摘要:

OFFICERS AND COUNCIL OF THE FARADAY DIVISION 1977-78 President Vice-presidents who have held ofice as President Prof C. E. H. Bawn CBE PHD FRS Prof G. Gee CBE SCD CCHEM FRlC FRS Prof Sir George Porter MA SCD CCHEM FRIC FRS Vice- Presidents Prof A. D. Buckingham MA PHD CCHEM FRIC FRACI FRS Prof P. Gray MA SCD CCHEM FRIC FRS Prof M. Magat DSC DPHIL Prof J. s. Rowlinsdn MA DPHIL CCHEM FRIC FRS Ordinary Members Dr W.J. Albery MA DPHIL Dr J. H. Baxendale DSC Prof Manse1 Davies SCD cCHEM FRIC Dr w.J. Dunning MBE PHD CCHEM FRIC Prof F. Franks DSC CCHEM FRIC Honorary Secretary Honorary Treasurer Faraday Division Members on the Primary Journals Committee Dr M. A. D. Fluendy MA DPHIL Prof F. Franks PHD DSC CCHEM FRIC Prof H.M. Frey BSC DPHIL CCHEM FRIC Dr D. Husain PHD DSC CCHEM FRIC Prof D. A. King BSC PHD CCHEM FRIC Editor Assistant Editor Editorial Ofice Pr0fD.H. Everett MBEMADSCCCHEMFRIC Dr T. M. Sugden CBE MA SCD CCHEM FRIC FRS Prof R.P. Bell MA CCHEM FRIC FRS FRSE Dr H. A. Skinner BA DPHIL CCHEM FRIC Prof F. C. Tompkins DSC CCHEM FRIC FRS Prof D. H. Whiffen MA DPHIL DSC CCHEM FRIC FRS Dr D. N.Hague MA PH D CCHEM FRIC Dr G. R. Luckhurst PHD Prof A. M. North DSC CCHEM FRIC FRSE Dr B. A. Thrush MA scD FRS Dr D. A. Young PHD DSC MINSTP Prof F. C.Tompkins DSC CCHEM m1C FRS Prof P. Gray MA SCD CCHEM mc FRS Prof H.R.Thirsk BSC PHD DSC DIC CCHEM FRIC Prof F. C.Tompkins DSC CCHEM FRIC FRS Dr D. A. Young PHD DSC MINST P Dr D. A. Young PHD DSC MINST P Mrs M. J. Grant BSC The Faraday Division of the Chemical Society previously The Faraday Society founded in 1903 to promote the stua'y of Sciences lying between Chemistry Physics and Biology Burlington House London WlV OBN telephone 01-734 9864 0 The Chemical Society

ISSN:0301-5696    

DOI:10.1039/FS97712FX001

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Nucleation Electrocrystallisation and Phase Formation Introductory Comments BY M . FLEISCHMANN Chemistry Department University of Southampton Southampton SO9 5NH Received 7th March 1978 The topics of this Symposium Nucleation Electrocrystallisation and Phase Formation cover a very wide field; fig. 1 is an attempt at summarising the main com- ponent parts and interconnections. One possible classification is to group these components under four main headings Processes in solution in particular the mass transfer of species to be deposited reactions generating species to be deposited which are coupled to mass transfer SOLUTION PHASE (mass transfer) .......w (reactions in solution) .......C (aacii rives) ......+ .......w ......+ ....................................c mass transfer reactions in solution ---*......* ......+-.-.-. (additives) ......+ ......)......* .................................... mass transfer -.-.-. (reactions in solution) ;:;::; additives 4 THE FIRST LAYER adsorption surface diffusion 2' dimemioncil nucteation and growth structure (properties) THICK DEPOSITS adsorption surface diffusion 3 dimensional nucteation and growth repeated 2 dimensionat nudeation and growth (inhibition of growth) Gle of distocations [special mechanisms for generating growth sites (edges kinks) I STRUCTURE AND PROPERTIES ' morphology instabilities orientation tetture properties FIG. 1.-Classification of the phenomena controlling the eletrodeposition of metals.Topics covered in earlier investigations are indicated by roman script. Topics awaiting investigation are in parentheses. Topics covered at this Symposium are indicated by italic script. +established connections; - - -+partially established connections; . -.bconnections to be established; ---b connections discussed at this Symposium. lNTRODUCTION and the mass transfer of species (including “additives ”) which affect the kinetics of reaction as well as the structure and properties of electrodeposits. The very initial stages of deposition on inert substrates which include adsorption the surface diffusion of adions or adatoms and two-dimensional nucleation and growth as well as the structure and properties of two-dimensional arrays.The formation of thick deposits which may be influenced by adsorption surface diffusion three-dimensional nucleation and growth repeated two-dimensional nucleation and growth of layers andfor the generation of layer planes by screw dislocations intersecting the surface. The inhibition of growth must clearly play an important part and there must be many special mechanisms for generating growth sites such as the edges of layer planes and the kink sites in the edges where lattice formation takes place (see below). The structure and properties of the deposits which demands investigations of the morphology and orientation as well as of the mechanical properties of the deposits. The topics which were investigated in the 1950’s and 1960’s (and in some cases at an earlier time) are indicated in roman type on fig.1. Thus mass transfer and homo- geneous reactions in solution close to the electrodes are reasonably well understood but the influence of surface structure has hitherto been ignored in such studies; equally the influence of mass transfer and of homogeneous reactions has been largely ignored in studies of electrocrystallisation. However these groups of phenomena are linked and it is for this reason that most of the interconnections are shown as awaiting establishment or as requiring further investigation. A diagram of this kind cannot show all the interconnections; at the same time a listing of topics under one heading does not imply that the phenomena are necessarily linked. Thus while the exact nature of two-dimensional nucleation and growth will certainly determine (and be determined by) the structure and properties of the surface layers it is not certain that adsorption and surface diffusion will necessarily be involved in two-dimensional nucleation and growth.The topics currently being investigated and which are covered by contributions to this Symposium are indicated in italics. The very initial stage of deposition on inert substrates has been intensively investigated in recent years and is covered by four papers. Of these the first three by Lorenz Schmidt Staikov and Bort by Bewick JoviCeviC and Thomas and that by Schultze and Dickertmann deal with adsorption and the kinetics of the reactions; structural evidence is derived indirectly using the coverage as the single measure of the degree of order.The observations are now well established the deposition is sensitive to the nature orientation and method of preparation of the substrate (the phenomena are in no sense truly two-dimensional!) and deposition takes place at a potentia1 positive to that for deposition of the bulk phase the so called “ underpotential ”. The favoured method of investigation linear sweep voltammetry shows much structure in the voltammograms. The interpreta- tion of the data is however in dispute. Thus Lorenz et al. using silver substrates convert the data into isotherms and if these are interpreted in terms of a Frumkin isotherm then the interaction parameters are such that continuous changes are indi- cated.Furthermore there is no three-dimensional nucleation on top of the ad- sorbed layers. On the other hand Bewick et al. show that for copper substrates there is strong hysteresis in the voltammograms. (Current time) transients at constant potential are characteristic of those predicted for phase transitions and the formation of a first layer precedes three-dimensional nucleation and growth. The data for the first layer are interpreted in terms of first and higher order phase transitions and if these mechanisms are established then it will prove to be of particular interest to INTRODUCTION investigate the kinetics of the latter processes the sensitivity of electrochemical meth- ods should permit detailed investigation of these phenomena.Schultze and Dickertmann interpret the data for the deposition of bismuth on gold (111) single crystal faces in terms of adsorption the formation of expanded epitactic and finally of a dense monolayer. These authors derive information on the rates of the processes and of the interconversion of the states by analysing the potential dependencies of key features such as the peaks observed in the cyclic voltammograms. Apart of the paper presented by Rangarajan is highly relevant to these investigations ; crystal growth is a highly non-linear process firstly in view of the nature of electrode reactions secondly in view of the character of nucleation and especially in view of the nature of the statistics of the " overlap " of growth centres. It follows therefore that the rates of individual steps can only strictly speaking be derived by appropriate convolution of the data and this is especially relevant for linear sweep voltammetry.It must also be remembered that surface and bulk diffusion may play a part (see the interconnections in fig. 1). This paper shows the two-fold role of theory in this field the exploration of models and the provision of a framework for the analysis and reduc- tion of experimental data to the key parameters of the models. It is evident that electrocrystallisation is always controlled by a set of such parameters and investiga- tions have hitherto relied heavily on potential step and mutiple potential step experi- ments. The use of more general relaxation techniques may therefore well prove useful both in providing diagnostic criteria and since at least one of the variables is changed independently during the experiments in effecting an economy of effort! The paper provides a framework for the exact analysis of a number of such experi- ments.The fact that the degree of order of the deposits has hitherto been inferred from measurements of the coverage has already been referred to above. It is most encour- aging that Beckmann Gerischer Kolb and Lehmpfuhl have found the first structural evidence for the formation of a superlattice using the classical methods of reflection high energy electron diffraction. This shows that it should prove possible to resolve some of the outstanding questions by using straightforward structural methods on suitable model systems.It is especially interesting that there is evidence of a super- structure on removing the deposit indicating the importance of structural reorganisa- tion of the surface for at least some underpotential deposition reactions. The importance of the development of models and of the theoretical analysis of experiments in this field has also already been referred to. A second group of three papers by Harrison and Rangarajan by Gilmer and by Rangarajan deals with these problems. The complexities are such that many of the questions will only be re- solvable by using simulation methods. The first paper deals in the main with the validity of the basic algebraic formulation of the role of the free and covered area in determining the overall kinetics the Avrami postulate.It is clearly of key importance to establish the correct way of handling the overlap of growth forms otherwise pro- gress will hardly be possible. In the second paper Gilmer shows that a kinetic Ising model fits the experimental transients for crystal growth. The simulations reveal further highly significant factors a roughening of the edges leading to a consequent lowering of the edge energies; a rate of nucleation faster than that predicted by the atomistic theory of nucleation in view of the contribution of clusters other than those of the minimum energy to the number distribution of cluster sizes; the enhancement of the rate of crystal growth as well as the enhancement of the oscillatory character of the (rate time) curves by surface diffusion for the particular models chosen which is especially relevant to growth from the vapour phase.It must be borne in mind that in the case of electrocrystallisation mass transfer in the adjoining solution phase will INTRODUCTION be important. The investigation also suggests an interesting new experiment the correlation of the rates of crystal growth on different crystal faces with theoretical predictions. The points raised by this investigation will certainly be discussed. It is a pity that no way has been found as yet for publishing the films of the computer output since it is these which show so clearly the role of the various phenomena! The paper by Rangarajan has already been referred to. A major objective is the relation of the kinetics of growth to nucleation at an earlier stage.This is a central feature of all investigations of the kinetics of crystal growth processes and progress will be limited unless this influence of nucleation is clearly defined and measured. The paper also presents an outline of the analytical forinulation of the repeated forma- tion of layers and of stochastic effects in crystal growth (stochastic effects are referred to further below). These phenomena are related as the observation of the first is de- pendent on the second. It should be noted that the models in the three papers have one common feature namely that the deposits are formed layer by layer. It will be important to determine in future work the extent to which the formation of a deposit at one level is correlated to that at earlier levels.We can predict two limits total loss of correlation due to repeated nucleation (although it could be argued that there would be some asymptotic value of the correlation functions) or total correlation if there is three-dimensional nucleation or if step propagation by dislocations is dominant. The remaining three groups of papers deal with the problems underlying the de- position of bulk phases the kinetics morphology structure and properties of the deposits. The third group of two papers by Gunawardena Hills and Montenegro and by Bostanov Budevski and Staikov is concerned with kinetics. The first deals with the determination of the number distribution of nuclei in the initial stages of deposition using sequential potentiostatic-galvanostatic and potentiostatic measure- ments.The appropriate description of nucleation in these early stages is still very uncertain. The flexibility in the design of complex electrochemical experiments and in the evaluation of data which is now feasible gives hope that progress can be made in this area. The second paper deals with step propagation due to the interaction of spiral dislocations. Simple cases are shown to be consistent with the formulation of Burton Cabrera and Frank and the parameters deduced from the measurements are in line with those which have earlier been deduced from experiments on two-dimensional nucleation and growth on perfect single crystal planes. Thus the two main mechan- isms for the generation of lattice growth sites have now been demonstrated and this leads to a number of questions which will have to be resolved in future work what is the relative role of the two mechanisms in practical cases; will it be possible to deal with randomly dislocated or pseudo-randomly dislocated systems ; are there other specialised (or general) mechanisms for generating growth sites indeed have the two classical mechanisms been found because the search for model systems was directed by theoretical predictions? In this connection I would like to draw attention to a recent study of the dissolution of iron where steps are shown to be produced by disso- lution of an atom at the apex of a pyramid and kinks by the intersection of two steps in a p1ane.l It seems to me that many specialised mechanisms not predicted by current theories will in due course be found to be operative.The next group of papers by DespiC DraziC and MirjaniC and by Epelboin Ksouri and Wiart is concerned with the link between the kinetics and morphology. For the deposition of cadmium on copper granular growth is observed under conditions where dendrite formation would be expected and inhibition by a solution constituent colloidal cadmium hydroxide is shown to be important. It has been known for INTRODUCTION some time that zinc deposits have complex morphologies and the second paper shows that the autocatalytic character of zinc deposition coupled to surface diffusion leads to instabilities and consequent formation of spongy layers whereas nucleation coupled to surface diffusion leads to dendrite formation.The various steps are necessarily introduced in a parametric manner and this study illustrates the great detail which will have to be included in future algebraic and simulation studies at the microscopic level. This paper again shows the highly detailed information (up to four coupled relaxation processes) which is now available from electrochemical measurements in this case of the impedance. The final group of two papers by Amblard and Froment and by Farr and McNeil is concerned with the structure and properties of nickel deposits as a function of the experimental conditions. A major task is to resolve the question as to where and when the ‘‘ decision ” for the formation of a particular structure is taken in the initial nucleation (possibly of a two dimensional layer) by preferential growth of certain faces or by inhibition of growth? The interpretation in the first paper of the complex dependence of the texture on pH and potential is that the events during growth are decisive and that inhibition by H Ni(OH)2 and H2are all important.In the second paper the deposition onto copper (100) faces is shown to pass through a succession of stages. A new type of dislocation pattern is proposed to account for the second stage of growth which serves to relieve the strain in the deposit caused by the mismatch of the lattice parameters; this is overtaken in the third stage by a differ-ent dislocation pattern. With these papers we come full circle but the circle is still broken.The structure and energetics of the deposits are unquestionably determined by the kinetics and the structures demand and cause imperfections in the deposits which in turn affect the kinetics fig. 1. The question is how is the loop to be closed? Any theory will certainly have to deal with the energetics and kinetics simultaneously. It is to be hoped that future work will be able to deal with the interconnections rather than with the individual topics. The papers in this meeting cover many other points and this introduction is simply a biased list of topics which have caught my attention. The coverage of the field by the papers presented at this Symposium is inevitably also fragmentary. We have chosen to restrict attention to metal deposition and thereby exclude not only aspects of metal dissolution but also the whole area of the electrocrystallisation of semi-conductors and insulators.Any conclusions drawn are therefore of a specialised kind. There is one particular gap in the topics which I regret especially and I would therefore like to close this introduction by referring to this field of work. Fluctuations in electrochemical systems are touched on by Rangarajan and instabilities are shown to be important by Epelboin Ksouri and Wiart. Nucleation electrocrystallisation and phase formation should certainly be regarded and analysed as a stochastic process at several levels the formation of the nuclei lattice formation the growth and over- lap of growth forms etc.Some of these effects are large compared to ‘< Nyquist ” noise and electrochemical methods have the sensitivity to measure the higher moments of the reaction rates. Indeed Blanc Gabrielli Ksouri and Wiart have shown that for the zinc system reported here the changes in morphology and orientation are corre- lated with changes in noise power.2 It is of interest that the rate constants determining quantities related to the second moment of the reaction rates (probability density autocovariance function power spectral density) appear in different combinations as compared to those determining the mean rate.3 A wealth of new kinetic information should therefore be available and the second moment also reveals phenomena not accessible by measurements of INTRODUCTION the mean.Thus a model for the stochastic formation of nuclei coupled to determin- istic growth shows that for an ensemble of transients the standard deviation divided by the mean current varies as (At)-* where A is the nucleation rate constant fig. 2. When still smaller electrodes are-used a succession of birth and death processes can be seen fig. 3 (the increase of a,/Iis due to the “death ”of crystal growth). Measure-ments of this kind should permit the definition of the role of such death processes which is currently obscure but evidently important in view of the microcrystalline 0.1 0.2 -1 3,s FIG.2.-Statistical analysis of the transients for the deposition of a-PbOz onto a 10 pm diameter Pt electrode. 0.05 a10 a15 am -.3 ,=-+ FIG.3.4tatistical analysis of the transients for the deposition of cr-Pb02onto a 2 ,urn diameter Pt electrode.character of many electrodeposits. The great detail which should become available from such measurements is perhaps best shown by an example from the field of bio-electrochemistry the effect of nucleation on ion transport through lipid bilayers. It is well known that the successive insertion of entities of the pore former alamethicin (an antibiotic polypeptide) into the membrane leads to a stepped response of the trans membrane ion ~urrent;~g~ an example is shown in fig. 4.’ The probability density of the fluctuations fig. 5 can be modelled in terms of the nucleation of a single pore the fluctuation in pore size being due to the insertion (and removal) of ala- methicin entities.The kinetics of interconversion of the various states can be derived by appropriate processing of a sufficiently large number of data points. Evidently electrochemical methods have sufficient sensitivity at this time to measure individual IN TR OD U C TI0N . ik a 0.8 0.6 0.4 0.2 sc. 0.1 0.2 0.3 0.4 0.5 tls FIG.4.-Fluctuations in the current flowing through a cholesterol/glycerol mono-oleate bilayer in contact with 2 x mol dm-3 alamethicin. Voltage across the layer 0.175 V. Electrolyte 0.1 mol dm-3 KCI. i/pA FIG.5.-Frequency distribution of the current flowing through a cholesteroI/glycerol mono-oleate bilayer in contact with 2 x loF8mol dm-3 alamethicin. Voltage across membrane 0.258 V.The zero current level was suppressed and the current sampled at 3 ps intervals. Data were accumulated in 100 channels and displayed with interpolation of 1000 points. events at the molecular level for appropriate and sufficiently small systems and it should therefore now prove possible to establish and characterise models at this level of detail. W. Allgaier and K. E. Heusler 2.Phys. Chem. N.F. 1975,98 161. G. Blanc C. Gabrielli M. Ksouri and R. Wiart Electrochim. Acfa in the press. P. Bindra M. Fleischmann J. W. Oldfield and D Singleton Faraday Disc. Chem. Soc. 1973 56 180. M. Fleischmann J. W. Oldfield and D. Singleton to be published. M. Fleischmann M. Labram and A. McMullen to be published. P. Mueller and D. 0.Rudin Nature 1968,217,713. L. G. M. Gordon and D. A. Haydon Nature 1970,225,451.

