ions (complexes) from the bulk.The equa- THEORY OF ELECTROCHEMICAL PHASE FORMATION tions could easily be written depending upon the dimensionality but several factors make an exact evaluation of the concentration profiles impossible. Even though the boundary conditions seem quite simple the boundaries are not! (a) For we deal with boundaryprofiles that are not only time varying but also are to be self-consistently determined by the diffusional fluxes themselves. (b)The influence of other centres poses an even greater challenge due to the stochastic components in their location and times of " birth ". (c) Moreoever one finds that whatever symmetry one may start with is easily lost by the distortions caused by other centres. But the problem is tractable under certain approximations.(I) To use '' lone-centre " models as far as concentration distributions go but employ Avrami's or those derived in paragraph 7 to relate S and S,. This is helpful to de- couple concentration and overlap effects but may underestimate in the process the fluxes at the centre. Reversible (electrochemically) hemispherical growth is a classic example. Assum-ing the concentrations at the periphery (cf. Nernstian) it is possible to obtain some interesting results as illustrated in table 2. TABLE 2.-ILLUSTRATING THE DIFFUSION-LIMITED GROWTH UNDER TWO TYPES OF CONDlTIONS; THE FUNCTIONS ~(z), p(z) ARE DEFINED IN EQN (50) (52). MORECOMPLEX SITUATIONS CAN ALSO BE APPROXIMATELY SOLVED. C( q) IS THE PERIPHERAL CONCENTRATION. D IS THE DIFFU- SION COEFFICIENT.model description radius R = 21v'Dt true " coverage " equation for A as a function of y and c* ~~ (A) hemispherical growth 2y-1A2eA2(e-A2 Adn-erf cA) instantaneous -in infinite dornain-= c(q) -c* s= R[1 -V(47'CNoA2Dl)] 3-D diffusion progressive s = R[1 -9(2nN&2Dt2)] (B) two dimensional growth y-'L2eA2 Ei (-A2) instantaneous -surface diffusion only = c* -c(q) S = 1 -exp (-4gN0A2Dt) progressive S = 1 -exp (-2gNoAA2Dt2) (11) The perturbation problem in this case viz to find the response in the sizes of centres (and the diffusion pattern) arising from a perturbation in the interfacial potential is even less straightforward. Under linearised conditions it is possible to obtain an explicit solution for 6R(t)but for the sake of brevity we will not take this up here.(111) Another problem that has been solved by us pertains to the 3-D diffusion to a 2-D growth centre. In this case a non-linear integral equation results and the analysis is then made by numerical or approximation procedures. Lastly we have also deduced series expansions for R(t)in the general case so that deviations from the other limit viz pure activation growth (section 3) can be esti- mated systematically. Thus it is possible to scan the models from the extreme kinetic control (no concentration polarisation) [where a linear law (R= K -t) holds] to diffusion controlled situations [where a square root law (R = 1'43 is obeyed]. The intermediate cases of course give rather involved functions of time (not reported here) for R.Remember however that these are for " lone-centre " models and hence corrections to the above results become necessary when R(t) -A the intercentre SARRIKHAI K. RANGARAJAN separation distance (-l/dHo for instantaneous nucleation and -l/Z/N,At for pro- gressive). The more dominant overlap effects could camouflage these errors. But the real limitation lies in the assumption of the spherical or cylindrical nature of growth. Even though the actual evolution of radii was “ self-consistently ” treated the more fundamental question of symmetry (or the lack of it) was not examined. In other words one must recognise that the centres do not grow in reality spherically or circularly. 9. MULTILAYER GROWTH When the growth is not confined to a monolayer at least two alternative descrip- tions become possible.Either two dimensional nucleation is followed by three dimensional growth or a cascade build-up-layer by layer each with its own rates of nucleation and growth-takes place. Both these models can be solved satisfactorily and their long time (and transient) behaviour analysed. The former approach is discussed briefly in paragraphs 7 8. We shall comment upon the latter here. Let each monolayer be characterised by the nucleation-growth law given by (para- graph 3) i =f(% t> say. The rate of build-up of such layers may not all be identical; we recognise this by using the subscript IZ as inf,. This problem discussed briefly in ref. (4) leads to the follow- ing expression for the Laplace transform of total current assuming thatf, the rate on the substrate is different from that of growth on subse- quent layersf,,f,.It can be shown that the steady state (t -t GO) value of the cur- rent is non zero and where Sx(t)is the “ extended area ’’ for the subsequent layers. One may note that eqn (55) is independent of the rate of formation of the first layer. In the special case of potentiostatic control S takes the form /3t (paragraph 3) and4 i +q,, . pivy + (56) For the “ 2-D progressive ” model /3 cc A(g)[K(g)12where A K(g) are usually as given by eqn (5) and (6). This results in the steady state potential dependence of im as i = [K(W3[A(W3. (57) The time constant for reaching this hit can be found as described in ref. (4). The corresponding result for the “ instantaneous ” case is im = K(v).(58) If the total charge q passed is measured [instead of i(t) = dq/dt] we may write THEORY OF ELECTROCHEMICAL PHASE FORMATlON where the " intercept in the asymptotic plot " is C and Irn (lorn ze-'. dz -e-"! dr) (1 e-sx di) c = O \2 Note that C is non-dimensional and depends on the characteristics of both the first and subsequent layers. In the special case S&) = Pt' (61) S,"(t) the "extended area " of the first layer We point out that eqn (59) and (60) are general expressions valid for time dependent potential profiles too [cf. potential sweep paragraph 4 with &(t) = 4B sinli4(Yt)]. Thus an analysis of Q against t plots asymptotically for the slope and intercept should be interesting and useful in deciding on the relative magnitudes of p and Po.The next question is how does one model three-dimensional growth-as hemi-spherical or as layer by layer ? It is difficult to assert but the latter seems more funda- mental. Any phase formation is strictly a build-up of lattice incorporation at the molecular/atomic sites on a substrate. Moreoever a hemispherical growth at a macro-level also implies a preservation of "memory " (cf. the centre of the nucleus) or symmetry. This does not rule out the possibility of observing this as a limiting behaviour. The nearest one can think of is the situation in which the growth on the substrate is the slowest. We can in principle test the two models by the theory (especially at t +co)sketched in paragraphs 7 to 9.Finally what form of potential dependence should be assumed for K(q)? The easiest seems to be the one in eqn (9,the well known exponential form. But we are considering rates of coverage of macro areas when we write dRldt cc K(q) (or flux) and hence it is reasonable to interpret K(q)as possessing " a finer structure " than that of a naive "electron transfer law ". To clarify further we ask should this circular growth of a " centre " itself not be considered as a cascade process? Just as we visualized the three dimensional growth as realisable with two dimensional layers as building blocks can we not think of a two dimensional growth uis & vis one dimen- sional periphery ? We are then nearer to the molecular picture and K( y) must possess a form not unlike that deduced for steady state currents [eqn (%)I.One can then correlate the observations to density of kinks and the lattice constants too. Details of such an analysis are available from the author. 10. STOCHASTIC NATURE OF THE MODEL The presence of "random elements " in the description of electrochemical phase formation is fundamental. Spatial randomness arises out of distributions of nuclei and temporal randomness from the activation. A coupling arises while evaluating S and it is no easy task to describe concentration polarisation in this framework. Two obvious questions are (1) is the " average " description presented above valid SARRIKHAI K. RANGARAJAN and (2) what are the fluctuation parameters and how does one exploit these measure- ments (correlation functions of current say) ? The available theories5 of monolayer formation are based on two important assumptions (i) Avrami’s formula (3) reflects the overlap effects of the randomly scattered growth centres at all times; (ii) the activation times are adequately simulated by a Poisson process.A rigorous formulation based on point-process theories has been worked out6 A formalism to cover non-Poissonian cases is also possible but there are still several problems that remain unanswered. These concern the rigorous stochastic description of multilayer and three dimensional growth processes. The fluctuations within the framework of the cascade model itself are amenable for analysis. But a more funda- mental approach would have to consider the stochastic activation times in the various layers as a branching process.Yet another feature which needs to be investigated concerns the interaction among centres. In the models hitherto considered the only “ interaction ” recognized is the so-called overlap. But competition for adatoms (or other species involved in the lattice incorporation) say by several centres is equi- valent to an interaction. A similar coupling of growth rates could occur via “ local ” potentials being different at the various centres. It is our belief that a primitive theory of non-uniform growth/dissolution (e.g. certain preferred morphological modes or in phenomena like pitting corrosion) can be formulated on this basis.Thanks are due to Prof. Thirsk and other colleagues in the Electrochemistry Group for useful discussions to the S.R.C. (U.K.) for financial support and to the University of Newcastle for hospitality and the Indian Institute of Science for leave of absence. M. Fleischmann and H. R. Thirsk Advances in Electrochemistry and Electrochemical Engineer- ing ed. P. Delahay (Interscience New York 1963) vol. 3 p. 123. J. A. Harrison and H. R. Thirsk Electroanalytical Chemistry ed. A. J. Bard (Marcel Dekker New York 1971) vol. 5 p. 67. R. D. Armstrong M. Fleischmann and H. R. Thirsk J. Electroanalyt. Chem. 1966,11,208. S. K. Rangarajan J. Electroanalyt. Chem. 1973 46 119. S. K. Rangarajan J. Electroanalyt. Chem. 1973 46 119. K. M. Mehata and S. K. Rangarajan unpublished results.THEORY OF ELECTROCHEMICAL PHASE FORMATION NOTATION coefficient in the potential dependent part of A non-dimensionalised form of a = nFa/4RT (eqn 27) nucleation rate constants eqn (6) non-dimensional parameters eqn (lo) (I 3) (25) intercept of q(t) against t in the limit t -+ 00 eqn (59) (60) eqn (8) (12) (not to be confused with the Faraday F) eqn (13) (26) rate of growth on the substrate rates of growth on the various multilayers Laplace Transform of yo,fi,eqn (54) a geometrical factor relating area to "radius " e.g. ;rc for a circle (table 1). current density Laplace Transform (Heaviside notation) of i(t) steady state multilayer current eqn (59 instantaneous current due to the bias eqn (34) modified Bessel function integrals defined in eqn (29) potential dependent faradaic rate eqn (5) bias value of K = K(y *) equilibrium rate constant eqn (9 (aK/ay) evaluated at y = Q* eqn (30) effective pseudo-constant inductance eqn (38) eqn (4% (51), density of growth-centre population eqn (49) not to be confused with the Laplace Transform variable eqn (49) (59, charge density monolayer charge density radius of a growing centre effective pseudo-constant resistance eqn (39) coverage/unit area of substrate " extended " coverage time variable sweep rate Vs-l non-dimensionalised sweep rate = nFv/4RT eqn (1 l) eqn (47h (50 eqn (14) transfer coefficients perturbations in i q Y respectively rectified component of q overpotential "threshold " overpotential angular frequency (y E as defined in table 1).(The numbers within the brackets refer to the equations where the symbols are defined or appear first.)

ISSN:0301-5696    

DOI:10.1039/FS9771200101

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Kinetics of Zinc Electrocrystallization Correlated with the Deposit Morphology MEKKIKSOURI WIART BY ISRAEL EPELBOIN AND ROBERT Groupe de Recherche no 4 du C.N.R.S. “Physique des Liquides et Electrochimie ” associk B 1’Universitk Pierre et Marie Curie 4 place Jussieu 75230 Paris Cedex 05 France Received 27th July 1977 A model for zinc electrodeposition with interfacial reactions localized on particular sites of the metal surface is proposed to account for the electrode kinetics studied by means of c.d. against potential plots and complex impedance measurements. This mechanism allows one to establish a close correlation between the electrode kinetics and the deposit morphology. On one hand a coupling between the reactions and the surface diffusion of the adions ZnIadsis shown to be the origin of the spongy deposits which arise at low c.d.On the other hand a strong acceleration of the nucleation rate as a result of the autocatalytic formation of the adions plays an outstanding role in the formation of dendrites triggering at high c.d. It is known that spongy compact and dendritic zinc electrodeposits can be suc- cessively observed with increasing c.d. This sequence relevant to the deposit mor- phology can be accompanied by the establishment of multiple steady-states revealed by three different c.d. appearing at distinctive values of the cathodic potential.’ Simultaneously an inductive impedance characterized by at least three time-constants is always obtained at low frequencies.2 Most of these results are interpreted in terms of interfacial reactions involving the autocatalytic formation of intermediate ZnIads adionsS2 However an inductive impedance can be partly ascribed3 to the nucleation process which ensures a permanent renewal of growth sites when it expresses the relaxation of the electrode area.4 The purpose of this paper is to propose a model for zinc electrocrystallization which takes the two standpoints into account and consequently explains better both the electrode kinetics and the origin of the three kinds of morphology.The main charac- teristic of this model consists in a localization of some of the interfacial reactions on particular sites distinguished with regard to the crystal gr~wth.~ INTERFACIAL REACTIONS Since zinc is deposited at potentials where hydrogen adsorption and hydrogen evolution take place a fraction Q1 of the electrode surface can be considered as covered with adsorbed hydrogen Hadsformed through Kl H+ +e ___f Hads (1) and consumed partially during the hydrogen evolution according to the frequently proposed path KZ H+ +H3dS-k e +HZ.(2) KINETICS OF ZINC ELECTROCRYSTALLIZATION In electrocrystallization theories several types of sites are generally distinguished on the metal surface where an adion can be more or less linked to the metal lattice and passes via different intermediate stages before its incorporation in the lattice.6 To describe zinc electrodeposition from cations Zn" which may be either complexed or solvated two types of intermediates are implied in the present model (i) the adions Znlads weakly linked to the metal and able to diffuse along the electrode surface.They cover a fraction 62 of the sites I belonging to planes or to zones with lattice imperfections. On these sites I the following reactions previously discussed' occur K3Zn" + ZnIads+ e 7-2Zn'ads (3) ZnIads+ Hads4cZn + H+ (4) K6ZnIads+ e __t Zn Zn" + e -Znrads.Ka (5) (6) The cations are adsorbed through reaction (6) and also through the autocatalytic reaction (3). Reactions (4) and (5) describe the incorporation of the adions on growth sites. These sites provided by the lattice defects need no renewal. (ii) the growth sites Zn* which occupy a fraction 63 of the sites I1 belonging to the growth steps of a perfect lattice.Such growth sites need to be regenerated through the nucleation reaction K, ZnIads+ e --+ Zn*. (7) As in the case of iron deposition,' the intermediates Zn* are assumed to catalyse reaction (8) which is still an overall process Zn* + ZnII + 2e Ks_l_ Zn + zn*. (8) This type of transfer occurring on a self-perpetuating kink has already been pro- posed for silver deposition. At a certain stage in the growth some kinks lose their activity Zn* KD Zn. (9) ELECTRODE KINETICS With simple assumptions (adsorption of Hadsand ZnIads according to Langmuir's isotherm nucleation rate proportional to the surface concentration of ZnIads) the electrode kinetics are governed by the following mass and electron balances pi d0 = Al(1 -01 -02) + AI(1 -01 -03) -A201 -A46182 (10) dt dO p2 2= A6(1 -01 -02) + (AS -A5 -A7)02 -A130z2-A40162 (1 1) dt p3 dt de3 = A7B2-Ago3 (12) J p; = (A + A,)(] -$1 -82) + Ai(1 -01-0,) + A261 + (As + A5 + A7102 -+ 2A803 (13) ISRAEL EPELBOIN MEKKI KSOURI AND ROBERT WIART where J is the c.d.I;is the Faraday and PI,p2 and p3 represent the maximal surface concentration of Hads,ZnIads and Zn*. The rate constants of the electrochemical reactions are supposed to vary with the potential Y according to Tafel's law Ki= kiexp (b,V)for the cathodic reactions and K3= K3 exp (-H3Y) for the anodic reaction. Terms Ai (in mol cm-2 s-l) are de- fined from the rate constants Ki as follows Al = Kl[H*] A2 = K2Pl[H+I A3 = K3P2[Zn(II)I A'3 = K'3p22 A4 = K4p1p2 A5 = K5p2 A6 = K6[Zn(II)] A7 K7P2 AS = &P3 [zn(II)I A = K9P3 The steady-state values of the coverage fractions can be written as 83 = fi7 02 A where The steady-state value of J and the deposition efficiency qare deduced J = 21."A281 + A40102 + (A + A7)02 + A831 (20) The electrode impedance 2 = R -jG is obtained considering the double layer capacity C,in parallel with the faradaic impedance 2,.The latter is calculated using a method described elsewhereg which consists in linearizing eqn (10)-(13) for small sinu- soidal perturbations of potential from steady-state conditions. We thus obtain the terms of eqn (22) where the first term represents the inverse of the charge transfer resistance R,. With appropriate values of the parameters Ai and bi chosen so that each transfer coefficient OC~(OC~ = biRT/nLF)remains between 0 and 1 there is a cathodic potential range where eqn (16) has three real roots between 0 and 1 to which correspond three values of 0 and 0 also between 0 and 1 and three values of J.Such multiple steady- states appear on the S-shaped curve 1 drawn in fig. l(a). As an example the imped- ance diagram simulated at polarization point A is shown in fig. I@). The capacitive semi-circle corresponds to the Rt-Cd circuit. At low frequencies the faradaic im- pedance prevails and three inductive loops corresponding to the relaxation of the KINETICS OF ZINC ELECTROCRYSTALLIZATION coverage fractions 01,O2 and O3 are observed. It is noteworthy that the lowest fre- quency loop corresponds to the slow relaxation of O3 because reactions (7) and (9) are supposed to be relatively slow compared with the others.A decrease in the Zn” concentration in the electrolyte corresponds to a decrease in the parameters A3 A6 and As. Such a simulation eliminates the multiple steady states and gives a c.d. against potential curve shifted towards cathodic potentials [curve 2 fig. l(a)] in agreement with Nernst’s law. To suppose that the nucleation N Q E -. fik Ik \ NI E 00 2 0 10 20 30 LO 1 VImV 0 0 006 (a 1 (b) FIG.1.-Simulation of the influence of Zn” concentration (a) on c.d. against potential curves with respect to an arbitrary origin and (b) on impedance diagrams. Curve 1 has been calculated taking the foliowing values for parameters br (in V-’) bl = 5 bz = 35 b3 = 33.8 K3 = 4.8 b5 = 38.6 b6 = 19.3 b7 = 29.3 bs = 64 and at V = 0 for parameters Ai(10-8 cm-2 s-l):A1= 2.3686 A2 = 0.7723 A3 = 11.86,A13 = 4.4785 Ad ==8.25,AS = 7.9448 A6 = 0.9992 A7 = 0.91754 x lo-’ As = 16.298 A 9= 0.01.Curve 2 has been calculated from the same set of parameters by multiplying A3,A6 and ASby 0.8 and A by 0.2. Impedance diagrams simulated at points A and B with the following para- meters Cd = 50 ,uF cm-’ h1= 10 Bz = h3= Po = 2.7 x lo-’ mol cm-’ (frequency in Hz). rate constant K7follows Tafel’s law is a rough approximation though this rate can be activated with the cathodic overpotential it is not at all clear why it should increase when the c.d. against potential curve as a whole is shifted towards cathodic potentials.In order to take account of this effect the decrease in the Zn” concentration has been simulated by diminishing A7 (by diminishing K7)in addition to A3,As and As. Such an influence is illustrated in fig. l(b) (diagram B) the faradaic impedance is clearly modified since a capacitive loop is observed here between 100 and 20 Hz approxi-mately. The simulated curves and diagrams of fig. 1 are in good agreement with the experi- mental results obtained during zinc electrodeposition. As an example fig. 2 shows the results of measurements performed in a sulphate electrolyte after eliminating the influence of mass transport. A comparison of fig. 1 and 2 shows that the orders of magnitude of the three time-constants of the faradaic impedance are fairly well ex- plained with coefficients PI p2 and /I3 which do not overflow the surface density po (2.7 x mol cm-2) of metal atoms.The measured efficiency q is also consistent with our model. As seen in fig. 3(a) the experimental results show that q increases with c.d. and with the concentration of ISRAEL EPELBOIN MEKKI KSOURI AND ROBERT WIART 0 0 003' 0 05 -1.OL vvs.S.C.E.Iv 03 (a1 (b) FIG.2.-Influence of the concentration c of Zn" (a) on the steady-state current-potential curves and (b)on impedance diagrams obtained at 26 "Cduring zinc electrodeposition with an acid sulphate electrolyte (1 mol dm-3 Nar SO4+ c ZnSO,; pH = 4.3) and a rotating disc electrode (area = 0.28 cm2 rotation speed 3000 r.p.m.).(a) curve 1 c = 1.5 rnol dm-3; curve 2 c = 0.2 rnol dm-3 (b)Impedance diagrams obtained at points C and D (frequency in Hz). 0.61 I 0.5-0 20 40 60 80 0 0 20 . LO 5 60 80 1 JlmA cm-2 JlmA em-* (a) (b) F FIG.3.-Influence of Zn" concentration on the efficiency against c.d. curves (a) plotted at 26 "C during zinc electrodeposition from a LeclanchC cell electrolyte (2.67 rnol dmd3NH4Cl+ c ZnCl, pH = 5.2; curve 1 c = 0.72 mol dm-3; curve 2 c = 0.24 rnol dm-9 with a rotating disc electrode (area 0.28 cm2 rotation speed 4000 r.p.m.) and (b)simulated with the same set of parameters as for fig. 1. zinc in agreement with the theoretical predictions [fig. 3(b)]. In addition it has been shown elsewhere2 that y decreases with a pH decrease in accordance with eqn (21).ORIGIN OF SPONGY DEPOSITS Here it will be shown that a coupling between the interfacial reactions and the surface diffusion of Znrads accounts for the spongy deposits arising at low c.d. For the sake of simplicity surface diffusion is supposed to be one-dimensional and to follow Fick's law. The parameters 01,e2 and e3and J denote the local values KINETICS OF ZINC ELECTROCRYSTALLIZATION of the coverage fractions and cd. all dependent on the position r on the surface. The local mass balances are written P3x - A,02 -A& (25) where Ds is the surface diffusion coefficient of Zn’,,,. Eqn (13) now gives the local c.d. J. In the steady-state eqn (23)-(25) lead to The r-independent roots of eqn (16) are obvious solutions for eqn (26).To determine the behaviour of the interface close to a uniform steady-state a classical techniqueloconsists in studying eqn (26) by the phase plane method i.e. in analysing the variation of p = d02/dr as a function of Sz. It turns out that If F(82) means a primitive 0ff(62) eqn (26) and (27) lead to p = *d2F(O2) -c (28) in which the integration constant Cois defined from the values of 0,(0) andp(0) in an arbitrary position r = 0. As an example thep(8,) curves calculated at potential Y = 0.4 mV and for various values of Coare represented in fig. 4. It will be noted that three singular points exist -1500 -FIG.4.-Phase trajectories of eqn (28) at potential Y = 0.4 mV (the values of terms Ai are given in fig. 1) calculated with p2Ds = lo-’‘ mol s-’ and various values for C,/108 3.4130 (curve l) 3.4133 (curve 2) 3.4060 (curve 3) and 3.3866 (curve 4).Increasing Y is indicated by arrows. ISRAEL EPELBOIN MEKKI KSOURI AND ROBERT WIART (0 = 0.15,0.22 and 0.64) corresponding to the multiple steady-states at this potential. Thep(0,) curves allow one to determine the system behaviour close to a uniform state for example when a small excess E of 0 appears at r = 0. Near 13~ = 0.15 a close trajectory is followed (curve 1) :eqn (26) has then a periodic solution whose amplitude is 0.11 and wavelength is A. Near 0 = 0.22 the solution is still periodic but with a tiny amplitude which never exceeds E. In contrast near O2 = 0.64 an infinite branch is followed (curve 4) :eqn (26) then admits no periodic solution.The existence of periodic solutions at low c.d. where 8 is low is essentially due to the coupling between surface diffusion and heterogeneous reactions (1) to (6) among which reaction (3) plays a major role. As a matter of fact a similar interface behaviour is found again when reactions (7) (8) and (9) are disregarded as shown in fig. 5. FIG.5.-Phase trajectoriesof eqn (28) at potential V = 0 calculated when reactions (1) to (6) only are considered (the values of terms At are given elsewhere),’ with BzDs = mol s-l and various values for C,,/108 cm-2 9.9284 (curve l) 9.9444 (curve 2) 9.9171 (curve 3) and 9.9119 (curve 4). Increasing Y is indicated by arrows. At low c.d. it is clear that periodic distributions of the intermediates called dissi- pative structures appear on the electrode and lead to c.d.distributions whose profiles have been already c0mputed.l The wavelength A depends on D, for example ;1 is N” 40 pm. for D = cm2 s-l. Both the uniform and the non-uniform solutions are stable with regard to small perturbation^.^ However the non-linearity of eqn (23) and (24) can destabilize a uniform steady-state because they can give rise to relatively high perturbation^.^ From eqn (16) the relative variation of O2 due to a local variation of any rate constant Aican be estimated as and small perturbations of Aican provoke large variations of 02. This is exemplified in fig. 6(b) which shows the c.d. against 1A02/821curves calculated as a consequence of a small perturbation (1 %) of the parameters Al (curve l) A5(curve 2) and A3(curve 3) when reactions (1) to (6) only are regarded.It is seen that IALe2/021can become high and even overflow 1 in the c.d. domain [see fig. 6(a)] where the multiple steady-states exist. It appears clearly (curve 3) that the system is particularly sensitive to the auto- catalytic reaction rate. KINETICS OF ZINC ELECTROCRYSTALLIZATION As in homogeneous kinetics,” a slight perturbation of a rate constant is conse- quently sufficient to trigger high variations in the adion concentration and in the c.d. If such a perturbation happens locally on the surface from a local heterogeneity of the deposit or the substrate it can destabilize a uniform c.d. distribution corresponding to the growth of compact deposit^.^ The evolution of the local coverage frac- tions and of the local c.d.is then given by a non steady-state analysis of the local mass and electron balances which we have computed using the Crank-Nicholson method.12 0 -5 0 +5 0.2 0.4 0.6 0.8 1.0 Y/mV (4 FIG.6.-(a) c.d. against potential curve simulated when reactions (1) to (6) only are considered [the values of terms Aiand bi are given in ref. (l)]. (6)c.d. against IAO,,!O,I curves as a result of a small perturbation (1 %) of the parameters Al (curve I) A5 (curve 2) and A3 (curve 3). As an example let t = 0 be the moment when there occurs a high perturbation AS2/S2= 100% located over a distance Ar < A(Ar/A = 2%) and imposed for the time AT. Then the system is left to itself and its evolution is observed in the perturbation neighbourhood with the boundary conditions AS2 = 0 for Y = 0 and Y = A.If AT is very short the system is found to come back to the uniform steady-state. In contrast if AT is long enough ix.,if the perturbation is larger than a critical size the system moves towards the non-uniform solution which becomes steady. Fig. 7 illustrates such an evolution for AT = 0.087 s; at time 2.65 s the system reaches the profiled steady-state (curve 4). The perturbation imposed in this example is very probable during the growth of a compact deposit because it corresponds to the formation of only one additional metal monolayer in the perturbed zone. The local c.d. peaks resulting from such a perturbation are able to initiate the formation of spongy deposits.ISRAEL EPELBOIN MEKKI KSOURI AND ROBERT WIART r/h FIG.7.-Variation with time t of the c.d. profile J(r)as a consequence of a Bzperturbation maintained for AT; t = 0 (curve l) t = AT = 0.087 s (curve 2) t = 0.947 s (curve 3) t = 2.65 s (curve 4). ORIGIN OF DENDRITIC GROWTH Though local c.d. peaks may also appear at high c.d.,l the dendritic growth does not result only from the coupling between surface diffusion and autocatalytic reaction. As a matter of fact the dendrite's birth is known to occur always with the formation of numerous nuclei,13 i.e. accompanied by a strong increase in the nucleation rate. Such nucleation acceleration can be accounted for by supposing that the nucleation rate vN is no longer proportional to 8 when 0 approaches 1 but that it follows for example the relationship vN = A7(8 + "-") i -e2 for 8 > 0 (30) depicted in fig.S(a) (curve 2) where 8 is a threshold close to 1. For 82 < O0,uN = A78 is still valid and the steady-state system is governed by eqn (15) (16) and (20) which give the variations O,(V) and O,(V) represented in fig. 8(b) and 8(c) (curves 1). I 0.5 Bo 1 FIG.&-(a) Nucleation rate uN as a function of 19~.(b) and (c) Variations of the coverages O2 and &; with potential Vcalculated assuming vN = A7e2(curves 1) and uN given by eqn (30) (curves 2). KINETICS OF ZINC ELECTROCRYSTALLIZATION For O2 > O0 the presence of Hadson the surface can be disregarded (6 -0) and the steady-state mass balances become A6(l -02)+ (A3 -Eqn (31) and (32) lead to the variations 02(Y)and Q3(Y)represented in fig.8(b) and 8(c) (curves 2) in the particular case where O0 = 0.95; the transition from curves (1) to curves (2) which is indeed continuous is indicated by a dashed line. It can be seen that (i) e2always remains lower than 1. (ii) O3increases more rapidly with Y and exceeds 1 as soon as Y = 2.4 mV. That means that the surface concentration of growth sites overflows the population Po of the atoms contained in a metal monolayer i.e. a roughness increase. Then dendrites are triggered and simultaneously steady-state conditions can no longer be maintained. As seen in fig. 8 such a phenomenon occurs at a relatively low overpotential because of the autocatalytic reaction which permanently provides a sufficient number of adions close to saturation (tY2 -1).The marked increase of the growth sites number due to this near-saturation concentration of adions co-operates with the surface diffusion-reactions coupling to explain the initiation of the dendritic growth at high c.d. CONCLUSION The present model of interfacial reactions based on the idea of active area intro- duced in terms of growth site concentration reasonably explains the kinetics of zinc electrocrystallization and the formation of non compact-structured deposits. This active area which increases with c.d. does not seem related simply to the deposit roughness which decreases in passing from a spongy deposit to a compact one.Con-sequently it is not surprising that the deposit roughness cannot be connected simply to the inductive impedance observed at low frequencies both in the cases of zinc and nickel dep0sition.l For tin and lead electrodeposition a similar correlation between the electrode kinetics and the deposit morphology has been fo~nd,~?~~ and this leads us to believe that similar elementary processes take place at the electrode. In addition such a correlation appears to promise a better understanding of how certain additives in- hibit the formation of spongy or dendritic dep0~its.l~ Finally it is noteworthy that other kinds of correlations between the electrode kinetics and the structural organization of the deposits can be obtained from the electrochemical noise study.It has recently shown16 that the noise power is connected directly either to the morphology or to the preferred orientation of the deposits. I. Epelboin M. Ksouri and R. Wiart J. Electroanalyt. Chern. 1975,65 373. I. Epelboin M. Ksouri and R. Wiart J. Electrochem. Soc. 1975,122,1206. R. D. Armstrong and A. A. Metcalfe J. Electroanalyt. Chem. 1976 71 5. W. Davison J. Harrison and J. Thomson Faraday Disc.Chem. Soc. 1973,56 171. M. Ksouri Thesis (Paris 1977). ti J. Bockris and G. Razumney Fundamental Aspects of Electrocrystallization(Plenum Press New York 1967). ISRAEL EPELBOIN MEKKI KSOURI AND ROBERT WIART ’W. Allgaier and K. E. Heusler 2.phys. Chem. Neue Folge 1975,98,161. T. Vitanov A. Popov and E. Budevski J. Electrochem.SOC. 1974,121,207. I. Epelboin M. Keddam and 9.C. Lestrade Faraday Disc. Chem. SOC. 1973,56,264. lo N. Rouche and J. Mawhin Equntions Diflirentielles Ordinaires (Masson Paris 1973) tome I p. 88. l1 R. J. Field and R. M. Noyes Faraday Symp. Chem. SOC.,1974,9,21. l2D. U. Von Rosenberg Methods for the Numerical Solution of Partial Digerential Equations (American Elsevier New York 1969). l3 M. Froment and G. Maurin Electrodeposition and Surface Treatment 1975,3,245. l4 M Ksouri and R. Wiart Proceedings INTERFINISH 76 Amsterdam (1976); Oberflache-Surface 1977 3 61. l5 J. Bressan M. Ksouri and R. Wiart 28th I.S.E. Meeting Druzba (1977). Extended Abstracts p. 341. l6 G. Blanc C. Gabrielli M. Ksouri and R. Wiart Electrochim. Acta 1977 in press.