ISSN:0301-5696    

DOI:10.1039/FS9771200007

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Metal Ion Adsorption and Electrocrystallization BY W. J. LORENZ,E. SCHMIDT, G. STAIKOV?and H. BORT Institut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe Germany and Institut fur Anorganische Analytische und Physikalische Chemie der Universitat Bern Switzerland Received 4th August 1977 Deposition of lead onto silver single crystal electrodes from perchlorate solutions has been studied in the undervoltage and low overvoltage regions employing twin-electrode thin layer and potential pulse techniques. Pseudo-Nernstian 8 isotherms exhibiting continuous coverage steps were found. 2D nucleation was not identified to be a kinetically relevant process. The rate of 3D nucleation decreases with increasing 8 thus indicating major structural dissimilarities between the 2D layer and the 3D nuclei.INTRODUCTION It is well known that in the initial stages of numerous metal electrocrystallization processes taking place at foreign solid substrates considerable amounts of the electro- active cation MeZ+ are deposited at potentials more positive than the MeZ+/Me,,, equilibrium potential building up strongly adsorbed (sub)monolayers at the electrode/ electrolyte interphase.lp2 Interest in these effects has grown remarkably during the last years as it became clear from the work of several authors3-6 that the kinetic and equilibrium properties of the emerging deposits are markedly influenced by the crystal- lographic orientation of the substrate electrode. There is now widespread (although not unanimous) belief that undervoltage de- position should be interpreted in terms of a nucleative epitaxial mechani~m~-~ assuming the Mez+ layer to originate in a sequence of 2D phase transitions initiated by discrete two dimensional nucleation acts.Subsequent lateral growth eventually would result in the formation of ordered adsorption structures in registry with the substrate lattice whose stability is restricted to well defined potential intervals within a more or less extended undervoltage range. Besides determining the shape of the pertinent adsorp- tion isotherms ordered coverages thus produced might also play decisive roles within the growth mechanism of Me bulk phase deposits providing for a suitable 3D nuclea-tion environment or even acting as a precursor matrix of developing lattice planes.It has been pointed however that 2D nucleation (which of course conflicts rather sharply with any continuous Me" adsorption model brought forward previ- + ously1*8) is still far from being unambiguously confirmed by experiment as a metal undervoltage mechanism of universal relevance. In order to acquire a more coherent picture of the low-coverage behaviour of a selected system Pb deposition onto Ag single crystals from perchlorate solutions has j' Permanent address Institute of Electrochemical Power Sources Bulgarian Academy of Science Sofia Bulgaria. W. J. LORENZ E. SCHMIDT G. STAIKOV AND H. BORT been studied in the undervoltage and low-overvoltage regions. This choice of the system was motivated by both the absence of complex formation in the Pb2+/C10,- couple and the inability of the perchlorate ion to adsorb specifically at Ag substrates.1° Consequently the observed polarization phenomena are supposed to be indicative of the interactions between the substrate and the Me coverage proper undisturbed by chemical complications and competitive or co-adsorption effects.The experiments performed include charge and coverage determinations by the concentrostatic twin-electrode thin layer method l1 as well as potential pulse experi- ments at chemically polished single crystal surfaces. For additional voltammetric and morphological studies Ag substrates made electrolytically by the Budevski capil- lary method12 were used. In this paper a brief account of the results obtained is given.Experimental details will be reported el~ewhere.l~-~~ UNDERVOLTAGE PROPERTIES OF THE Pb2+,ClO;i/Ag SYSTEM COVERAGE ISOTHERMS Voltammetric twin-electrode thin layer experiments have been carried out with chromate-polished l6Ag single crystals of (loo) (110) and (111) orientation using bulk Pb as a Pb2+ reversible generator electrode.ll Typical undervoltage voltammograms are shown in fig. 1. At the low potential sweep rates employed (IdE/dtI <1 mV s-l) there is reasonable symmetry between the 1 - -50 0 50 150 250 E -Epb/pb2*/mV METAL ION ADSORPTION AND ELECTROCRYSTALLIZATION 6 5 4 16) 3 2 1 N I 50 Q I *_\ -1 -2 -3 -4 -5 -6 -56-0 FIG.1 .-Twin-electrode thin layer voltammograms of the Pb2+,ClO:/Ag(hkl) system.(a)Ag(100); (b) Ag(ll1). Electrolyte 0.5 mol dm-3 NaC104 + 0.005 mol dm-3 HC104 + 2 x mol dm-3 Pb2+;chromate-polished electrode surfaces; T= 298 K; IdE/dt 1 = 0.42 mV s-'. (A) anodic curves; (K) cathodic curves. -i; ---ig. anodic and cathodic current curves indicating reversibility of the undervoltage process at the time scale of the experiment. In all systems multiple peak structures have been found (table l) the main peaks being A and A at the (100) and (1 lo) and A at the (1 11) crystal faces respectively. The peak potentials obtained agree fairly well with the corresponding values reported by Bewick17 and by Dickertmann et aL1* According to the operating principle of the twin electrode method the current i measured at the Me adsorbing electrode corresponds to the global charge flux due to the variation of the surface charge density whereas the generator current ig is equiva- lent to the amount of Pb2+ deposited per unit time.Assuming equilibrium to have been established at the initial and final potentials E and E, of a given voltage scan W. J. LORENZ E. SCHMIDT G. STAIKOV AND H. BORT surface charge and Pb surface concentration increments may be determined simply by integrating the corresponding i and igvoltammograms TABLE PEAK POTENTIALS OF THE PbZ+,C104 + Ag(hkl)SYSTEM 1 .-UNDERVOLTAGE A JmV A2/mV A ,/mV A4/mV From &/ATpb correlations thus obtained the charge/coverage coefficient of the Pb undervoltage deposit ZE = F-1(a4/arPb)E7 (3) is calculated.2 is found to coincide with the Pb2+ionic charge within the limits of experimental accuracy ZE = 2 & 0.1 [PbZf ClO,/Ag (100); (110); (ill)]. (4) This implies that in analogy with the Pb2+/C10i system with plycrystalline elec- frodes,I1 Pb2+ is the only ionic species substantially incorporated into the inner double layer. Procedure (2) results in a direct AT determination which in contrast to charge-coverage evaluations of conventional single electrode voltammograms does not depend on apriori suppositions with respect to 2,. Because rpb is likely to vanish if E -00 in the absence of specific anion adsorption absolute Tpb data are obtained by eqn (2) provided that a sufficiently high starting potential E, is applied E rPb(E,Cpb2+) =Ea+CO lim (2F)-1\Ea dt' (5) The experimental limit values of rpb thus determined with E approaching the Pbb,,,/ Pb2 equilibrium potential Epb/pb2+ consistently come close to the packing density + of the bulk Pb (1 11) lattice plane allowing for a roughness factor of -1.2 TABLE 2.-EXPERIMENTAL AND HYPOTHETICAL Pb SURFACE CONCENTRATIONS (CHARGE EQUIVALENTS) rs,m Ad1101 exp.0.38 0.02 rs,Fb Ad100) exP 0.37 rt 0.02 rs,m Ad111) exP. 0.34 & 0.02 Pb(1 1 1) calc. 0.302 Ag(l11) -3(2 x 2)Pb calc. 0.336 Ag(100) -c(2 x 2)Pb calc. 0.193 Ag(100) -42 x 2)Pb -42 x 2)Pb calc. 0.386 METAL ION ADSORPTION AND ELECTROCRYSTALLIZATION Hence one might speculate that in the Pb layer at potentials near Epb/pb2+ a similar close packed structure is present.” Notice however that as a consequence of the rather large Ag/Pb misfit which is of the order of 20% close-packed arrangements of Pb atoms cannot be planar in direct contact with any Ag crystal face unless some non- spherical deformation of either the substrate or part of the adsorbate particles is permitted.In the Ag(100) system I-‘,,,, would also be compatible with a square twin- layer c(2 x 2) -c(2 x 2) structure.13 Due to the nearly ideal q/I-‘stoichoimetry as expressed by eqn (4) unified CpbZ+-inde- pendent coverage isotherms are produced with each crystal orientation when the 1 .o Q (0) 0.5 “..,,_ A 0 1.0 0 (b) 0.5 0 1.0 0 (c1 0.5 a FIG.2.-Coverage isotherms B(E-Epb,pb2+) of the Pb2+/C10j system.Electrolyte 0.5 mol dm-3 NaC104 + 0.005 mol dm-j HC10 + x mol dmW3Pb2+ < x < lo-”>.(a) Ag (111)/Pb2+ (6) Ag(100) Pb2+,(c) Ag(ll0) Pb2+. W. J. LORENZ E. SCHMIDT G. STAIKOV AND H. BORT 19 experimental set of rpb data (normalized with respect to rs,pb) as obtained for different cPbz+values is plotted against the undervoltage E -Epb/pbz+ rPb(E,cpbZ+)/rs,Pb *,E -EPb/Pb2+) if 2 = 2 (7) (" pseudo-Nernstian " metal adsorbateig). As seen in fig. 2 the resulting 8 curves each exhibit a sequence of rather drawn out coverage steps that correspond to the voltammetric current peaks of the respective substrate orientations. Attempts to identify a clear-cut correlation between the fully developed steps and hypothetical surface concentrations of simple submonolayer superstructures20 have been unsuccessful so far except in the (100) system where the total rpb of peak Al strongly suggests formation of a 42 x 2) Pb single layer.Characteristically neither isotherm reveals any 6 against E discontinuity thus indicating perfectly continuous transition from one coverage level to another. Roughly approximating each step individually by a mean field (Frumkin) model values of the lateral interaction parameter g were determined from experimental 0 slopes that lie safely within the continuity range of a Frumkin adsorbatei5 (gex,< 3.5). Poor step separation also indicates considerable overlap of successive deposition stages. Such equilibrium behaviour clearly is at variance with the concept of 2D phase-like 6 singularities existing in the undervoltage region that undergo first order trans- formations when E is crossing distinct two-phase coexistence lines.It would how- ever support the idea of the Pb deposit occupying continuously a limited number of adsorption sites. Preferential stability of ordered intermediate structures would not be excluded by such a model as long as merging intervals of homogeneity exist which enable the system to establish a steady sequence of 6 against E equilibrium states. Notably a very similar coverage pattern is observed in Pb undervoltage experi- ments with single-faced Ag substrates capillary-grown by the Budevski te~hnique.'~*~~*~~ Minor irregularities notwithstanding voltammograms taken with this class of elec- trodes l3 are virtually identical to those obtained with chemically polished macro crystals as far as peak position and peak width is concerned.Thus basic congruence of the underlying isotherms with respect to both step structure and continuity is demonstrated (fig. 3). Non-discontinuous 0 increase particularly may not be attri- buted to accidental distortion of the evolving monolayer by surface defects such as screw dislocations and subgrain boundaries as both types of imperfections are absent from Budevski crystals but appears to be a genuine phenomenon of the regular equili- brium surface. It is not known to what extent the Pb layer will be influenced by kinks and steps of monoatomic height produced by microroughening when the substrate is exposed to the adsorband electrolyte.Doping Budevski surfaces artificially with Ag growth pyra- mids which increase the step line density by about 5 x lo5 cm/cm2 was not found to alter the undervoltage properties of Pb appre~iab1y.l~ POTENTIAL PULSE RESPONSE At Pb2+ concentrations 5 x mol dm-3 < cpb2+ < mol dm-3 cathodic potential pulse polarization leads to monotonously decreasing i against t curves regardless of the step width of the voltage signal provided that E > Epb/pbZ+. The most prominent feature observed is a distinct shoulder which appears when large pulses are applied within the potential ranges of the voltammetric current peaks (fig. 4) * As the current is substantially smaller than that predicted by a semi-infinite diffu- METAL ION ADSORPTION AND ELECTROCRYSTALLIZATION -1 OOOL 0 100 200 3 0 f-fPblPb2* ImV FIG.3.-Cyclic voltammogram of Pb2+with Ag(ll1) electrode grown electrolytically by the capillary method.Electrolyte 0.5 mol dm-3 NaC104 + 0.005 mot dm-3 HCI04 + 0.05 mol ~Irn-~ Pb(C104)2 IdE/dt[ = 10 mV s-l. sion model the curves cannot be explained by mere transport controlled adsorption.' Transients of similar shape and magnitude? however may easily result from homo-geneous first order Pb2 transfer kinetics + drPbldt = Kad(E.hb)(cPb2+ -'(E,rPb)) (8) assuming Kad varies appropriately with rpb. The c(E,rPb).parameter denoting the Pb2+ equilibrium concentration as a function of E and rPbis defined by the actual 0 isotherm.For Frumkin type systems with pseudo-Nernstian 9 against E dependence eqn (8) reads explicitly [cf. ref. (7)] where a = kO(1 -0)-l exp [-go] and w = exp [2F(E -EPb/Pb2+)/RT]. Eqn (9) was used to calculate the pulse response in the main peak region of the Ag(ll1) system neglecting the influence of the satellite peaks A and As. As seen in fig. 5 remarkable agreement with experiment is thus achieved. Within the concentration range investigated rising transients? which might be due to nucleative 2D phase formation have not been observed. Likewise asymptotic transient analysis that would identify non-adsorptive currents in a composite adsorp- tion-nucleation model with 2D phase growth being slow compared with adsorbate rela~ation,~~ did not give evidence of coverage processes other than continuous F increase according to eqn (8) and (9) respectively.? a E s 2 msl division FIG.4.-Cathodic potential pulse undervoltage transient. Electrolyte 0.5 mol dm-3 NaC104 + 0.001 mol dm-3 H2S04 + 0.01 mol dm-3 Pb(C104)2. Electrode Ag(l1 l) chromate-polished E = Epb/pb2+ + 200 mV; E = Epb/pb2+ + 60 mv. [Toface page 20 W. J. LORENZ E. SCHMIDT G. STAIKOV AND H. BORT It is concluded therefore that in accordance with isotherm continuity as found voltammetrically undervoltage deposition kinetics in the Pb2 ClO,/Ag system + is dominated by a homogeneous sorption mechanism phase formation-like processes being absent or at least kinetically irrelevant. -801. Q -40 ~ p7 I 2 -20 -I OLO 2.5 5.0 7.5 10.0 tlms FIG.5.-Calculated cathodic potential pulse undervoltage transient.- Calculated by use of eqn 2.35; 0.6; k 7.47 x lo-'; 2 Fkadca= 1.03 A cm-'; 0.38 mC (9) g = a = 0.4; p = = 2FI's,pb = cm-2. Pulse as in fig. 4. 0,Experimental as in fig. 4. UNDERVOLTAGE-OVERVOLTAGE TRANSITION The only nucleative process unambiguously identified in the present system is the onset of Pb bulk phase deposition. -Epb/p$+ 7-25 mv) starting from a low-undervoltage initial potential (0 < E -Epblpb2+ < 100 mV) rising i against t curves are obtained as shown in fig. 6. Their shape appears to be consistentl4 with diffusion controlled 3D nucleation as known from phase growth at polycrystalline Ag.24*25 The overall current density depends on both the pulse width and the substrate used.In general i is substantially larger at Ag(100) than at Ag(ll1). Phase growth proceeds in the presence of a more or less fully developed under- voltage layer whose rPb increases gradually as the pulse is applied. Therefore a falling transient is superposed on the nucleative current establishing (metastable) equilibrium or steady state conditions in the layer within a few tenths of a second. As E is close to Epb/pbZ+ the corresponding charge flux usually is small compared with that due to the phase growth process. There is a remarkable correlation between the overall rate of deposition and the initial state of the undervoltage layer. As seen in fig. 7 the nucleative current de- creases sharply when (at constant final E) Tp is increased by shifting E towards &b,pbZ+.Since under such conditions the growth kinetics of single nuclei is not affected significantly the rate of nucleation evidently is reduced as rPbapproaches ,!?>(0is pulsed into the near overvoltage region EWhen METAL ION ADSORPTION AND ELECTROCRYSTALLIZATION the packing density of the full coverage deposit which is in equilibrium with bulk Pb at EPblPb2+. This almost definitely rules out a closer structural relationship between the bulk phase lattice and ordered 2D domains whose stability and/or frequency increases with TPb, because in that case enhanced nucleation would result from higher coverage. The most appropriate way to overcome this discrepancy is to assume a major dissimi- larity between the 2D layer and the substrate/3D deposit interface.Nucleus forma- tion then would involve a rearrangement requiring a certain intrinsic mobility of the layer. As this structure gradually becomes more rigid by denser packing nucleation is obstructed in agreement with experience. -500 (Y ' -250-5 Q 3 .. 0 2 4 6 8 3 tls FIG.6.-Overvoltage potential pulse transients. Electrolyte:0.5 rnol dm-3 NaC104+ 0.005 mol dmW3 HC104 -/-0.01 KlOl dm-3 Pb(C104)Z. E = Epb/pbZ+ + 75 mV; E = Epb,pb2+ -16 mv. Iiz situ information on the 2D layer of course is inaccessible. Substrate/nucleate epitaxy however is readily ascertained by Nornarski interference microscopy 26 of deposits obtained with Budevski Ag electrodes.On both (1 11) and (100) substrates a limited number of isolated tri- and hexagonal Pb crystallites is seen (fig. 8). From crystal symmetry and edge orientation with respect to the absolute substrate axes Pb/Ag epitaxy according to (111)Pb [I (111)Ag; [11O]Pb 11 [11O]Ag and (11l)Pb I[ (1OO)Ag; [11O]Pb [I [11O]Ag is found. Thus close-packed El101 lattice rows of both Ag and Pb line up in parallel in the substrate/nucleate interface of either system. As seen from the distances of adjacent [110] rows in the planes involved [Ag(100) 2.88 A; Ag(l11) 2.50 A; Pb(l11) 3.03 A] the row-by-row misfit in the Pb(lll)/Ag(100) system is only 5% whereas with Ag(l1 I) a 5 6 periodicity is approximated. Both epitaxial structures consequently might ensure relatively unstrained contact between Ag and Pb.In view of serious mismatch with natural adsorption sites however both row-by-row configurations must be considered inadequate arrangements for continuously evolving 2 D systems which would probably prefer low strain structures such as Ag(100) -c(2 x 2). Structural identity of 2D layer and substrate/nucleate interface is there- fore most unlikely. 0.1 sl division FIG. 7.-Influence of E on overvoltage pulse transient. Electrolyte as in fig. 6. E =EPblpbz++AE; E =Epb/pb2+ -18 mV; BE = 75 mV (upper curve); 50 mV; 30 mV; 10 mV (lower curve). [oil1 [ioiI [iioI [Ol1I LroilI FIG. 8.-Pb deposits at capillary-grown Ag electrodes (Nomarski interference microscopy).Electrolyte as in fig. 6; E =Epb/pb2 + -3 mV. (a)Ag(ll1); one set of crystallites with parallel edge orientation. (b)Ag(100); two sets of crystallites rotated 30". [Toface page 22 W. J. LORENZ E. SCHMIDT G. STAIKOV AND H. BORT CONCLUSION The validity in the Pb2+ ,ClO,/Ag system of the 2D phase concept of metal under- voltage deposition was not confirmed by the experiments reported. Isotherm dis- continuities that would positively identify any (first order) 2D phase transition have not been recognized. Nucleative components of potential pulse i against t undervoltage transients have not been found. Moreover undervoltage deposition and 3D phase formation appear to be rather disjunct phenomena. Ideally organized 2D layers might even effectively impede 3D nucleation.Homogeneous adsorption models therefore are considered more adequate for describing this system. It should be said however that this statement applies strictly to the present in- vestigation. It is not precluded that there might be other systems or foreign com- ponents in the Pb/Ag system such as adsorbing anions which might produce (or mimic) phase transition or nuleation like effects. Further work will help to clarify this issue. E. Schmidt and H. R. Gygax J. Electroarlalyt. Chem. 1966,12,300. 'W. J. Lorenz H. D. Herrmann N. Wuthrich and F. Hilbert J. Electrochein. SOC.,1974 121 1167. A. Bewick and B. Thomas J. Electroanalyt. Chenz. 1975 65 91 1. A. Bewick and B. Thomas J. Electroanalyt. Chenz. 1976 70,239.J. W. Schultze and D. Dickertmann Surface Sci. 1976 54,489. R. Adzic E. Yeager and D. Cahan J. Electrochenl. SOC.,1974 121,474. K. Juttner G. Staikov W. J. Lorenz and E. Schmidt J. Electroalralyf. Chem. 1977 80 67. H. D. Herrmann N. Wuthrich W. J. Lorenz and E. Schmidt J. Electroarralyt. Chem. 1976 68 273 289. A. I. Briggs H. N. Partonand R. A. Robinson J. Amer. Chem. SOC. 1955,77,5844. lo L. Rainaley and C. G. Enke J. Electrochem. SOC.,1965 112 947. l1 E. Schmidt and H. Siegenthaler Helv. Chim. Acta. 1969 52,2245. l2 E. Budevski and V. Bostanov Electrochim. Acta. 1964 9 477. l3 G. Staikov K. Juttner W. J. Lorenz and E. Budevski Electrochim. Acta 1977 in press. l4 G. Staikov K. Juttner W. J. Lorenz and E. Budevski to be published. l5 K.Jiittner H.Bort W.J. Lorenz and E. Schmidt to be published. l6 T. Fukazawa cit. Chem. Abstr. 1961,55 14279. A. Bewick and B. Thomas J. Electroaizalyt. Chenz. in press. l8 D. Dickertmann F.D. Koppitz and J. W. Schultze Electrochim. Acta 1976,21 1967. l9 E. Schmidt Helv. Chim. Acta 1969 52 1763. 'O F. Hilbert C. Mayer and W. J. Lorenz J. Electroanalyt. Clzem. 1973,47 167. E. Budevski V. Bostanov T. Vitanov Z. Stoinov A. Kotzeva and R. Kaishev Electrochim. Acta 1966 11 1697. 22 E. Budevski V. Bostanov T. Vitanov Z. Stoinov A. Kotzeva and R. Kaishev Phys. Stat. Solidi 1966 13 577. 23 G. Staikov K. Juttner W. J. Lorenz and E. Schmidt Electrochim. Acta 1977 in press. 24 J. A. Harrison J. Electroanalyt. Chem. 1972 36 71. 25 J. A. Harrison R. P. J. Hill and J. Thompson J. Electroarzafyt. Chem. 1973,44,445. 26 G. Nomarski and A. R. Weill Rev. Metallurg. 1955 52 121.