ISSN:0301-5696    

DOI:10.1039/FS9771200115

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Granular Growth of Electrochemically Deposited Metals BYALEKSANDAR DRAGUTIN AND MILUTIN R. DESPI~ M. DRA~I~ D. MIRJANI~ Faculty of Technology and Metallurgy University of Beograd Beograd Yugoslavia Received 8th September 1977 Conditions of deposition of cadmium from cadmium perchlorate solutions on copper electrodes leading to the appearance of granular deposit (boulders) have been investigated. It was found that this type of deposit appears in a limited pH range only (pH 3 to 6) in which colloidal cadmium hydroxide is found to appear. The probability of appearance of granules is diKerent at different crystal planes of the copper substrate. The rate of growth of the granules has been determined microscopically. It was found that the size of the granules increases proportionally to the square root of time.This indicates that the rate of growth is controlled by the spherical diffusion of de- positing ions from the bulk of solution. Fundamental research in electrodeposition of metals in recent years has advanced to the extent that basic steps leading to the formation of the first few monolayers of the deposit are now fairly well understood and the theory has been developed to a semi-quantitative level. In the deposition of thicker metal layers however only the understanding of phenomena relating to difficulties in the transport of the reacting species (amplification of surface roughness dendritic growth and the levelling effect of some addtitives) seems to have reached a similar 1evel.l Except for some speculations concerning predominant orientation of crystal^,^-^ understanding of the development of texture of thicker deposits has made little progress since that reviewed in the classi- cal treatise of Fischer.6 In particular little seems to be known about conditions caus- ing the appearance of granular deposits of relatively high porosity and highly developed surface area which are obtained in some instance^.^ This type of growth has attracted our attention for some time n0~.~9~ In a study of the deposition of granular cadmium from solutions of simple cadmium salts9 it was shown that such a deposit dissolves anodically more readily than does a compact deposit not only because of the larger specific surface area but also because of a somewhat higher activity of the metal in such a state.Yet such deposit growth is clearly distinguishable from that leading to the formation of dendrites. The metal particles are of similar dimensions in all directions and in the extreme tend to become globular with outwardly poorly developed crystal structure.1° Hence it is obvious that the reasons for its appear- ance should not be sought along the lines of the theory of dendritic growth.llJ2 Globular growth of copper on graphite has been obtained upon the addition of an adsorbing and codepositing polyelectrolyte (polyvinylpyridine) to the so1ution.l' Hence the search for conditions leading to granular growth from simple salt solutions has been directed to the study of some solutions containing species which might exhibit similar action to that of the polyelectrolyte and in particular to the effect of the hydro- lysis of salts at increasing pH values.Also since granular growth has been observed as a rule on some parts of the electrode surface only while on others a fine-grained relatively smooth deposit is obtained the effect of the crystal orientation of the substrate on the appearance of the granulae has been studied. A. R. DESPIC D. M. DRA~I~ AND M. D. MIRJANIC EXPERIMENTAL Cadmium was deposited on copper electrodes from cadmium perchlorate solutions with perchloric acid and sodium perchlorate as pH adjusting electrolytes using the potentiostatic technique with simultaneous microscopic observation. ELECTRODES Copper electrodes were made from 99.95% copper wire 2 mm in diameter which was subjected to special thermo-mechanical treatment (repeated stretching and annealing) leading to an increase in grain size.When cut across and polished the cross sectional surfaces were found to consist of a very few grains and in some cases of a single grain only. Hence deposition on individual grains could be followed. The orientation of the grains was deter- mined by X-ray examination. Two orientations were found to predominate the (I 11) and (200) crystal planes appeared on the surface at inclinations to the axis of the wire ranging from 0.8 to 14". By mechanical polishing to a mirror finish followed by electropolishing layers of higher indices were removed and smooth surfaces of a given orientation exposed. In some instances anodic dissolution was extended to the appearance of dislocation pits.ELECTROLYTIC CELL A thin layer cell was used with an optical window through the counter electrode facing the electrode under Observation. This consisted of the wires described above embedded in Teflon. The counter electrode was a thin foil (80 pm) of pure cadmium (99.95%). Its surface was about 160 times larger than that of the working electrode so that it could serve also as a reference electrode. The gap between the two electrodes was 0.2 mm and the electrolyte was made to flow through the gap at a rate of 0.6 dm3 h-I in all the experiments. SOLUTIONS The solutions were prepared by dissolving cadmium oxide (" Zorka "-Sabac) in perchloric acid (" Merck "-p.a.)and triply distilled water to a concentration of 1.5mol dm-3.Stoichio-metric amounts of the oxide and the acid gave solutions of pH 6.40,with some oxide remaining undissolved. The solutions were therefore opaque with particles in the colloidal range (passing through fine grade filter paper). The pH was lowered by adding acid; solutions became clear below pH 5.20. However time effects and some hysteresis characteristic of colloidal systems were encountered in titration of the solution with the acid and retitration with alkalis. It appears that in the pH region between 5 and 6there is a maximum concentra- tion of Cd(OH)2 dissolved or in acolloidal state with colloidal particles below the turbidity limit. PROCEDURE Prior to the experiments the electrolyte was made to flow through the cell and the working electrode was potentiostatted with aWenking potentiostat to a potential 10 mV more positive than that of the cadmium reference electrode.The electrode was then subjected to a poten- tial step of a selected constant cathodic overpotential and the current was recorded on a Hewlett-Packard X-Y recorder for a period of up to 110 s. Simultaneously microscopic observations were made using a Reichert Zetopan Pol. microscope with a magnification of 400 (in some experiments 500x ). When granular growth appeared photographs were taken with an automatic exposure system at regular time intervals (5 s). At the end of the cathodic step the polarity was reversed and the electrode was n~aintained at the anodic overpotential 128 GRANULAR GROWTH OF ELECTROCHEMICALLY DEPOSITED METALS until the current dropped to zero.The electrode surface could then be seen to return to its original state. Experiments were carried out at room temperature (25-27 "C). RESULTS Out of a total of 7 electrodes subjected to the above treatment granular growth was observed on two electrodes only both having at least one larger grain with the plane (200) exposed to the electrolyte while the others had none. In a sequence of in-E 0 10 20 30 40 50 60 t/s FIG.1.-Time responses of current to steps of different cathodic overpotentials in the case of appear-ance of granular growth pH = 5.33. creasing cathodic overpotential a series of time responses obtained in the cases when granular growth was observed in the microscope is shown in fig.1. At any given time there is a rather sharp increase in current with overpotential (10-fold for 20-30 mV). The amount of deposited cadmium within the duration of the overpotential step could be obtained by integrating the time response curve. By anodic dissolution it was found that cathodic deposition occurred with roughly 100% faradaic efficiency. For a given overpotential the amount of deposited cadmium was found to depend on pH. As shown in fig. 2 this dependence exhibits a maximum at around pH 5. Cor-respondingly microscopic observations revealed a maximum incidence of granular growth in the same pH range. Below pH 4 granular growth was rare and below pH 3 this type of growth was never observed. At a given pH the number of granulae in the field of vision increases with increasing overpotential as shown in fig.3 although at the highest overpotential used some decrease is observed. The granulae are evidently becoming more even in size while the average size is increasing. PLATE 1.-Microphotographs of granular cadmium deposit on copper. (a)Example of a well grown hexagonal grain; (6) area of the electrode where granulae appear upon the application of cathodic potential step (arrows point to locations where nucleation occurs) ; (c)-(f)a sequence taken during growth at pH 4.98 and overpotential of 50 mV at 10 s intervals. [Toface page 129 A. R. DESPI6 D. M. DRAilc AND M. D. MIRJANIC PH FIG.2.-Total amount of electricity passed during 50 s as a function of pHfor different constant values of cathodic overpotential.0 t i 4 O /,pH 4'9s 5.92 I 30 40 50 __I 1' mV FIG.3.-Number of granulae counted in one and the same field of vision as a function of overpotential. A typical sequence of microphotographs recording the growth of granulae during a single overpotential pulse is shown in plate I. In some instances ideally hexagonal crystals grew as seen in picture (a) indicating that nuclei are formed with the hex- agonal plane lying flat on the substrate. Most granulae however were deformed exhibiting a tendency to spheroidize. The majority of the granulae appeared at some points where some imperfection (different from a pit-producing dislocation) occurs on the electrode surface (black dot).Some granulae however appeared at the edge or even at the bottom of triangular dislocation pits. Others developed at locations at which nothing but a flat crystal surface could be seen before the current pulse as shown in the plate (picture b). 130 GRANULAR GROWTH OF ELECTROCHEMICALLY DEPOSITED METALS When a series of cathodic deposition pulses was employed followed by total anodic dissolution of the deposit it was observed (fig. 4) that the majority of the granulae appeared repeatedly at the same locations. Some new locations however were also activated as the overpotential was increased while at some others growth was absent. A general finding was that once the granules start developing no new ones appear. u. 0 L aJ n E C Location FIG.4.-Number of pulses which produced granulae at a certain location. Type of location I-imperfection of uncertain origin ; D-dislocation pit ; shaded-flat surface. Series of micrographs of the type shown in plate I for different pH and different overpotential enabled a quantitative evaluation of growth. The rate of growth could be estimated by measuring the change in the linear dimension of the granulae with time. A typical example is shown in fig. 5. It is seen that in one and the same overpotential pulse all crystals do not grow at the same rate. Also fluctuations in the rate of growth are observed which are outside the limits of the error in the measure- ment. Nevertheless all the growth followed a square root time dependence as shown in 4 0 1 I I I I FIG.5.-Growth of a number of granulae with time pH = 5.95; 7 = 50 mV; A-the average size.L-the size of the largest measured granula; S-the size of the smalIest measured granula. A. R. DESPI~,D. M. DRA~I~ AND M. D. MIRJANI~ fig. 6 for a set of overpotential pulses. Even though the average size of a number of crystals is taken the growth is seen to be somewhat erratic at lower overpotentials while at 50 mV a very smooth linear dependence is found. The slopes of the t* dependences seem to be equal in all cases i.e. independent of either the pH or the overpotential as seen in fig. 7. The straight lines however do not extrapolate to the origin of coordinates. In some cases there is a positive intercept with ordinate indicating a faster growth at the very beginning.In others however the growth seems to exhibit a delay. 30 20 E \\ 0 10 0 / I b /I 1 I 1 I I 01234567 "'2 1 22 Frc 6 -Plot nf the si7e of the average ~ranirla against saiiare root of time for different overnntentials 8 LO 132 GRANULAR GROWTH OF ELECTROCHEMICALLY DEPOSITED METALS DISCUSSION Granular growth in electrodeposition of cadmium on copper is found to occur in a relatively narrow range of conditions (pH -5 -+ 1; overpotential 30-50 mV) and on certain electrodes only. This latter finding indicates that different crystal planes favour different types of nucleation. A possible representation can be seen on the model representation of a (1 1 1) and a (200)plane in fig.8. A two dimensional nucleus can be better situated on the (1 1 1) plane exh adatom of cadmium falling close to the ( 111 1 FIG.8.-Model of formation of a hexagonal nucleus of cadmium on two crystal planes of copper. recess between copper atoms in the plane. This implies that epitaxial growth in con- tinuation of the copper lattice at steps or kinks should also be more favourable on the (111) plane. On the (200) plane on the other hand two-dimensional nucleation produces less stable nuclei and hence a delay in two-dimensional growth occurs which makes room for three-dimensional nucleation. This idealized picture is of course complicated by the fact that at imperfections or dislocations at which most of the growth was found to occur the atom arrangements in the substrate could be significantly different from those shown in the model.Hence other structural elements in the surface must also have a role. This is sup- ported by the fact that granules also appear at some parts of the surface which accord- ing to the shape of the dislocation pits must be of the (1 11) orientation. As for the supply of cadmium adatoms for a continuous growth of the three- dimensional nuclei into granulae of considerable size (20-30 pm) one can calculate the necessary current by the following reasoning if we assume that granulae are approximately spherical a granulus of measured linear dimension a,consumes a vol-ume of metal rc V=-a3. 6 The change in volume with time dV/dt is related to the change in the molar amount of metal dN/dt and further to the current by the expression A.R. DESPI~,D. M. DRA~I~ AND M. D. MIRJANIC Hence by differentiating eqn (1) and substituting into eqn (2) one obtains Fpx da I=-a2-M dt' (3) The supply of atoms by the current given by eqn (3) can occur by discharge on the substrate or on the granules. The fact that the number of granulae within the field of vision does not increase once the granulae start developing supports the view that adatoms deposited at the substrate are transferred to the granulae by the mechanism of surface diffusion (the " clear field effect " observed by Markov Boynov and Toschev).I3 It is however difficult to conceive that this is the main supply route considering that the required amount of material increases as a2and that the surface diffusion path to the point of incorporation also increases with the size of the granulae.Hence it was assumed that most of the supply is met by discharge on the granulae themselves. In such a case the local current density on the granulae is . I (FpnIM)a2(da/dt) l=-=-S a2n (4) i.e. it is directly proportional to the slope of the a against t graph. Since the linear a against t dependences obtained in most experiments provide more precise values of the slope k one could further relate i with k in the case when the straight line passes close to the origin of coordinates from the following a = kt2 (5) and hence da k2 -=-dt 2a so that . Fpk2 1 1=-2M a (7) and I=-Fpnk2 2M a.It is seen that as long as the crystal growth follows the t* dependence the current density is inversely proportional to the diameter of the granule and the total current directly proportional to it. That is a characteristic of steady-state spherical diff~si0n.l~ This as well as the virtual independence of the rate of growth from overpotential indi- cates that once the granules start growing the rate of growth is diffusion controlled. In such a case14 . 2FDCO 1=-a12 . (9) Hence the slope k can be estimated theoretically from eqn (7)and (9) as k=(--). 8MDCO Taking D -loq5cm2s-l one obtains k -7 x cm s-* which is close to the slopes arising from fig. 7. 134 GRANULAR GROWTH OF ELECTROCHEMICALLY DEPOSITED METALS The fact that the i against t3 dependences often do not go through the origin can be due to two effects (a)At an early stage of growth the supply of material from that discharged on the substrate by the mechanism of surface diffusion can be significant and hence the growth be faster than if supplied by spherical diffusion only.This must lead to posi- tive intercepts with the ordinate and eqn (5) should read a2-a2(t=o,= 2kt. (5') (b)At low overpotentials nucleation of the granulae can be slow so that an induc- tion time ti is expected. In such a case the correct eqn (5) should be a = k(t -ti)+. (5") The observed behaviour is a consequence of the interplay of the two effects; the fact that experimental data fit the approximate eqn (5) fairly well indicates that these two disturbing effects (a) and (b)are together quite small.Also the fact that a delay in the development of the grains and a generally smaller grain size after a given period of time is observed at lower overpotentials indicates that the second effect then pre- vails. An indirect insight into the number of granulae over the entire electrode surface area n' can be obtained if it is assumed that at least at the advanced stages of growth all the current is used for their development and that the current spent on epitaxial growth is negligible. In such a case n' is found by dividing the total recorded current with that spent on developing an average granula. The latter was evaluated for each of the reviewed experiments using eqn (9) and on using the corresponding total current data presented in fig.9 were obtained. These confirm the finding that A 500 /pH 4.98 I 400 -c 300-3.46 200 -100-1 I 0 b the incidence of granular growth is largest around pH = 5 and that it increases with increasing overpotential. The sharp increase in the total current with overpotential at any given pH is actually due to the increased rate of nucleation since the rate of growth of individual nuclei is unaffected by overpotential under the conditions of diffusion control. A. R. DESPIt D. M. DRAiIC AND M. D. MIRJANIk Finally one notes that undisturbed growth under diffusion control should lead to the development of dendrites-l The fact that the granulae remain spherical throughout the growth period can be explained only if one assumes the existence of a dendrite suppressor in the electrolyte.Colloidal hydroxide might very well play such a role since it is likely to be adsorbed faster at micro-protrusions appearingon the crystal than on flat crystal planes and might prevent their further development with an overall effect of spheroidization. This as well as a possible effect of the adsorption of colloids on two-dimensional nucleation explains the fact that a maximum in the granular growth is found in the pH range where the formation of colloidal hydroxide occurs. The authors are indebted to NSF (USA) and to the Research Fund of SR Serbia whose grants have made this work possible. cf. A. R. Despid and K. J. Popov Transport-controlled Deposition and Dissolution of Metals in Modern Aspects of Electrochemistry ed.B. E. Conway and J. O’M. Bockris (Plenum Press New York 1st edn 1972) vol. 7 chap. 4 p. 199. K. M. Gorbunova 0. S. Popova A. A. Sityagina and Y. M. Polukarov Crystal Growth (Rept. Congr. Crystal Growth March 1 1956 Akad. Nauk S.S.S.R. Moscow 1957) p. 58. N. A. Pangarov and St. Rashkov Bull. Inst. Phys. Chem. 1960 1 79; Compt. Rend. Acad. Bulgare Sci. 1960 13 555. N. A. Pangarov and S. D. Vitkova Electrochim. Acta 1966 11 1733. A. K. N. Reddy J. Electroanalyt. Chem. 1963,6 141. H. Fischer Elektro lytische Abscheidung iind Elektrokristallisation von Metallen (Springer Verlag Berlin 1954). ’J. O’M. Bockris Z. Nagy and D. Draft J. Electrochem. SOC. 1973,120,30.J. N. JoviCeviC D. M. DraiiC and A. R. DespiC Electrochim. Acta 1977,22 589. J. N. JoviCeviC A. R. DespiC and D. M. DraLiC Electrochim. Acta 1977 22 577. lo A. R. Despid G. SaviC MagliC and M. Jadovid Paper presented at the 28th Meeting of ISE Varna Sept. 1977. J. L. Barton and J. O’M. Bockris Proc. Roy. SOC.A 1962,268,485. l2 J. W. Diggle A. R. DespiC and J. O’M. Bockris J. Electrochem. Soc. 1969 116 1503. l3 J. Markov A. Boynov and S. Toschev Electrochim. Acta 1973 18 377. l4 cf. P. Delahay New Instrumental Methods in Electrochemistry (Interscience London 1954) p. 61.

ISSN:0301-5696    

DOI:10.1039/FS9771200126

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

New Interpretation of Texture Formation in Nickel Electrodeposits BY JEAN AMBLARD AND MICHELFROMENT Groupe de Recherche n”4 du C.N.R.S. “Physique des Liquides et Electroc hime” associ6 & 1’UniversitC Pierre et Marie Curie 4 Place Jussieu 75230 Paris Cedex 05 France Received 1st August 1977 Experimentally observed fibre textures in thick Ni electrodeposits are not satisfactorily explained by any theoretical treatment. The purpose of this work is to put forward an alternative interpreta- tion based on a critical analysis of the most important current theories (bidimensional nucleation geometrical selection) and a quantitative study of the texture exhibited by Watts-deposited Ni samples prepared in well-defined conditions. This new interpretation takes into account the effect near the cathode of various inhibitors (Ni(OH)Z gaseous Hz,Hads) which result from hydrogen codeposition.Since the earliest X-ray examinations1p2 it is well-known that the different crystallites of a metallic electrodeposit are never randomly oriented. They very often exhibit a one-degree orientation (like a fibre texture) in such a way that every crystallite has a tendency to possess a definite crystallographic axis [hkl]along the electric field direction. This tendency is more or less pronounced according to the nature of the metal being deposited and according to depositing conditions. Nickel is a good ex- ample among many other metals for giving numerous well-defined preferred orienta- tions. In order to understand the origin of such an anisotropy a great deal of work- both experimental and theoretical-has been devoted to the subject.We quote here as a basic work the early contribution of Finch and coworkers who showed by elec- 394 tron microscopy and diffraction that there are two different stages during the electro- lytic growth of a metal first an epitaxial stage where the orientation of the thin de- posit is identical with that of the substrate then an independent stage where the texture axis of thicker deposits is solely determined by the other depositing conditions. We shall restrict this Discussion to the latter case. Many theoretical explanations have been put forward to account for the different textures experimentally observed. We give in a first section a critical survey of two of the most important ones which start from quite opposite standpoints according to the first hypothesis anisotropy is the result of competitive while for the second theoretical treatment the same anisotropy stems from a growth competi- tion.8-10 A confrontation of both theories with recent experimental data which are recapitulated in section 2 proves that they are no longer adequate to account for the whole set of the results now available.The discrepancy mainly origin- ates from the unpredicted stability of textures like {110) and (21 1) whose crystallites systematically contain specific structural defects.” Thus a new interpretation has to be proposed. For this purpose we carefully analyse and discuss in section 3 the results of a systematic and quantitative study of the preferred orientations en- countered in Watts-deposited Ni samples in terms of three relevant parameters the JEAN AMBLARD AND MICHEL FROMENT Ni partial current density JNi (closely related to the cathodic potential at a given temperature) the bulk solution pH (pH,,,) and the electrolyte composition.1. CRITICAL SURVEY OF CURRENT THEORIES OF TEXTURE FORMATION 1.1. BIDIMENSIONAL NUCLEATION According to Pangar~v,~-~ the texture of a bulk deposit results from an anisotropy occurring in the nucleation process during which bidimensional nuclei are formed on inert sites of the substrate. Hence the only problem in predicting what kind of texture axis must be expected in given electrolysis conditions is to determine what kind of bi-dimensional nucleus is then most likely to be formed a calculation Ieads one to evalu- ate the work of formation of a (hk1)-type nucleus as a function of the overvoltage q and to determine the expected texture axes sequence for increasing values of r.For every f.c.c. metal the texture axes would then appear in the following order [lll] +[ZOO] -[110] -+ 113111+[210]. However many serious objections can be raised to this kind of theoretical treat- ment deposition is supposed to occur in " pure conditions " which means there are no disturbing effects from the substrate surface or from adsorbed species. Both conditions appear to be unrealistic requirements on the one hand metallic surfaces are seldom defect-free and we know that growth may occur on a screw-dislocation for example without requiring any nucleation process; on the other hand it is quite unlikely that a transition metal of high surface energy like nickel would ever exist without any adsorbed species.The last reason explains why Pangarov explicitly excluded the case of nickel from the field of application of his theory at least in his third paper7 if not in his previous w~rk.~*~ 1.2. GEOMETRICAL SELECTION Under this heading we gather a number of considerations developed by several authors especially by Reddy and coworkers &lofor the actual case of nickel deposits. The common idea is that anisotropy arises during the growth process during which are preferentially developed those nuclei which were initially favourably positioned on the cathodic substrate.The whole problem consists here in determining which factor is responsible for " favourable positioning ''-According to WilmanI2 the decisive factor is the initial orientation inside each crystallite of the most densely-packed reticular planes (i.e. the (1 11) planes for f.c.c. materials) since those planes have the lowest growth rate along their normal f.c.c. deposits should tend preferentially to develop (1 11) octahedral facets and hence exhibit either a [11 I] texture axis (in the so-called lateral mode of growth) or a [l 101preferred orientation (for an outward mode of growth). The essential contribution of Reddy has been to generalize Wilman's ideas to cases where slow growing faces are no longer the planes of highest reticular density but any kind of less-dense planes whose growing rate is slowed down because of the adsorption of hydrogen atoms (Had,).Admitting that hydrogen gas is preferentially adsorbed on less-dense planes (which seems now to be an erroneous concIusion)'3 and moreover that nickel electro- TEXTURE FORMATION IN NICKEL ELECTRODEPOSITS deposits only grow with an outward mode he concludes the preferential formation of facets to be in the following sequence 1111)+{loo}+(1 lo} *{21I} for an increasing disturbance of growth by Hads. Hence the following preferred orientations would be successively observed with increasing values of Hads coverage [110] +[loo] -[210]. Here again numerous objections must be raised against Reddy's theory.Of course the theory seems initially more satisfactory because it does not neglect the important disturbing effect of cathodic codeposited hydrogen. But Hads is far from being the sole chemical species capable of disturbing nickel electrocrystallisation since other species like H20 OH- NiOH+ Ni(OH), etc. . . . do exist permanently close to the cathodic surface. Another important feature of geometrical selection theories lies in their implication with regard to the morphology of electrodeposits they consider the deposits to be made of a mosaic of singre crystals for which the difference in growth rate of various reticular planes are doubtlessly the unique cause of anisotropy. Moreover not only must the texture axis be of a certain kind but we must observe simultaneously the preferential formation of particular facets.Such requirements seem to be very con- stricting because Ni deposits do not generally exhibit definite facets except for (21 1) and (1 10) textures whose crystallites are very often limited by (1 11) planes. We shall see below that both textures have to be excluded from Reddy's theory because of the very peculiar arrangement of their crystallites which systematically contain twin planes l4 and thus are never single crystals. 2. EXPERIMENTAL DATA The results we intend to discuss in the next section have been collected during a ten-year investigation in our laboratory. They all concern thick Ni samples (15 ,um or more) electrodeposited from a Watts type solution and examined with both X-ray diffraction and electron microscopy techniques.We shall present first the results obtained with an organic-free bath,15 then the effects of two typical addition agents on the structural properties of Ni deposit^.^^*^' 2.1. TEXTURES OF DEPOSITS FROM AN ORGANIC-FREE BATH 2.11. ELECTRODEPOSITION PARAMETERS We know from experience that texture like other physical properties of Ni electro- deposits critically depends on plating conditions. For this reason special care has been taken to control every electrolysis parameter. In all cases the solution was com- posed of NiS04. 7H20(300 g dme3) NiC1,. 6H20(35 g dm-3) and H3B0,(40 g dm-3) and its pH was adjusted with slight additions of either concentrated H2S04(d = 1.84) or NH40H (d =0.92) to values between 0 and 5.The temperature was maintained at 50 "Cand stirring was ensured by rotation of the cathode (a mechanically polished brass cylinder of diameter 28 mm) at a constant angular velocity (2000 r.p.m.) so that Ni deposition is never diffusion-controlled. Plating was carried out under potentio- static conditions and the duration of each experiment was chosen to obtain a deposit JEAN AMBLARD AND MICHEL FROMENT 139 of an effective thickness of 55 pm such a high value is required by our X-ray diffracto- metric method of texture quantitative analysis.18 In a solution of a given composition which relevant parameters govern the stability of textures? An earlier studylg dealing with this problem led to the conclusion that at a given value of pHsola change of texture axis occurs at a definite cathodic potential (after an appropriate ohmic drop correction) whatever the bath temperature and cur- rent density.Then by varying both cathodic potential and pHso value a diagram was obtained showing definite areas of stability for different textures. Such a dia- gram appears in fig. l where results are plotted against the same two parameters. d 0 u) 0 Ip upd CPO 0 0 0 Ol I I 1 n\ I I I3 It 1 I I 0.2 0.3 0.5 1" 23 5 10 20 30 'Ni min /A dm-2 1 I I I -700 -800 -900 cathodic potential /(mV/ S.C.E.) FIG.1 .-Stability diagram for the various textures encountered in thick Ni electrodeposits obtained from an organic-free Watts bath against cathodic potential (or Ni partial current density) and pH,,,.The arrow indicates how the (21 1) -+ [loo] frontier is shifted when the bath does not contain NH4+ions. For reasons given elsewhere l5 it seems however more accurate to determine the partial current density [JNimin) rather than the cathodic potential so we have plotted both scales in the abscissa. JNimin is computed from thickness measurements at the points of the disc cathode where the deposit is thinne~t.'~?~~ 2.12. TEXTURE DIAGRAM The diagram shows that according to the deposition conditions four different textures appear two of them have a stability restricted to definite pH values ([210] 140 TEXTURE FORMATION IN NICKEL ELECTRODEPOSITS for acid media and (21 1) for pHsol values 2 2.5) while the others exist in the full pH range.Regarding now the current density range we note that (1 10) only appears for very low values of JNimin in opposition to [210] which is associated with the highest current densities. The location of any frontier between two textures is very sensitive to a slight variation in deposition conditions; this is particularly true for the (211) -[loo] frontier which shifts towards higher current densities and more acid pH values when the solution does not contain its proper amount of NH4+ions.15 The comparison of our texture diagram with theoretical predictions proves that it is not possible whatever the pH,, value to recognize any predicted texture axes sequence. According to Reddy's theory for instance we should expect the sequence [210] -[loo] -+ [llO] with increasing current density (as the cathodic surface becomes free from HadJ and the results show just the opposite sequence at least at low pHsol values! 2.13.FURTHER INVESTIGATIONS If theoretical predictions are thus proved to be quite inadequate we must now try to understand why texture changes occur with pHsol and JNimin. In view of this objective we made further investigations in two main directions (1) a careful electron microscope ~tudy~~.~' of the crystallite arrangement for each texture reveals a great difference between <I 10) and (21 1) on the one hand and [loo] and [210] on the other the latter do not show any structural particularities while the former have a quite specific internal organization where crystallites systematically contain a given number of vertical twin planes which give them either a two-fold or a five-fold symmetry.Hence crystallites of both (21 1) and (1 10) textures are never single crystals; that is why we use the symbol { ) of a zone axis to represent both preferred orientations. Very recent work shows there is now strong evidence that such crystallites degenerate from tridimensional clusters possessing perfect icosahedral or decahedral structures.11 (2) A quantitative analysis of the textural perfection (Qhkl)as a function of pH and JNimin inside each texture domain gives relevant additional data 15917 { 110) deposits appear to exhibit the textures of lowest perfection and the shortest fibre coherent lengths; the more so in less acid media where { 110) deposits very often show a multi- component orientation ((110) + (211)).(211) deposits are generally of high per- fection with much longer fibres; by keeping constant the cathodic potential (around -810 mV/SCE) we have shown that an increase of pHsol without addition of NH40H was accompanied by a decrease in QZl1,while an addition of NH4+ions without varia- tion of pHsol induced an increase in Qzl1. [loo] deposits exhibit long fibres and tex- tures of high perfection; keeping the cathodic potential constant ( N -900 mV/SCE) we have observed a distinct degradation of this texture (= lower perfection shorter fibres) when going to lower values of pHsol a degradation caused by increasing hydro- gen evolution. In a quite opposite manner the perfection Qzlo of [210] deposits in- creases with acidification of the medium with an addition of NH4+ions or with an increase in JNi that is to say in every case where the evolution of gaseous hydrogen is enhanced.This conclusion has been recently confirmed by a complementary study of Qzloas a function of bath temperature and stirring efficiency,21 which proves that the best (210) textures are encountered in conditions (low temperature low stirring) favouring an inhibition of nickel growth by gaseous hydrogen. JEAN AMBLARD AND MICHEL FROMENT 141 2.2. MODIFICATIONS OF TEXTURES BY ORGANIC ADDITIVES We know from the literature that standard addition agents like acetylenic alcohols (levelling agents and brighteners) or aryl sulphonic compounds (brighteners) induce strong modifications in the crystal growth and therefore markedly affect texture^.^^^^^ Starting from an organic-free bath at a constant pHsol value (= 4.5) we have investi- gated how variable was the texture axes sequence (( 110) -+(21 1) -[loo]) with progressive additions to the Watts solution of two typical compounds butynediol (but-2-ynyl 1.4diol) and sodium benzene sulphonate.Both brighteners exert a common effect by producing grain refinement and simul- taneously a degradation of texture perfection but they modify the texture axes se- quence in a quite specific way the addition of butynediol leads to a quick disappear- ance of textures other than (211),16 while the sulphonic compound enhances the stability of It is noteworthy that such a specific behaviour may be related to the competition of cathodic discharge between Ni2+ and H+ ions.By measuring the rate of pHsol increase during Ni deposition we found that butynediol strongly im- poverished the cathodic layer in H+ ions while sodium benzene sulphonate did not have the same effect.17 3. NEW INTERPRETATION 3.1. INHIBITED DEPOSITION Compared with many other metals Ni deposition appears to result from a highly inhibited cathodic process in organic-free baths an overpotential of 200 mV is often required to initiate the metal deposition so that nickel has been regarded as an electro- chemically inert metal.23 Moreover Ni deposits are particularly fine-grained and frequently incorporate foreign materials. All these facts suggest that Ni electro- deposition is hindered probably due to a strong interaction between the metallic surface and every chemical species capable of being adsorbed upon it.3.2. WHAT KIND OF INHIBlTION ? We must now try to discover what kind of chemical species is the most likely to provoke an inhibition according to electrolysis conditions. Let us first of all examine in what conditions we may expect the strongest inhibition by Hads. Starting from equilibrium potential for the Ni2+ -/-Ni system (21 -500 mV/SCE) we know that Ni deposition begins as soon as the H+ discharge becomes diff~sion-controlled~~ (for a cathodic potential of about -690 mV/SCE in our conditions). Thus in the low current density range the metallic surface is expected to be almost entirely covered with €Iads; this has been experimentally c~nfirmed.~~ It is no longer the case for higher current densities because of a permanent renewal of Ni surface thanks to a faster crystallization without newly arriving protons (since they are still diffusion- controlled) Thus in a medium current density range we may expect the cathodic surface to be relatively free from Hads.And now what about the highest values of JNimin? Here again an inhibition has to be considered since we observe an import- ant H2 gas evolution; the more so for more cathodic potentials and more acid media. This gaseous hydrogen was supposed to come from the reduction of adsorbed H20 molecules.26 The fact that H+ ions arriving at a Ni cathode are readily discharged and ad- sorbed has as a main consequence the marked pH rise of the ~atholyte,~~.~~ which TEXTURE FORMATION IN NICKEL ELECTRODEPOSITS may cause precipitation of Ni(OH)2 close to the Ni/catholyte interface.Examination of the Pourbaix diagram for Ni,29which we have reproduced on the left hand side of fig. 2 enables one to predict in what electrolysis conditions we must expect the strongest inhibition by Ni(OH)2 both for less-cathodic potentials and less-acid media where the thermodynamically stable species is no longer Ni but its hydroxide. 3.3. AN ALTERNATIVE MECHANISM OF TEXTURE FORMATION The first experimental evidence is that for Ni deposition high overvoltages are required in such a way that every kind of nuclei must be formed during the nucleation process.This has been experimentally confirmed even under a very strong epitaxial influence:30 whatever the initial orientation of a single crystal Ni substrate and what- ever the current density we have observed the formation of tridimensional nuclei like those which lead to (1 10) and (21 1) textures. Hence texture must be the result of a competition which occurs during the growth process. Ni(OH1 /1 Ni potential /(mVIS.C.El FIG.2.-Comparison between Pourbaix' diagram for and the textures diagram of fig. 1 which shows the parallelism of Ni(OH)2/Niand (21 l>/[lOO] frontiers. But even though such a first conclusion resembles the starting point of geometrical selection theories it is no longer possible to suppose that anisotropy is only due to geometrical factors since we know that some of the various nuclei are necessarily non-single crystals the presence inside them of structural defects gives rise to a sharp anisotropy,20 far more pronounced than the anisotropy arising out of geometrical factors only.Moreover one must wonder how the various chemical species adsorbed on the cathodic surface play a role in the growth competition. It seems unlikely that a defin- ite chemical inhibitor Hadsfor example hinders the growth of any kind of nucleus in the same way. On the contrary the comparison between our experimental results JEAN AMBLARD AND MICI-IEL FROMENT in fig. 1 and the considerations developed in paragraph 3.2 strongly suggests that there is a close correlation between the stability of a given texture and the prevalence of a definite foreign species near the cathode/catholyte interface (i) (1 lo} appears at low current densities when it is mostly Hads which inhibits the deposition (ii) I12101 has a domain of stability restricted to conditions where gaseous H evolution is the strongest.We have shown that even the texture perfection is increased when H evolution is enhanced. (iii) (21 1> exists only for high pHsolvalues and relatively low current densities in the very domain where we expect a strong perturbation because of Ni(OH),. More-over if we compare in fig. 2 our texture diagram with the Pourbaix form there appears a parallelism between the (21 1) -[loo] frontier and the limit [eqn (2) of Pourbaix] of Ni(OH) and Ni domains respectively.Then taking into account the effects of Hads inhibition which shifts both pH and potential scales it is possible to ascribe (211) texture of Ni deposits to a specific inhibition by Ni(OH),. This hypothesis is reinforced by our results concerning butynediol this additive broadens the (21 1> domain as long as it impoverishes the cathodic layer in H+ ions thus favouring a Ni(OH)2 precipitation. (iv) conversely [loo] cannot be associated with any definite inhibition. This texture appears in conditions where the cathodic surface becomes relatively free from Hads,Ni(OH) or gaseous H,. Thus we consider it corresponds to thefree mode of growth for electrolytic Ni. Such a conception has allowed us to explain a good deal of data from the literature [loo] Ni deposits exhibit the highest d~ctility,~' the lowest internal stress and 11ardness.~~ Besides it is on a (100)-oriented Ni substrate that epi- taxial growth gives the best result~.~~'~~ CONCLUSION Our alternative explanation of texture formation in Ni electrodeposits has led us to distinguish a free mode of growth which favours the [loo] fibre axis and several hind- ered modes of growth each of them being closely related to a definite preferred orienta- tion (110) has been ascribed to a selective inhibition of the Ni/catholyte interface by Hads,(21 1> to Ni(OH) and [210] to the presence of gaseous hydrogen.This inter- pretation not only explains satisfactorily our own results but it gives a better under- standing of classical results taken from the literature concerning physical properties of Ni electrodeposits.R. Glocker and E. Kaupp 2.Phys. 1924,24 121. R. M. Bozorth Phys. Rev. 1925 26,390. G. I. Finch and C. H. Sun Trans. Faraday Soc. 1936,32,852. G. I. Finch H. Wilman and L. Yang Disc. Faraday SOC., 1947,1,144. N. A. Pangarov Electrochim Acta 1962 7 139. N. A. Pangarov Electrochim. Acta 1964,9 721. N. A. Pangarov J. Electroanalyt. Chem. 1965 9 70. a A. K. N. Reddy J. Electroanalyt. Chem. 1963 6 141. A. K. N. Reddy and S. R. Rajagopalan J. Electroanalyt. Chein. 1963,6 153. lo A. K. N. Reddy and S. R. Rajagopalan J. Electroanalyt. Chem. 1963,6 159. 11 I. Epelboin M. Froment and G. Maurin Comm. at the 28th ISE Meeting (Druzhba near Varna September 1977).l2 H. Wilman Trans. Inst. Met. Einishiirg 1955 32 281. l3 W. M. H. Sachtler G. Dorgelo and W. van der Knaap J. Chiin.phys. 1954,51,491. lJM. Froment and C. Maurin J. Microscopie 1968 7 39. l5 J. Amblard M. Froment and N. Spyrellis Surf. Technol. 1977 5 205. I44 TEXTURE FORMATION IN NICKEL ELECTRODEPOSITS l6 J. Amblard Th. Costavaras A. Hugot-Le Goff and N. Spyrellis Oberjlache-Surface 1977 18 1. J. Amblard Thesis (Paris 1976 C.N.R.S. A.O. 12387). l8 J. Amblard M. Froment and G. Maurin Electrodeposition Surf. Treutment 1974,2,205. l9 I. Epelboin M. Froment and G. Maurin Plating 1969,56 1356. 2o G. Maurin Oberjlache-Surface 1970,11,297,309; 1971,12,8,24,47 54. 21 J. Amblard M. Froment and S.Vitkova Comm. at the 28th ISE Meeting (Druzhba near Varna September 1977).22 Th. Costavaras M. Froment A. Hugot-Le Goff and C. Georgoulis J. Electrochem. SOC.,1973 120 867. 23 R. Piontelli and G. Serravalle Trans. Inst. Met. Finishing 1957 34 293. 24 R. K. Dorsch J. Electroanalyt. Chem. 1969 21 495. 25 Ph. Morel Thesis (Paris 1968 C.N.R.S. A.O. 2346). 26 L. B. Harris J. Electrochem. Sac. 1973 120 1034. *’ A. G. Ives J W. Edington and G. B. Rothwell Electrochim. Acta 1970 15 1797. S.I. Berezina L. V. Burnasheva A. N. Gil’manov I. Kh. Muzeev and R. M. Sageeva Elektro-khimiya 1974 10 948. 29 M. Pourbaix Atlas d’iquilibres dectrochimiques a 25 “C(Gauthier Villars Paris 1963) g. 333. 30 J. Thevenin J. Microsc. Spectr. Electron. 1976 1 7. 31 F. Denise and H. Leidheiser Jr J. Electrochem. SOC.,1953 180,490. 32 D. J. Evans Trans. Faraday Soc. 1958 54 1086. 33 B. Rivolta L. Peraldo Bicelli and G. Razzini J. Phys. D Appl. Phys. 1975 8,2025. 34 M. Froment G. Maurin and J. Thevenin Compt. rend. l969,269C 1367.