ISSN:0301-5696    

DOI:10.1039/FS9771200014

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Phase Formation in the Underpotential Deposition of Metals BY ALANBEWICK,JOVAN JOVICEVIC AND BRIANTHOMAS Department of Chemistry Southampton University Southampton SO9 5NH Received 22nd August 1977 The structures of the two-dimensional layers formed in the underpotential deposition of lead onto carefully prepared single crystals of copper are shown to depend upon the substrate orientation for (lll) (100) and (110) surfaces. Nucleative growth processes are observed for first order and for higher order phase transitions. Comparison is made with the behaviour observed on silver sub- strates and the differences are ascribed to the change in atomic radius and in electronegativity. Formation of the underpotential layer is shown to be a necessary precursor to overpotential deposition the mechanism of which is markedly dependent on substrate orientation.Investigations of the deposition of metals onto foreign metal substrates at poten- tials positive to the reversible potential for bulk metal deposition i.e. in the under- potential region have proved to be of considerable interest in their own right as well as being of relevance to studies of the initial stages of bulk metal deposition. Until recently underpotential deposition (UPD) was believed to be caused by the formation of a layer of adsorbed atoms1 Subsequent investigations 2-7 using carefully prepared single crystal substrates with a variety of orientations have revealed a range of more complex processes the detailed nature of which varies with the substrate orientation.Coulometric measurements indicate the formation of epitaxial layers and the con- version of these to close-packed layers which are non-registered but which can be distorted by the structure of the underlying substrate. The formation mechanisms of some of these phases appear to be first order processes while others are of second or of higher order. It has also been dem~nstrated~-~ both for cases involving first order transitions and those involving higher order transitions that the deposition of the phase at constant potential requires the formation and growth of two-dimensional nuclei. These recent developments point to a considerable parallelism between the nature of the phases and the phase transitions observed in underpotential layers and those observed in adsorption onto solid surfaces from the gas phase studied by con- ventional methods and by LEED.Although the electrochemical systems are not amenable to direct structural investigation they have the advantage in readily en- abling the dynamics of the phase formation processes to be investigated. This aspect should be particularly valuable in probing the properties of two-dimensional systems and for example the applicability of new theories of melting in two-dimensional systems.s Our detailed measurements on single crystal surfaces have been restricted to a single substrate material silver. Since we expect the underpotential processes to depend not only on the difference in electronegativity between the substrate and the depositing metal,g but also upon the relative sizes of their constituent atoms a factor which controls epitaxy and registration we have extended the work to other substrates.In this paper deposition of lead onto single crystals of copper will be reported together with preliminary results on the correlation between underpotential deposition and overpotential deposition of lead onto silver.1° ALAN BEWICK JOVAN JOVICEVI~: AND BRIAN THOMAS EXPERIMENTAL It has already been pointed out that quantitative reproducible results depend markedly upon careful chemical polishing of the single crystal surfaces. The technique used for the silver electrodes has been described.* In the case of copper single crystals modified chemical polishing procedures had to be developed for each of the orientations employed (1 1 l) (100) and (110); these will be reported elsewhere.ll Copper is also sensitive to minute traces of oxygen; specially rigorous precautions were necessary to ensure that contamination was below a detectable 1evel.l' Precise potential control was essential for some of the experiments; this was ensured using a HiTek Instruments potentiostat type DT2101 and making use of the internal DVM to calibrate the programming waveform generator.All electrode potentials are quoted with respect to the reversible potential for bulk metal deposition in the solution employed. RESULTS AND DISCUSSION UPD OF LEAD ONTO COPPER (i) LINEAR SWEEP VOLTAMMETRY. Typical linear sweep voltammograms for the three substrate orientations are shown in fig.1 2 and 3 for deposition from perchlorate solutions. No essential -4 N fj -2 4 E N 2 \ .-0 4 0 200 400 €/mV vs Pb FIG.1.-Linear sweep voltammogram at 3 mV s-'; Cu(ll1) electrode; electrolyte mol dmW3 Pb(OAc)2+ 0.5 mol dm-3NaCIO + mol dm-3 HC104. 26 PHASE FORMATION IN UNDERPOTENTIAL DEPOSITION OF METALS I I I I I I 0 200 400 f/mV voPb FIG.2.-Linear sweep voltammogram at 5 mV s-'; Cu(100) electrode; electrolyte mol dm-3 Pb(OAc)2+ 0.5 mol dm-3 NaC104 + rnol dm-3 HC104. differences were observed using acetate or nitrate solutions or using lead concentrations of lov3 mol dm-3 and 10-1 mol dm-3 although the peak positions showed a concen-tration dependence of about 15 mV per decade.'l On the (111) surface deposition occurs in a single sharp peak and there is a single stripping peak which is less sharp.The small shoulder following the sharp deposition peak and the corresponding feature preceding the stripping peak appear to be associated with parts of the electrode surface not possessing the (1 11) orientation. This can be demonstrated by gradually reconstructing the copper surface.l' At very low sweep speeds (-1 mV s-l) the deposition peak is very sharp with a width of about 3 mV at the half peak height and even at this sweep speed the separation of the deposition and stripping peaks is -50 mV. These features suggest a sharp phase for- mation process which is probably first ~rder.~?~ Integration of the deposition and stripping peaks gives a charge value of 229 x C cm-2 table 1.Analogy with the results obtained on ~ilver~.~ would suggest a comparison with the charge required for a close-packed non-registered monolayer which is 310 x C cm-2. The difference is much too large to be accommodated by a change in the extent of anion adsorption. There is very good agreement however with the charge required to form the closest packed epitaxial layer fig. 4 as shown in table 1. A factor of 1.1 to allow for roughness and for a difference in anion adsorption gives perfect agreement. On the (100) surface fig. 2 deposition occurs in two steps with a small shoulder preceding a relatively sharp peak. Corresponding features are observed on the stripping sweep. The total charge involved in the deposition or the stripping processes ALAN BEWICK JOVAN JOVICEVIC:AND BRIAN THOMAS -8.--4- N k e E N I 0 .-\ *-0.-4.- I I I I I I I FIG.3.-Linear sweep voltammogram at 10 mV s-’; Cu(ll0) electrode; electroIyte mol dm-3 Pb(OAc)2+ 0.5 mol dmb3NaC10 + mol dm-3 HC104.is shown in table 1. Again it is too low to correspond to the formation of a close packed plane of lead atoms but there is excellent agreement with the charge required to form the epitaxial layer with the structure shown in fig. 5. It should be noted that this epitaxial structure is very close to that of the (100) face on bulk lead. Comparison with the earlier results obtained on silver leads to the conclusion that the shoulder represents initial random adsorption of lead atoms at favourable coordination sites TABLEMEASURED VALUES OF CHARGE c Cm-’) ASSOCIATED WITH FEATURES ON LINEAR SWEEP VOLTAMMOGRAMS FOR THE UPD OF Pb ON Cu COMPARED WITH CALCULATED CHARGE VALUES FOR VARIOUS STRUCTURES.substrate charge associated charge associated charge for a close orientat ion with the deposition with epitaxial mono- packed layer peak layer of fig. 4 or 5 or 6 310 (100) total charge 273 243 310 prepeak only -50 (110) 1st peak 190 178 310 total charge 322 28 PHASE FORMATION IN UNDERPOTENTIAL DEPOSITION OF METALS FIG.4.-The structure of a complete epitaxial layer of Pb on Cu(ll1). and the sharp peak shows the formation of the epitaxial phase layer the phase transition being of higher order.On the (110) surface the deposition and stripping processes give rise to two over- lapping peaks fig. 3. Each of the peaks is relatively sharp. The charge associated with the first peak is approximately 190 x loe6 C cm-’ compared with a theoretical value of 178 x C cm-2 for the close-packed epitaxial layer shown in fig. 6. Once more there is agreement within a factor of 1.1. It should be noted that the epitaxial structure shown in fig. 6 is very similar to that of the (1 10) face on bulk lead. The total charge encompassed by the two peaks is 322 x C cm-’ which is close to the value required to form a layer of closely packed lead atoms. It appears there- cu (100) aixm 1.28 A FIG.5.-The structure of a complete epitaxial layer of Pb on Cu(100).fore that for this orientation the deposition process follows a very similar pattern to that observed using a silver ~ubstrate.~ The initial process is the formation of an epi- taxial adsorbed layer. Before this layer is fully completed it begins to reorganise into a close-packed structure. Although this layer is likely to be distorted by the substrate as was observed on silve~,~ there is no evidence in the present case for the ALAN BEWICK JOVAN JOVI~EVI~ AND BRIAN THOMAS cu (110) FIG.6.-The structure of a complete epitaxial layer of Pb on Cu(l10). deposition of a second layer in the underpotential region before the onset of bulk deposition. In the preceding discussion possible structures for the surface layers have been inferred by the comparison of observed charge values with those calculated for simple structures related to the arrangement of atoms in an undistorted substrate surface.Although considerable relocation of surface atoms and the reconstruction of surface structures has frequently been observed in other studies [e.g. see ref. (12)] it appears to be unnecessary to introduce this additional complication in the present case. (ii) POTENTIAL STEP EXPERIMENTS Considerable information on the mechanism of phase formation can be obtained by the analysis of the current against time transients observed after initiating the phase formation at constant potential using a potential step. In particular the participation of a nucleation process can be distinguished and the growth geometry and the detailed kinetics of the slow step can be found.This technique was applied to the present system by stepping the potential into the deposition region from a rest potential well positive from this. Fig. 7 shows examples of the transients obtained for the (1 11) surface for a series of growth potentials scanning through and beyond the region of the single sharp peak seen on the voltammograms. For all potentials within or beyond this peak the current against time transients show a well-formed peak which is characteristic of crystal growth from two-dimensional nuclei. The initial part of the rising portion of these transients is linear implying that the layer is formed by the two-dimensional growth of nuclei produced just at the start of the potential step.Further analysis confirms this conclusion. Fig. 10 shows a reasonable linear plot for the data from one of the transients according to the well known equation for this growth mechanism :l3 I= zFnMNok2texp (-nM2Nok2t2/p2). * P 30 PHASE FORMATION IN UNDERPOTENTIAL DEPOSITION OF METALS t I ~o-~s FIG.7.-Current against time transients at a Cu(ll1) electrode in lo-' rnol dm-3 Pb(0Ac)' + 0.5 rnol dm-3 NaClO + mol dm-3 HClO in response to a potential step from +390 mV to (1) +130 mV (2) +120 mV (3) +110 mV (4) + 105 mV (5) + 100 mV. Since the observed nucleation is instantaneous and not progressive it must be con- cluded that the single crystal surfaces contain quite high concentrations of defects. One further property of the peaked transients is of special importance.Integration of any of them leads to the same value of charge and it corresponds to the formation of a complete layer of the close-packed epitaxial structure shown in fig. 4. This is true even for those transients obtained at a potential just at the very start of the deposition peak on the voltammogram. The implication is that the phase formation is a true first order process and the finite width of the peak on the voltammogram is due to kinetic effects even at 1 mV s-l. Details are given elsewherel' of the further analysis of these transients to yield other kinetic data. FIG.8.-Current against time transients at a Cu(100) electrode in mol dm-3 Pb(OAc)* + 0.5 rnol dm-3 NaC10 + rnol dm-3 HClO in response to a potential step from +370 to (1) +70 mV (2) +65 mV (3) +60 mV (4)$55 mV (5) 150 mV.The transients obtained for deposition onto the (100) and (1 10) surfaces are shown in fig. 8 and 9 respectively. In these cases also it is apparent that growth proceeds via a nucleative mechanism but the transients have an additional feature a substantial falling component due to adsorption. This is readily understandable for these two cases since the substrate surface affords particularly favourable sites for adsorption. ALAN BEWICK JOVAN JOVICEVIC AND BRIAN THOMAS I I 0 10 2b 30 4’0 t/ ~o-~s + 0.5 FIG.9.-Current against time transients at a Cu(ll0) electrode in mol dm-3 P~(OAC)~ mol dm-3 NaC104 + mol dm-3 HC104 in response to a potential step from +365 mV to (1) +85 mV (2) $75 mV (3) $65 mV (4) +55 mV (5) +45 mV.I 0 I000 2600 3000 4000 5000 15 10-6s* FIG.10.-Plot of log i/t against t2 for transient (5) in fig. 7. After the application of the potential step nucleative growth develops slowly because of its kinetic limitations whereas adsorption can proceed quite rapidly. Thus ad- sorption can dominate at shorter times even though the final stable form of the deposit is a phase layer. For the (100) surface the adsorption sites and the sites of the lead atoms in the epitaxial layer are the same. However it is reasonable to postu-late that adsorption could proceed by random deposition until approximately half of the sites have been filled and the adatonis are still quite widely separated.Further deposition necessitates bringing adjacent atoms into very close proximity fig. 5 and this requires the development of nuclei to overcome the electrostatic repulsion between separate adatoms connected to the surface by strongly polar bonds. PHASES AND PHASE TRANSITIONS SILVER AND COPPER SUBSTRATES COMPARED The general pattern observed for the UPD of lead5 or thallium2 onto the (1 11) or the (100) or the (1 10)surface of silver was that of adsorption at more positive potentials 32 PHASE FORMATION IN UNDERPOTENTIAL DEPOSITION OF METALS up to a full epitaxial monolayer followed at more negative potentials by a nucleative phase transformation process to form a phase layer which was coulometrically equiva- lent to a close-packed crystal plane.The adatoms in the epitaxial layer were in the most favourable adsorption sites and on the (1 11) surface which does not possess particularly favourable sites the layer was never fully developed. On the other two surfaces the layer could be fully formed but depending upon the concentration the phase transformation could start before completion of the epitaxial layer. A close-packed layer of lead or of thallium would not be registered with the silver substrate but there was evidence that the layer was distorted and partially moulded by the sub- strate structure. On all three surfaces thallium formed a second underpotential layer on top of the first close-packed layer; the details of this deposition were still dependent on the substrate orientation. It was observed that lead formed a second layer ody on the (1 10) substrate.The nucleative phase transformation process appeared to be first order on the (1 11) surface and of higher order on the other two. On changing from silver (atomic radius 0.142 nm) to copper (atomic radius 0.128 nm) there is a significant decrease in size and a significant increase in electronegativity. This decrease in size leads to a larger number of special adsorption sites per unit area on copper ;the sizes of lead and thallium are such (0.175 and 0.170 nm respectively) that the same fraction of these sites can be filled on silver and on copper. As a result the lead or thallium atoms in an epitaxial monolayer are considerably closer together on copper (see fig. 4,5 and 6) than on silver and in the former case they form a layer closer in structure to a further layer of the substrate.Thus it might be expected that the adlayer on copper would more easily participate in a band structure extending over substrate and adlayer thus allowing the development of the properties of a well-defined phase. Further deposition beyond that required for the fully formed epitaxial layer is found only with the (1 10) substrate and the second deposition process always starts at a more positive potential than that required for completion of the first. The epitaxial structure shown in fig. 6 shows the lead atoms arranged in parallel chains with a wide spacing between adjacent chains. It might be expected that further material would be accommodated in a second set of chains situated between and a little above the first set.The measured charge is insufficient for the completion of this process and it must be concluded that as on silver it is energetically more favour- able to form a close-packed structure even though this involves loss of detailed registra- tion. The difference in electronegativities implies stronger bonding to copper than to silver and this will be an additional factor favouring the epitaxial structures which are observed to be more dominant on copper. It is interesting that on both copper and on silver the phase transformation process is first order on the (111) surface and it involves the formation of the phase on an almost bare surface. On the other surfaces the phase transformations are of higher order; they involve phase formation on a surface which already has an appreciable coverage by adsorbed material.There appears to be no correlation between the order of the phase transformation and the degree of registration of the phase; on the (1 11) surface of silver the phase is non registered whereas on copper it is fully registered. This is contrary to the trends which have been reported in other work.14 It is of particular interest that a nucleative growth mechanism is observed for the higher order phase transitions. Electrochemical methods can therefore be used to probe the dynamics of such processes. These kinetic and mechanistic data will be a valuable complement to the structural information obtained by LEED and related methods for phase formation on solid surfaces from the gas phase.For a higher order process proceeding at constant potential it is not clear whether the density of the growth centres will vary with size or to what extent the growth rate constants will vary with ALAN BEWICK JOVAN JOVIE6VI6 AND BRIAN THOMAS the size of the patches. Some indications of variations in these quantities has been obtained.6 OVERPOTENTIAL DEPOSITION OF LEAD ON SILVER In inany cases a very low nucleation overpotential is observed for bulk metal depo- sition in those systems for which UPD is known to occur. However the progression from underpotential to overpotential deposition has not been examined. Harrison et aZ.15 did investigate the overpotential deposition of lead on single crystals of silver but their data for UPD suggest that the surface preparation was not as good as can now be achieved; they observed no effects of substrate orientation in the overpotential region.Similar measurements lousing single crystal electrodes prepared in the same way as for the UPD studies have produced rather different results. In all cases even for deposition at very high overpotentials these studies show that the initiation of bulk deposition by three-dimensional nucleation does not occur until the under- potential monolayer has been laid down; the underpotential layer appears to be an essential precursor to normal bulk deposition. The current against time transients in response to a single potential step into the overpotential region fig. 11 12 and 13 2 4 t/s FIG.11.-Current against time transients at an Ag(l11) electrodein 5 x lo-’ mol dm-3 Pb(OAc)2+ 0.5 mol dmb3 HC104.Potential stepped from +300 to 0 mV for 1 s to preform the underpotential layer then to (1) -13.4 mV (2) -14.5 mV (3) -15.4 mV (4) -15.9 mV (5) -16.8 mV. show interesting variations with substrate orientation. Their major characteristics are (a) rising transients are observed at overpotentials in excess of -13 mV and they are very potential-sensitive as observed by other workers;15 (b)the transients level off to a limiting current at longer times those for higher potentials passing through a maximum due to non-steady state planar diffusion as expected for three-dimensional growth; (c) on the (100) and (1 10) surfaces the rise of current is linear with t2initially indicating the three dimensional growth of nuclei formed instantaneously and with the slow step occurring at the surface of the growing centres; (d)on the (1 11) surface the initial current varies as tY2 indicating that mass transport through hemispherical diffu- sion zones to progressively nucleated three dimensional centres is rate-determining.16 It is clear that the deposition mechanism on the (111) surface differs both in the type of nucleation invoIved and in the nature of the slow step from that on the other two surfaces.This difference will almost certainly be due to the structural reIation- ship between the substrate the underpotential layer and the three-dimensional layer. The underpotential layer is a close-packed plane and the preferred orientation of the 34 PHASE FORMATION IN UNDERPOTENTIAL DEPOSITION OF METALS I t 5 10 t/s FIG.12.-Current against time transients at an Ag(100) electrode in 5 x mol dm-3 Pb(OAc)2 + 0.5 mol dm-3 HC104.Potential stepped from +300 to 0 mV for 1 s to preform the underpotential layer then to (1) -14.2 mV (2) -14.4 mV (3) -14.8 mV (4) -15.2 mV (5) -15.5 mV. -0*4- U 0 2 4 t/s FIG.13.-Current against time transients at an Ag(ll0) electrode in 5 x mol dmF3 Pb(OAc)2 + 0.5 mol drn-3 HC104. Potential stepped from + 300 to 0 rnV for 1 s to preform the underpotential layer then to (1) -15 mV (2) -15.5 mV. three-dimensional layer will be expected to be with a high-density plane parallel to the surface.The closest structural relationships therefore will be met by the (111) system; the other two will possess considerable mismatch. In view of this it is not surprising that the lattice growth rate is considerably higher on the (111) surface and that the nucleative process is progressive. E. Schmidt and H. Gygax J. Electroanalyt. Chem. 1966,12,300; W. J. Lorenz H. D. Hermann N. Wuthrich and F. Hilbert J. Electrochenz. Soc. 1974 121 1167. A. Bewick and B. Thomas J. Electroanalyt. Chem. 1975 65,911. A. Bewick and B. Thomas J. Electroanalyt. Chem. 1976,70 239. A. Bewick and B. Thomas J. Electroanalyt. Chem. in press. A. Bewick and B. Thomas J. Electroanalyt. Chem. in press. A. Bewick and B. Thomas in preparation. ’ D. Dickertmann F. D. Koppitz and J. W.Schultze Electrochim Acta 1976,21,967. * J. M. Kosterlitz and D. T. Thouless J. Phys. C Solid State Phys. 1972 5 124 and 1973 6 1 I81 ; R. L. Elgin and D. L. Goodstein Phys. Reu. 1974 A9,2657. D. M. Kolb M. Przasnyski and H. Gerischer J. Electr.onnalyt.CIiefIi. 1974 54 25. lo B. ‘Thomas PA,D. Thesis (University of Southampton 1976). ALAN BEWICK JOVAN JOVICEVI~:AND BRIAN THOMAS A. Bewick and J. JoviCeviC in preparation. l2 R. Riwan C. Guillot and J. Paigne Surface Sci. 1975 47 183. l3 M. Fleischmann and H. R. Thirsk Advances in Electrochemistry and Electrochemical Engineer- ing ed. P. Delahay (Interscience New York 1963) vol. 3. l4 See for example the review by J. G. Dash Films on Solid Surfaces (Academic Press New York 1975). D. J. Astley J.A. Harrison and H. R. Thirsk J. Electroanalyt. Chetn. 1968 19 325; J. A. Harrison J. Electroanalyt. Chem. 1972,36,71; W. Davison J. A. Harrison and J. Thompson Faraday Disc. Chem. SOC.,1973 56 171. l6 M. Fleischmann J. A. Harrison and H. R. Thirsk Trans. Faraday SOC.,1965,61,2742; D. J. Astley J. A. Harrison and H. R. Thirsk Trans. Faraday Soc. 1968 64,192.