ISSN:0301-5696    

DOI:10.1039/FS9771200136

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Electrocrystallisation of Nickel on Copper BY J. P. G. FARR AND A. J. S. MCNEIL Department of Industrial Metallurgy The University Birmingham B 15 2TT Received 3 1st August 1977 A detailed electron microscopic study has been made of the very early stages of growth of nickel electrodeposits on to characterised (100) copper substrates. These observations have shown the elec- trocrystallisation of nickel on copper to be fundamentally different from its growth from the vapour involving the production of a specific type of defect the "growth dislocation ",to reduce misfit strain which has hitherto gone unreported. The importance of electron microscopy in the study of nickel electrodeposit struc- tures is well recognised yet while this facility has been applied fairly extensively in conjunction with replica techniques,l to the examination of deposit morphology [e.g.ref. (2)-(S)] its use for systematic structural investigations of nickel electro- crystallisation has been comparatively cursory. In particular we know very little yet about the earliest stages of deposition when events are occurring that may well determine the characteristic structures of the thicker deposits. This paper presents the results of an electron microscope study of the first stages of the growth of nickel on to copper single crystal (100) substrates. Such an approach inevitably demands some acquaintance with the techniques of electron microscopy and with the behaviour of dislocations in metals. The exposition of the former topic in ref.(9)-(14) (the last concerning Moire patterns) is more than adequate for the present purpose. A suitable treatment of dislocations in metals is given in ref. (9) (13) (15)-(17) with the first two considering dislocations in the con- text of electron microscopy. ELECTRON MICROSCOPY STUDIES OF NICKEL ELECTRODEPOSITION ON COPPER The most thorough study of the first stages of nickel electrodeposition has been made by Gaigher and van Wyk.ls-*O These authors used thin (100) copper films pre- pared by vapour deposition on to rock salt having -5 x 10' dislocations cm-2 and a low density of microtwins. Gaigher and van Wyk observed different nickel be- haviour on the two sides of the copper films which they attributed to contamination and oxidation. On the side adjacent to the rock salt which they called the clean side no signs of nucleation were seen.On the other side which had been exposed through- out the preparation procedure nickel growth commenced by three-dimensional nucleation. Nickel deposits on the clean copper substratesl8 showed no features up to -2 nm thickness; the stripped films were essentially continuous. Between 3 and 10 nm thickness the films showed strong contrast effects which were attributed to holes in the nickel layer. These nickel deposits displayed two types of dislocations first a ELECTROCRYSTALLISATION OF NICKEL ON COPPER " very low " density of scattered dislocations -100 nm long at 5 5 t 5 10 nm; and a second for t 2 10 nm long straight dislocations of -2 (1 lo} type generally with Burgers vectors b inclined to the film plane but sometimes with b parallel to the film plane.Gaigher and van Wykls measured the misfit between the nickel and copper lattices using the MoirC fringe spacing and the splitting of diffraction spots (curve c in fig. 7). Gaigher and van WykI9 repeated this work using the exposed sides of their copper substrates. They found that nickel growth now commenced with the formation of three-dimensional nuclei 5 15 nm across which revealed themselves by their strained condition on the copper substrates. The nickel layers quickly became continuous usually by -5 nm. The misfit of these nickel deposits with their copper substrates increased rapidly from 0.016 at 10 nm to near the maximum 0.0259 by -1 5 nm which is in marked contrast with the behaviour of the deposits on " clean " substrates (fig.7). The authors gave no information on the formation and type of dislocations in these deposits however. The nickel deposits also displayed large block-like growths 50-300 nm in size which were nearly always bounded by (100) directions though some- times by (110) and were present in all the electroplate examined up to 30 nm. Gaigher and van Wyk suggested that these formed on oxide on the copper films. The same authorsZo went on to investigate the influence of codeposited foreign substances on the growth of nickel by varying the pH of the solution. They found that the Ni/Cu misfit increased with decrease in pH at any given thickness (see curves b c and din fig.7). Gaigher and van Wyk tentatively concluded that the nickel lattice was elastically strained to match the copper substrate but noted that the measured values of misfit could not be correlated with elastic strain because the degree of lattice expansion by codeposited substances was unknown. Accurate measurements of the lattice parameters of the nickel deposits from each of the solutions revealed values very close to that for bulk nickel indicating that no lattice expansion had occurred and that the nickel layers were truly elastically strained. Gaigher and van Wyk ob-served dislocations in short lengths and found that their density was higher and their glide was easier in deposits from low pH solutions. They then explained the differ- ences between the misfit curves (b),(c) and (d)in fig.7 and also their generally low values in terms of codeposited material impeding dislocation motion. Thompson and Lawless 21 have presented observations on interfacial dislocations lying between 20 nm thick nickel deposits and (100) and (1 11)copper substrates which resembled the defects seen by Gaigher and van Wyk.20 The traces of these disloca- tions lay in (1 10) directions and produced a local reduction in Moir6 fringe spacing implying a corresponding increase in misfit and relief of elastic strain. They sug- gested that the length and straightness of these dislocations were related to their glide on (1 11) planes and proposed two types of dislocation for the nickel deposits first an ingrown edge type with b contained within the film plane; and second a mixed edge and screw type with b inclined at 45" to the film plane.The second type is not as efficient in reducing misfit as the first but is the only type that can be produced by gliding of pre-existing dislocations or by nucleation of fresh dislocations at the free nickel surface. Finally Nakahara and WeilZ2 have studied the growth of nickel on vapour de- posited copper films under a variety of conditions. The copper substrates were annealed to reduce the defect density to -loS twins cm-2 and " a number " of disloca- tions. These workers found that nickel growth generally commenced with the forma- tion of three-dimensional epitaxial crystallites (TEC) but that their formation and character depended on the deposition conditions.For example no TEC were seen J. P. G. FARR AND A. J. S. MCNEIL in deposits from solutions buffered to pH 3. When TEC were formed the deposit attained continuity between 2 and 5 nm but otherwise continuity was achieved almost immediately. The continuous films exhibited elastic strain Moir6 fringes and thick- ness variations; the first feature was relieved by the formation of dislocations accom- panied by a splitting of the Ni/Cu diffraction spots. In the deposits forming either large TEC or none at all there were long straight dislocations of 2 (1 10) type with 2 edge character. These defects disappeared when the nickel films were stripped from their substrates showing that they had been lying in the bicrystal interface. Those deposits which displayed small or irregular TEC developed less regular dislocations which did not lie in the Ni/Cu interface but in the nickel layer.This work was con- tinued by Weil and WU,~~ who studied the defects formed by the coalescence of crystal- lites. STRUCTURE OF VAPOUR DEPOSITED FILMS It is necessary to consider vapour deposited films here because this is a well under- stood area and one closely related to electrodeposition. Single crystal vapour de- posited films have been to grow both by spreading monolayers and also by the formation of three-dimensional nuclei followed by their growth and coalescence into a complete film. We confine ourselves here to the former case. A theoretical study of monolayer growth was first made by Frank and van der Merwe,28 which has since been extended by van der This author has shown that it is energetically favourable for the deposit layer to strain elastically so as to reduce the misfit between the two lattices to an extent depending inter alia on the bulk misfit and the deposit thickness.Frank and van der MerWe28 distinguished a critical misfit up to which the first few deposit monolayers follow the substrate lattice perfectly; conditions change with growth however and dislocations are generated at the free surface of the deposit because the energy to strain it elastically increases with thickness. In all cases the model assumes that the deposit is homogeneously strained. A number of experimental studies [e.g. ref. (33)] established the existence and identity of the postulated dislocations.Other studies [e.g. ref. (34) (35)] though providing some quantitative support for the model noted that the observed reduction in elastic strain was smaller than predicted. Matthew~~~9~~ and Cabrera36 both con- sidered that difficulties in the generation and movement of dislocations in the deposit might account for this discrepancy. Two mechanisms have been proposed for the provision of dislocations to relieve strain. The first 34 involves the extension of disloca- tions already in the substrate while the second35 involves the nucleation of a fresh dislocation at the free deposit surface followed by its extension through the film and down to the interface. GROWTH OF NICKEL ON COPPER FROM THE VAPOUR Two studies have been made of the vapour deposition of nickel on to copper which may be related to its electrocrystallisation.Matthews and Crawford 37 prepared a single crystal nickel film in which there was a thickness gradient. They found that the nickel was strained to match the copper base up to -1.5 nm when interfacial dislo- cations appeared increasing in number as the film thickened so that the strain in the nickel was quickly reduced (curve a in fig. 7). The critical thickness at which the dis- locations appeared was in agreement with the van der Merwe m~del,~*-~~ as was the ELECTROCRYSTALLISATION OF NICKEL ON COPPER development up to -5 nm. Thicker films showed more elastic strain than the theory predicted but Matthews and Crawford were able to eliminate this discrepancy by adapting the model to take into account dislocation interactions in the nickel layer.Gradrnann3' also studied the vapour deposition of nickel on to copper and ob- tained results similar to those of Matthews and Cra~ford.~' EXPERIMENTAL SUBSTRATE PREPARATION AND CHARACTERISATION The substrates used were (100)-oriented single crystal films of copper -100 nm thick. These were prepared by vacuum evaporation on to (100) single crystal faces of rock salt fol- lowing the procedure of Brockway and Marc~s.~~,~~ The cleaved rock salt faces were polished on moist filter paper and then rinsed in distilled water and in methanol; this eliminated the larger cleavage steps and surface debris on the rock salt and also resulted in a copper film with a refined structure and a smoother topography.The copper films were annealed on their rock salt substrates in a hydrogen atmo~phere.~~*~~ It was found that all annealing treatments were accompanied by the formation of holes in the copper films which produced perturbations in the nickel deposits. The precise nature of the hole-forming reaction could not be ascertained though the observation of what appeared to be CuCl around the holes suggests an interaction between the copper and the rock salt. A satisfactory structure was produced in the copper films by annealing in hydrogen at 1 atmo- sphere pressure at 540 "C for 5 min. Although the rock salt substrates could be quite uneven the copper layers quickly de- veloped smooth surfaces during vacuum deposition.The annealing treatment produced large defect-free areas in the copper films bounded by long stacking faults lying in (1 lo} directions (fig. 1). This is very unlike the usual structure of evaporated films which is a combination of subgrains short planar defects and tangles of dislocations typically 101o-lO1l lines cm-2.39-41 NICKEL ELECTRODEPOSITION Practical difficulties in handling the fragile films and in avoiding as far as possible con- tamination of the films and the electrolyte restricted the choice of electroplating equipment and procedures. The copper films were floated on the electrolyte surface electrical contact was made with a fine probe wire and nickel was deposited on the underside [see ref. (21)]. This procedure has the advantages of involving very little mechanical handling of the film no organic masking materials and no pre-plating surface treatment for the copper film can be plated within a few moments of its removal from the annealing furnace.There are serious limitations however. First the copper film is in contact with the electrolyte for a period of time (up to -4 min) before plating starts and some surface attack may occur in that time. Second plating on the underside of a floating film certainly involves a pattern of convective flow different from that operating at a vertical cathode; the situation is not hydrodynamically well-defined. Plating was performed in a U-shaped cell which could be tilted to allow the films to be floated on to the electrolyte easily.A perspex jig on one arm of the cell carried a fine copper probe which could be lowered just to make contact with the copper film. Current was sup- plied galvanostatically using a 180 V supply and a large series resistance. A Tektronix 564 storage oscilloscope was used to monitor the voltage across aknown resistance in the plating circuit and thereby to display both plating current and time. Overpotential was not measured. Immediately before plating each small 42x 2) mm2,copper substrate film of known area was hydrogen-annealed on its rock salt substrate. The copper film was stripped from the rock salt in N/120 hydrochloric acid to prevent oxide growth. The film was inverted at this stage so as to deposit nickel on the smooth copper surface developed during vapour FIG.1 .-The structure of the annealed copper substrates comprising large defect-free areas bounded by long stacking faults.The electron image also shows (200) and (220) extinction contours meeting in the upper left corner each of which is flanked by finer subsidiary fringes produced by higher order reflections. [Toface page 148 J. P. G. FARR AND A. J. S. MCNEIL deposition. After plating the Ni/Cu bicrystal was removed from the cell rinsed in methanol and folded in a double (oyster) electron microscope grid. It was found that this could be accomplished most easily with the film and grid resting on filter paper soaked in methanol whose surface tension held the film steady. Nickel deposits were prepared from a standard Watts solution buffered to pH 3 [see ref.(2)]. Four deposit thicknesses were produced 1 5 10 and 30 nm at two current densities 5 and 40mAcm-2. Plating times for the thickest deposits were 17 and 2.1s respectively. After transmission examination of the Ni/Cu bicrystals in an AEI EM6G electron micro- scope the nickel deposit topographies were replicated with platinum/carbon [see ref. (l)]. RESULTS INTRODUCTION Because we are dealing with a Ni/Cu bicrystal which carries a certain amount of macrostrain the exact nature of the contrast in the electron image depends on the way the film lies in the electron beam. All the micrographs presented here have been taken with the copper side uppermost i.e. the beam passed first through the copper and then through the nickel.As has been made clear in the previous section the experi- mental conditions were chosen to ensure as perfect a substrate as was reasonably possible. All observations of the nickel deposits were made in the defect-free regions shown in fig. 1 avoiding the stacking faults and holes with which anomalous nickel deposition was associated; all the structural features seen in the micrographs were contained within the nickel layers. The transmission micrographs of the Ni/Cu bi- crystals contain a large amount of information although their interpretation is by no means straightforward relying upon an understanding of the sources of image contrast.9-14 It is useful to bear in mind that in looking at the growth of nickel on copper we see a situation governed both by misfit and by epitaxy.The copper substrate has a lattice parameter -24% larger than that of the nickel; it would require a considerable stress to stretch the nickel to that extent in the bulk condition so that plastic deformation would occur. Nonetheless? the two lattices are similar enough in nature and dimen- sion for the nickel initially to attempt to continue the underlying copper structure rather than suddenly to create its own. Both series of nickel deposits displayed two apparently unrelated types of growth; first discrete "primary " crystallographic features which were largely inactive and were quickly engulfed by the second type the nickel deposit proper. PRIMARY GROWTHS The primary growths marked G in the micrographs showed common characteris- tics and behaviour.First they all displayed a crystallographic appearance initially square with {loo} edges and later square with {1lo} edges. Secondly they showed only a small size range with the upper limit being -250 nm across and -50 nm high but with no definite lower limit. They were all rapidly overgrown by the surrounding nickel layers and had disappeared by a deposit thickness of -30 nm. Thirdly all the primaries showed a measure of strain contrast of a polarity light -+ dark in the positive direction of the diffraction vector g (which we refer to as L +D in +g) that indicated a radial inward pull on the copper substrate due to the misfit between the nickel and copper lattices (fig. 2). Finally and most strikingly the primary growths were quite free of defects at all stages of deposition.ELECTROCRYSTALLISATION OF NICKEL ON COPPER I 1 I I f C" FIG.2.-The distribution of lattice strain associated with certain contrast features. (a)A large primary growth pulls the surrounding copper lattice planes inwards producing L -+D contrast. (b) D +L contrast features can be produced by holes as shown for clarity here or by non- uniform strain. (c) Thickness variations can produce lattice strain and thereby contrast in the electron image. GROWTH OF THE NICKEL DEPOSITS The development of the nickel deposit topographies followed a simple pattern. Both series of Watts deposits were consistently smooth though at 30 nm they appeared to be developing a common characteristic topography [fig.4(c)] bearing small pits that might possibly be the precursors of the pyramidal pits seen in thick (100)-oriented deposits el~ewhere.~.~ The structural development of the nickel deposits fell into three stages and the transmission observations are treated accordingly. STAGE 1 FORMATION OF A CONTINUOUS LAYER In the first stage shown by the 1 nm deposits the nickel layers exhibited very little contrast. The only definite features to be seen (marked H in the micrographs) were small with a dark to light contrast polarity (D -+ L in +g). This indicates that the copper lattice planes were pulled outwards by a symmetrical radial stress. It is not possible to interpret the contrast more exactly; these features may be holes in the nickel layer as shown in fig.2 or they may be regions of non-uniform strain. What-ever their exact nature these features indicate that by 1 nm thickness the nickel de- posits were essentially continuous over the copper substrates. There was a clear difference at this stage between the two 1 nm deposits; the 40 mA cm-2 deposit dis- played more numerous and " contrasty "features than the 5 mA cm-2 deposit. J. P. G. FARR AND A. J. S. MCNEIL 151 STAGE 2 GENERATION OF LOCALISED DEFECTS The start of the second stage of nickel growth was signalled by the appearance in the deposit of two related features a strong rippled or periodic contrast and an array of very short dislocations marked R and D respectively in the micrographs. The latter features are a specific hitherto unreported type of defect ; they will be referred to as growth dislocations to distinguish them from the misfit or interfacial dislocations observed here in the later stages of nickel growth and also by other workers in electro- deposited and vapour deposited films (see Introduction).The ripple contrast patterns were always aligned perpendicular to the diffraction vector S and their polarity (D +L in +g) indicated a radial outward strain in the nickel. The almost uniform state of strain in the earliest deposits had broken down to give a non-uniform strain distribution with some regions bearing more than the overall degree of strain. The strain contrast fields were extended in directions per- pendicular to g in the electron image thus producing the rippled appearance.The development of non-uniform strain shortly preceded the appearance of the growth dislocations. These varied in length extending as deposition proceeded but by the standards of bulk materials they were very small most being 5 40 nm long with many appearing only as dot-like features. The majority of the growth dislocations were situated in the highly strained regions while the remaining number were small and more or less evenly distributed. Their generation and extension reduced the degree of ripple contrast but by no means eliminated it. The rate of generation was extremely high; in the 5 mA cm-2 series for example 101o-lO1l lines cm-2 (equivalent to a severely cold-deformed metal) had been produced at -10 nm after their first appearance at -5 nm.The rate of formation was even higher at 40 mA cm-2. These values are close to those observed in the thickest deposits so it seems that the majority of growth dislocations were produced in the early stages of deposition (before -10 nm) and the rate of production subsequently diminished. It proved very difficult to characterise the growth dislocations. Their behaviour under different conditions of tilt was unusual; this is attributed to the particular nature of the specimens for the dislocations were exceedingly short and close to the specimen surface. A number of observations were made however first the growth dislocations were almost always seen with their lines approximately normal to the diffracting vector g showing only a small variation about that alignment thus very few dislocations were observed with more than one g; secondly all dislocations were short and straight generally 540 nm long; finally they were largest and most numer- ous in the highly strained regions of the deposits though they only partly relieved the strain there.With the formation of growth dislocations in large numbers MoirC fringes appeared in the transmission images of the deposits accompanied by a splitting of the spots in the diffraction patterns. Both features indicated the development of a significant misfit between the two crystal lattices. The MoirC fringes resulted from the periodic interference between the nickel and copper lattices; the diffraction spots split as the lattice parameter of the nickel changed from the copper value to which it had been stretched.In their early stages of formation the MoirC patterns were faint patchy and highly distorted but later they became clearer and more regular. In all deposits displaying Moirk patterns fringe-free areas could be seen which had an associated L -+ D strain contrast. The larger areas were almost certainly the remains of primary growths which were being engulfed by the surrounding nickel deposit and in some micrographs [e.g.,fig. 4@)] the Moiri patterns can be seen grow- ing over them. It is not certain that all the fringe-free areas were primary growths ELEC'I'ROCRYSTALLISATION OF NICKEL ON COPPER and in fact micrographs such as that in fig. 3(d),make it clear that in many cases they are simply dislocation-free regions which are lagging behind the overall deposit development.In all cases however the fringe-free areas gradually shrank often becoming quite round and had almost disappeared by 30 nm. The fully developed MoirC patterns (e.g. fig. 5) displayed a number of features characteristic of specific structures in the deposits. They clearly revealed a high dis- location density typically -loll lines cm-2 close to the direct counts of the growth dislocations at lesser thicknesses. They also revealed the non-uniform condition of the deposits and in a number of ways. First they showed a degree of " mosaic " character comprising small areas with a relative misorientation indicating that the nickel was locally misoriented with the underlying copper to the extent of -1 '.This misorientation also showed itself in the diffraction patterns where the nickel spots were streaked in a small arc with an angular spread of -1'. Secondly the consider- able variation in fringe spacing and finally the light and dark patchiness of the MoirC patterns both indicated non-uniform strain which produced localised variations in the diffracting conditions in the Ni/Cu bicrystals. STAGE 3 PRODUCTION OF LARGE-SCALE COOPERATIVE DEFECTS The last features to appear in the nickel deposits marked the start of the third stage of the growth; these will be referred to as interfacial disIocations (ID in the micrographs) to distinguish them from the second stage growth dislocations. The interfacial dislocations were all aligned in (1 10) directions often with lengths of a few microns and generally only appeared in the 30 nm deposits though they occasionally appeared at 10 nm.They were not major features even at 30 nm however and were unevenly distributed. The interfacial dislocations appeared in the MoirC patterns and could be detected by their normal dislocation contrast and by their disruption of the fringe array [fig. 3cf)l. None of the 30 nm deposits showed any signs of twinning or polycrystallinity. MISFIT MEASUREMENTS The diffraction patterns were used to plot the development of misfit between the nickel and copper lattices shown in fig. 7. The relative rnisfit,f is defined by f= (b -ah where a and b are the lattice parameters of the overgrowth and substrate respectively.Thus the misfit can be determined from the diffraction pattern by f= (hi -RCu)/&u where R is the radial distance from the (000) difii-action pattern origin to the respective spot. The unstrained or bulk misfit betwen the lattices of nickel (a = 0.3524 nm) and copper (a = 0.3615nm) is 0.0259. This diffraction method of misfit measurement is a through-thickness method and so gives some average value lying between the ex- tremes of the Ni/Cu interface and the free nickel surface. The plot shows that at a current density of 40 mA cm-2 most of the misfit had been attained by -5 nm thick- ness and there was little subsequent increase. The curves also show a small decrease in misfit when the current density was reduced from 40 to 5 mA cm-2.While the misfit curves are equivocal on this point the transmission micrographs have made it FIG.3.-The series of Watts deposits produced at 5 mA cm-2. (a) 1 nm showing primary growths G hole-like features H and a pre-existing dislocation in the copper film D (Cu). (b)5 nm now showing dot-like growth dislocations D and ripple contrast R. (c)and (d)10 nm displaying a faint and distorted Moire pattern M punctuated by fringe-free areas F which are lagging behind the general deposit development. (e) and (f) 30 nm showing the fully developed Moire pattern and interfacial dislocations ID in certain areas. [Toface page 152 FIG.4.-Watts deposits produced at 40 mA cm-2. (a) 5 nm already showing a faint and highly distorted Moir6 pattern and small fringe-free areas F.(b) 10 nm showing the MoirC fringes M extending into the primary growths G. (c) 30 nm a Pt/C single stage replica revealing small pits P in the nickel deposit surface. [Toface page 153 J. P. G. FARR AND A. J. S. MCNEIL abundantly clear [compare fig. 3(b) (c),(d)and 4(a) (b)]. The other curves will be dealt with in the discussion. DISCUSSION PRIMARY GROWTHS Despite their numerous formation it is clear that the primary growths were not the stable product of nickel deposition for they rapidly disappeared from both deposit series. It is difficult to explain their formation when the stable form of nickel deposi- tion was by continuous layer growth. It is suggested therefore that these primary features formed during the " incubation period " when the copper film was floating on the electrolyte prior to plating.It was repeatedly observed that the copper sub- strate had suffered extensive dissolution around holes and along stacking faults by local cell action and this would have to be balanced by the deposition of an equivalent quantity of nickel. Such a deposition occurring in localised areas would account for the observed primary growths and its occurrence during the incubation period would account for the disproportionate amounts of material seen in the micrographs of the early deposits [fig. 3(a) and 3(b)]. The rapid disappearance of the primary growths suggests that the nickel ion supply was adequate. Were this not so their growth would have been enhanced especially at the higher current density; this was not seen.Gaigher and van Wyk19 found large block-like features in their Ni/Cu bicrystals and showed them to be nickel in agreement with the present observations. Their sug- gestion that they formed at sites of copper oxide (Cu20)growths is not supported by the present work because the preparation method completely removed all oxide from the copper substrates. STAGE 1 GROWTH Though it is not possible to identify the D -+ L contrast features in the 1 nm deposits with any certainty they are clearly not discrete nickel growths and so tell us that by 1 nm the nickel had formed an essentially continuous layer over the copper base. The interpretation of these features as regions of non-uniform strain however is consistent with the incorporation of more structural disorder in the deposit with increasing deposition rate as will be discussed more fully with reference to stage 2 growth .The observations on stage 1 growth are consistent with the results of other trans- mission studies. Lawless5 has reported complete coverage by very thin nickel de- posits on copper. Nakahara and Wei122 found layer growth under the conditions used in the present work. Gaigher and van Wyk18 also found total nickel coverage occurring early on clean copper substrates; they observed no features in deposits 53 nm thick; this may be due to their use of a low current density (1 mA cm-') for the present observations indicate a decrease in the number of defects and contrast features in the early stages when the current density is reduced.STAGE 2 GROWTH There were considerable problems in imaging the growth dislocations which meant that the normal methods of dislocation analysis could not be applied. In normal practice for example with longer dislocations in a bulk metal the Burgers vectors b characterising the defects are identified by tilting the specimen so as to view the disloca- ELECTROCRYSTALLISATION OF NICKEL ON COPPER tions using a number of diffracting vectors g. The fact that a dislocation becomes invisible when gis perpendicular to b enables the dislocations to be identified uniquely. In the present work however it was found that the growth dislocations could be imaged only with one g; under other conditions of tilt they were not visible and the normal methods of dislocation analysis could not be used.The reasons for this possibly lie in the extremely small size of these defects and their closeness to the nickel surface which would certainly reduce their strain field (thus reducing contrast) and may introduce other imaging problems. The experimental results are complex and in some instances conclusions have had to be drawn from a collection of related observations rather than from direct observa- tion or measurement. Nevertheless taken as a whole the pattern is seif-consistent and is in good agreement both with established knowledge and with other experimental observations. The evidence indicates that the non-uniform strain field is an intrinsic feature of the growth of nickel on copper by layer spreading.The discrete D -+ L contrast features in the 1 nm deposits then appear as precursors of the periodic strain field. The micrographs show this non-uniform strain to be closely connected with the appearance of the growth dislocations though their precise relationship is not obvious The high strain in the deposits apparently favoured their formation and extension yet was not essential for some dislocations albeit few and small did appear outside the regions of high strain. The Moirk patterns showed short extra half lines (as at D in fig. 5) indicating that dislocations were still being formed at 30 nm when substantial misfit had developed between the nickel and copper lattices with a conse-quent reduction in strain in the nickel.The majority of growth dislocations were formed very quickly however following the development of non-uniform strain ; subsequent formation was at a slower rate. The micrographs show when the growth dislocations appeared in the deposits but not whereabouts they were formed. It seems clear however that they must have been generated in the growing nickel surface. In the observed absence of extensive dislocation glide strain relief must have involved the introduction of “ extra ” nickel planes in the deposit. There is no way of doing this in the bulk of the specimen for what is given to one region for the relief of strain must be taken from another. The only source of “extra” nickel in the deposit is the deposit/solution interface i.e.the free nickel surface. This conclusion is supported by the observation that most of the growth dislocations were generated in the highly strained regions; they must be surface phenomena and would therefore have no influence on any interfacial mechanism of dislocation formation. Although it was impossible to characterise the growth dislocations by the usual rigorous methods9Tl3 it seems reasonable to conclude that as the optimum imaging condition occurs when g is parallel to the Burgers vector b of a dislocation the growth dislocations have their Burgers vectors perpendicular to their lines thus mak- ing them edge types. Two types of dislocation are then possible unit a (110) dislocations and a(1 1I} Frank partials.15-” The presence of partials can be dis- 3 missed on two counts first because the stacking fault energy of nickel at 180-240 erg cmU2 [ref.(1 51 (42) (43)] is too high; and secondly because the consequent frac- tional displacements in the Moire fringes were not observed [fig. 5 and ref. (9) (14)]. The evidence thus indicates that the growth dislocations observed in the micrographs are unit dislocations taking the form of loops with both ends lying in the growing nickel surface. FIG.5.-Moirk pattern of a 30 nm 5 mA Watts deposit displaying certain structural features dislocations with 1 and 2 extra fringes (A and B respectively) multiple dislocations (C) and short fringes (D). [Toface page 154 J. P. G. FARR AND A. J. S. MCNEIL Two types of unit dislocation loop can be formed both a (1 10) and with strong 2 edge character.They are otherwise radically different however in behaviour and mechanism of formation. The first type (a) in fig. 6 is a prismatic dislocation wholly edge in nature and formed by the insertion of two extra (1 10) half planes like a wedge into the growing nickel surface. The second (b),is a shear-type dislocation loop with b contained within the loop plane; it is formed by the shear of a small region of the nickel surface on a (111) slip plane and has a mixed edge and screw character. loop plane . loop plane 3 FIG.6.-Dislocation loops in the growing nickel surface. (a)Prismatic loop (i)b inclined at 45" to thefilm plane (ii) b parallel to the film plane. (6)Shear-type loop with b at 45" to the film plane.It turns out that type (b)is the interfacial dislocation that has been observed in the third stage of deposition here as elsewhere in electrodeposits20*21 and in vapour de- posit~.~~*~~*~~*~~*~~ This defect is able to glide laterally through the deposit layer to produce the long straight dislocation lines seen in fig. 3(f). The radically different nature of the growth dislocations makes it clear that they must be type (a) the pris- matic dislocation. This conclusion is supported by two observations first the gener- ation of the shear-type loop depends solely on the presence of very high stresses in the nickel surfaces and this would probably be preceded by the formation of the prismatic type of dislocation which would be assisted by strain in the nickel surface but not be dependent on it ; second the prismatic dislocations are revealed in the Moirk patterns (as at B in fig.5) which all display dislocations with two extra fringes; these must be dislocations with b in the film plane which can only be prismatic dislocations. It is difficult on the present evidence to gain any clear understanding of the man- ner of generation of growth dislocations in the nickel deposits. However the delay in their formation the importance of deposition rate and of surface strain imply the presence of a kinetic barrier to nucleation. This suggests that the dislocations are not built into the lattice atom by atom but are generated by the rearrangement of a small ELECTROCRYSTALLISATION OF NICKEL ON COPPER element of nickel in the surface possibly with a minimum stable size.This is similar to the manner of formation of prismatic dislocations in bulk metals which is by aggre- gation of atoms or of vacancies to form an extra lattice From this view- point the deposition rate probably influences the rate of dislocation formation through its effect on the state of order in the nickel surface; there is evidence for a considerable degree of surface disorder. The early MoirC patterns [fig. 3(d) and 4(a) for the 5 and 40 mA cm-2 deposits] which indicate the condition of the nickel surface layers dis- play a high degree of disorder much greater than those from the 30 nm deposits [fig. 3(e) and cf)] which relate more to the bulk of the deposit.Thus the mechanism of growth dislocation formation is put on something of a statistical basis influenced by strain in the nickel and also by deposition rate. It is of course quite possible that a number of dislocations are generated by what might be called " random fluctuations " in the deposition process. This cannot be examined in the Ni/Cu system where deposition is dominated by the Ni/Cu misfit but could usefully be investigated in the growth of nickel on nickel. It is clear from the micrographs that the growth dislocations are not mobile in the deposits in the same manner as are the interfacial dislocations of stage 3; yet the growth dislocations were observed to be extending in the deposits. This observation is easily catered for by the prismatic loop shown in fig.6(a),for it is amenable to ex- tension by the incorporation of nickel atoms at the ends of the dislocation line. This process would be especially favourable to the growing nickel deposit for it would introduce " extra "material and so further reduce strain. The process is clearly shown in some of the micrographs e.g. fig. 3(b) and (c) and is directly equivalent to the pro- cess of negative climb observed in bulk materials.15-17 In the bulk metal climb is dependent upon high temperatures to provide the necessary diffusion. Clearly no such diffusion could be occurring in the bulk of the nickel electrodeposits but at their free surfaces there is a very high flux of discharging atoms that would act as the diffusing species. This process of dislocation extension which we may perhaps call " surface climb " is thus a two-dimensional analogue of the three-dimensioml bulk phenomenon.The large multiple dislocations revealed by the Moirk patterns (as at C in fig. 5) are aggregates of single growth dislocations and it seems feasible that they were formed by surface climb of individual dislocations. Repeated localised nucleation of single growth dislocations can be discounted for the formation of each defect by reducing the local strain would make subsequent dislocation formation less likely. Certainly surface climb seems to offer a simple means for the nickel deposit to adjust to the varying and localised constraints of growth. For example the mosaic texture of some of the MoirC patterns fig.3(e) and 4(b) could well have been produced by surface climb of the growth dislocations into low energy configurations ; such arrange- ments may provide the basis for subsequent polycrystallinity. In this context it would be interesting to look at the growth of nickel on (1 11)-oriented copper sub- strates for such deposits rapidly become polycrystalline whereas { 100) nickel deposits usually remain monocrystalline to considerable thicknesses beyond the limitations of the electron micro~cope.~*~*~~ Surface climb results from the incorporation of " extra " nickel atoms at the ends of the growth dislocation lines but impurity atoms could be incorporated just as well which could influence the extension and possibly the mobility of those defects. This aspect could be examined by preparing nickel deposits from solutions of differing purity; one would perhaps expect to see long possibly mobile dislocations in the pure deposits and short possibly bent ones in the impure deposits.This could be done in a more controlled way by varying the solution pH as did Gaigher and van J. P. G. FARR AND A. J. S. MCNEIL Wyk,20 who found a greater incorporation of foreign matter from solutions with higher pH. So far we have seen how effective were the growth dislocations in reducing strain in the nickel i.e. increasing misfit with the copper substrate (fig. 7). Yet this was a short-term phenomenon only for at some later stage a new and more effective mechan- ism of strain relief had to be introduced-the interfacial dislocation.The reason seems to lie in the immobility of the growth dislocations for their nature means that they 0.026 0.022 1 0.018 -. Y 0.014 v) E 0.010-0.006 . -..... 2 4 6 610 20 30 40 nickel thickness /nm FIG.7.-Misfit curves for the growth of nickel on copper. (a) Vapour dep~sition.~’ (6) Electro-deposition 1 mA crn-’ pH 2.4.20 (c) Electrodeposition 1 mA cm-’ pH 3.3.’8*20 (d) Electro-deposition 1 mA cm-2 pH 5.7.20 (e) Electrodeposition 40 mA cm-’ pH 3 (fig. 4). (f)Electro-deposition 5 mA cm-2 pH 3 (fig. 3). cannot glide laterally through the deposit but are restricted to the cylindrical glide surface defined by b and the dislocation line which terminates in the Ni/Cu interface. It may be however that the growth dislocations do not enjoy even this limited mobility.Observations such as the difficulty of imaging the growth dislocations and also the faintness of the early Moir6 patterns suggest that these defects having formed in the nickel surface remained stationary and only slowly extended as they were buried deeper in the deposit by further growth. Such immobility could be accounted for by image forces attracting the dislocations to the nickel surfa~e.~~’~~ Furthermore the incorporation of impurity atoms would help to lock them in position,” and finally the high dislocation density would make any dislocation movement even more diffi- cult. The literature on the early stages of nickel electrodeposition makes no mention of the two major features of stage 2 growth :non-uniform strain and growth dislocations.They may well have been seen but attributed to perturbations in the deposition pro- cess by substrate defects or to the defects themselves. In the present work however the high degree of substrate perfection has revealed these features as intrinsic to the nickel deposition process. Gaigher and van Wyk18 seem to have produced these features in their Ni/Cu bicrystals without recognising their nature. They observed a D -tL contrast and a very low density of short dislocations in nickel deposits 3-10 nm thick They ignored the dislocations whose low density may well have been due to the low current density of 1 mA cmY2 and attributed the D +L contrast to holes in the nickel these being found in the stripped deposits.It is possible however that these holes were artefacts for Weil and Wu23found that their thin nickel deposits suffered some dissolution during stripping from their copper substrates. ELECTROCRYSTALLISATION OF NICKEL ON COPPER STAGE 3 GROWTH Probably only the earliest features of the third growth stage have been revealed in this work. This stage is characterised by the appearance of large scale cooperative changes the first being the interfacial dislocations which glide laterally through the deposit and down to the interface. Structural features such as twinning polycrystal- linity and deposit texture belong in this stage being common in (1 11)-oriented deposits though not really a feature of (100) deposits until considerable thicknesses have been attained.5*6944 The interfacial dislocations produced in this work are identical to those seen by other workers in electrodeposits20~21 Their length and in vapour dep~~it~.~~*~~*~~*~~~~~ and straightness in (1 10) directions indicates that they are produced by dislocation glide on the inclined {l 1l} nickel planes; the shear dislocation loop in fig. 6 will be- have in this way. This dislocation glides by expansion of the loop in its own plane; the lower edge part glides down to the Ni/Cu interface there taking a mixed edge/ screw character while the two screw-type ends lying in the nickel surface glide laterally in (1 10) directions. Cross-slip is a basic property of screw dislocations and so the interfacial disloca- tions can glide in either of the mutually perpendicular [110] and [IT01 directions in the (001) film plane.Although it is difficult to determine when a MoirC pattern is superimposed it appears that a fair degree of cross-slip has occurred in the area of nickel deposit shown in fig. 3(f). PERSPECTIVES Having established a self-consistent pattern of behaviour from the micrographs we are now in a position to assess the results from a broader point of view. EXPERIMENTAL PROCEDURE This work has shown that studies can be made of deposition on to highly perfect clean thin film substrates under realistic plating conditions and avoiding the produc- tion of handling defects such as deformation twinse6 Problems have been revealed notably the substratelsolution contact before deposition which is thought to have produced the primary growths.It is considered that their presence has not affected the growth of the nickel deposits but such a possibility should be explored. GROWTH DISLOCATIONS IN THE ELECTROCRYSTALLISATION OF NICKEL The development of nickel deposits studied here and also elsewhere 18-20937 is summarised in the misfit plots of fig. 7. All the curves show a lower rate of misfit development than predicted by the van der Merwe model 28-32 though Matthews and Crawford 37 were able to match theory and experiment (curve a)by taking into account the dislocation interactions in the film. We are able to relate misfit measurements directly to elastic strain for Gaiglier and van Wyk20 have demonstrated the absence of any lattice expansion by codeposited substances.The difference between the curves (e)and (c) at 10 nm must be due en- tirely to the density of growth dislocations in the two types of deposit. Gaigher and van Wyk 18*20observed only a " low density " of short dislocations in their 1 mA cm-2 deposits whereas 101o-lO1l cm-2 had been produced by that thickness in the 40 mA cm-2 deposits. This is consistent with the view of growth dislocation formation as a J. P. G. FARR AND A. J. S. MCNEIL fundamentally kinetically controlled process. The close match between the curves (a) and (e) reveals the effectiveness of these defects in producing misfit and so relieving elastic strain. Matthews and Crawford 37 found interfacial dislocations nucleating at a thickness of 1.5 nm in their vapour deposited nickel (curve a) whereas these de- fects did not appear in the Watts deposits until after -10 nm and were not numerous even at 30 nm.The very rapid rise in misfit (curve e) was produced entirely by the growth dislocations. Gaigher and van Wyk’s ‘O observations of a low interfacial dislocation density in their 10 nm deposits (curves b c and d)imply that the differences at that thickness must have been due to the influence of pH on the generation of growth dislocations. Suoninen and Hakkarainen 45 have shown pH variations to have a pronounced in- fluence on the nickel deposit structure which they attribute to a colloidal layer of Ni(OH)2 on the cathode. We have found that the presence of the organic addition agents 1,3,6,-naphthalene trisulphonic acid and coumarin in the nickel plating solu- tions is accompanied by considerable reductions in growth dislocation density; it is plausible that a layer of Ni(OH) would have similar effects on the generation of growth dislocations.With increasing pH and thus stronger inhibition by Ni(OH), fewer growth dislocations would be formed leading to a lower Ni/Cu misfit. After 10 nm further misfit was produced in Gaigher and van Wyk’sZ0 deposits by the nucleation and glide of interfacial dislocations ; these authors attributed the differences between the curves to the differing levels of incorporated material impeding dislocation glide. Examination of the curves (b),(c) and (d) quickly shows however that the increases in misfit produced by these defects shown by the rises in the curves between 10 and 40 nm are approximately the same at all pH values.The residual strain in the thickest deposits had in fact been determined by the influence of pH on the growth rather than the interfacial dislocations. The corollary of this deduction is that far from being impeded by incorporated material the interfacial dislocations in Gaigher and van Wyk‘sZ0 deposits were unaffected. This seems at first to be a rather unusual state of affairs especially when considering the amounts of such material seen by those authors at high pH,’O yet the above conclusion is in keeping with the known ability of the screw dislocation to cross-slip and thus avoid small obsta~les.~~-’~ This explan- ation seems plausible but the fact remains that the nickel electrodeposits show a much slower increase in misfit produced by interfacial dislocations (curves b c and d; 10-40 nm) than do vapour deposits (curve a; 1.5-10 nm).This point is discussed more fully later in connection with vapour deposition. The results of the present work are consistent with the speculations of Hoar and Arr~wsmith,~~ who suggested that one source of internal stress in electrodeposits is the preponderance of edge dislocations of a particular sign. The formation of growth dislocations has been seen to be sensitive to current density and Gaigher and van Wyk’sZ0 results have been reinterpreted in terms of these features. It seems likely therefore that the effects of current density and pH47 on internal stress in nickel electro- deposits could be explained in terms of growth dislocations.The stresses in thick deposits are not extreme; e.g.,a stress of -20 x lo3psi (-14 kg rnmw2) typical for Watts corresponds to an elastic strain of only 0.0007 (Young’s modulus values from Saf~anek~~ and Thompson and Lawless 48) whereas elastic strains approaching 0.01 have been observed in the present work. This study has clearly demonstrated the importance of growth dislocations in nickel electrocrystallisation ; it is curious therefore that they have hitherto gone un- remarked. This is probably due to the use of imperfect and uncharacterised sub- strates and low current densities typically 1 mA cm-2.18-22*49 Moreoever it may well be that the growth dislocations so prominent here play little or no part when growth ELECTROCRYSTALLISATION OF NICKEL ON COPPER involves the coalescence of discrete nuclei.For example Gaigher and van Wykl’ found a very rapid almost linear increase in misfit in nickel deposits on contaminated substrates which had almost reached the bulk value by 15-20 nm thickness (compare curve c in fig. 7). The manner of growth of these deposits by nucleation rather than by monolayer spreading suggests that the misfit was attained in a different way probably by dislocation formation during the coalescence stage. The growth of nickel has been examined here when it is dominated by the misfit between itself and the copper base; this may have obscured other fundamental aspects of the electrocrystallisation process.It is important for example that the growth of nickel on nickel be studied for the present results imply that growth dislocations may be generated solely by the electrodeposition process itself with consequences for the kinetics of growth. Furthermore other morphological 2-4 and ~tructural~~*~~ studies have revealed fundamental differences between growth on {loo} {11 l} and (1 lo] surfaces and the structural studies presented here could usefully be extended to other crystal planes. ELECTRODEPOSITION AND VAPOUR DEPOSITION It is clear that the monolayer growth of nickel on copper from the vapour 37 is adequately described by the van der Merwe mode1,28-32 yet the model does not account for the electrolytic growth of nickel on the same substrate.There are two major anomalies. First in Gaigher and van Wyk’s18,20 deposits produced at low current density and with a low density of growth dislocations the production of misfit by the interfacial dislocations was much slower than demanded by the model. Second in the present work we have seen how the development of non-uniform strain and the generation of growth dislocations features not considered in the model played a large part in producing misfit. The first difference might arise simply from greater quantities of incorporated foreign material in the electrodeposits compared with the vapour deposits which im- pede interfacial dislocation glide were it not that Gaigher and van Wyk’s20results discussed earlier strongly suggest that these defects are not affected in this way.An alternative explanation is that this difference is due to the formation of growth dis- locations in the deposit. The van der Merwe model assumes that interfacial disloca- tions can be generated by stress in the growing deposit without undue difficulty and the observations of Matthews and Cra~ford~~ indicate that this is the case with nickel vapour-deposited on copper for the development of their deposit up to -5 nm was as predicted by the model. Since the nucleation of these defects is wholly dependent on stress however any mechanism which relieves that stress will delay or even prevent their formation. The present results have clearly demonstrated that the production of growth dislocations provides significant stress relief and greatly delays the appear- ance of the interfacial dislocations.What is suggested by the juxtaposition of our results with those of Matthews and Cra~ford~~ is that the growth dislocations continue to form after the appearance of the interfacial dislocations perhaps too slowly usefully to lower the strain but probably in sufficient numbers to reduce the rate of interfacial dislocation formation and therefore to slow down the development of misfit. The production of large numbers of growth dislocations with consequent de-velopment of misfit and of non-uniform strain were features not considered by van der Merwe whose model predicts that where the conditions allow the attainment of equilibrium the minimum energy configuration of the deposited layer before the appearance of interfacial dislocations is one of homogeneous train.^^?^^ It may be J.P. G. FARR AND A. J. S. MCNEIL then that the differences between the electrodeposited nickel observed here and else- where,18*20 and the vapour deposited appear as a result of the use of high elec- trodeposition rates compared with those common to vapour deposition. The deposi- tion rate used by Matthews and Cra~ford~~ in their preparation of nickel vapour deposits is unknown but almost certainly very low. High electrodeposition rates could reasonably be expected to prevent the achievement of equilibrium and therefore of homogeneous strain in the deposit layers. Certainly an increase from 5 to 40 mA cmm2 current density has been seen here to produce a significant increase in the rate of development of non-uniform strain and the formation of growth dislocations.It is perhaps worth remarking that in nickel plating terms current densities of 1 mA cm-2 (-0.35 nm s-l) are low while the same rate would be quite high for vapour deposition certainly at substrate temperatures typical of electrodeposition. It would therefore be interesting to extend the present structural study to very low current densities 4.1 mA crnV2. CONCLUSIONS Detailed structural observations of the early stages of nickel electrodeposition on to {loo} copper have been presented. The electrocrystallisation of nickel involves a fundamental difference from its growth from the vapour the production of a specific type of defect to reduce misfit strain which is not considered in the models of epi-taxial layer growth and which has hitherto gone unrecognised in electrodeposition studies.We thank W. Canning and Co. Ltd. for the award of a research scholarship (A.J.S.M.),and Prof. D. V. Wilson for the provision of laboratory facilities and for his continuing interest. J. P. G. Farr and A. J. S. McNeil Surface Technology 1976,4 59. J. P. G. Farr and A. J. S. McNeil Surface Technology 1975,3 399. J. K. Dennis and T. E. Such Nickel and Chromium Plating (Newnes-Buttenvorth London 1972). M. Froment and J. Thkvenin Electrodeposition and Surface Treatment 1973/4,2 355. K. R. Lawless Physics of Thin Films 1967 4 191. K. R. Lawless J. Vacuum Sci. Technol. 1965,2,24.R. Weil and H. C. Cook J. Electrochem. Soc. 1962,109,295. J. K. Dennis and J. J. Fuggle Electroplating and Metal Finishing 1967 20 376; 1968 21 16. P. B. Hirsch A. Howie R. B. Nicholson D. W. Pashley and M. J. Whelan Electron Micro- scopy of Thin Crystals (Wiley N.Y. 1964). lo A. Howie in Techniques for Electron Microscopy ed. D. Kay (Blackwell Oxford 1965). l1 R. S. Alderson and J. S. Halliday ref. (10). l2 K. W. Andrews D. J. Dyson and S. R. Keown Interpretation of Electron Diffraction Patterns (Hilger and Watts London 1967). l3 J. W. Edington Monograph 2 Electron Diflraction in the Electron Microscope and Monograph 3 :Interpretation of Transmission Electron Micrographs in the Practical Electron Microscopy in Materials Science series (Macmillan London 1975).l4 J. W. Menter Adv. Phys. 1958,7,299. l5 D. Hull Introduction to Dislocations (Pergamon Oxford 1965). l6 W. T. Read Jr. Dislocations in Crystals (McGraw-Hill,N.Y. 1953). l7 A. H. Cottrell Dislocations and Plastic Flow in Crystals (O.U.P. London 1953). lS H. L. Gaigher and G. N. van Wyk Thin Solid Films 1973 15 163. l9 H. L. Gaigher and G. N. van Wyk Electrochim. Acta 1973,18,849. 2o H. L. Gaigher and G. N. van Wyk Electrochim. Acta 1974,19,383. z1 E. R. Thompson and K. R. Lawless Appl. Phys. Letters 1966,9 138. 22 S. Nakahara and R. Weil J. Electrochem. Soc. 1973,120 1462. 162 ELECTROCRYSTALLISATION OF NICKEL ON COPPER 23 R. Weil and J. B. C. Wu Plating 1973 60 622. 24 D. W. Pashley Adu. Phys. 1965,14 327. 25 D.W. Pashley in Thin Films (Amer. SOC. Metals N.Y. 1964). 26 J. W. Matthews Physics of Thin Films 1967 4 137. 27 J. W. Matthews in Epitaxial Growth ed. J. W. Matthews (Academic Press N.Y. 1973 part B. F. C. Frank and J. H. van der Merwe Proc. Roy. SOC.A 1949,198,216. 29 J. H. van der Merwe J. AppZ. Phys. 1963,34,117 and 123. 30 J. H. van der Merwe Phil. Mag. 1962 7 1433. 31 J. H. van der Merwe in Single CrystaZ Films ed. M. H. Francombe and H. Sat0 (Pergamon Oxford 1964). 32 J. H. van der Merwe and C. A. B. Ball in Epitaxial Growth ed. J. W. Matthews (Academic Press N.Y. 1975) part B. 33 J. W. Matthews in Single Crystal Films ed. M. H. Francombe and H. Sat0 (Pergamon Oxford 1964). 34 J. W. Matthews Phil. Mag. 1966 13 1207. 35 J. W. Matthews and W.A. Jesser Acta Met. 1967,15,595. 36 N. Cabrera Surface Sci. 1964,2 320. 37 J. W. Matthews and J. L. Crawford Thin Solid Films 1970,5,187. 38 U. Gradmann Ann. Physik 1964,13,213; 1966,17 91. 39 L. 0.Brockway and R. B. Marcus J. Appl. Phys. 1963,34,921. 40 L. 0.Brockway R. B. Marcus and A. P. Rowe in Single Crystal Films ed. M. H. Francombe and H. Sat0 (Pergamon Oxford 1964). 41 G. A. Bassett and D. W. Pashley J. Inst. Metals 1958/9,87,449. 42 R. E. Smallman Modern Physical Metallurgy (Butterworth London 1970). 43 F. Haussermann and M. Wilkins Phys. Stat. Solidi 1966,18,609. 44 H. Leidheiser and A. T. Gwathmey J. Electrochem. SOC., 1951,98,225. 45 E. J. Suoninen and T. Hakkarainen J. Nat. Sci. 1968,3,446. 46 T. P. Hoar and D. J. Arrowsmith Trans.Inst. Met. Fin. 1958/9,36 1. 47 W. H. Safranek The Properties of Electrodeposited Metals and Alloys (Elsevier N.Y. 1974). 48 E. R. Thompson and K. R. Lawless Electrochim. Acta 1969 14,269. 49 A. G. Ives J. W. Edington and G. P. Rothwell Electrochim. Acta 1970,15,1797.