ISSN:0301-5696    

DOI:10.1039/FS9771200024

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Kinetic Investigations of Structural Changes and Desorption of Metal Adsorption Layers on Single Crystal Planes BY J. WALTERSCHULTZE AND DIRKDICKERTMANN Institut fur Physikalische Chemie und Quantenchemie der Freien Universitiit Berlin 1000 Berlin 33 Thielallee 63-67 W. Germany Received 2nd September 1977 At the surface of noble metal electrodes foreign metal ions from the solution (S) may be bound in a random layer (C),in an ordered structure (B) or in a condensed layer (A). Owing to structural differences desorption processes include various diffusion steps (d) and the charge transfer (t). Models are discussed in analogy to electrocrystallization. Potentiostatic pulse measurements were carried out with the system Au(l1 l)/Bi3 +,for which different Iayers with the structure A B and C exist.A charge transfer step is rate-determining in all cases. The exchange current densities of the desorption of layer A( <1 pA cm-2) B (1 mA cm-2) and C (10 mA cm-2) increase with the distance of next neighbours in the adsorption layer. Hence the desorption transients of all three layers differ and can easily be distinguished. At low potentials the desorption of A proceeds by a transfer of ions leaving a layer of B but the intermediate formation of B cannot be proved at high potentials. The anodic dissolution of B starts at the edge of homogene ous islands of B. Atoms diffuse to the free surface and ar-e then desorbed. Layers of B and C coexist not only at an unique equilibrium potential but in a range of less than 6 mV which can be explained by the non-ideal behaviour and the small size of areas with ordered structures of B.1. ELECTROCRYSTALLIZATION AND METAL ION ADSORPTION At the interface metal/solution the cathodic deposition of metal ions can take place on electrodes of the same metal (electrocrystallization) or of a foreign metal (adsorption). Since the charge transfer takes place in the Helmholtz layer these processes seem to be equivalent. The potential energy of the discharged atom on the surface however differs in both cases due to the different interaction with neighbour- ing atoms and the underlying layer. In electrocrystallization the lateral attraction is so strong that the removal of an atom from a place within the surface is impossible. Even for the kink site the lateral attraction is strong.Hence the direct charge transfer process kink site -+ solu-tion is less probable than the stepwise process kink site -+ edge -ad-atom -so1ution.l Further two-dimensional nucleation occurs due to the lateral 293 attraction of adsorbed atoms. In the case of metal ion adsorption the interaction substrate-adsorbate was assumed to be dominant. It increases with the work function difference of the Between the adsorbed atoms on the other hand lateral repulsion was assumed due to the incomplete discharge of the This assumption however is not correct for all systems. Recent investigations of metallic adsorption layers on single crystal planes have proved that lateral attraction is important for many system^.^ In con- trast to the simple Langmuir model two-dimensional condensation and nucleation phenomena can be expected also in the case of adsorption.Further surface diffusion WALTER SCHULTZE AND DIRK DICKERTMANN 37 which could not be detected in experiments with polycrystalline metal^,^-^ may have a strong influence on adsorption processes. Nucleation phenomena in metal ion adsorption were observed first by Bewick and Thomas for the system Ag(hkZ)/Tl+ and Ag(hkZ)/Pb2+ 9~10but the evidence was con- tested by Juttner et aZ.I1 We observed phase formation phenomena during anodic desorption in the system Au( 1 1 l)/Bi3+. Galvanostatic transients in this system de- monstrated that under certain conditions the desorption takes place only at the edge of complete islands.12 The process was analysed and discussed by analogy with the processes of electro~rystallization.~~ Further investigations of nucleation and phase formation in this system have been carried out by potentiostatic pulse experiments.The results will be presented and discussed in this paper. 2. MODELS OF ADSORPTION Due to the complicated kinetic behaviour of the system Au( 11 l)/Bi3+ experiments and their interpretation must be based on models of adsorption layers structural changes and desorption mechanisms. On single crystal planes three models of layers may be distinguished :these are shown in fig. 1 (a)for the adsorption of Bi on the (I I 1)-plane of gold (i) The dense monolayer of a hexagonal structure. Since the ratio of radii rBi/rAu,exceeds unity the monolayer is non-epitactic and the adsorbed atoms differ in C B FIG.1 .-Models of adsorption layers on the (1 1 1)-plane of f.c c.-metals and desorption paths.A = hexagonal monolayer; B = p(d? x d%-structure B’ = hexagonal rings C = adatom; S = ion in solution; d = diffusion parallel to the surface; t = charge transfer to the solution. their position relative to the substrate e.g. in fig. l(a) two of three atoms are in a surface trough but the third is in a top position. (ii) At lower coverages epitactic ordered structures may exist which are well known from LEED experiments in the gas phase. Fig. 1(a)shows the p(d3 x 61-structure (B) and an array of hexagonal rings (S’)as examples of possible structures. KINETIC INVESTIGATIONS OF STRUCTURAL CHANGES (iii) In contrast to models with definite structures a statistical adsorption accord- ing to the Langmuir or Frumkin model is possible.In the case of weak attraction (Frumkin constant a <4) it may be applied up to 8 = 1. If a > 4 on the other hand a random layer exists at low coverages only but at higher coverages layers of A or B are formed by two-dimensional condensation. Regarding the desorption mechanism processes parallel and normal to the surface must be distinguished [fig. l(b)]. This discussion is similar to common theories of electrocrystallization. The charge transfer t consists of a movement of adsorbed bismuth ions (A B C)normal to the surface into the solution (S). The rate of this process increases with increasing potential e.If lateral attraction is absent ions can desorb from all positions. In the case of strong lateral attraction however the re- moval of ions will take place only from the less-covered parts of the surface (C) or from the edge of compact layers (A or B). The surface diffusion d has no influence on the adsorption/desorption kinetics in the case of Langmuir adsorption but it becomes important for phase formation. The process d parallel to the surface begins with the removal of an atom from the kink site or the edge of the two-dimensional lattice. Then the atom can diffuse along the edge of an island to the free surface or to the lattice position in another structure. The movement of the atom parallel to the surface is approximately independent of potential.According to this argument the total process of desorption will follow one of three types of reaction paths (I) The direct path A B C& S all over the surface which corresponds to common adsorption models. (IT) The direct path A B 1,S at the edge of homogeneous islands of structure A or B. This path is equivalent to the direct charge transfer kink site edge &S in electrocrystallization. (111) The indirect path A B dLB C S corresponding to the Stranski d d model of crystallization kink site +edge __t ad-atom s01ution.l~ To investigate the mechanism of desorption potentiostatic transients i(t) were recorded and analysed in dependence on t and Q,respectively. The shape of the transient depends on the desorption mechanism and the rate determining step.The rate equations for suitable models are summarized in table 1. In the case of the Langmuir model the desorption current density is proportional to the number of adsorbed atoms and decreases exponentially with time. If the desorption follows path (11) i is proportional to the length I of the edge which increases with time. The i(t)-transients for the case of progressive and instantaneous nucleation were calculated by Bewick Fleischmann and Thirsk.I5 For a desorption according to path (111) either the transition of the atoms from the edge to the free surface (d) or the following transfer to the solution (t) can be rate determining. In the first case the rate is given by the length of the edge and the models described above can be applied.In the latter case the desorption rate is proportional to the free surface13 and increases exponenti- ally with time. The analysis of experimental i(t)-transients will be based on the de- rivatives and characteristic data given in table 1. These models are derived for ideal layers. In practice however inhomogeneities of the surface and of real phases may limit their validity. Further complications may arise from changes in the electro- sorption valency 7 i.e. the discharge of adsorbed ion^.^.'^ WALTER SCHULTZE AND DIRK DICKERTMANN TABLE1 .-PREDICTIONS FOR THE POTENTIOSTATIC TRANSIENTS OF METAL ION DESORPTION ACCORDING TO VARIOUS MODELS. instantaneous progressive desorption from Langmuir nucleat ion nucleation the free surface 1 -Had i-I i-I i-A ..i = 2aiQmont. i y-3apQmontZ I = 1AAo exp( -Qmon exp (-ail2) exp (-at3) exp (")Qmon a) definitions il = i(B = 1) ai= mVoi12/Qmon2ap = ITN'~~~/~Q~~~~A = fractionoffree Qmon= charge on a monolayer iL= current cm-' of the edge N' y-nucleation rate surface at t = 0 iA= current cm-2 No= number of of free surface nuclei 3. EXPERIMENTAL The single crystals were prepared as already described.17 For the experiments in this paper only the (1 ll)-plane was used. The misorientation of the electropolished faces was <lo. Thus the concentration of steps is <2%. 1 mol dm-3 HC104 was used as support- ing electrolyte prepared from 70% perchloric acid (Merck Suprapur) and water which was boiled with KMn04 and distilled twice in a nitrogen stream.mol Bi203then were dis- solved in 1 dm3 of electrolyte. The experiments were carried out in an electrochemical cell specially designed so that only the oriented face of the electrode was in contact with the electrolyte.18 Oxygen was excluded by bubbling nitrogen (99.995%) through the electrolyte; during the measurements nitrogen was passed over the surface of the solution. Potentials were measured against a mercury sul- phate electrode but all potentials E = E -cBiin this paper are referred to the reversible ~~ potential &Bi of a bismuth electrode in the same solution (E = 0.23 V against NHE). The potentiostat consisted of an operational amplifier (LF 357) with an additional power booster which could deliver more than 0.3 A to the cell.A differential amplifier was con-nected to a resistance between the output of the potentiostat and the counter electrode. Its output voltage was proportional to the current and could be fed back to compensate the ohmic drop. The charge was measured by electronic integration. Current and charge as a function of the time were recorded with a digital oscilloscope (Nicolet 1090 input unit 92). The resolution in time and the maximum current in the experiments were restricted to t > 0.2 nis and i < 100 mA cm-2 for several reasons. During desorption the Bi3+ con- centration of the electrolyte near the surface rises and causes a diffusion overvoltage. If Bi-ions equivalent to 100 pC are desorbed by a current of 100 mA within 1 ms the over- voltage at the end of the current pulse amounts to 15 mV.At currents of 100 mA the error due to the compensation of the ohmic drop (k0.la)gives rise to an error in potential of +-lo mV. Although a variation in the feedback resistance by 0.1 S2 does not change the shape of the current peak appreciably the peak currents and times can be changed by KINETIC INVESTIGATIONS OF STRUCTURAL CHANGES 30%. Due to the limited output current of the potentiostat and the settling times of the amplifiers measurements are reliable at tiines >0.2 ms after the potential pulse. 4. SYSTEM Au(lll)/Bi3+ The general behaviour of adsorption systems can be seen from potentiodynamic adsorption or desorption spectra7 Fig. 2 shows both spectra of Au(lll)/Bi3+ re- corded with a very slow sweep rate de/dt = 0.2 mV s-l.In the adsorption spectrum two broad peaks appear at 210 and 130 mV respectively. During the anodic sweep B \ ‘?gmuir 0.1 2 3 potenti 1 Er/V FIG.2.-Potentiodynamic adsorption and desorption spectrum of Au( 11 l)/Bi3+. 1 mol dm-3 HC104 cgj3+ = mOl dm-3; E = & -EBi; d&/dt= 0.2 mV S-’. --corresponding Langmuir spectrum for two species A and 9. the corresponding peaks appear at 220 and 160 mV respectively. The asymmetry of the curves indicates a strong irreversibility even at the lowest current densities. For comparison the corresponding desorption spectrum for two adsorbed species obeying a Langmuir isotherm is plotted too (dotted line). The experimental peaks A and 13 have a half width of 20 and 5 mV respectively instead of 30 mV in the case of a Langmuir isotherm.This indicates a strong lateral attraction for species B where the formation of a two-dimensional phase may be discussed as a possibility.12 From p(~)-isotherms at constant coverage,6 the electrosorption valency y = 2.4 was obtained for species B. The deviation from y = 3 which had already been observed on poly- crystalline gold,6 is due to the difference in electronegativity Ax = 0.5 which causes WALTER SCHULTZE AND DIRK DICKERTMANN a polarity in the adsorption bond.19 The y-value of species A is almost 3 but could not be obtained with the same rzliability. The structure of the layers can be derived from the E( Q)-isotherm (fig. 3) which was measured by anodic desorption after potentiostatic prepolarizatisn.At E = 0 the total charge Q is 400 pC cm-2. Using y = 2.4 a surface concentration of 1.04 x lOI5 cm-' is obtained which agrees well with that of the hexagonal monolayer 4 FIG.3.-Adsorption isotherm of Au(l1 l)/Bi3+. Q = desorption charge; 1 mol dm-3 HC104 CBi3f = mol dm-3. [model A in fig. 1(a)],calculated with the radius rsi = 1.66 A. * The charge of species B is 280 ,uC cm-2. Using y = 2.4 a surface concentration of 7.3 x 1014cm-2 is calculated which is similar to 6.96 x 1014 calculated for structure B' in fig. l(a). Thus structures A and B' of fig. l(a) may be suggested as stable layers but the existence of others is also possible e.g. for lower coverages p(d3 x 43) [structure B in fig. l(a)] for which 4.64 x loi4 cm-2 is calculated corresponding to a charge Q = 178 pC cm-2.A random layer C exists at very low coverages (see section 8). 5. PROBLEM OF PHASE FORMATION A strong lateral attraction favours the formation of two-dimensional adsorbate phases. Then the slope of the isotherm dQ/dE should be infinity. Experimentally the slope is <100pC cm-2 mV-l. Following the Frumkin analysis of isotherms the attraction constant a is 3.5 but not 2 4 as necessary for phase formation. It may be no accident that for other adsorption systems a = 3.7 was found but never 4." The common thermodynamic analysis presumes infinite homogeneous layers but two- dimensional phases on single crystal planes are finite ;local inhomogeneities must not be neglected.A first limitation on the size of homogeneous phases arises from the growth mechanism. Nucleation takes place at many sites and growing nuclei will * For rBivalues from 1.5 to 1.82 8 are quoted20*21 depending on the method of determination. I .6 8 was found in LEED experiments.20 KINETIC INVESTIGATIONS OF STRUCTURAL CHANGES come in contact. If the nuclei do not fit one another two-dimensional grain boundar- ies are formed as has been shown by computer simulation.22 Further monoatomic steps with a distance of -100 A may exist even on well prepared gold single crystal planes. For both reasons the diameter of homogeneous phases will not exceed 100 A and the edge energy must be taken into account. Further at steps and grain bound- aries the adsorption enthalpy may change by some kJ mol-' within a distance of some A.These effects are not negligible but may change the slope of the isotherm from dQ/de = infinity to some finite value. 