ISSN:0301-5696    

DOI:10.1039/FS9771200145

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. J. A. Harrison and Dr. D. R. Sandbach (Newcastle) said We have recently been reconsidering the problem of the metal-electrolyte double layer structure.l In connection with this problem we have made measurements of differential capacity against potential curves for Ag Pb Cu and Cd in contact with common aqueous electrolytes.2 Measurement of the frequency dependence of the capacity shows that after chemical or electropolishing the surface is relatively rough. It would probably be useful to make similar measurements on the surfaces used in this paper. Prof. W. J. Lorenz (Karlsruhe) said The double layer capacity of polycrystalline and monocrystalline gold and silver electrodes has been measured by using galvano- static pulses as well as by the impedance techniq~e.~-~ However the experimental results depend strongly on the electrode potential and cannot be interpreted in terms of the roughness factor of the electrodes without doubt.On the basis of coverage measurements we have estimated a roughness factor of our electrodes used of about 1.1-1.3 in agreement with the results of other authors. Dr. R. Wiart (Paris)said A comparison of your fig. 1 and 3 shows clearly that the voltammograms are strongly dependent on the experimental conditions such as the concentration of lead perchlorate the scan rate or the technique used for the elec- trode preparation. On fig. 1 three peaks appear instead of two on fig. 3. What is your opinion on the origin of the different peaks observed on the voltammograms and which experimental condition determines why one of these peaks does not appear on fig.3? Prof. W. J. Lorenz (Karlsruhe) said The electrolytically grown Budevski surface used in fig. 3 contains many fewer crystal imperfections than the surface of the macro crystal used in fig. 1. It has been found in the system Ag(hkZ)/Pb2+as well as in the system Ag(hkZ)/Tl+ that the Al peak might be associated with surface singularities such as step lines and/or dislocations. Moreover a slow structural rearrangement of the Ag(ll1)face has been observed in the potential range between the peaks A2and A3(see the answer to Kolb’s question). As a result the relative heights of the peaks Al A2 and A3 on the Ag(ll1) face depend on the electrode pretreatment and the polarization technique used.Prof. M. Fleischmann (Southampton) said The application of cyclic voltammetry to the direct determination of the equilibrium properties and kinetics of transforma- tion of two dimensional layers is fraught with difficulties. The kinetics of phase I. L. Cooper and J. A. Harrison Electrochim. Acta 1977,22,1361 1365. I. L. Cooper J. A. Harrison and D. R. Sandbach EZectruchim. Acta in press. H. D. Herrmann N. Wuthrich W. J. Lorenz and E. Schmidt J. EZectruanaZyt. Chem. 1976 68 289. K. Engelsmann Dissertation (Karlsruhe) in preparation. K. Juttner M. Klimmeck and W. J. Lorenz unpublished results. 164 GENERAL DISCUSSION formation are highly non-linear in the independent variables as discussed by Ran- garajan at this Symposium; similar effects will be important in the case of adsorption.It would therefore be surprising if cyclic voltammograms can in general be directly related to equilibrium isotherms on the one hand or to kinetic parameters on the other. Such parameters can really only be derived by appropriate deconvolution of the experimental data e.g. in the case of phase formation by taking into account nuclea- tion phase growth and overlap ; isotherms derived from experimentally measured transients must be broadened by the interaction of the various effects. It should be borne in mind that surface diffusion (and possibly bulk diffusion) is yet another factor which will distort the response as was shown by simulation methods for the potentiostatic deposition of nickel on mercury.2 These effects will also have to be taken into account in relating experimental data to theoretical models and if they are important then it would be advisable to use potentiostatic rather than cyclic voltammetric methods so as to simplify the kinetics.Could the authors comment as to whether their derived isotherms are free from such interfering factors and whether the kinetic data can be interpreted unambiguously? Prof. W. J. Lorenz (Karlsruhe) said We completely agree with the conception of Fleischmann that the equilibrium properties and kinetic parameters of underpotential metal deposition cannot be determined directly from cyclic voltammograms as had been done by other authors. However our thermodynamic data have been derived from real equilibrium measurements (see the answer to Bewick's question).On the other hand the kinetic interpretations of our work are based on potentiostatic or galvanostatic step meas~rements.~-~ Prof. J. W. Schultze and Dr. D. Dickertmann (Berlin) said The determination of thermodynamic data from potentiodynamic desorption spectra is possible only if the currents involved are smaller than the exchange currents of the system. In the system Au(l1 l)/Bi3+ the exchange current density for structure A is lower than pA ~m-~.' Thus spectra recorded with sweep rates of 1 mV s-' or more do not re- flect the equilibrium state. At a sweep rate of 20 mV s-' even the different adsorption structures A and B cannot be distinguished as can be seen in ref. (8).To overcome this difficulty measurements in our paper were carried out by poten- tiostatic pulse measurements after a long prepolarization period to attain an adsorp- tion equilibrium. Dr. B. Thomas (Southampton) (communicated) Lorenz et al. imply in their paper that it is possible to study the overpotential growth of lead on silver at varying degrees of surface coverage by the underpotential monolayer and that their results indicated that 3D growth was hindered by the presence of the monolayer. However my own workg [in the solution 5 x mol dm-3 P~(OAC)~ +0.5 mol dm-3 HClO-] is at 1 S. K. Rangarajan this Symposium. 2 M. Fleischmann J. A. Harrison and H. R. Thirsk Trans.Faraduy Soc. 1965,61,2742. 3 H. D. Herrmann N. Wuthrich W. J. Lorenz and E. Schmidt J.Electroanalyt. Chem. 1976; 68,273; 1976,68,289. K. Juttner G. Staikov W. J. Lorenz and E. Schmidt J. Electroanalyt. Chem. 1977,80 67. G. Staikov K. Juttner W. J. Lorenz and E. Schmidt EZectrochim. Acta 1978 23 305. G. Staikov K. Juttner W. J. Lorenz and E. Budevski Electrochim. Acta 1978,23 319. 'J. W. Schultze and D. Dickertmann paper presented at the ISE-Meeting in Varna/Bulgaria, 1977. D. Dickertmann and J. W. Schultze,Electrochim. Acta 1977 22 117. B. Thomas PhD Thesis (University of Southampton 1977). GENERAL DISCUSSION variance with these results. The 3D growth current transient at a given overpotential was found to be completely independent of the starting potential Ea in the under- potential region (where 0 -E -E pb/pb2+ < 250 mV) and moreover was found to be independent of whether the monolayer was preformed in a pulse prior to the 3D growth pulse.An investigation of the first few milliseconds of current against time transients corresponding to steps in potential from a value where the electrode surface was bare to values in the overpotential region revealed a feature corresponding to the forma- tion of the monolayer. This indicates that it is impossible to study 3D growth in this system in the absence of the monolayer or as Lorenz et al. suggest at various degrees of coverage by the monolayer. The relevance of the monolayer to the formation of the 3D deposit was emphasized in experiments involving a nucleation prepulse (at -92.5 mV vs Epb/pb2+) prior to the growth pulse at (-14.7 mV).It was found that prepulses of length between 0 and 2.6 ms had no effect on the growth transient at -14.7 mV. Prepulses longer than this however produced a marked increase in the growth current. It was found that the critical time of 2.6 ms corresponded exactly to that required for the formation of the monolayer at -92.5 mV. No 3D nuclei can apparently be formed until the mono- layer is complete showing that the formation of the underpotential monolayer is an essential precursor to the formation of thicker deposits. An explanation for the varia- tion observed by Lorenz et al. in fig. 7 of their paper might be that the potential in the pulse was not constant at different starting potentials [e.g. for the (100) face an in- crease of 1.0 mV in the overpotential causes the rate of growth at constant time to increase by a factor of three].Prof. W. J. Lorenz (Karlsruhe)(communicated) (1) The experiments described by Thomas may not be directly compared with ours. Whereas our solutions were free of surface active anions Thomas’ electrolyte contains 0.1 mol dmm3 acetate which might adsorb at Ag surfaces thus strongly influencing both the kinetic and equilibrium properties of the evolving Pb adsorbate. (2) The constancy of our pulse potentials was within & 0.1 mV. We cannot accept therefore Thomas’ interpretation of our results. Dr. A. Bewick (Southampton) said In their paper Lorenz et al. express doubt on whether nucleative phase formation processes are involved in the development of the two-dimensional layers formed in the underpotential region.They insist on finding a discontinuous isotherm indicative of a first order phase transition before accepting the participation of a nucleative process. We now present further data for the deposition of Pb onto Cu(ll1) which allows us to construct an isotherm approaching very closely to this ideal form. Using more positive potentials and very accurate control of potential we have been able to obtain transients like those shown in fig. 7 of our paper but on a much longer time scale fig. 1. The relationship between these transients and the structure shown on a linear sweep voltammogram at low sweep speed can also be seen from the figure. On a time scale up to 30 min a peaked transient corresponding to the formation by a nucleative mechanism of a complete epitaxial monolayer is obtained at all potentials more negative than 3-147 mV.Thus at 3-147 mV a complete monolayer is formed in about 30 min whereas at a potential just 1 mV more positive only a very small amount of lead is deposited and the (cur- rent time) transient is monotonic. Note that +147 mV is right at the foot on the positive side of the peak seen on the voltammogram. Fig. 2 shows a (coverage potential) isotherm calculated by integration of these (current time) transients. GENERAL DISCUSSION t /min FIG.1 .-Deposition of Pb on Cu (1 11) in mol dm-3 Pb(OAC)2 + mol dm-3 HC104 + 0.5 mol dmW3 NaC104. 1 q = +148 mV us Pb; 2 q = +147 mV us Pb; 3 q = +146 mV us Pb; 4,q = 145 mV us Pb; E = +400 mV us Pb.Inset Q = 286 pC cm-2 at 1 mV s-'. 300-7 5 0 a '200- wn loo-&-130 140 150 160 +QImV vs Pb FIG.2.-Isotherm of coverage plotted against potential for Pb on Cu(ll1) in + mol dm-3 HClO + 0.5 mol dm-3 NaC104. mol dm-3 Pb(OA(& +?I 400 156 153 149 148 147 146 145 144 143 142 141 140 138 QP 22 18 20 18 32 283 280 278 280 279 282 278 276 278 GENERAL DISCUSSION This has an almost discontinuous rise changing from a coverage of about 10% to that of a complete layer over an interval of 1 mV. These measurements also show how difficult it is to obtain data approximating to equilibrium conditions for a nucleative process; this is due of course to the strong potential dependence of the rate of nucleation.It is clear from fig. 1 that a very slow linear potential sweep would lead to a voltammogram which has a very sharp current peak located between +147 and +148 mV in contrast to that illustrated for a sweep speed of 1 mV s-l. This would require a sweep speed no faster than 1 mV in 30 min i.e. slower than 10-6V s-'. In general therefore one must not expect linear sweep voltammograms obtained at realistic sweep speeds to show the characteristics of a first order phase change free from the effects of kinetic limitations. In view of this the work of Rangarajan in predicting the form of the voltammograms taking into account the kinetic effects is particularly interesting. This discussion prompts me to put two questions to Lorenz and Schmidt. (i) Do you accept our "thirty minute isotherm " as proof of the nucleative mechanism which we had formerly advocated on the basis of kinetic evidence? (ii) Are you sure that the isotherms you have presented are free from kinetic effects and does a comparison of linear sweep voltammetric data for ordinary and dislocation free electrodes as given in your paper provide sufficient evidence that surface heterogeneity is not camouflaging sharp features on the isotherms ? Prof.W.J. Lorenz (Karlsruhe)said (1) By any experimentally reasonable standard of continuity the charge isotherm of the Cu(111)/Pb2+ C104- acetate system pre- sented by Bewick should be accepted as being discontinuous indeed thus strongly sug- gesting a 2D first order phase transition in that particular system.We nevertheless prefer to uphold our statement saying that 2 D nucleation " . . .is still far from being unambiguously confirmed . . . as a metal undervoltage mechanism of universal relevance . . . " since as a matter of triviality Bewick's result neither proves global applicability of a nucleation model to any undervoltage process conceivable nor does it disprove our own experiments evidencing continuous non-nucleation layer formation in the Ag/Pb2+ C104- system. It has been proposed elsewherel that undervoltage discontinuity might be enhanced by interaction between the evolving Me layer and a suitable specific anion adsorbate whose absence is known in the Ag/Pb2+ C104- system whereas in Bewick's experiments formation of a specific acetate adsorption layer cannot be excluded.(2) The charge and coverage data presented in our paper have been obtained by equilibrating the system at both the starting and final potentials of slow voltage sweeps.2 The Ag(100) and Ag(ll0) isotherms are considered to represent true equilibrium data. At Ag(l11) more recent results suggest a slow structural transformation of the Pb layer similar to that observed in the Ag(lll)/Tl+ system (see the answer to Kolb's question). As for the role of Budevski surface imperfections refer to our paper. Prof. J. W. Schultze Dr. D. Dickertmann and Dr. F. D. Koppitz (Berlin) said In the system Ag/Pb2+ Lorenz et aL3 observed a maximum surface concentration of Pb2+ which is almost independent of the substrate orientation (see table 2 of their paper).This result confirms our opinion that near the equilibrium potential forma- tion of a substrate independent monolayer is a rule which has very few exceptions. G. Staikov K. Juttner W. J. Lorenz and E. Schmidt Electrochim. Actu 1978 23 305. H. Bort K. Jiittner W. J. Lorenz and E. Schmidt J. Electruanulyt. Chem. in press. W. J. Lorenz E. Schmidt G. Staikov and H. Bort paper at this Symposium. GENERAL DISCUSSION Table 1 shows a comparison of data for various systems.l” The experimental surface concentration near the equilibrium potential is given by Qmaxwhich can be referred to the charge of a monolayer Qmono. Qmono is calculated assuming a hexagonal monolayer using the data given in table 1. It can be seen that for most systems the ratio emax/ em,, is almost unity independent of the crystal plane.That means that a close packed monolayer is formed independent of the substrate orientation. Exceptions to this rule are the systems Au(l1 l)/Tl+ the systems Cu(l1 l)/Pb2+,4 and the epitactic 1 .-RATIO OF EXPERIMENTAL MAXIMUM DESORPTION CHARGE em,, TABLE AND CALCULATED CHARGE OF emon, MONOLAYER DESORPTION. WAS CALCULATED WITH ypb2 + = 2 yBi2+ = 3 )’TI+ = 1 and Ypb2i = 1.74 A Ygj3+ = 1.76 A and YTlf = 1.70 A. Qmonol Qmaxl Qmono pCcm-2 (111) (100) (1 10) ref. Ag/Pb2 305 0.96 0.99 0.95 (2) Cu/Pb2 305 0.75 0.89 1.05 (4) + Au/Pbz+ 305 0.95 1 .o 0.93 (1) + Ag/Bi3 450 1.06 1.04 1 .o (3) + Au/Bi3 450 0.97 0.89 0.93 (1) AuITl 160 0.68 1.06 1.06 (11 monolayers of the Au/Cu2+ systern.l For the system Au/Bi3+ values between 0.89 and 0.97 are obtained which are obviously < 1.This difference is caused by the electro- sorption valency which is smaller than 3 for this ~ystem.~ Prof. W. J. Lorenz (Karlsruhe) said In the systems Ag(hkl)/Pb2+ Clod- and Ag(hkZ)/Tl+ ,C104- our saturation coverage values rSdepend slightly but significantly on the orientation of the silver substrate. From these data from the different peak structures of the voltammograms as well as from the shapes of the equilibrium iso- therms we conclude that only at the Ag(ll1) face a close packed monolayer can be assumed. The adsorption behaviour on Ag(100) and Ag(ll0) faces is better explained by assuming 2c(2 x 2) and 3c(2 x 2) superlattice structures for Pb and T1 saturation coverages respectively.6 Dr.D. M. Kolb (Berlin) said The results of our RHEED investigation strongly suggest that there is a surface rearrangement when Cu is deposited onto a Au(ll1) surface in the underpotential range. Did you find in your electrochemical experiments any evidence for such a structural change of the surface during monolayer deposition? Prof. W J. Lorenz (Karlsruhe) said Investigation of the Ag/Tl+ system has shown that fractional T1 monolayers at Ag( 1 1l) obtained in perchlorate and sulphate solu- tions are not stable under potentiostatic polarisation conditions. When these J. W. Schultze and D. Dickertmann Surface Sci. 1976 54 489. D. Dickertmann F. D. Koppitz and J. W. Schultze Electrochim. Acta 1976 21 967.F. D. Koppitz Thesis (Freie Universitat Berlin 1977). A. Bewick J. Jovicevic and B. Thomas paper at this Symposium. J. W. Schultze and D. Dickertmann paper at this Symposium. G. Staikov K. Juttner W. J. Lorenz and E. Budevski,Electrochim. Acta 1978,23,319. ’H. Bort K. Juttner W. J. Lorenz and E. Schmidt J. Efectroanalyt. Chem. in press. H. Siegenthaler K. Juttner E. Schmidt and W. J. Lorenz Electrochim. Acta in press. GENERAL D I S CUSS I ON deposits are held at their formation potentials for a sufficiently long period of time (~2 000 s) about two thirds of the T1 originally present is redesorbed to the solution whereas the remaining fraction of the deposit is bound more strongly to the substrate than before. When complete T1 monolayers are built up by subsequent cathodic polarisation the electrode exhibits distinct memory effects which disappear on either repeated potential cycling or shifting the potential to high anodic values.The most obvious interpretation of this phenomenon is a slow structural rearrangement of the Ag( 11 1) surface in analogy to Kolb’s model of the Au( 11 1)/Cu2+ system leading to partial annihilation of the adsorption sites available as well as incorporation of re- maining TI species into the uppermost layer of the substrate lattice. A more detailed account will be given in a forthcoming report1 Prof. S. K. Rangarajan (Bangalore) said There seems to be a misconception that the nucleation phenomenon would always reveal itself in (4 E)or (i E)curves through the appearance of some sort of discontinuity associated usually with certain phase transitions.The nature of transients and potential sweep response observed by Lorenz Bewick and Schultze are not too different from those obtained for example with the calomel or Ag deposition where nucleation/growth are fairly certain to have been present Hence it does not seem proper to look a priori for “ abrupt changes ” or infinities to affirm or deny the existence of 2-D condensed phases. The second comment relates to the often-used Frumkin isotherms in these monolayer situations. The implicit notion that the observed Frumkin constant g (being (4) can disprove the existence of phase formation seems rather an oversimplification. Apart from the fact that g may be varying with the potential and coverage (cf.multi-peak case) it may not even be needed for phase transitions! After all models with no such attractive component (e.g.hard spheres hard rod) are known to exhibit the required features on geometric or packing considerations alone. Nor does this mean that a “ sharp ’’ peak implies a phase transition @so facto. In nucleation growth models such peaks can be related solely to kinetic parameters with no appeal to thermodynamics. Even the phase transformations-suggested in the papers by Bewick et al. and Schultze et al. based on symmetry or density changes -could well be described phenomenologically. For example let A -jB with A B possessing differing 2-D structures. If the temporal growth of A is followed by its coverage SA(t) it is possible to visualise “ the phase B ” nucleated on A through a certain Avrami-like rate equation fAB(t) say (with or without a threshold potential).Consequently the coverage is dt) =,d SA(tlfAB(t -r> and the observed current i(t) cc d(s + sB)/dt. The individual coverages must be obtained by judicious modelling for AB and deconvolution. Multipeak situations deserve more detailed analysis. One may consider if the various phases are formed ‘‘sequentially ” (transformations) ; if there are critical potentials or supersaturations of the ‘‘ mother phase ” for formation; if the parameters (nucleation rate rate con- stant etc.) associated with each of these phases are consistent with both the potential sweep and potentiostatic experiments.I now address some specific queries to Lorenz. (a) How does one reconcile the shapes of “isotherms” especially the non-saturation behaviour reported in fig. 2 with Frumkin’s expressions ? H. Siegenthaler,K. Juttner E. Schmidt and W. J. Lorenz Electrochim. Acta in press. 170 GENERAL D I S CUSSION (b) Eqn (8)-(9) have been employed to reconstruct the potential pulse response (fig. 5). Obviously it must be possible with the same choice of constants to predict the potential sweep response too. Has this been done? (c) The influence of the 2-D layer on the 3-D formation has been reported [cf. fig. 8 (b)]. Has the converse been investigated uiz. the effect of 3-D nuclei on the 2-D growth ? Can the potential be momentarily shifted cathodic to bulk-deposition potentials so as to ensure deposition 5 1 monolayer and then be brought back anodic- ally to grow the 2-D phase? (d) Is it possible to choose the metals A B so as to underpotentially form B on A first and A on B (monolayer) subsequently? The solid state physics of this stack formation (at the moment imaginary!) could be very interesting.(e) Can one say that “ the two dimensional over-layer ” behaves as a polarisable electrode in the region of potentials anodic to “ the bulk deposition region ”? Can a study of redox reactions on such an overlayer substrate give useful information on the nature of substrate bonding ? cf) Finally a comment on the state of the theory. The reported data by Lorenz as well as by Bewick indicate a strong “adsorption component” in the model.Thus a better description probably more general than a naive adsorption picture and the elementary nucleation growth models is worth seeking. I shall be happy if Bewick can also comment on the above queries especially in the light of his reflectivity measurements. Prof. W. J. Lorenz (Karlsruhe) (communicated) Generally we agree with the com- ment of Rangarajan that an exact separation of phase transformation effects and ad- sorption phenomena is rather difficult in case of the formation of 2D underpotential metal deposits. We have always stated that the characteristics of the observed non-steady state signal responses cannot be considered as a sufficient criterion for the distinction between different models.1*2 On the other hand a discontinuity of an equilibrium rE, p-isotherm has to be regarded as a real criterion for a first order phase transformation.It is clear that the Frumkin isotherm only represents a first approximation of a mean field theory. A more realistic treatment on the basis of statistical thermo- dynamics as well as Monte-Carlo simulations has been carried out very re~ently.~ Concerning the specific questions (a) The procedure is described elsewhere for the thallium ads0rption.l (b) No because the calculated sweep diagram corresponding to the isotherm will not provide new information. (c) Experiments of this kind are unreasonable since the process of under-potential metal deposition cannot be suppressed before 3-D nucleation and growth take place.(d) The formation of Sandwich structures A-B-A-B . . . of different metal adsorb- ates cannot be realized electrochemically. (e) Extended investigations concerning the influence of underpotential metal deposits on different redox reactions have been carried out re~ently.~ cf) The experimental results obtained in systems free of non-metallic cosorption K. Juttner G. Staikov W. J. Lorenz and E. Schmidt J. Electroanalyt. Chem. 1977,80,67. G. Staikov K. Juttner W. J. Lorenz and E. Schmidt Electrochim. Acta 1978 23 305. Van der Eerden D. Kashchiev,G. Staikov W. J. Lorenz and E. Budevski Monte-Carlo Simula- tion of Underpotential Metal Ion Adsorption. Paper presented at the 28th ISE-Meeting Varna 1977 (to be published). C. Mayer K. Juttner and W.J. Lorenz J. Appl. Electrochem. in press. GENERAL DI S CU SSI ON processes are well described by simple adsorption models. Up to now first order phase transformations have been detected only in systems in which non-metallic cosorption processes seem to be involved. However higher order phase transforma- tions might occur but their experimental proof seems to be rather difficult. Dr. D. G. Lovering (Shrivenham) (communicated) Are the apparent discrepancies between the Lorenz et al. and the Bewick et al. interpretation of underpotential depo- sition partly semantical ? At these potentials a condensed-state layer strongly inter- acting with the substrate may be intuitively expected theoretically predicted and experimentally observed. RHEED results prove the considerable extent of these interactions and optoelectrochemical results confirm the unique physical properties e.g.refractive index of the new surface layer. No-one is surprised; so when therefore is an adsorbed film not an adsorbed film? And can the extent to which ions are discharged to become partially charged adsorbed ions or strongly interacting ad-atoms unequivocally be determined? Does it really matter or would a quantum mechanical approach be a more appropriate aproach to avoid these hardsphere conceptual difficulties ? Prof. W. J. Lorenz (Karlsruhe) (communicated) (1) In the sense of Gibbsian sur-face thermodynamics each surface film that is characterized by a definite coverage iso- therm depending on the intensive system parameters should be termed an adsorbate.This term therefore should be applied to metal undervoltage deposits irrespective of their origin and/or structure unless they are shown to grow three dimensionally pro- ducing alloy bulk phases. However it remains to be decided experimentally whether or not 2 D layer formation proceeds through a sequence of 2 D phase transition like structural transformations (discontinuity against continuity of isotherms) giving rise to nucleative growth processes (discontinuity vs. continuity of the adsorption mechanism). In our opinion conclusive evidence in favour of nucleative layer building as an universal undervoltage deposition model is still lacking. (2) Charge and coverage measurements do not reveal the true state of charge of the adsorbed particles.The so called electrosorption valency which is identical to (aq/a& merely describes the interdependence of Me and non Me adsorption. (3) In our opinion an appropriate quantum mechanical approach of the compli- cated underpotential metal deposition process cannot be realized at present Dr. A. Bewick (Southampton) (communicated) The distinction between the forma- tion of a two-dimensional phase layer by a first order nucleative mechanism and the formation of an adsorbed layer by a simple discharge mechanism following a continu- ous isotherm is certainly not a matter of semantics. Both Lorenz et al. and ourselves agree on the nature of the distinction and the way in which this is defined in terms of thermodynamics and kinetics.The difficulty lies in obtaining the ideal evidence from real systems in which effects such as surface heterogeneity and slow kinetics can cause problems. I believe we have obtained evidence acceptable to all parties for a nuclea-tive phase formation process in Pb deposition on Cu(l11). We believe that this well proven example allows one to look at similar systems for which there is strong kinetic evidence for analogous processes and make the same inference. Lorenz et al. prefer to advocate an adsorption mechanism for all systems for which conclusive proof to the contrary has not been obtained. Dr. S. Fletcher (Ottawa) said Fig. 7 of Bewick’s paper shows that current densi- ties at small times have values of 29mA cm-2. Hence there appears the possibility GENERAL DISCUSSION of IR drop effects such that the potential at the electrode-electrolyte interface would rise only slowly.Since the effect of IR drop is also to broaden the (i t) responses expected in potential step experiments it would be interesting to estimate the size of Ra here. Were any special precautions taken to avoid this problem? Dr. A. Bewick (Southampton) (communicated) When making measurements of the kind shown in fig. 7 of our paper we take great care in adjusting the position of the Luggin capillary to minimise the effects of IRu(R,being the uncompensated resistance). We use a fine capillary and then adjust its position to obtain a first order cancellation between IR effects and electrical screening of the electrode as indicated by the double layer charging transients.I would estimate the residual R,value to be about 0.2 to 0.3 ohm cm-2. Thus the R,C (Cd = double layer capacity) time constant would be about 5 x s and the variation of potential over the major portion of transient 5 would be about 1 mV. Prof. J. W. Schultze and Dr. D. Dickertmann (Berlin) said Bewick et a2.l ascribe some differences of the systems Ag/Pb2* and Cu/Pb2+ to the differences of electro- negativities or work functions of Ag and Cu. In spite of the general this influence seems to be negligible for these special systems. This can be seen from fig. 1 where the under-potential difference (taken for the most anodic desorption peak) is plotted versus the work function difference of the ~ystem.~ According to Kolb Gerischer and Przasnyski,2 &,k should increase linearly with Av.This correlation is valid for the (1 10)-plane at high Aq-val~es.~ For the (100)- and (111)-plane and especially for the systems Ag/Pb2+ and Cu/Pb2+ it is less justified. Dr. A. Bewick (Southampton) said In reply to Schultze and Dickertmann I would like to reiterate what we have already said about the correlation between work func- tion differences and underpotential shifts. We have always emphasised6-* that the work function correlation appears to be very successful when the whole area of under- potential deposition is viewed on a broad canvas (Au values from 0 to 2.3 eV) but that a detailed examination over a narrower range e.g. a comparison of the differences observed on a single substrate with changing orientation shows that the simple correlation is not valid.We suggested that this was due mainly to the neglect of the structural factors which play a major role in determining the magnitudes of several of the components of the overall energy of the underpotential layer. It is now clear that the structure of the substrate surface and the relative sizes of the atoms of substrate and deposit control the epitaxy and registration and thus the interaction energies between substrate and deposit and between atoms in the deposit. When the work function correlation was proposed by Kolb et al. underpotential deposition was thought to be a simple adsorption process and the importance of these other factors was not apparent.A. Bewick J. JoviCeviC and B. Thomas paper at this Symposium. D. M. Kolb M. Przasnyski and H. Gerischer J. Electroanalyt. Chem. 1974,54,25. J. W. Schultze and D. Dickertmann Surface Sci. 1976 54 489. J. W. Schultze and F. D. Koppitz Electrochim. Acta 1976 21 327. S. Trasatti J.C.S. Faraday I 1972 68 229. A. Bewick and B. Thomas J. Electroanalyt. Chem. 1975 65 91 1. 'A. Bewick and B. Thomas J. Electruanalyt. Chem. 1976 70,239. Paper at this Symposium. GENERAL DISCUSSION I would like to conclude with a warning which is relevant to all attempts at the interpretation of underpotential shifts. We have found that the underpotential shifts are dependent upon the metal ion concentration (at constant ionic strength) in most of the systems we have studied.This effect needs to be allowed for in com- parisons between the various systems. The concentration dependence is of course of (111) (110) 0.8 -0.6--w Y a G 0.4-0.2-0-018 OL 0.8 FIG,1.-Relative potentials &pk of the most anodic desorption peak of metal adsorption layers in dependence on the difference of work functions Aq great interest in its own right and we are preparing to submit a contribution on this subject. Dr. D. M. Kolb (Berlin) said When we derived the correlation between under- potential shift and work function difference for polycrystalline substrates,l we con- sidered the work function as an appropriate measure for the electronegativity of the metal atoms involved in the formation of the adatom-substrate bond.Testing this correlation for different single-crystal surfaces by simply using their work function values is a doubtful approach since these values reflect differences in band structure and lattice symmetry of the surface. By splitting the single-crystal work function into contributions from the bulk and the surface (chemical potential and dipole layer) it becomes evident that the first term which represents the position of the Fermi level and which is the same for different surface orientations is the one that describes best the adsorptive properties of the substrate and hence should be used for any comparison. The results however presented by Schultze where the underpotential shift for various metal adatoms on one single-crystal surface is plotted against work function differences still indicate that other (e.g.structural) effects do play a significant role beside the Ay at least for systems with relatively small Ap-values. D. M. Kolb M. Przasnyski and H. Gerischer J. Efectroanafyt.Chem. 1974,54 25. J. W. Schultze and D. Dickertmann Surface Sci. 1976 54 489. GENERAL DISCUSSION Prof J W. Schultze and Dr. F. D. Koppitz (Berlin) said The very interesting phe- nomenon of surface reconstruction is similar to or almost identical with the alloy formation which has been found earlier in various systems. In general alloy forma- tion increases strongly with decreasing potential due to the increase of mole fraction of the less noble alloy component as has been shown for the system Au/Cd2+.l Similar observations have been made for the system Au(poly)/Cu2+ but in this case the observed effect of alloy formation was smaller.Fig. l(a)shows the total charge 14-0.8-Q of copper desorption after potentiostatic prepolarization at various potentials in dependence on the polarization time.2 Q is almost constant and smaller than the charge of a monolayer at potentials E > cCu i.e. place exchange reactions and alloy formation could not be detected under these conditions. At lower potentials E 6 cCu,however Q increased strongly with time which was presumably due to place exchange reactions (or surface reconstruction). The total charge exceeded that of a monolayer by a factor of 2. The deposition of bulk copper could be excluded under these conditions because of the large nucleation overvoltage.Time effects were also observed in the Ag(lOO)/Tl+ ~ystem.