6. TRANSITION A B + S Potentiostatic pulse experiments were carried out in the following manner. A definite layer of B was prepared by potentiostatic prepolarization at ep = 170 mV for 300 s. Then another potential c = 50 mV was switched on and the adsorption current i(t)and the charge Q(t)were recorded on the oscilloscope. During this pro- cess ions from the solution (S) are adsorbed on the layer of B and form the dense layer A B+S+A. Fig. 4(a) shows the adsorption curve. After a short induction period i is almost constant for some seconds. Then i decreases exponentially.The corresponding desorption process can be observed by measurements using E = 60 mV (formation of FIG.4.-Current against time transients for the potentiostatic adsorption and desorption of Bi3 + on Au(ll1). Prepolarization potential E = 170 mV for adsorption (structure B) and 60 mV for de- sorption (structure A). A) and e = 190 mV which is shown in fig. 4(b). The influence of Q on i can be seen from fig. 5. The adsorption curve shows a large plateau and then a linear decrease corresponding to Langmuir behaviour. In the anodic curve two linear regions and a smaller plateau at intermediate charges can be distinguished. The extrapolation of the linear curves to the complete layer A (380 pC cm-2) and the layer €3 (280 ,uC cm-2) respectively yields the anodic currents i and i,' and the cathodic current i- which may be used for the characterization of i as well as the plateau current densities i+*' and i-p'.A change in the pulse potential E i.e. the overvoltage affects the value of the current density but not the shape of the transients. The potential dependence of WALTER SCHULTZE AND DIRK DICKERTMANN 501 350 300 FIG.5.-Adsorption and desorption current as a function of charge Q. Prepolarization potential E = 170 mV for adsorption and 60 mV for desorption respectively. i ,i-,i and i-pl can be seen in the Tafel plot of fig. 6. The cathodic slope is 76 mV while the anodic one is 23 mV at low and 39 mV at higher current densities. The potential dependences of i-p' and i-and of i+P1 i and i+' respectively agree.Hence there is no basic difference between the processes corresponding to these currents. The small exchange current density of about 1 pA cm-2 indicates a very slow ad- sorption/desorption process and explains the low reversibility of peak A in fig. 2. This result which is in agreement with galvanostatic meas~rements,~~ is reasonable for Er/V FIG.6.-Tafel plot of the current densities i+,l LP1,it. and i-for the reaction A +B + S. Prepolarization potential 8 = 170 mV for cathodic values and 60 mV for anodic values respectively. KINETIC INVESTIGATIONS OF STRUCTURAL CHANGES desorption since the atoms of A are strongly bound by lateral attractions similar to an atom in a smooth metal surface. The adsorption of Bi3+ in a hole on the other hand may be hindered due to the necessary desorption of water or rearrangement of neighbouring Bi-atoms.According to fig. 5 adsorption and desorption do not follow a single reaction scheme. The Langmuir model for example can explain only the second part of the adsorption line but the current in the first horizontal part is much smaller than the extrapolated Langmuir current (dotted line). Therefore nucleation phenomena may influence the growth of layer A. The comparison with the equations in table 1 shows however that none of the models can be applied since di/dQ = 0. This result could be explained only by a one-dimensional growth of nuclei e.g. from a step of the substrate surface perpendicular to the step. The desorption curve is not the same as the reversed cathodic curve; indeed it looks even more complicated.The plateau is much smaller than in the cathodic case and does not extend to Q = 280pC cm-2 as could be expected from the cathodic curve. The two different linear parts of the desorption curve and the corresponding currents i and i+’ indicate two different layer states. Distinct from the cathodic process the anodic process can take place in two differ- ent ways. Either B is left on the surface during the desorption of Bi3+ or all ions of layer A are desorbed at first and layer B is formed by a subsequent cathodic deposi- tion. Since the i(Q)-transients and their potential dependence on both reaction paths should be similar they cannot be distinguished here.7. TRANSITlON B-S The desorption of layer B was investigated by anodic potentiostatic pulse measure- ments for various values of E and E. The desorption charge Q was almost independ- ent of E in the range from 170 to 200 mV but the state of layer B i.e. the degree of homogeneity and the number of imperfections may change. Fig. 7 shows some i(t)-transients and the correspondent i(Q) plot. The most striking feature of the i(t)-transients is the bell shape which indicates a phase transition. The experimental slope (di/dQ),= M s-l is neither negative as predicted by the Langmuir model nor infinity as predicted by the models of instantaneous or pro- gressive nucleation but it fits reasonably the model of desorption from the free surface FIG.7.-Current against time and current against charge transients for the potentiostatic desorption of Bi3 (structure B) for different prepolarization potentials 8,.+ WALTER SCHULTZE AND DIRK DICKERTMANN which was also used for the explanation of the galvanostatic tran~ients.'~.'~ This means that the desorption of B starts at local inhomogeneities and then proceeds by diffusion of atoms of B to the free surface (layer C) where they are desorbed by a rate determining transfer process. Using (di/dQ),= = iA/Qm, = lo3 s-l and Qmon= 280 pC cmV2,iA= 280 mA cm-2 is obtained. For t = 0 the current should be i = iAAO. From fig. 7(a) i = 10 mA cm-2 is obtained. Hence A. is z3% which is a reasonable value for the fraction of the free surface at t = 0. If the removal of atoms from their lattice position is slow and the transfer process fast a potential-independent limiting current should be observed.Experimentally the peak current ipkdepends strongly on E as can be seen from fig. 8. The Tafel line 220 240 260 280 300 E,/ mV FIG.8.-Tafel plot of the peak currents ipkof the potentiostatic transients as shown in fig.7. cP = 190 mV. with a b-factor of m20 to 25 mV and an exchange current density of 1 mA cm-2 d indicates a rate-determining transfer process. Since the observed process B __t C S is the fastest desorption process it must be concluded that the direct transfer B S is too slow (io < 1 mA cm'2) due to the strong lateral attraction. It should be mentioned however that the model presented does not fit all experi- mental results.For example the model is applicable for small desorption charges only otherwise the peak would be on the left side of fig. 7(b)but not in the mean range. This failure of the model may be due to the decreasing transfer overvoltage. Since the equilibrium potential of the layer increases by some mV the transfer over- voltage decreases under potentiostatic conditions. This decrease is enlarged by the overvoltage of the diffusion in solution which increases with desorption charge Q. For other models the fit of experiments is worse. No models explain the influence d of E on the slope of the i( Q) curves. Hence the proposed mechanism B -C & S gives the best explanation of the experimental transients despite some inadequacies.KINETIC INVESTIGATIONS OF STRUCTURAL CHANGES 8. TRANSITION C +S AND B -tC +S In the adsorption isotherm c(Q) a steep increase is observed at E > 220 mV. The stability of phase B which was discussed before is limited to lower potentials and charges Q > 80 ,uC cm-2. At E z 220 mV layer C becomes stable. The total coverage is so small that a random layer is most probable. The desorption of this species extends over a larger potential range up to 350 mV so that it cannot be clearly distinguished in the potentiodynamic spectrum fig. 2. In the following desorption 1 I c-s t /ms FIG.9.-Current against time transients for potentiostatic desorption of Bi3+adsorbed on Au(ll1) (structure B + C). Desorption-potentialE = 0.26 V. experiments at E = 260 mV about half of species C is measured by Q,.Fig. 9 shows the i(t)-transients for E = 260 mV and various values of E, which determine the coverage of C and B respectively. In the desorption curves two species can clearly be separated. At first the current must be due to species C but the peak appearing after 2 ms is the same as in fig. 7 and due to the desorption of B. For E 2 222 mV only species C can be seen but not B. Kinetic interpretations of the very rapid transition C fL S must be confined to t > 200 ,us and i < 100 mA cm-2 due to the limitation of electronic equipment. Therefore only the rapid decrease in i with decreasing coverage of C can be confirmed. Further the current density increases strongly with potential. This means that a charge transfer process is rate-determining.Figs. 9 and 10 show clearly that Q increases with decreasing QB. That means that the surface is occupied by B or C alternatively. Fig. 11 shows the linear relation between QBand Qc quantitatively. This behaviour is characteristic of the existence of two different phases. At low coverages only the random layer C exists but with increasing coverage Q > 80,uCcmW2, two-dimensional condensation occurs due to the strong lateral attraction. As pointed out in section 5 phase B is not ideal. Hence the statement of a finite slope dE/dQ in fig. 3 and 10 is not in contradiction to the two- phase model. The kinetic separation of the species B and C is possible only in the case of a fast charge transfer and a slow diffusion process.This is not consistent with the model of fast diffusion and slow charge transfer discussed in section 7. There-fore the layer state or desorption mechanism in the experiments of fig. 9 must differ from those of fig. 7. For example the mean diameter of homogeneous areas of B may increase at low coverages if steps are absent. Then the diffusion length in- creases and the diffusion is no longer fast enough. During desorption of B the WALTER SCHULTZE AND DIRK DICKERTMANN \ FIG.10.-Charge on 0structure B (QB)and x structure C (Q,) as a function of the potential E,. -0 1 10 FIG.11 .-Charge on structure C (&) as a function of that of structure B (QB)for Bi3 on Au(ll1). + KlNETIC INVESTIGATIONS OF STRUCTURAL CHANGES model of section 7 may be applicable only in the vicinity of B but not for the whole surface.9. TRANSITION A -+B + S -+ S In section 6 the desorption of structure A was discussed for low potentials only i.e. for conditions where B or B' is left on the surface. If desorption experiments are carried out at E > 230 mV phase B will be also desorbed. Fig. 12shows such a transi- ent. At first the current decreases to i < 1 mA cm-2. After a period of ~0.1 s a broad desorption peak appears. Comparison with the anodic Tafel line in fig. 5 -. ! FIG.12.-Current against time transient for the potentiostatic desorption of structure A (prepolariza-tion potential E = 60 mV; desorption potential E = 260 mV) for Bi3+ on Au(l11). The thin curves are estimated from kinetic data of structure A and B.I + 1. I 0 0.1 0.2 Ep /v FIG.13.-Logarithmic plot of the peak currents iPkof Bi-layers adsorbed on Au( 111) as a function of the prepolarization potential 8,. Desorption potential E as parameter equals + 280 mV; 0,270 mV; x 260 mV. WALTER SCHULTZE AND DIRK DICKERTMANN shows that the small desorption current fits into this current against potential curve for 260 mV i.e. the first desorption current seems to be due to the SIOW reaction A -B + S. Consequently an assumed i(t)-transient for this reaction was plotted in fig. 12. Then the following peak should be due to the reaction €3 -& S as dis-cussed in sections 7 and 8. In fact the i(t)-transient seems to be very similar to that in fig.7 the current density however is much smaller (1 instead of 100 mA Hence this explanation is insufficient because of quantitative discrepancies. An-other explanation may be based on the direct path A&S taking place at the edge of homogeneous islands. In this case the desorption current should be smaller than for B due to the stronger attraction forces. The potential dependence could be ex-plained by the rate-determining charge transfer process. The peak of the i(t)- transient should be due to an increasing edge length of the islands. On the other hand the first decrease in i at very short times would then have to be explained by inhomogeneities in layer A which is not very probable. -____-0 7-I -2 I /A-BB-S (10 9260mV) \ 400 300 ‘200 100 Q/pC cm-2 FIG.14.-Logarithmic plot of current i as function of charge Q for potentiostatic desorption of dif-ferent layers of Bi adsorbed on Au(l11).ICI N E TI C I N V E S TI GA TI ON S OF S TRU C T U R A L C H AN GE S 10. CONCLUSIONS For the system Au(l1 l)/Bi3+ various desorption processes could be distinguished. At constant desorption potential the peak current density depends strongly on the prepolarization potential. Fig. 13 shows log ipkas a function of E,. The desorption current increases in the order A < B < C,i.e. with increasing distance of next neigh- bours. This fact shows the importance of lateral attractions. The unusual behaviour of metallic layers can be seen also from fig. 14 which shows log i as a function of the desorption charge Q for various transients.It can be seen that the initial layer con- dition i.e. the structure A B and C respectively has a much stronger influence than the value of Q. Again this is due to the lateral attractions. These cause the phase formation of structure B which can be proved by the bell shaped i(t)-transients of desorption and the kinetic separation of two species B and C. Charge transfer processes are rate-determining in general. Limiting currents independent of potential which are expected for a rate-determining removal of ad- sorbed atoms from their lattice position parallel to the surface were not observed. Surface diffusion from islands to the free surface is involved in the desorption of structure B but for structure A desorption takes place by direct charge transfer at the edge of islands.Electrocrystallization models seem to be useful as a first approxi- mation but they cannot describe all the details of desorption since the variety of adsorbed states is greater than for pure metals. The support of this work by the Deutsche Forschungsgemeiiischaft is gratefully ackno wledgeci. K. J. Vetter Electrochemical Kinetics (Academic Press New York 1967) p. 282. ’E. Budewski W. Bostanoff T. Witanoff Z. Stoinoff A. Kotzewa and R.Kaischew Electro-chim. Acta 1966 11 1697. H. R. Thirsk and J. A. Harrison A Guide to the Study of Electrode Kinetics (Academic Press London 1972) p. 115. H. Gerischer D. M. Kolb and M. Przasnyski Surface Sci. 1974,43 662. ’J. W. Schultze Bev.Bunsenges. phys. Chem. 1970 74 705. J. W. Schultze and K. J. Vetter J. Electroanalyt. Chem. 1973 44 63. J. W. Schultze and D. Dickertmann Surface Sci. 1976 54 489. W. J. Lorenz H. D. Herrmann N. Wuthrich and F. Hilbert J. Electrochem. Suc. 1974 121 474. A. Bewick and B. Thomas J. Electroanalyt. Chem. 1975,65,911. loA. Bewick and B. Thomas J. Electroanalyt. Chem. 1976 70 239. l1 K. Juttner G. Staikov W. J. Lorenz and E. Schmidt J. Electroarralyt. Chem. 1977,80,67. l2 D. Dickertmann and J. W. Schultze Electrochim. Acta 1977 22 117. l3 J. W. Schultze and D. Dickertmann paper presented at the ISE-meeting in Varna Sept. 1977. l4 I. N. Stranski 2.phys. Chem. 1928,136,258. l5 A. Bewick M. Fleischmann and H. R. Thirsk Trans. Faraday Soc. 1962,58,2200; M.Fleisch-mann and H. R. Thirsk Advances in Electrochemistry and Electrochemical Engineering ed. P. Delahay (J. Wiley N.Y. 1963) vol. 3 p. 123. l6 R. Adzic E. Yeager and B. D. Cahan J. Electrochem. Soc. 1974,121,474. l7 D. Dickertmann J. W. Schultze and K. J. Vetter J. Electroarralyt. Chenz. 1974 55 429. l8 D. Dickertmann F. D. Koppitz and J. W. Schultze Electrochim. Acta 1976,21 967. l9 J. W. Schultze and F. D. Koppitz Electrochim. Acta 1976 21 327. 2o A. Sepulveda and G. E. Rhead Surface Sci. 1975 49 669. 21 Gmelin Handbuch der Aizorg. Chemie (Verlag Chemie Weinheim Bergstrape 1964) vol. 19 (Erganzungsbd.) p. 299. 22 G. Ertl and J. Kuppers Surface Sci. 1970 21 61.