~ Fig. l(6) shows that the desorption charge in- creases considerably with the prepolarization time and follows a filaw. This can be explained by place exchange reactions between Ag and T1 atoms. Can Kolb specify the potential dependence of surface reconstruction in his experi- ments ? Dr. D. M. Kolb (Berlin)said We have observed a RHEED pattern from the bare Au(ll1) surface after deposition of Cu in the underpotential region. This apparent reconstruction of the surface is found after deposition of 2/3 of a monolayer as well as of a complete monolayer. As mentioned in our paper bulk Cu deposition has a much more pronounced effect on the Au surface obviously due to the immediate form- ation of an alloy for E < E,.Dr. J. Jovitevi6 (Southampton) said We find the results presented by Kolb et al. showing reconstruction of the surface of the substrate very interesting because as we J. W. Schultze,F. D. Koppitz and M. M. Lohrengel Ber. Bunsenges. phys. Chem. 1974,78,693. G. Toro Diplomarbeit (Freie Universitat Berlin 1970). F. D. Koppitz Thesis (Freie Universitat Berlin 1977). GENERAL DISCUSSION pointed out in our paper we had been looking for reconstruction effects in our UPD systems but had not found it necessary to invoke them in order to explain the results. The effects observed in the system used by Kolb et al. are not surprising because it is well known that gold and copper readily form alloys.Therefore reconstruction might well be expected to follow from the disruption of the surface region caused by alloy formation. In the case of a copper substrate we have been able to produce surface reconstruc- tion effects but only by inducing actual dissolution and decomposition of the copper itself. We have used the UPD behaviour of Pb on Cu as a sensitive tool for detecting and following the course of the reconstruction. In the UPD of Pb on Cu(l1 l) the single deposition/dissolution peak system shown in fig. 1 of our paper was sometimes supplemented by a second peak system depending upon how well the surface was pre- pared fig. l(a). On continuous cycling such that the anodic limit was just 1 or 2 mV into the CU+~/CU dissolution region this second peak system became more pro- nounced while the first one decreased in size and finally disappeared fig.l(b) and (c). These voltammograms were taken at 30 min intervals during the sweeping period. The new peak system fig. l(c) was similar in charge values and peak potentials to that seen on Cu(100). It appears therefore that the Cu(l11) surface reconstructs to a structure similar to Cu(100) during the cycling but only if actual dissolution of copper takes place. This conclusion is supported by the observation that similar cycling of the Cu(100) electrode appears to improve the substrate surface. These results show that a reconstruction of the substrate surface can be readily detected on UPD volt- ammograms because of the great sensitivity of the energetics kinetics and structural characteristics of the underpotential layers on the substrate structure.In view of this they also indicate how well the surfaces are prepared for UPD studies (a question already raised in this discussion). It is interesting to note also that there seems to be evidence for a related effect in the case of the Ag(ll1) system. Lorenz et al. have shown voltammograms of lead deposition onto a dislocation free Budevski type Ag(ll1) surface (fig. 3 in their paper). This is almost free of the peaks Al and A3 [see either fig. 1 in the same paper or ref. (l)] observed on the normal chemically polished single crystal electrodes. It appears therefore that the peaks Al and A3 are associated with defect structure on these crystals as was suspected1 from the dependence of Al and A3 on surface preparation.By comparison therefore between Cu(1 1 1)/Pb (absence of Al and A3) and the Budev- sky type Ag(l1 l)/Pb it can be concluded that the chemically polished Cu(ll1) surface is very close to ideal. Dr. M. Froment (Paris)said Have you obtained detailed information concerning the chemical composition of the surfaces. The annealing treatment of the samples can give rise to the segregation of impurities on the surface. It is well known that some elements like sulphur2 cannot be removed from the surface during further elec- trolytic treatment. It would be interesting to follow the surface composition after annealing and after cycling and electrolytic polishing of the gold samples.Dr. D. M. Kolb (Berlin) said These first experiments were carried out under normal high vacuum conditions in a conventional RHEED-apparatus. Therefore we could not use Auger or ESCA for surface analysis. Cyclic voltammetry performed on our samples before and after annealing did not give any indication for changes in surface A. Bewick and B. Thomas J. Electroanalyt. Chem. 1977,84 127. Ph. Marcus N. Barbouth and J. Oudar Compt. rend. C. 1975,280 1183. GENERAL DISCUSSION -0.3 Tioe2 a .'=-E 0.1 0 0.1 0.2 TlmVvsPb flmVvsPb t -1.0 --0.5-r E Q: E O-*\N 0.5-1.0 1 0 100 200 300 4W NmV vs Pb FIG.1.-Linear sweep voltammograms for the deposition of Pb onto Cu(ll1) showing the gradual reconstruction of the surface during continuous sweeping just into copper dissolution.(a)volt-ammogram on a freshly prepared surface at 30 mV s-l (b)after 30 min at 15 mV s-' cycling and (c) after 60 min cycling. Solution lod2mol dm-3 lead acetate mol dm-3HC104,0.5 mol dm-3 NaC104. GENERAL DISCUSSION composition other than reconstruction. However we plan to use more surface sensitive methods like those mentioned above to investigate this important aspect. Dr. J. Jovitevik (Southampton) said The results we have obtained for deposition of lead on vitreous carbon confirm our view that the results of Kolb et al. are caused by alloy formation. As it can be seen fig. 1 the amount of lead deposited on the carbon in the underpotential region increases with the number of linear sweep cycles to which the electrode has been subjected.Since the voltammogram of a lead free supporting electrolyte in a region of potential appreciably exceeding the UPD region (curve 1 in fig. 1) in both cathodic and anodic directions does not show any sign of c FIG.1.-Linear sweep voltammograms for the deposition of lead on vitreous carbon. The full lines are curves recorded at intervals of 5 min during the continuous sweeping process. The dashed line is the voltammogram for the base electrolyte free from lead. Solution 0.1 mol dm-3 lead acetate mol dm-3 HC104 0.5 mol dmP3 NaC104 at 5 mV s-l. reaction other than current flowing due to the double layer charging the changes in the UPD behaviour are attributed to the rearrangement of the substrate surface.It is known that lead like mercury can diffuse into vitreous carbon. It appears that lead deposited in the underpotential region penetrates into the substrate and changes the structure of the surface region of the carbon. When removed during dissolution the lead leaves its " fingerprint " in the form of a carbon structure which promotes in- creasing amounts of lead deposition. As every subsequent deposition cycle increases the extent of the reconstruction the UPD becomes more pronounced. This change in structure also has a considerable effect on the kinetics of the overpotential deposi- tion of lead on vitreous carbon substrates. Prof. S. K. Rangarajan (Bangalore) said In any nucleation/growth model a proper identification of No the number of " dissolution-sites " is necessary.Can Schultze give his own ideas on the nature of such nuclei-centres? To what extent are these controlled by the history of their formation and the topography of their formation and the topography of the original substrate? Are these regions of misfits of two or more crystallites or due to point (or line) defects of the overlayer? The experiments reported seem to ignore the details of the overall electrochemical reaction with the possibility of adsorbed (charged!) intermediates very much present. GENERAL DISCUSSION An overall phenomenological coefficient like the electrosorption valency may not suffice. Are these fears exaggerated? Again from the analysis presented here " the coexistence of the three phases " in contrast to the successive formation at well defined potentials is a possibility-at least in certain range of potentials.Do you consider this realistic? My comments on the previous papers as regards the phase transitions vis-6-vis lateral attractive interactions (and Frumkin isotherms) are relevant to this paper too where the steric and packing effects seem even more important! Finally I wish to draw Schulze's attention to the fact that the diffusion-controlled 2-D nucleation-growth is indistinguishable in form from the Langmuir-case. This refers to entries in table 1. Prof. J. W. Schultze (Berlin) said Regarding the question for the nature of nuclei centres I must say that the most important question by Rangarajan leads us unfortun- ately to the field of speculation.We don't know the real topography of our single crystal planes. The misorientation of the planes is < 1" and the concentration of surface defects (estimated from etch pits) is <lo4 cm-2. We assume that point de- fects will be negligible but steps in the substrate surface will be important since they limit the growth of two-dimensional ordered structures. Two-dimensional grain boundaries between homogeneous areas built up by different nuclei are line defects as well. Depending on the history of the adsorbed layer the size of homogeneous areas and the number of the grain boundaries (line defects) will vary but not the substrate topography. More detailed assumptions would be speculative. The problem of adsorbed intermediates is not ignored.For example the problem was studied so far as possible for layer B. In this case the electrosorption valency is constant. Therefore it gives a good phenomenological description of the layer state. It must be mentioned that the electrosorption valency is not an overall coeffi- cient but a true thermodynamic partial derivative describing the adsorption process. The coexistence of three phases was not proved in our experiments. It may be possible that under rapid desorption processes three phases exist simultaneously but we proved only the coexistence of two adsorbate phases B and C in equilibrium. Prof. A. R. Despic (Beograd)said In the case of discharge of multivalent ions like Bi3+ responses to perturbations can be complicated by complex discharge mechanisms involving intermediate-valency species.It seems possible to interpret the result of fig. 3 (and correspondingly that of fig. 2) by a two step mechanism in which first a monolayer of Bif is formed at potentials around +0.22 V which is subsequently reduced to Bi" at 3-0.13 V. The electro- sorption valency of 2.4 is anyhow closer to 2 than to 3. How does one distinguish between this possibility and the model suggested in the paper ? Prof. J. W. Schultze (Berlin) said We assume an ordered layer of type B of bis-muth atoms bound on the gold surface by a polar bond corresponding to an electro- sorption valency y = 2.4 & 0.1. The complete discharge of this layer (280 pC cm-2) would require an additional charge of 70 pC cmw2 which is much smaller than the additional charge of 100 to 120,uC cm-2 measured experimentally.Therefore further adsorption of bismuth ions must take place during the transition B + C -jA. This means that there must be a difference in packing density of layer A and B. This becomes stronger if one takes into account that even the monolayer A may not be discharged completely. From the correlation between y and the difference of electro- GENERAL DISCUSSION negativity Ax we expect for the system Au/Bi3+ given Ax = 0.5 a value y = 2.4 & 0.3 but not 3.0.l This expectation is supported by the fact that the total charge of a Bi-layer A on Au is about 10% smaller than on Ag where the Bi-layer will be dis- charged completely (see our comment on the monolayer formation).In addition to these quantitative arguments we want to say something about the physical meaning of the electrosorption valency in case of metal ions. Similar to ad-atoms the electron gas of the substrate metal will extend over the layer of adsorbed ions. The only difference to the bulk metal will be the lower electron density due to the polarization of the adsorption bond. This was shown schematically in a previous paper1 fig. l(6). Due to the continuous change of electron density at the adsorbed ion the definition of a special intermediate Bi+ is not reasonable. We expect an effective charge something smaller e.g. 0.6. Dr. S. Fletcher (Ottawa) said I have two comments on Schultze’s paper. First I am surprised by the data of fig.7 and in particular by the ‘‘ sharpness ” of the (i,t) transients. Because the current densities are so large (>50 mA cm-2) it would be interesting to re-estimate the accuracy of the ohmic compensation in this case. Furthermore the separation of the non-Faradaic and Faradaic currents is also unusual on this time scale and this also implies that some large ohmic factor might be present. This could be an overcompensation of RQ,or possibly a slow rise-time of the potential at the electrode-electrolyte interface. Similar comments also apply to fig. 9. The value of the rise-time mentioned in the experimental section (0.2 ms) 0 0.5 1.o 4/qr FIG.1.-Theoretical data for i/imagainst q/qT. would mean that it is extremely dangerous to record data within an order of magnitude of this figure particularly when i in the transient is comparable to the double-layer charging current.It seems to me that the effects of such a procedure on the nuclea- tion mechanism are likely to be profound. = co for instantaneous or progressive-nucleation is only accurate at very small values of Q (<1 % coverage) and then only in the case Secondly the test of (di/dQ) ,,= of no background currents. For comparison the theoretical data are shown in fig. 1. I wonder if some experimental data were accumulated on longer time-scales to check this point? ’J. W. Schultze and F. D. Koppitz Electrochim. Acta 1976,21 327. GENERAL DISCUSSION Prof. J. W. Schultze (Berlin) said The ohmic resistance between working and reference electrode about 1.20 was determined by galvanostatic pulse measurements prior to the experiments.The accuracy was &O.ln. A variation of compensation by this amount did not affect the shape of the transients significantly; notably the separation of double layer and adsorption currents was not changed. A large over- compensation was impossible due to oscillations of the potentiostat anyhow. The limit of resolution of 0.2 ms as given in the paper refers to all possible errors and includes the rise-time of the potentiostat (z10V ms-l) as well as the registration of the current. After 0.2 ms the accuracy of the measurements was better than 2%. Although the test (di/dQ),= = GO will be difficult to prove our (current charge) curves are significantly different from the calculated (i Q) transients for instantaneous or progressive nucleation especially as there were no background currents in our experiments.Transients recorded with lower overvoltage and thus on longer time scales are analogous to those shown in the paper. Prof. S. K. Rangarajan(Bangalore) said I find the presentation by Gilmer interest- ing on several counts. First his fig. 1 is not unlike the ones Harrison and I obtain in our simulation studies. What is surprising in this similarity is that our approach is not necessarily molecular (see table 1 our paper) and assumes specific growth geometry (square in the loc cit). Obviously in a true molecular simulation randomness arises at various stages of modelling and introduces a spatial roughness that can be characterised by a wide spectrum of wavelengths.However the similarity seems to indicate that the small wavelength limit (dominant in the fluctuations associated with the geometry of the individual centres) decreases as the coverage increases. One may recall that the origin of the “ 2-D roughness ” in our pictures is entirely due to the overlap effects. This observation is interesting from the view of the theory of simulations that interests us at the moment. A comparison of fig. 2 of Gilmer with the theoretical curves computed from the analytical exact theory available as well as the numerical simulations of Armstrong et al. reveals yet another similarity. Considering that the latter models employed a phenomenological description of the multilayer (cascade) and monolayer (Avrami) formation this similarity makes one optimistic of providing suitable theories for the Gilmer-type simulations too.In this context I would appreciate it if the location of the various maxima the limiting rate of growth etc. can be given as a function of the para- meters like k+,k- k, Ap etc. This similarity (mentioned above) too is not entirely unexpected if we remember that certain details of a model may become irrelevant for large numbers (central limit theorem) or at long times (t -GO). Prof. G. J. Hills (Southampton) said I would like to make some general comments on the papers by Gilmer and by Harrison and Rangarajan. Gilmer’s paper and the film represent a tour de force and lead to an immediate appreciation of many of the factors involved in nucleation and phase formation.The paper by Harrison and Rangarajan is another example of the power of numerical methods in extending analytical methodologies and freeing them from the irritating approximations so frequently necessary to constrain them to a manageable form. Both papers use com- puter simulation to calculate quantities algebraically inaccessible and of course such procedures produce no insights not already in the minds of the authors. This is not to belittle the use of numerical methods but rather to draw a distinction between what might be called confirmatory or interpolatory methods and those speculative or exploratory methods where a genuine uncertainty is investigated. Thus in the latter GENERAL DISCUSSION 181 category and in the field of electrochemical nucleation it is possible by means of com-puter simulation to ask important questions for which there is as yet no obvious answer.For example given a good understanding of the properties of a metal or any other material in an actual and well characterised state it is possible to ask what are its properties in two-dimensions. Under what conditions can it exist in 2D? What is the probable structure of a small cluster in 2D or 3D? When does a disc of hard spheres of necessity assume a raspberry-like structure ? These fundamental questions can be explored by the methods used by Gilmer and have been investigated by our- selves1 and especially by B~rton.~,~ His work is of considerable significance in the field of nucleation and suggests that macroscopic quantities such as volume melting point homogeneity and interfacial tension should be used with caution in the con- sideration and description of microscopic systems such as nuclei.Our own molecular dynamic calculations on clusters of 64 molecules indicate for example that the effect of the surface state on such a small ensemble is such that the properties of “ core ’’ molecules are quite different from those in the surface. The melting temperature structure factors and diffusion coefficients are quite different from those in correspond- ing fully bounded conditions. Thus although Gilmer’s calculations relate to in- finitely bounded conditions in the x,y plane his model of the system in the z co-ordinate may impose characteristics on the system that in fact it does not possess.I would therefore be interested in Gilmer’s comments on the relation between the results of his computer simulations and those say of Burton on microclusters. Dr. G.H. Gilmer (New Jersey) said In reply to informal comments made by Hills I feel that new insights can be obtained from most of the simulation models but that the models must be chosen carefully to suit the problems. For example Ising model calculations have contributed far more to the understanding of critical point phe- nomena than have molecular dynamics studies. New and surprising results have been discovered about the behaviour of density fluctuations and their relation to symmetry dimensionality and the interactions between particles.Weeks et al. have used the Ising model to explore the roughening transition in the crystal-vapour interface and have found some unexpected results including an apparent divergence in the inter- face width at the transition temperature [see ref. (11) of my paper]. Molecular dy- namics techniques are simply not practical for the investigation of cooperative effects involving large groups of particles. Detailed calculations of the trajectories of the particles require much computer time. As a result the technique is presently confined to systems containing small numbers of particles and short runs and the accuracy is limited by the amount of phase space available for performing the averages. Of course there are many phenomena for which the molecular dynamics technique is to be preferred.The small clusters mentioned by Hills often assume configurations where some particles occupy positions that are not related to any bulk lattice structure. The lattice of the Ising model would impose unnatural constraints and it is better to allow continuous coordinates by assuming a pair potential and using the molecular dynamics technique. The bulk melting transition is another phenomenon where models with continuous coordinates is more appropriate. In answer to the question on the relation between our studies of crystal growth and the work on microclusters I believe that the cluster configurations are quite different F. M. S. S. Fernandes and G. J. Hills to be published. J.J. Burton Catalysis Rev. 1974 9 209. C. L. Briant and J. J. Burton J. Chem. Phys. 1975,63 2045. GENERAL DISCUSSION in these two cases. The crystal growth process at low temperatures involves the addition and removal of atoms at a limited number of sites at the surface and hence is ideally suited to the Ising model. Also the strong bonding to the surface tends to produce 2D clusters. But freely suspended 3D microclusters are best treated with models that permit continuous particle coordinates. In our model the only extra restriction imposed on the system in the z-axis direction is the exclusion of overhangs. These configurations become significant at temperatures close to the melting point but the confinement of the atoms to bulk lattice sites is questionable in this region as well.In conclusion I believe that the greatest progress in understanding a pheno-menon is derived from the simplest model that can exhibit most of the effects associated with it. Dr. R.Wiart (Paris)said Your fig. 1 reveals an increase of the surface roughness defined at the atomic scale with an increase of the driving force. It would be inter- esting to know quantitatively how the surface state varies with the driving force because our impedance measurements carried out during the electrocrystallization of some metals such as zinc lead to the idea of an increase of the number of kink sites with the overpotentia1.l From your simulations it would be of interest to determine a parameter characteristic of the surface state for example this number of kink sites.Can you give some quantitative information on the variation of the roughness as a function of the overpotential (mainly under steady-state conditions) and to what ex-tent this variation possibly depends upon the metal lattice? Dr. G. H. Gilmer (New Jersey)said Data relating the number of kink sites to the overpotential (or Ap) on a low index face were published in ref. (6) of my paper. These results do show a decided increase with Ap below the roughening transition temperature; but above this point the kink site density is already large at Ap =0 and there is only a small increase for larger Ap values. Since the kink sites are located in the edges of steps it is apparent that the number of these sites is roughly propor- tional to the total length of steps present on the face.Most electrocrystallization experiments are performed at temperatures far below the roughening transition point and in this case the number of steps is determined largely by the crystallographic orientation of the face and by the growth mechanism. For example the classical theory predicts that the step length associated with a growth spiral is proportional to Ap. Recent computer simulations have confirmed this result over a range of Ap; but important deviations occur at large values where 2D nucleation competes with spiral growth [see ref. (18) of my paper]. Also competition between adjacent arms of the spiral may occur at large Ap when surface migration is important. On a perfect low-index face the step length is determined by the steady-state density and size distri- bution of the 2D clusters.Approximate values for the kink site densities may be obtained from the classical models together with expressions for the densities of kink sites in the edges of the steps [see e.g. ref. (19) of my paper]. Dr. D. E. Williams (Birmingham) said Gilmer’s paper refers solely to crystal growth by vapour deposition in vacuo and the experimental results quoted do refer specifically to this situation. The effect of the presence of a solvent has not been con- sidered. However in his film presentation he showed the effect of a small amount of an impurity species present in the vapour and I wondered if he had considered the case where the “impurity ” was present in large excess and could be incorporated into I.Epelboin M. Ksouri and R. Wiart paper at this Symposium. GENERAL DISCUSSION the surface layer but not into the bulk as would be the situation if the " impurity " were a solvent? I would guess that the binding energy of the solvent to the surface would be an important parameter and might have an effect similar to that of the ratio of surface mobility to evaporation rate high and low extremes of which Gilmer showed gave respectively two and three dimensional nucleation. Since 2 and 3-D nucleation can in principle be distinguished experimentally simulation studies on the effect of a solvent could therefore lead to some interesting discussion on the nature of the metal-solution interface. Dr.G. H. Gilmer (New Jersey) said We did examine a situation involving a vola- tile impurity that was similar to a solvent in some respects. The parameter that describes its effect on the surface is p' = pAA + qgB -2qAB where ~)AA,~BB and ~AB are the bond energies between two host atoms two impurities and the host and impurity atoms respectively. When q'> 0 there is a range of values for the tempera- ture and chemical potential of the impurity pUB where the surface layer is dominated by the impurities but the concentration in the bulk is small. There is also a first order surface phase transition associated with this since the surface composition may change abruptly from an A-rich phase at small values of pBto a B-rich phase at large values. The surface rich in volatile B atoms is inherently more disordered and hence the effect is similar to that of a high temperature.The interface between the B-rich layer and the A-rich crystal may also be more disordered than the pure crystal-vapour interface if p' < vAA. In fact a simple model of the crystal-solvent interface is obtained if one assumes that the solvent occupies all of the sites not occupied by host atoms [see ref. (6) of my paper]. This system is clearly isomorphous with the pure crystal-vapour interface model studied in our paper and the new effective bond energy is exactly p'. Thus if pAB> (oBB/2 then (0' < qAA and the solvent effect is again equivalent to a high surface temperature. Steric effects of the solvent molecules may also be im- portant but the Ising model is not suited to a study of this.Prof. M. Fleischmam (Southampton) said The use of cyclic boundaries in simula- tion experiments seems to impose a degree of correlation which does not correspond to the experimental conditions in effect the growth of a centre close to one boundary of the simulation area becomes correlated to crystal growth at the opposite boundary. Is there any information on the effects of the size of the simulation area on the form of the transients? It should also be possible to use simulations to determine whether there are any order parameters other than those indicated by the rate against time response (or coverage against time response). Such order parameters may well be more appro- priate for the testing of models of adsorption and phase transformation than those currently used (which depend exclusively on the rate against time responses or on data derived from such responses).Is there any information available on this point at this time? Dr. G. H. Gilmer (New Jersey) said There are two different boundary effects that should be considered. First enhanced nucleation may occur when the critical nucleus is large in comparison with the simulation area. The cyclic boundary condi- tions permit the cluster to interact with a reproduction of itself at the boundary and this decreases the probability of its dissolution. In our simulations a critical cluster contains only about four atoms on a 60 x 60 surface and this effect is negligible. A more serious complication arises when the time between nucleation events is larger than the time required for a stable cluster to expand and cover the surface.Then each GENERAL DISCUSSION nucleation event results in the growth of a new layer; and the growth rate is directly proportional to the nucleation rate and hence to the simulation area. The transi- tion from the size-dependent to the size-independent growth rates as the nucleation rate increases is discussed by Bert0cci.l In our simulations 40-50 nucleation events occurred during the growth of a layer on the 60 x 60 surface and the results should be quite close to the infinite area limit. As a further check the same process was repeated on a 40 x 40 surface and the results were consistent with those on the larger surface.Some order parameters describing the structure of the crystal surface have been suggested. For example Leamy et al. [ref. (11) of my paper] showed that the mean of the squared difference in height between two points on the surface is sensitive to the precise condition of the surface. Below the roughening temperature this parameter approaches a finite value in the limit of an infinite lateral separation between the points but at high temperatures it diverges. I feel that experimental and theoretical investigation of structural parameters of this type would greatly increase our under- standing of crystal growth. Prof. S. K. Rangarajan (Bangalore) said Budevskii with the present investiga- tions has verified the two limiting theories of the two modes of crystal growth in the electrochemical context viz.the classical nucleation theory and the spiral growth. I have a few queries to make. (a) The results reported here are for a single dislocation only. How does one adapt these to the case when the growing dislocations are in close proximity and interfere with one another? Can one model these in a fashion similar to the ‘‘ growing cones ”? In this context the term “ steady state ” needs a more careful definition since there are now two levels of observations viz. at the level of a lone dislocation with its own rate of propagation and then at the overlap stage. What are the orders of time involved in such steady states from the experimentalist’s point of view ? (b) Is it proper to ignore classical nucleation mode (as is usually attempted) when ledges formed by dislocations of opposite sign are assumed present? Note that as pointed out in this paper a critical potential-not very different from that associated with the classical nucleation-is involved in the dislocation mode too.(c) Finally I wish to know Budevskii’s opinion on the role of dislocations present in the substrate A when a dzflerent phase B is grown on it. In the case of the overlayer formation (the so called underpotential deposition) B is further assumed to be two dimensional. In such 2-D deposition on real surfaces how do dislocations influence nucleation phenomena ? For example Lorenz et al. claim that the substrates prepared with your technique (with or without artificially doping them with Ag growth pyramids) were not very different from the others as regards “ undervoltage ” properties and voltammograms.What are your comments? Prof. E. Budevski (Sofia) said (a)The kinetics of growth of a singular face depends essentially on the step density and the step propagation rate. The latter being a con-stant at a given supersaturation it is the change of step density that mostly affects the kinetics of growth. The step density produced by a spiral is a constant (a constant overvoltage assumed) as long as the distance between the emergence points of the dislocations is larger than the length of the critical nucleus and hence does not depend on the number of screw dislocations piercing the growing face. The case where this condition is not fulfilled is the subject of the paper under discussion.Bertocci Surface Sci. 1969 15 286. GENERAL DISCUSSION As the step density (number of steps per unit length cm-l or the total length of step per unit area cm cm-2) determines the current density a steady state is attained only when a time independent step density is set up i.e. when the whole surface of the face is covered by the steps produced by the growing spirals at the given supersatura- tion. (b) The two-dimensional nucleation has to be taken into account in the process of growth at higher overpotential regardless of the presence of screw dislocations and spiral steps. The complex growth behaviour of a face under these conditions has not been treated theoretically at least to my knowledge.(c) The emergence points of screw-dislocations as well as other surface defects could affect the process of adsorption by changing the adsorption energy. Steps produced by screw-dislocations could affect this process additionally. Under normal conditions however the area of the surface affected by these defects seems to be small enough and their contribution to the overall adsorption process appears to be undetectable as found by Lorenz et al. Prof. M. Fleischmaun(Southampton)said It is interesting that the edge energies of silver deduced by a variety of methods are unexpectedly low. In consequence two- dimensional nucleation must be an inherently more likely event that would other- wise be expected. In addition the frequency factors for two-dimensional nucleation may well be much higher than those predicted by classical nucleation theory.It is particularly interesting that the Monte Carlo simulations have shown that non-equilibrium forms of the nuclei may well have to be counted in the distributions thereby enhancing the rates1 In this connection it may be noted that an early exam- ination of an extensive set of data for the three-dimensional nucleation of lead dioxide as a function of both electrode potential and overpotential (using solutions covering a wide range of pH and plumbous ion activity) in fact showed that the experimental frequency factors were higher by a factor of lo5than the calculated values.2 High rates of two-dimensional nucleation have been consistently observed in our earlier work on the formation of monolayers of non-metallic phases.In some cases the difference in potential between the two-dimensional nucleation of the phase and the converse two-dimensional nucleation of holes can be made as low as 1-2 mV. It is also relevant that the overpotentials (or underpotentials!) for the formation of the layers are small. A possible interpretation of both these effects is that the layer and edge energies are reduced by electrostatic imaging in the conducting metal and solu- tion phases. A similar phenomenon could be responsible for the low edge energies observed for metals if the atoms at the edges carry a partial charge. Even if the electrosorption valencies for the layers indicate virtually complete charge transfer the atoms at the edge may still carry a substantial charge.Prof. S. K. Rangarajan(Bangalore)said It is comforting to note in Hills’ paper that the limiting solution [eqn (2) valid for t -01 of the Stefan-like problem is not too different from the author’s numerical procedure [eqn (3)]. I have looked into this problem too by no means completely solved in view of the overlap of diffusion regions associated with the various growth centres-and it appears that eqn (2) of Hills follows from mine [table 2 (A)] when 3 (or R)-+ 0 (refer to column 2 of table 2) as a special case. Even though both the approaches use “ lone centre ” models table 2 of my paper also gives the overlap effects. I hope a fuller interpretation of the observa- G. H. Gilmer paper at this Symposium.’ M. Fleischmann and H. R. Thirsk Electrochim. Acta 1959 1 146. GENERAL DISCUSSION tions of Hills will become available soon and the location of maxima and their depend- ence on potential the asymptotic envelope etc. be made clear. Prof. M. Fleischmann (Southampton) said following informal discussions with Hills and others The formation of a limiting number of nuclei at the peaks of the galvanostatic transients fig. 6 may be due to a number of contributory factors which include (i) a fall in the nucleation rate with decreasing potential in the region past the maximum. (ii) a redissolution of clusters of subcritical size as the potential falls in view of the concomitant increase in the critical size with decreasing potential.(iii) the conversion of a limited number of preferred sites into nuclei with increas- ing time. With regard to (iii) it is noteworthy that nucleation is confined to a relatively short region of time fig. 6 which corresponds to the " instantaneous " nucleation of a defined number of nuclei at preferred sites in potentiostatic experiments.l This "instantaneous " nucleation will not be as sharp in galvanostatic as in potentiostatic experiments as the number of sites is itself dependent on the potential. Dr. J. A. Harrison (Newcastk) said The (i t3) plot in fig. 5 does not look to me to be very satisfactory. Would it not be more convincing to describe the data of fig. 4 predominantly by an (i t) dependence? Such dependences are observed in a number of other reversible systems.2 If this is the case then probably the galvanostatic pulse used does not create the conditions assumed by the authors.Dr. G. A. Gunawardena Prof. G. J. Hills and Mrs. I. Montenegro (Southampton) said It is not easy to see the full significance of Harrison's question. These nuclei are known to be isolated hemispheres growing under mass transfer control. That being so the corresponding current must be a linear function of t3. In any case the relationship is only used to determine the nuclear density which can be and has been checked by independent means. Prof. M. Fleischmann (Southampton) said The tabulation1 of the standard rate constants for the Hgi+ + 2e 2Hg reaction referred to by Hills shows that a number of methods give values of the order 2 x cm s'l; there is a tendency for the observation of higher values when relaxation methods are used at very short times or high frequencies.It should be noted however that this tabulation refers to perchlorate solutions. The potentiostatic experiments1 have been carried out under conditions (in a special thin layer cell) such that the concentration polarisation would be less than in the experiments reported here but even under those conditions the measurements showed a rapid transition from kinetic to diffusion control. The derived kinetic data did not follow a simple Tafel relation. The low value of the standard rate constant may therefore be due to the use of nitrate solutions a deviation of the kinetics from a sim-ple Tafel relationship or else concentration polarisation.P. Bindra A. P. Brown M. Fleischmann and D. Pletcher J. Electruarzalyt. Chem. 1975,58,39. J. A. Harrison J. Electruanalyt. Chem. 1972 36,71. GENERAL DISCUSSION Dr. S. Fletcher (Ottawa) said In fig. 4 of Hills’ paper a small falling transient may be observed on a time scale of -0.1 s. What is the origin of this phenomenon and how does it relate to the galvanostatic result of fig. 2? Also why do the data of fig. 5 not extrapolate through the origin? I would like to ask about the de- convolution process. Is all of the rising section of the (E t) response (fig. 2) due to non-faradaic effects or would a potential maximum still be observed (on a similar time scale) in the absence of charging currents? These curves clearly have a complex shape.Dr. G. A. Gunawardena Prof. G. J. Hills and Mrs. I. Montenegro (Southampton) said The small falling transient evident in fig. 4 of our paper occurs over a time scale of up to 0.1 s depending of course on the magnitude of the applied overpotential. It is the result of the relaxation of the double layer charging current and possibly of the simultaneous relaxation of ad-atom concentration as stable nuclei emerge. Clear evidence of this is given in a forthcoming paper. The minimum in current might also be related to an induction period preceding the formation of stable nuclei. The in- duction time is also evident in fig. 5 and is the reason why the linear relation between current and t3 does not pass through the origin.The minimum is not easily related to the shape of fig. 2 although the underlying phenomena are of course the same in both experiments. In answer to the second question the rising portion of the present (q t) curves is certainly not due only to non-faradaic effects but rather to a combination of double layer charging ad-atom deposition and formation of nuclei. A potential maximum might still be observed in the absence of any double layer charging. This is so for two reasons. (1) The falling part of the potential transient is inevitable because the in- creasing area of electroactive (mercury) surface relaxes the faradaic current density and therefore the overpotential. (2) The rising part could also result from monolayer formation or any other initial process requiring a lower overpotential than the prin- cipal deposition step.Dr. H. P. van Leeuwen (Wageningen) (communicated) The correction for capaci- tance current applied to the galvanostatic current in the PGP signal is based upon the value of the differential double layer capacitance Cd. This value is obtained from the initial part of the galvanostatic transient and is related to the potential of the first potentiostatic pulse. During the galvanostatic part of the PGP pulse train over- potentials up to some 300 mV are reached and there seems to be no certainty as to the C values for the graphite-solution interface at these potentials. Besides by the time these potentials are realized parts of the graphite surface are covered with mercury nuclei and the mercury-solution interface has different capacitance characteristics.From the numbers of fig. 2 it can be calculated that the extent of this coverage can easily be of the order of 20% of a monolayer. The questions that arise are did the authors consider the potential dependence of cd for the graphite-solution interface and how did they rule out the contribution to the charging current of the mercury- solution interface ? There seems to be a need for an experimental determination of C in situ the overall cd for the graphite 4-mercury-solution interface. This could be realized by using coulostatic pulses at different stages during the galvanostatic part of the PGP-pulse. Even if fast electrode processes can take place at the interface quite reasonable results can be 0btained.l Alternatively (or in addition to the foregoing point) a H.P. van Leeuwen and J. H. Sluyters J. Electroanalyt. Cheni. 1972,39 233. GENERAL DISCUSSION second galvanostatic pulse could be applied in such a way that &/dt is forced to be Zero. As in the classical galvanostatic double pulse method the faradaic current at that certain moment is directly measured. The quality of these experiments can be very good because a second coulostatic or galvanostatic pulse can be made to follow the first galvanostatic pulse within less than a microsecond. Dr. G A. Gunawardena Prof. G. J. Hilis and Mrs. I. Montenegro (Southampton) said We are grateful to van Leeuwen for his comments and for drawing attention to his earlier paper describing a wide variety of multiple pulse trains.We agree that it would be valuable to use say a potentiostatic-galvanostatic-coulostatic pulse train to determine (i) the interfacial capacity and (ii) the faradaic current. It would be parti- cularly useful to determine the latter quantity at lower overpotentials than those arising out of the present PGP method. Turning now to the specific question relating to possible errors in the deconvolu- tion of the capacitance current it was realised from the beginning that the assumption of a constant value of C,over the entire potential excursion is only an approximation. It was for this reason that we chose to use the current densities and overpotentials at the galvanostatic maximum where at least cd dy/dt =0 irrespective of the vdue of cd.It could of course be argued that qmaxdCd/dt # 0,but because the measurements were made at high ionic strengths and because the area of electroactive (mercury) surface and the rate of change of that area with time are still quite small it was thought to be a good approximation to assume the charging current at the galvanostatic maximum to be negligible. Moreover although the coverage may correspond to 20% of a monolayer the total area of hemispherical nuclei at the peak potential was cm2 as compared with the area of the graphite electrode which was 0.32 cm2. It therefore seemed entirely reasonable to neglect the contribution to the charging current from that of the mercury/solution interface. Even if this approximation is acceptable there remains the error in average nuclear size as evaluated from the expression Again because the variation of cd for graphite is not markedly potential de- pendent except in dilute solution it might be thought that the error is small but no firm conclusions can be drawn about this point until direct determinations of the type described by van Leeuwen have been made.Dr. L. M. Peter (Southampton) said I should like to ask Harrison if the Avrami theorem is applicable to the case of progressive nucleation followed by one-dimen- sional i.e. needle-like growth. Recently we have found that the (current time) transients for the deposition of monolayers of CdS on cadmium amalgam resemble the transients expected for instantaneous nucleation followed by two-dimensional gr0wth.l Since under similar circumstances we find in agreement with Fleischmann et al.that Cd(OH)2 clearly grows by the progressive-2D mechanism and since also the liquid surface is uniform we considered as an alternative explanation for the CdS results that in this case progressive nucleation is followed by essentially ID growth. We have carried out simulations3 similar to those discussed by Harrison and Rangarajan and I. da Silva Pereira and L. M. Peter in preparation. M. Fleischmann K. S. Rajagopalan and H. R. Thirsk Trans. Favaday SOC.,1963,59,741. I. da Silva Pereira and B. Scharifker unpublished results. GE NE R A L D I S CU S S I ON the results are shown in the form of a reduced variable plot in fig.1. We prefer this type of linear plot for the diagnostic examination of experimental and simulated transients. The simulated transient deviates from the experimental result for t > tmax suggesting that the model is oversimplified. The experimental transient also deviates considerably from the well-known analytical solution for the instantaneous-2D mechanism. .* ........_ I --1.0 2.0 3 I.O t/tm FIG.1 .-Comparison of the simulation of ths progressive-lD mschanism (opircles) v analytical solution for the instantaneous-2D mechanism (dotted line) The continuous line is an experimental result obtained for the growth of CdS on 1% Cd(Hg) in 0.1 mol dm-3 NazS + 1.0 mol dm-3 NaHC03 (tmax3.7 s). The details of the simulation were L x L = 20 x 20 N = 5 G = 1 ; average of 20 runs.In our opinion a more general simulation of monolayer growth would be worth- while. Such an approach should consider the possibility that the growth rate depends on the crystal edge and varies during the lifetime of the growing centre. In the case of a liquid substrate the random movement of the nuclei on the surface can lead to coalescence phenomena which should be included in the simulation of the (i t) transient. This effect must be of particular importance when the film grows slowly. Dr. G. H. Gilmer (NewJersey) said I would again like to consider the physical basis for Harrison and Rangarajan’s treatment of multilayer deposition. The current to layer n + 1 in eqn (3) may involve an unstated approximation regarding the struc- ture of the crystal surface.To see this let us first calculate the current to an ensemble of electrocrystallization systems each containing a complete layer of atoms at level n. Suppose that the deposition process was initiated at various times z in the different systems where 0 < z 6 t. If the fraction of systems initiated in the interval (z z + dz) is chosen to be proportional to i,(z)dz then eqn (3) is exact.* That is the total current to all layers at level n + 1 in the ensemble is proportional to the number of systems initiated at time z multiplied by the currentf,(t -z) and summed over all of the systems. Does this equation apply also to an ensemble where the deposition in each system starts at level 1 at t = O? Clearly i,(z)dz is proportional to the area of layer n deposited in the interval (7 z + dz); hence the area on which the deposition * Here in(r)is chosen to be equal to the current to layer n during the multilayer deposition that starts at layer 1.GENERAL DISCUSSION of layer n + 1 begins to take place is identical with that in the first ensemble. How-ever the surface is quite different in the two cases. In the first ensemble layer n is complete and n + 1 empty at the instant the deposition of layer n + 1 begins; but in the second ensemble both layers are incomplete. An incomplete layer n should reduce the deposition rate at level n + 1 in comparison with that of the first ensemble. But the clusters already deposited at level n + 1 will have the opposite effect. Because of these opposing influences the two ensembles may have similar currents; but apparently only the first one is exactly given by eqn (3).Therefore I would like to ask the authors whether they are convinced that eqn (3) is exact for the case they have considered; and if not whether they have any estimate of the accuracy of the approximation. Dr. S. Fletcher (Ottawa)said My first comment relates to question (a)asked at the beginning of Harrison’s paper. As far as I am aware the derivation of the Avrami theorem does not depend on geometrical assumptions; so that geometries other than circular should be adequately described. However the probability of encountering various nuclei should be the same in all directions from any given point in the space and also the number density of nuclei should be limitingly high.It might therefore be interesting to consider some non-random distributions of nuclei also. My second comment relates to question (c). Although I agree two types of ran-domness are involved in the theoretical picture the temporal one is of little significance to eqn (1) because the surface coverage is evaluated at each instant hence eliminating any contribution from possible time-dependent processes (i.e. nucleation). In the calculation of (i t) responses in the electrochemical case some sort of integration over time is obviously necessary which may (or may not) be possible. However I do not see how this reflects on the fundamental efficacy of the Avrami theorem. A third point which follows from the above concerns the “ ingestion effect ”.(I take this to mean the nucleation of “ ghost ” nuclei in areas already covered in the 2-D plane.) It seems to me that this type of nucleation is automaticaZZy taken care of by the Avrami theorem via S,. There appears to be no need to evaluate a non-linear differential for S, rather S,should simply be the sum of the extended areas of all nuclei c‘ghost ” or otherwise) on the electrode surface at any given instant. If the above be the case it remains to explain the discrepancy between the simula- tion and the Avrami theorem. Could this discrepancy possibly be caused by either (a) the finite size of the simulation or (b)the large number of “ catastrophic ” collisions between adjacent nuclei since these are all square and have similar orientations in space? It might be expected that such collisions would produce singularities in the simulation response particularly for small N.Dr. D. G. Lovering (Shivenham) (communicated) I am not clear how the surface charge on the metal substrate and any residual or mirrored charge on the ad-“ atoms ” e.g. as in a partially-charged intermediate may be accounted for in simulation. Dr. R. Wiart (Paris)said It appears that the curves depicted in Harrison’s fig. 1 correspond to the formation of successive monolayers so that the isimincrease cor- responds to the development of nuclei and the isimdecrease to the overlapping. To what extent the origin of such a cyclical current could be the result of your assump- tion according to which a nucleus moving over a boundary is systematically reintro- duced at the opposite edge of the square matrix? As a matter of fact one wonders if the time-lapse appearing in fig.1 does not correspond essentially to the time necessary for the five simultaneously formed nuclei to propagate through the matrix GENERAL DISCUSSION from one edge to the opposite one. In other words what is the influence of such cyclical boundaries on your cyclical results ? Prof. M. Fleischmann (Southampton) said I would like to clear up one particular point concerning the growth of three-dimensional centres on a substrate. It appears from this paper that our earlier analysis of the growth of right circular cones on a substratel is incorrect but at this stage I cannot see that there is any error in that ana- lysis.I also wish to refer to the application of the equation i = nFk' 1 -exp -L-given by our analysis to the electrocrystallisation of nickel on vitreous carbon sub- In this equation k mol cm-2 s-l is the rate of crystal growth parallel and k' mol cm-2 s-l the rate of crystal growth perpendicular to the surface. Mg mol-l is the molecular weight p g the density and A s-l the nucleation rate constant. Fig. 1 shows a computer fit of the equation to an experimentally observed transient. Nuclea-tion rate constants may be deduced from double potential pulse experiments (using a high negative potential of short duration to form the nuclei followed by a low negative potential to observe their growth) in this case applying the equation where No is the number of nuclei formed in the first pulse.It follows that the two rate constants k and k' can be compared fig. 2 shows that they are proportional to each other and approximately equal. It follows that no special mechanism is needed to propagate crystal growth in this case. In particular if dislocations were active then we would predict that k' cc k2 which was observed for the case of the growth of mercuric 0xide.l A conclusion similar to that for the case of the electrocrystallisation of nickel has been reached for the case of the growth of lead dioxide3 (but in that case using different premises). Prof. A. R. Despit (Beograd) said It would be very useful for simulation purposes to establish equivalent circuits for the phenomena considered in the paper.Could Rangarajan offer some at least for the linear perturbation conditions? Dr. D. E. Williams (Birmingham) said Rangarajan has described in some detail the theory of the potential sweep method. I wish to raise the question of its applica- tion to experimental results. Results obtained with this method are particularly sensitive to the value of the resistance Ra between reference electrode tip and working electrode surface because the true potential scan rate at the working electrode utrueis different from that applied utrue= Y -Rn(dI/dt). R. D. Armstrong M. Fleischmann and H. R. Thirsk J. Electruanalyt. Chem. 1966 11 208. M. Abyaneh and M. Fleischmann to be published. M. Fleischmann and H. R. Thirsk Electrochim.Acta 1959 1 146. 192 GENERAL DISCUSSION r 3150 --2450-4 .w C -L L 3 1250-1050-350-t/s FIG.1 .-Computer fit of the equation of the experimental results for the electrodeposition of nickel at a potential of -0.875 V (SCE). The fit gives the following parameters. PI = i = 65.7 f7.9 PA ; 18.2pA; P3 =; sA P2= zFk‘ = 3548 -l = 2.16 x -l 6.9 x 10-6s-3; P4 = r = 1.11 i 3P 0.14 s. ST = standard error in fit = 7.4 Log k& -4.0 -3.4 -2.8 -2.2 -1.6 I I 1 I I I I I I -1.82 -2.24 log k’ -2.66 -3.08 -3.50 FIG.2.-Plot of log k’ against log k; the slope is found to be about 0.97. GENERAL DISCUSSION 193 Since the current can vary rapidly with time especially at high scan rates the difference can be considerable and the effects are marked.l A recent discussion2 of this effect using a simple model3 in which the current is proportional to the area of the electrode left uncovered by deposit indicates that the dependence of peak current on scan rate varies from i,ccu towards i,,ocu+ as the value of Ra increases.Comparison with eqn (22) and (23) of Rangarajan’s paper shows therefore that the experimentally determined variation of peak current with scan rate is not particu- larly sensitive to the details of the model chosen to represent the results. The peak potential variation is similarly insensitive. As an example of the insensitivity of the peak parameters to the details of the chosen model I can again cite some work by Arvia et al.In an investigation of the formation of anodic films on Pt in molten KSCN using cyclic ~oltammetry,~ the peak parameters were interpreted in some detail using the simple model cited above.3 However in an earlier paper in which the same system was investigated by the galvanostatic meth~d,~ the data were interpreted in terms of a nucleation and growth model in which the current is proportional to the edge length of the developing nucleus.6 The fact that these are two very different models which can be distinguished in other ways7 em- phasises the point that the scan rate variation of peak parameters in cyclic voltammetry is insensitive to the nature of the model chosen to represent them. Certainly the whole shape of the current response in a potential sweep experiment contains within it considerable information on the details of the electrode reaction.However until a reliable method of recovering the true shape from the experimentally measured shape is obtained (as can be done to some extent for diffusion-limited processes)* then the potential sweep method must remain semi-quantitative only. Dr. S. Fletcher (Ottawa) said My first observation concerning the paper of Ran- garajan relates to the question of nomenclature as used in his sections 3 and 4. It is clear that two types of nucleation law are considered under potentiostatic conditions ; zero order (“ instantaneous ” nucleation of No nuclei) and first order (c‘ progressive ” nucleation with N = No&). There are however difficulties in interpreting these simple relationships when q is varied as in the case of linear potential sweep (L.P.S.).As an example suppose that a given system is characterized as “ instantaneous ” by the potential step method. What will its (i t) response be to L.P.S.? It certainly will not be eqn (8)-(12) of Rangarajan because the extreme potential dependence of No has not been explicitly taken into account in his derivation [see eqn (4)]. The assumption of N = No = constant is therefore physically unreasonable. Of course it would be possible to fix No by the application of a large potentiostatic pre-pulse prior to the L.P.S. but then the derivation can hardly be said to be for simple L.P.S. Note also that a large pre-pulse in the progressive case would also render the same “instant-aneous ” response to the subsequent L.P.S.It seems best to reserve the terms “ instantaneous ” and “ progressive ” (properly D. E. Williams and G. A. Wright Electrochim. Acta 1976 21,1009. N. R. de Tacconi A. J. Calandra and A. J. Arvia Electrochim. Acta 1973,18 571. S. Srinivasan and E. Gileadi Electrochim. Acta 1966 11 321. A. J. Arvia A. J. Calandra and M. E. Martins Electrochim. Acta 1972 17 741. A. J. Calandra M. E. Martins and A. J. Arvia Electrochim. Acta 1971 16 2057. D. A. Vermilyca Advances in Electrochemistry and Electrochemical Engineering ed. P. Delahay (Interscience New York 1963) vol. 3 p. 211. ’D. E. Williams and G. A. Wright Electrochim. Acta 1977 22 505. P. E. Whitson H. W. VandenBorn and D. H. Evans AnaZyt.Chem. 1973,45 1298. GENERAL DISCUSSION applicable only under potentiostatic conditions) for the generaldescription of particular systems under consideration even though zero-order and first-order nucleation will not be observed when these systems are subjected to simple L.P.S. or any other varia- tion of potential one might chose. Hence on this view what Rangarajan has calcu- lated in eqn (8)-(12) is the response of both instantaneous and progressive 2D nuclea-tion and growth to a “ P.P.L.” waveform i.e. a potentiostatic pre-pulse followed by L.P.S. The other case considered by the author (labelled “ 2-D progressive ”) also ignores the variation of No with q and hence is exceedingly unlikely ever to be observed in practice. A second observation relates to the complete form of the (i t) response governed by eqn (8)-( 12) in the limit of high v.These equations correspond to a case considered by numerical simulation techniquesf My result is illustrated in fig. 1. The coverage at the maximum is identical to that predicted by Rangarajan. It is worth noting that 44 FIG.1 .-i& plotted against q/qT. it should be comparatively easy to test this result experimentally provided ohmic complications can be avoided. My third observation relates to the problems raised by Williams. Using numerical techniques [based on equations similar to (3) and (4) of Rangarajan except that a term for the potential dependence of No is included] it is possible to investigate the effects of Rn on the L.P.S. response of any chosen nucleation and growth mechanism.2 Without going into details the results indicate that RQis indeed of crucial importance in the analysis of L.P.S.data because of the extreme potential dependences of the various nucleation and growth parameters. A posteriori compensation is difficult without prior knowledge of either the nucleation mechanism or the exact value of Rn. In turn it seems that L.P.S. techniques are not highly diagnostic of the many possible 2-D nucleation and growth mechanisms and hence potential step methods are much to be preferred for this purpose. Of course potential step techniques are also subject to iR-drop considerations but in these cases the effect of I& is minimal at short times in the rising transient. If l S.Fletcher unpublished data. R,G Barradas F. C. Benson and S. Fletcher Electrochim. Acta 1977 22 1197. GENERAL DISCUSSION desired the complete ohmically-distorted transient can be computed by numerical methods similar to those described above.’ Prof. S. K. Rangarajan (Bangalore)said Fletcher seems to think that the problem of “ instantaneous ” and “ progressive ” nucleation models applied to linear sweep is more than one of nomenclature. The concern is understandable but the conclusions that the results given in the paper refer to only PPS rather than LPS are not. A fairly general description of the nucleation rate can be dN/dt = NoA(q) exp {-i A[ q(z)]dz} which reduces to dNldt --t No6(t) (instantaneous) -t NoA(q) (progressive) according as A +co or A -+ 0.There is therefore no basic obstacle to extend- ing the two basic nucleation models to the case of time varying overpotentials. The only question that remains is how accessible are these limits? When = ut and A = exp (-3 dN/dt = NAo exp (-a‘lE) exp [-E2 (%)-where E2 is the exponential integral defined E2(z) =,(:xp (-zt) dt/t2. Hence the accuracy with which one may use the instantaneous or progressive model depends on the magnitude of [AoE-E2(a’/E)/V] = A. t Ez (a’lE) being >> or < 1. This may be compared with the analogous condition in the potentiostatic case uiz. A. exp (-a‘/E)t 9 or < 1. And hence at any time or potential of observation in the LPS the accessibility of the two limits is modified by the function exp (a’/E) E2(a’/E) which is bounded on the two sides by In other words accessibility to the instantaneous case is less (not denied) over the initial period zi sa/v.If this time constant zi < z, the characteristic time constant for overall growth (cf-the B factor) there is no loss of generality at all assum- ing the I-model at t = 0. There is no such limitation on the onset of the progressive model. To sum up it is not correct to suggest that the analysis given in my paper is limited to PPL and also that there are basic difficulties in postulating instantaneous/progressive limits to the case of time varying potentials. However we should not forget the domains of validity of such limiting models whether the technique is potentiostatic or potentiodynamic.R. G. Barradas F. C. Benson S. Fletcher and J. D. Porter J. Electroanalyt. Chem. 1977 85 57 67. I96 GENERAL DISCUSSION The models for N,-variation [over and above the A(q)factor] are not clear and are empirical at this juncture. The arguments given above are fundamentally the same even in this case even though the (i E)curves will be modified. We are not concerned in this paper with all possible models for potential variation of the nucleation constant and so this question is not taken up now. Both Fletcher and Williams raise the important question of iR corrections. We recognise this vexed problem but do not include this aspect as it will impede the ease of discussion. The results reported here are valid if the ohmic compensation can be satisfactorily made and remembering that they can be made even if not completely! The more generalised model is too involved to discuss now.It is difficult here to take up the question of adequacy or inadequacy of the earlier treatments of this question referred to by Fletcher and Williams. Both Fletcher and Williams have argued very appropriately (and not too soon) the need for better diagnostic procedures. I agree with this but I shall not go all the way with them in ruling out linear sweep voltammo- grams for this purpose. The limiting laws (22)-(23) are not the quintessence of the LPS-they are just the residue! For example a better version of eqn (22)-(23) is (ip/V) over the entire range. -coth (3) Dr. R. Wiart (Paris) said The point I would like to raise concerns the electrode impedance you have calculated at a frequency much larger than the time constant of the system which is not under steady state conditions.What is the physical meaning of the inductive impedance [obtained eqn (38)] that you have found out in the case of a progressive nucleation? Is it related to a relatively fast change in the active area and to what extent this inductance can be connected with the inductive impedance which has been observed in many cases of electrocrystallization1*2but this time in the range of very low frequencies ? Prof. S. K. Rangarajan (Bangalore) said The physical measuring of the inductance element (giving the approximate representation of 2-D nucleation/growth model) is at the present moment not clear.It arises mathematically and can be traced to the con- volution integral associated with the progressive nucleation. The reference to high frequencies becomes essential since the system (cf. area) is changing continuously and the small signal measurements have to be meaningful. There seems to be no obvious relationship with the inductive impedance referred to by Wiart except that the activated state of a centre may be thought of as an intermediate. Prof. M. Fleischmann (Southampton) said A major concern of this paper is the examination of the validity of the Avrami postulate using simulation methods as applied to the overlap of crystal growth centres as well as the ingestion of the sites where nucleation would otherwise take place.However it seems to me that the statis- tical treatment by the Avrami postulate of the random nucleation and growth of two- dimensional growth centres on an area or of three-dimensional growth centres in a volume (though not of other more complex cases) always takes correct account of all classes of overlap and in particular of the ingestion of nuclei. The stochastic mean for potentiostatic experiments deduced from any simulation of these cases should therefore be equal to the deterministic mean predicted by algebraic analysis and if this is not so then this points to an inadequacy of the simulation rather than of the Avrami postulate. I. Epelboin M. Ksouri and R. Wiart paper at this Symposium. I. Epelboin and R. Wiart J. Electrochem. Soc. 1971 118 1577.GENERA L DISCUSS I ON I would also like to refer to the form of the (current time) transients predicted for the repeated formation of layers by two-dimensional nucleation and growth. Our early simulation results lY2 showed that the oscillations due to repeated layer formation do not die out nearly as rapidly as is suggested by the form of the transients calculated by analysing the deposition as a cascade pro~ess~~~ and are much more in accord with the data deduced by recent Monte Carlo simulation^.^ It seems to me that nucleation and growth in the second and subsequent layers is never totally random since the proba- bility of overlap of a growth centre formed on an underlying centre is dependent on the distance of the nucleation site from the periphery of the underlying centre a degree of correlation is therefore introduced and this must have the effect of accentuating and maintaining the successive oscillations due to repeated layer formation.Prof. S. K. Rangarajan (Bangalore) said I rephrase the questions posed by Gilmer Wiart and Fleischmann as (i) how good is Avrami’s equation? (ii) how reliable is the multilayer equation? (iii) how safe are the cyclical boundary conditions? The answer is not apriuri obvious in the case of Avrami’s equation. There are prob- lems associated with the surface effects of small areas and small numbers of centres. The coverage probability of n identical centres of area a and perimeter I “ randomly dropped ” on a plane domain of area A and perimeter L is for example (2nA + L1)”A = [2n(A + a) + ZL]”’ We can demonstrate how this leads to the usual Avrami (Poissonian) limit S = 1 -exp (-Sx) if n -w 00.There are then also questions of ingestion effect geometry/symmetry of the centres evaluation (discrete or continuum?) of S, etc. Our simulations emphasise the need to consider these. If Avrami’s equation had not been disproved it is not entirely due to the merits of the equation. The conditions of simulation have been chosen not unfavourably to reach such a conclusion. Nor should these be taken to support Fleischmann’s contention about the average of the stochastic simulation equalling the algebra of the averaged process. We are dealing with nonlinear functionals of stochastic events and also doubly stochastic processes.Avrami’s average theory could well be inadequate. It has been shown formally in the case of S that this theory can easily be extended to cover ingestion effects and the fluctuations associated with (and their transforma- tions via) Avrami’s individual centres. Further simulation studies are necessary in this direction but I am not however so sure of the realisability of these features in experimental observations. The multilayer eqn (3) is again like Avrami’s an example of successful modelling of a complex phenomenon by a simple relationship; so are its limitations. The equa- tions model the system where the deposition starts at t = 0 and the possibility of A. Bewick M. Fleischmann and H. R. Thirsk Trans. Faraday SOC.,1962 58,2200.A. Bewick Ph.D. Thesis (University of Newcastle-upon-Tyne 1961). R. D. Armstrong and J. A. Harrison,J. Electrochem. Soc. 1969 116 328. S. K. Rangarajan J. Electroanalyt. Chem. 1973,46 119. G.H. Gilmer paper at this Symposium. GENERAL DISCUSSION layers at all levels (n = 0 1,2 . . .) is granted. Eqn (3) is not the whole story and is related to similar equations governing other levels. Together these determine in(t). At any time t we obtain therefore the entire array {in(t)> n = 0,1,2 . . . . If my assumption of the model is to be termed " crucial " it is the ansatz that the transition to level (n + 1) from levels lower than n is considered unlikely. There is still plenty of manouverability possible within the context of eqn (3).The rate of phase-forma- tion,f (t),can be modelled more carefully considering that we may be dealing with small systems (in the initial stages at least) and also the layer to layer characteristics can depend on n. I believe that eqn (3) is a reliable conceptually and operationally starting point. It also explains the oscillations. The cyclical boundary conditions are well accepted features of simulations. One interesting motivation at least is to "enlarge " the finiteness of the domain to the infinite region i.e. to transcend the limitations of space inherent in the experimental system. This is no doubt imperfectly achieved by cyclical boundary conditions in that a certain type of correlation is set up. I do not consider this to be really serious if certain precautions are taken.In our simulations we had checked this by varying the mesh-size. The maximum in i is definitely not caused by this. Analytical solu- tions for e.g. in fig. 1 nT = 9 and L = 39 make the possibility of the cyclical condition causing a maximum in current highly unlikely. This does not mean that cyclical conditions are always trouble-free! One must be careful in avoiding " aliasing-like " effects known in fast Fourier transforms (though in the time-axis instead of the two dimensional space as here). Prof. A. R. Despi6 (Beograd)said Spongy zinc deposit is known to occur simul- taneously with intensive hydrogen evolution (and local increase in pH) at low current densities before massive zinc deposition starts. Hence the highly disordered struc- ture has been thought to result from effects of adsorption of hydrogen and zinc hydroxo complexes (possibly colloidal hydroxide).On the other hand at high current densities diffusion control over the deposition process has been shown to account well for the phenomena leading to the development of dendrites and dendritic and powderous metals are known to form onZy under condi- tions of limited supply of depositing ions from the bulk of solution. How does the new model account for the effect of adsorption of species foreign to the deposition process as well as for bulk diffusion limitations? Dr. R. Wiart (Paris)said According to our model the origin of spongy deposits is ascribed to a coupling between the interfacial reactions and the surface diffusion of Znais.This coupling is prevailing at low c.d. under conditions where any bulk diffu- sion can be disregarded and where most of the electrode is blocked by adsorbed hydrogen. Periodic distributions of the surface concentrations of intermediates on the electrode are then obtained with local c.d. peaks corresponding precisely to local maxima of Znais concentration and local minima of Hadsconcentration. Conse-quently our model accounts clearly for the inhibiting effect of Hadson zinc electro- deposition. Moreover since this inhibiting effect of Hads occurs at low values of mean c.d. where hydrogen evolution and consumption are relatively intensive our model is in good agreement with the possibility of an inhibition by Hadswhich could effectively be strengthened by the local adsorption of hydroxide as a result of a local pH increase.At high c.d. the development of dendrites is fairly well explained in terms of a GENERAL DISCUSS ION 199 limited supply of depositing ions. However this diffusion-controlled process seems not sufficient to account for the dendrite’s birth. As a matter of fact during zinc deposition on a rotating disc electrode the formation of very small dendrites has been observed at relatively high rotation speeds where the influence of mass transport can be considered as eliminated.1*2 In addition the analysis of the structural features of zinc dendrites has shown that the dendritic growth is not the result of the only local development of the underlying compact metal since it needs a nucleation pro~ess.~ The birth of zinc dendrites can be reasonably explained by the autocatalytic reaction (3) since this reaction is able to give rise to a strong acceleration of the nucleation rate even at a very low overpotential.That is the reason why we are led to think that the reaction mechanism is closely connected with the dendrite’s birth which has to be distinguished from the dendrite’s development undoubtedly governed by a diffusion p~ocess.~ Prof. M. Fleischmann (Southampton) said It is interesting that the formation of dendrites is accompanied by an increase in the rate of nucleation. However it is surprising that this increase can take place at such a low overpotential. While eqn (30) can predict this behaviour it is not clear why an equation of such a form should describe a nucleation process.Is there a physical explanation for the form of this equation ? A somewhat related question concerns the observation of the rather sharp capaci- tative loops at low zinc ion concentrations and low frequencies. It is surprising that there should be such sharp loops in the Faradaic region and they again seem to require a rather special behaviour of the nucleation rate. Is it possible to justify this at the present time in terms of a more detailed physical model? Dr. R. Wiart (Paris) said (i) Reaction (7) describes the nucleation which is here the formation of new growth sites Zn* from the adions Zn&. It can be reasonably admitted that the nucleation rate uN is proportional to the Zn& surface concentration (uN = A762) provided that this concentration remains low enough in our paper this condition is expressed by 62 < 0 where Oo is an arbitrary threshold close to 1.In contrast when O2 approaches 1 which is allowed to occur at a very low overpotential because of the autocatalytic formation of Znais the mean distance between these adions tends to be very short so as to increase markedly the probability for clusters to attain the critical size and give nuclei. Consequently a strong increase of the nuclea- tion rate uN is logically expected when the number of adions comes close to satura-tion. Eqn (30) which is supposed to be valid only for 8 > O, is proposed as an ex- ample able to formulate such a strong increase of oNwith a near-saturation 8,.Since the autocatalytic reaction (3) allows 62 to attain 1 at a very low overpotential eqn (30) can be logically applied at a very low overpotential. (ii) In contrast to the lowest frequency inductive loop which corresponds to the slow relaxation of the number of growth sites Zn* governed by slow reactions (7) and (9) the capacitative loop which is observed at low zinc concentrations is not dependent on the nucleation rate. This faradaic relaxation process is indeed governed by much faster reactions which form [reactions (3) and (6)] and consume [reactions I. Epelboin M. Ksouri and R. Wiart J. Less Conzmon Metals 1975,43 235. M. Ksouri and R. Wiart Proceedings Interfinish 76 Amsterdam (1976); Oberfluche Surface 1977 3 61 ; Metalloberflliche 1978 32 63.M. Froment and G. Maurin Electrodeposition and Surface Treatment 1975,3,245. A. R. DespiC and K. I. Popov Modern Aspects ojElectrochemistry (Butterworth London 1972) vol. 7 p. 199. GENERAL DISCUSSION (4) and (5)] Znafis. This relaxation of Znafis concentration can give rise to either an inductive loop as at high Zn" concentrations or a capacitative loop as at low Zn" concentrations according to the relative values of the rates of these fast reactions. Dr. D. E. Williams (Birmingham) said Since surface diffusion could be interfered with by specifically adsorbed species have the authors considered the effects of for example trace organics on the deposit morphology in relation to their mechanism? Dr.R. Wiart (Paris) said With the presence of some additives in the electrolyte (lead acetate tetrabutylammonium bromide benzylacetone) the irregular deposition of zinc is inhibited and compact deposits can be obtained over a larger range of current densities. This inhibiting effect of the additives has been shown to be accompanied by changes in the electrodeposition kinetics proving that specifically adsorbed species influence the interfacial processes. As a matter of fact these additives increase the cathodic overvoltage decrease the current efficiency eliminate the multiple steady- states in acid electrolytes and modify markedly the shape of impedance diagrams. These experimental results are interpreted by a slackening of the autocatalytic forma- tion [reaction (3)] of Znafis and an enhancement of the hydrogen adsorption [reaction (l)].In a sulphate electrolyte a pH decrease has been observed to influence these reaction rates in a similar way. Nevertheless the inductive loop corresponding to the slow relaxation of the surface concentration of kink sites Zn* reveal a difference be- tween the influence of H+ ions and the additive molecules one. As a matter of fact an acceleration in the nucleation rate is observed in the presence of an additive but not with a pH decrease. This specific influence of the additive molecules on the renewal of kink sites is closely connected with the changes in the deposit growth which result from the presence of these molecules in the electrolyte. Dr. R. Wiart (Paris)addressed his next remark to DespiC Since the growth of the granulae is found to be diffusion controlled an acceleration of the diffusion rate should prevent the development of these granulae.To eliminate the granular growth have you made such an attempt with an increase of the electrolyte flow in your cell or perhaps more easily by using a rotating disc at a sufficiently high rotation speed ? Prof. A. R. Despit (Beograd)said I should first say that we did not want to elimin- ate the granular growth since the purpose of our study was to find out optimum conditions of their appearance. Hence we did not try to do so in the way Wiart suggests. However even if we did I do not expect we would have obtained a straight- forward effect. For it is spherical diffusion at microscopically small particles which seems to be rate-controlling and this is usually not affected by the hydrodynamics of solution flow unless very thin hydrodynamic boundary layers are formed by intensive stirring.Effects could be expected at some later stage of growth when the granulae grow to size sufficiently large to penetrate the boundary layer. Mr. J. R. B. Gilbert (Birmingham) said Arising out of your reply to a previous question in which you made it clear that the electrolyte flows past the deposits at quite a high rate in your experimental apparatus I should like to ask about the adherence of granular deposits to their substrates. I had assumed on no good grounds at all that such deposits would only be very loosely adherent. I would be grateful for any J.Bressan and R.Wiart J. Appl. Electrochem. 1977 7,505. GENERAL DISCUSSION 201 comments you can add on the nature and degree of adherence in your systems cad-mium granules on copper substrates copper granules on graphite substrates and any other combinations you may have tried. Have you in particular any experience with deposits of a metal onto a substrate of the same metal please? Prof. A. R. Despit (Beograd)said Our experience is that granular deposits gener- ally exhibit a much better adherence to the substrate than dendritic or powdery de- posits. Cadmium granules on copper were not seen to be removed by the stream of electrolyte before an anodic current undercut their roots. Copper granules on graphite adhered so well that little of the deposit was transferred to a cellotape which was first sealed to the deposit and then torn away.However in the latter case de- position was carried out in the presence of a codepositing polymer (polyvinyl pyridine- co-methyl methacrylate) whose presence is likely to contribute to adherence. We have no experience with granular growth onto a substrate of the same metal. Dr. D. E. Williams (Birmingham)said Presumably the authors are considering a mechanism by which the formation of granular deposits is related to the adsorption of a positively charged colloid at the negatively charged metal surface. Therefore have they considered the effect of variables which might alter the colloid surface charge such as the ionic strength or the anion composition of the solution? Prof.A. R. Despie (Beograd)said The only variation in experimental condition made so far which could affect the state of cadmium hydroxide was that of pH. Further research is being carried out oriented towards establishing the validity of the colloid-effect hypothesis by varying other conditions known to affect the colloidal state as are also the ones suggested by Williams. Prof. M. Fleischmann (Southampton) said It is not immediately obvious why the coverage of the nickel surface by adsorbed hydrogen atoms should fall with increasing current density. The surface area of the nickel deposits is presumably nearly constant in these experiments while the rate of the hydrogen evolution is also constant over most of the potential range (at the limiting value).A fall in the coverage must therefore be due to a rather special mechanism for the hydrogen evolution reaction; simple combinations of known reaction steps would not predict such a trend. Could the reduction in coverage be due to competitive coverage by nickel adatoms or adions? In view of the importance of the hydrogen coverage to your interpretation of the development of texture would you make some further comments as to the evidence that the hydrogen coverage decreases with increasing negative potential ? Dr. J. Amblard (Paris)said In para. 3.2 of our paper we give the main features of hydrogen codeposition during nickel electrocrystallization for the low current density range the H+ discharge is diffusion-controlled and Hads covers almost entirely the metallic surface.2 In these conditions we find <110> oriented deposits.Now the question is what happens when the cathodic potential is increased to- wards more negative values? We cannot expect a more intensive arrival of H+ ions since they are still diffusion-controlled; conversely we may expect a reduction in Hadscoverage because of a more intensive flux of Ni2+ ions (which are not yet diffu- R.K. Dorsch J. Electroanalyt. Chem. 1969,21,495. Ph. Morel Thesis (Paris 1968 CNRS A02346). GENERAL DISCUSSION sion-controlled) and hence a faster renewal of the metallic surface. The occurrence of such a dynamic effect has been already pointed out by B0ckris.l The picture is different for the high current density range in the very conditions we find [210] oriented deposits we also observe a strong H evolution.Since there are still no new protons to be discharged this evolution must arise from another mechanism for the hydrogen reaction. The most likely is to suppose that H2 then originates directly from the numerous adsorbed H,O molecules2 which in turn may come from the dehydration of solvated Ni2* ions. Dr. R.Wiart (Paris)said Concerning the hypothesis of a decrease of the hydrogen coverage of a nickel cathode with an increase of the overvoltage which has been put forward by Amblard and Froment in their paper we have some recent results obtained by impedance measurements which reveal the existence of two relaxation processes I... 4 b0.16 FIG.1 .-Impedance diagram obtained during nickel electrocrystallization (Watts electrolyte pH = 0.5 temperature = 50 “C,cad.= 5 mA crn-’ electrode area = 0.2 cm2 electrode rotation speed = 2000 r.p.m.). The frequency is indicated in Hz. at low pH as shown in fig. 1. While the inductive loop observed between 0.25 and 0.016 Hz has been previously ascribed to NiOH ad~orption,~ the inductive loop ob-served between 0.001 and 0.016 Hz is obviously connected with the process of hydrogen adsorption since (i) it appears only at low c.d. in the very range where the current efficiency is lowest and (ii) a pH decrease markedly widens the c.d. range in which this inductive loop can be observed. Such an inductive behaviour means probably that the electrode coverage by Hads diminishes with an increase of the cathodic potential.Dr. F. Santter (Frankfurt)said The proposed mechanism as it is given in para 3.3 strongly correlates the stability of a given structure with the amount of hydrogen either adsorbed or evolved as a gas. While it is difficult to predict the gas content of nickel deposits from the amount of gas evolved a gas analysis may help to clarify the stituation. I would therefore J. O’M. Bockris and G. A. Razumney Fundamental Aspects of Electrocrystallization (Plenum Press New York 1967) p. 119. L. B. Harris J. Electrochem. SOC. 1973 120 1034. J. Bressan M. Ksouri and R. Wiart Compt. rend. 1977 285C 467. I. Epelboin and R. Wiart J. Electrochem. SOC. 1971 118 1577. FIG.1 .-Nickel deposits from Ni(NH2S03)21 mol dm-3 pH 2.(a)45 "C; on Ni(Ol1) 13 mA cm-2. (b)45 "C; on Ni-P; 9 mA cm-2 NiC12 1 mol dm-3 pH 4 + 30 g dm-3 H3B03 (c) +30 g dm-3 H3B03; 25 "C; on Ni-P; 50 mA cm-' p.0. 1121 I]. [Toface page 203 GENERAL DISCUSSION like to ask the authors whether the nickel deposits have been analysed for hydrogen or even whether the total amounts of hydrogen discharged have been determined. In a previous investigation,l it was found that under experimental conditions similar to those reported here the amount of hydrogen occluded did not vary from pH 2.0 to 4.0 and current densities from 0.5 to 3.0 A dm-2. Prof. P. Cavallotti and Mr. D. Colombo (Milan) said In studies on the electro- crystallization of metals having electrochemical kinetic inertness nickel and cobalt have been deposited from aqueous solutions of their salts without any addition such as buffering levelling or brightening agents; even the presence of other cations such as sodium or ammonium ions has been carefully avoided.The anion chosen was sul- phamate because by depositing from sulphamate solutions it is possible to grow definite structures exhibiting low internal stresses. Our results as far as they concern the obtained p.o.s generally are in good agree- ment with those presented by Amblard and Froment. In particular we agree with the following findings (a) the sequence of the p.0.s with increasing the current density is [110] + [loo] +[210]. The last one was observed by us in particular conditions such as when boric acid was added to the solution or cupric ions were present in the bath; (b) we have also observed a great difference between (1 10) and (21 1> p.0.on the one hand and [loo] and [210] on the other just as have Amblard and Froment less perfection observed by RHEED techniques and crystallites never being single crystals in the first case. Moreover we have observed that even when depositing onto the (011) face of Ni single crystals only one-dimensional orientation was observed for [110] p.0. In fig. 1 the columnar structure of the [110] p.0. is observed; the single crystallites correspond to dendrites with tips having typical twinned structure with five or two symmetry axes. 2-degree [loo] p.0. is observed for deposition on (001) and also on (011) faces. By depositing on the (001) Ni face the perfection was maintained also at high thickness in the range of several microns.The [211] p.0. was observed by us only when chloride ions were present in the bath. We have also observed a close relationship between the kinetic behaviour and the obtainment of the different p.0.s. As one can see from fig. 2 there is a low current density range where the rate of nickel discharge is low and the electrode voltage increases steeply; here the [llO] p.0. is obtained. An inter- mediate current density range where Ni and H2 discharges follow the Tafel law with slopes of about 60 and 120 mV/decade respectively the related p.0. is [loo]. By in- creasing the current density we meet a third region where precipitation phenomena are observed.Similar results are obtained during the electrocrystallization of Co (see fig. 3). In the first region (11.0) p.0. is evidence while in the second one the p.0. is {10.0). As far as the interpretation of texture formation is concerned we agree on the very important role of adsorbed species and also on the relative role of HLs water Nif& and Ni hydroxide on the development of the different p.0.s. However we want also to underline the specific role of the closest packing direc- tions in the development of these p.0.s. It is when the closest packing direction is perpendicular to the surface that we obtain [110] p.0. and when Ni2+ions are present in the adsorption layer the closest packing direction becomes parallel to the deposit. The same behaviour is found in the cobalt electrocrystallization.Cobalt deposits E. Raub and F. Sautter Metallobevjlache,1959 13 129. G. Caironi P. Cavallotti D. Colombo and U. Ducati 28th ISE Meeting (Druzhba near Varna September 1977); P. Cavallotti and D. Colombo preprint. GENERAL DISCUSS I ON T-I I 1 1 I LI 0.1 I i/mA cm-* 10 100 FIG.2.-Polarization curves of Ni and H2 in Ni (NH2S0& 1 mol dm-3 solution at pH 2 cathode Ni-P 45 "C. show p.0.s. corresponding to those of nickel in the different regions. [ll .O] p.0. with a closest packing direction perpendicular to the base is observed in the first region; [10.0] P.o. with a closest packing direction in the basal plane in the second one. We have also studied the chemical reduction of cobalt by hypop1iosphite.l The 800-700-w E B LL1 600- 500-I 1 I I I I I 0.1 1 i/mA cm-2 10 100 FIG.3.-Polarization curves of Co and HZin CO(NH~SO~)~ 1 mol dmh3 solution at pH 1.5 cathode Ni-P 45 "C.general behaviour of chemically reduced cobalt resembles that of the electrochemically crystallized one; the main difference is the presence of the reducing agent in the solu- tion phase. When cobalt hydrolysed species prevail in the layer adjoining the surface we obtain [lO.O] P.o. when H2P02-overcomes Co2+in the layer the p.0. changes to- wards [ll .O]. The increase of the surface coverage degree by the cobalt species leads P. Cavallotti and S. Noer J. Material Sci.,1976,11,645 ; P. Cavallotti S. Noer and G. Caironi J. Material Sci. 1976 11 1419; P.Cavallotti and G. Caironi Surfuce Tech. 1978 7 1. GENERAL DISCUSSION to attainment of the [00.1] p.0.; this texture is obtained with difficulty because its growth occurs when the baths show inhibition phenomena. This [00.1]p.0. exhibits very good magnetic properties such as a saturation magnetization of about 130 e.m.u. 8-l and a very high intrinsic coercivity 2.35 kOe (with a low squareness),l while the results hitherto reported for Co-P magnetic films give a maximum value in the range of 1 kOe. Dr. M. Froment (Paris) said Farr and McNeil observed the first epitaxial layers of electrodeposited nickel on copper substrates at two different current densities 5 and 40 mA cm-2. According to our own results during the steady state these conditions involve the formation of thick deposits with respectively {110) and (21 1) texture axis due to a specific inhibition of the nickel electrolyte interface.It has been observed that even under a very strong epitaxial influence and whatever the crystallo- graphic orientation of the single crystal-substrate would be these two textures are generated by tridimensional nuclei2 Conversely at higher current densities the growth is relatively free the epitaxy is easy and the polycrystalline deposits exhibit a (100) texture axis.3 Did you observe the structure of the first epitaxial layers ob- tained in the conditions corresponding to the formation of (100) textured electro- deposits (higher current densities of electrolyte more concentrated in SO:-) ? In the positive case do you know if the interfacial and growth dislocations have the same structure as before ? Dr.J. P. G.Farr and Dr. A. J. S. McNeil (Birmingham)said We have not in fact used the higher current densities and more concentrated sulphate electrolytes referred to by Froment and we regret that our experiments do not permit us to speculate on the corresponding growth structure. The question suggests an interesting extension of our study. Prof H. R. Thirsk (Newcastle),in closing the Symposium said An important part of these meetings is to identify progress in the area under scrutiny; hopefully to see this as a positive quantity and to make some comment perhaps a rather hazardous task about future possibilities. However in making this review of the present meeting I also wish to state that academics also teach and for the benefit of our younger colleagues as well as interested visitors with less specialised interests I propose to identify some items by quoting references to papers having a large review content.The ultimate success of studies in electrocrystallisation will be when there is a total convergence of kinetic and structural results and by this I mean information concern- ing internal structure topography and chemical characterisation and as I have al- ready implied a valuable product of this present meeting has been the opportunity to assess the progress to this end and to appraise the effectiveness of the experimental and theoretical means now available. A point I wish to emphasise is that the overall timescale of these studies has already been surprisingly long; the way the work in the field has developed historically in part accounts for this feature.I found it an interesting exercise in judging progress to turn to three earlier Dis- cussions of the Faraday Society which are particularly relevant to my present summary. I refer to the meetings44 in 1935 1947 and 1949. G. Asti G. Caironi P. Cavallotti and D. Colombo INTERMAG 78 Firenze. J. Thevenin J. Microsc. Spectr. Electron. 1976 1 7. J. Amblard and M. Froment paper at this Symposium. The Structure of Metallic Coatings Films and Surfaces General Disc. Furaday SOC.,1935. Electrode Processes Disc. Furauhy SOC.,1947 1. Crystal Growth Disc. Furaduy SOC.,1949 5. GENERAL DISCUSSION Electrodeposition in 1935 when concerned with microstructure was already very much a device for producing material for epitaxial or similar studies as exemplified by the contribution to that meeting by Finch Quarrel1 and Wilman.(It is interest- ing incidentally to note the clear exposition by Tronstad in this discussion of the appli- cation of ellipsometry to surface problems and the fact that D. L. Chapman was clearly still interested in interfacial problems but was applying the method to studies of the hydrogen oxygen reduction of platinum.) About 1937 when I was working in Finch’s laboratory with a contemporary E. G. Whitmore we became very interested in single crystal Kikuchi patterns obtained by electron diffraction. These patterns were recognised as being of great value in problems of crystal orientation and surface preparation.Having developed as a stage in our work a general method for indexing these useful diffraction patterns and looking for other types of material to examine other than naturally occurring gem- stones and of more general availability synthetic metal oxide crystals which we were using as substrates for chemical reactions the almost chance detection by Cochrane working in G. P. Thomson’s laboratories of Kikuchi patterns from a specimen of a copper single crystal led me to the task of trying to make strain-free characterised single crystal faces on the few metal single crystals that were obtainable at that time. The newly current methods of electrolytic polishing developed by Jacquet helped con- siderably in this matter and the preparation of such faces became a not-too-difficult routine procedure.Unfortunately due to a reorganisation of activities which many of us suffered in 1940 these results on metals were not adequately published. There is an article by myself in 19401in a rather obscure journal (but one I should say viewed with affection by members of Imperial College). However it was not until the same material that I used then and which was reproduced in a much referred to contribution by Finch Wilman and Yang in the Discussions of 1947 that I think the entire feasibility of using routinely metal single crystals as a substrate for electrodeposition was made generally clear. Many years elapsed before such usage became generally widespread in electro- chemical studies and still with very variable quality of preparative techniques since very often workers do not have access say to RHEED or LEED to check their pre- parations.This is a serious restriction. The point I wish to emphasise most strongly however is the purely structural content of this early work; the thought of the kinetics hardly entered the areas of consideration. During this same early period however (middle and late thirties) there was ex- tremely interesting work developing in publications by Erdey-Gruz and Volmer2 on concepts of nucleation and growth in metal deposition and with developing ideas on the nature of the potential dependence it is easy to follow the development of this work through the researches of Kaischev et al.and later in elegant form Budevski and his collaborators. Considerations of nucleation and growth moved away from the earlier con- siderations with the ideas generated first in 1949 by Frank and van der Mer~e.~ Elegant though the theories of crystal growth originating at dislocations were the concept was not really helpful to the progress of the study of electrocrystallisation. Indeed it is as recent as in this present Symposium that this type of growth is at last l H. R. Thirsk Sci. J. Roy. College Sci. 1940 10 35. * T. Erdey-Gruz 2.phys. Chem. 1931 157 165; M. Volmer 2.phys. Chem. 1935 172 157 R. Kaischev and I. N. Stranski 2.phys. Chem. B 1934 26 317; Phys. Z. 1935 36 393 M. Volmer Kinetik der PhasenbiIdung (Leipzig 1939).F. C. Frank and J. H. van der Merve Pruc. Roy. SOC.A 1949,198,216. GENERAL DISCUSSION seen kinetically as in the contribution by Budevski in being an illustration of a spiral growth mechanism. Two other papers in the 1947 Discussions are very relevant to the development of our studies a kinetic contribution on ax. methods by Randles which undoubtedly was a real starting point of the application of this important perturbation technique and we have some glimpse of the development of this method to electrocrystallisation in the paper by Epelboin et al. [see ref. (7) and (8) for subsequent developments] and as far as I know a little-referred-to contribution by Levich on electrode hydrodynamics including the appropriate results for the case of the rotating disc electrode.By the middle fifties and early sixties step perturbation methods for studies of nucleation and growth were well developed although not well recognised. The studies were of anodic and not cathodic processes but if I take a contribution to the CITCE meeting of 1953l as the approximately earliest date for the establishment of this technique (subsequent developments have been thoroughly re~iewed)~*~ for the study of electrocrystallisation we can claim that some very important experimental methods are quite dignified by age; some 40 30 and 25 years respectively. A necessary opportunity is available in connection with the present meeting to examine the convergence which can be seen to be progressing with structural and kin- etic measurements.They are still impeded by very considerable experimental diffi- culties and unfortunately by the limited likelihood of a single research centre posses- sing the diverse instrumentation often required. If we look at some papers from this meeting kinetic techniques have become more sophisticated for example the papers by Lorenz et al. Bewick et al. Schultze et al.; in the related areas of sparse electrode coverage; sophisticated structural work for example the papers by Beckmann et al. and Farr and McNeil may be quoted and as a bridging concept in the study and understanding of crystal growth increasingly elab- orate simulation techniques as in contributions by Gilmer and Harrison and Ranga- rajan are of importance. Much interest has focused on the resolution of processes occurring in the underpotential regions.The papers by (1) Lorenz Schmidt Staikov and Burt; (2) Bewick JoviCeviC and Thomas dealing with deposition in underpotential regions and (3) Schultze and Dickertmann concerned with dissolution are all relevant to similar degrees of coverage of the substrate at potentials positive to the reversible potential. Perhaps not really electrocrystallisation but an area that must first be fully. understood. The papers contain an analysis of the kinetics which is strongly dependent on the assumption of models. In some ways these simple models relate to simulation tech- niques and are an essential part of the analysis to be seen both with these problems and a.c. perturbation methods.Interesting problems remain in the interaction of deposit with substrate and the adsorption of anions as well as with the considerable experimental difficulties. The preparation of single crystal faces possessing the assumed geometry and freedom from preparative artefacts is a very necessary prerequisite of convincing experiments. This evidence is unfortunately still often absent from experimental accounts. The association of more of this work with parallel epitaxial studies by LEED would be of interest and could well reveal that a wider range of deposit orientations M. Fleischmann and H. R. Thirsk 5th Meeting of CITCE Stockholm 1953 (Buttenvorth). M. Fieischmann and H. R. Thirsk,Advances in Electrochemistry and Electrochemical Engineering ed.P. Delahay (John Wiley New York 1963) vol. 3 p. 123. J. A. Harrison and H. R. Thirsk ElectroanaZyticaZ Chemistry ed. A. J. Bard (Marcel Dekker New York 1971) vol. 5 p. 67. GENERAL DISCUSSION could exist. In other areas of epitaxial studies less obvious alignments between major areas of substrate and deposit than the simple postulates made in the present contri- bution are found; the real situation must be established by appropriate structural evidence. If one goes right back to early epitaxial studies and this interest in them had great experimental impetus in the late thirties-well before the 1949 Discussion it will be discovered that examples of “ misfit ” controlling close epitaxy are somewhat selective of the available experimental data.There is a great need for more direct determina- tion of the orientation of these primary deposits in order to confirm the assumptions made in the models. The most obvious technique is the greater use of LEED but in this connection the paper by Beckmann Gerischer and Kolb on the use of RHEED to examine under- potential deposit structures is quite remarkable in that it does seem to yield useful information by a technique which intuitively one would have thought would have yielded too much substrate information to be so unequivocal in its information on surface layers. Clearly more work of this kind could be rewarding. I shall return to some further comments on structural work later in references to the papers by Amblard and Froment and Farr and McNeil.I referred earlier to simulation methods bridging the structural and kinetic contri- butions. We have had two papers specifically associated with simulation methods. They are both of course computer based but I think they differ in an important way; both approaches are clearly of value. The contribution by Gilmer is of a method that is relatively free from bias towards any particular experimental method of forming the deposit but does include atomic processes to the extent of making the final growth transients in increasingly satisfactory accord with experimental measure- ments. Intrinsically based on a simpler type of simulation the procedures outlined by Harrison and Rangarajan are more closely associated with some of the ideas that have already been incorporated into the simple models used in analysis of a good deal of electrochemical kinetic data.To a considerable degree the calculations have been used to strengthen the justification of assumptions made in earlier kinetic analysis for example some confirmation of the correctness of the use of the Avrami equations is of considerable significance and also to emphasise the relation between real and simula- tion parameters. There is no question that further development of both these types of calculation is eventually going to help to identify the most realistic models for growth in electro-chemical deposition. The films generated by Gilmer’s work are also dramatically attractive. A broad generalisation can be made in that much of the present understanding of growth mechanisms in electrocrystallisation is dependent on ideas of two and three dimensional nucleation and growth.As has been referred to above in the paper by Bostanov et al. there is a reminder that with refined experiments the theory of spiral growth as developed by Frank et al. can now be seen to have considerable experimental relevance on actual kinetic investigations. This is not readily seen under the conditions of the majority of electrocrystallisation experiments and again the long interval before the elegant ideas formulated by Frank and the demonstration at this meeting is note- worthy. A different theoretical problem but equally desirable in the experimental analysis of our problems is the overall assessment of the theoretical side of electrocrystallisa- tion studies and particularly the interaction of this method of kinetic experiment and the fundamental features of the phenomena.In his paper Rangarajan has continued GENERAL DISCUSSION his examination of the logical aspects of the theory which I think is becoming ex- tremely helpful for the design of future experiments. To revert again to experimental papers. There were a number of contributions referring to thicker deposits and the rather difficult problems that have to be resolved. Epelboin et al. deal with a model for zinc deposition studied by a.c. perturbation methods which is highly dependent on the apportioning of different kinds of lattice sites1 and as in many a.c. experiments a model is developed against which to test the experimental observations.The same laboratory have given indications2 that noise power when measured with the same system may be a more sensitive function of morphology or changes in orientation than changes in the complex plane impedance diagrams. Hopefully there is soine- thing that may be of considerable interest here and I had hoped for more extensive reporting. We do also have the comments by Fleischmann in his introduction of some analogous developments. Amblard and Froment reported on the sources of fibre textures in thick electro- deposits examining this problem with nickel plated from conventional baths ; prob-lems which extend backwards incidentally at least to the 1935 Discussion. Fortu-nately the workers associated with these two contributions (I mean Froment and Epelboin and their collaborators) are close neighbours ; as the problems become clearer a likely combination of techniques could ensue to the enlightenment of all of us in these areas of great practical importance.The elegant experimental work communicated by Farr and McNeil indicates the extent to which the metallurgical aspect of electrocrystallisation may be explored. Unfortunately the task of associating such experiments because of the preparative methods necessarily used with the restraints required in kinetic studies offers possibly but hopefully not insuperable problems. There are however techniques increasingly available with modern scanning electron microscopes which have been shown to be of value in the study of solids that should be more vigorously employed.I refer to the possibilities of exploring the use of channelling patterns from single crystal substrates3 extended to the use with electro-deposited layers. Other papers concerned with single substrates also appear using X-ray Kossel patterns. Such methods can be associated more readily with kinetic measurements for there is no severe problem in making single crystal rotating disc electrodes even if with a large defect structure of a size suitable to SEM use and therefore combining available electrochemical methods with a thorough exploitation of these techniques. This of course makes extremely heavy demends on instru- mentation which few of us can meet. A final comment must be made.This short meeting has been almost exclusively concerned with metal electrocrystallisation. It has however been studies of anodic electrocrystallisation that has assisted so substantially in the development of many of our electrochemical tools as can for example be seen in ref. (8) and (9). There is no need to emphasise how central the understanding this aspect of electrocrystallisation and phase formation is in the problems basic to electrochemical power sources passivity and corrosion. Structurally the final evaluation will always be less elegant than with metal deposition but knowledge of the essential chemistry other than the electrochemistry must progress with increased application of spectroscopic skills. J. Bressan and R. Wiart J. Appl. Electrochem.1977 7 505. G. Blanc C. Gabrielli M. Ksuori and R. Wiart Electrochim. Acta in the press. See for example for the method G. Booker Modern Difraction and Imaging Techniques in Material Science (North Holland 1970) p. 613. Man Hoat Nguyen J. Poulignon and S. Offret Electrochim. Acta 1975,20,675. GENERAL DISCUSSION Indeed there is still to my way of thinking a very serious lack of co-ordination between structural studies (and by this I refer broadly to spectroscopic methods as well as those normally implied) and kinetics. As was stated at the beginning of this sum-mary the coordination should be a progressive one. It is the development of thicker layers which is really what electrocrystallisation is about in practical deployment in the understanding of electrodeposition corrosion and power sources.Very positive efforts must be made to accelerate this co-ordination. If not con- vincing studies will not emerge and progress will continue to be disconnected and rather slow. Undoubtedly this Symposium has been valuable in assessing our present state of knowledge and I think identifying the areas requiring vigorous investigation. The interest is a specialised one and the meeting has been valuable in giving an opportunity for a thorough exchange of views.

ISSN:0301-5696    

DOI:10.1039/FS9771200163

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

AUTHOR INDEX* Amblard J. 136 201 Beckman H. O. 51 Bewick A. 24 165 171 172 Bort H. 14 Bostanov V. 83 Budevski E. 83 184 Cavallotti P. 203 Colombo M. 203 Despit A. R. 126 178 191 198 200 201 Dickertmann D. 36 164 167 172 Drazit D. M. 126 Epelboin I. 115 Farr J. P. G. 145 205 Fleischmann M. 7 163 183 185 186 191 196 199,201 Fletcher S. 171 179 187 190 193 Froment M. 136 175 205 Gerischer H. 51 Gilbert J. R. B. 200 Gilmer G. H. 59 181-183 189 Gunawardena G. A, 90 186-188 Harrison J. A. 70 163 186 Hills G. J. 90,180 186-188 Jovicevic J. 24 1 74 177 Kolb D. M. 51 168 173-175 Koppitz F. D. 167 174 Ksouri M. 115 Lehmpfuhl G. 51 Lorenz W. J. 14 163-165 167 168 170 171 Lovering D. G. 171 190 McNeil A. J. S. 145 205 Mirjanik M. D. 126 Montenegro I. 90 186-1 88 Peter L. M. 188 Rangarajan S. K. 70 101 169 177 180 184 185 195-197 Sandbach D. R. 163 Sautter F. 202 Schmidt E. 14 Schultze J. W. 36 164 167 172 174 178 180 Staikov G. 14 83 Thirsk H. R. 205 Thomas B. 24 164 van Leeuwen H. P. 187 Wiart R. 115 163 182 190 196 198-200 202 Williams D. E. 182 191 200 201 * The references in heavy type indicate papers submitted for discussion.

ISSN:0301-5696    

DOI:10.1039/FS9771200211

出版商:RSC    

年代:1977

数据来源: RSC