ISSN:0301-5696    

DOI:10.1039/FS9771200036

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

RHEED Investigations of Copper Deposition on Gold in the Underpotential Region HEINZ GERISCHER BY HANS0.BECKMANN DIETERM. KOLB*AND GUNTER LEHMPFUHL Fritz-Haber-Institut der Max-Planck-Gesellschaft Faradayweg 4-6 1 Berlin 33 W. Germany Received 31st August 1977 The underpotential deposition of a Cu monolayer on single crystal gold electrodes of (111) and (100) orientation is investigated by cyclic voltammetry and after removal of the electrode from the electrochemical cell and subsequent transfer into a vacuum chamber by reflected high energy elec- tron diffraction (RHEED). It is found that underpotential deposition of about 2/3 of a Cu mono- layer causes a (d3'x 4%R30 superstructure to appear in RHEED. After stripping a faint superstructure of the same type is still visible in the RHEED pattern.Deposition and stripping of bulk Cu also rearranges the Au electrode surface in a characteristic way producing an additional (2 x 2) superstructure. No such structure is seen when the electrode potential is cycled only in the double layer charging region of Au and in the oxygen adsorption region. The observed RHEED patterns are discussed in terms of surface rearrangements during Cu deposition due to the formation of ordered surface and bulk alloys. The underpotential deposition of metals on foreign metal substrates that is to say the deposition of metal atoms from their ions in solution up to a monolayer at elec- trode potentials positive to the respective Nernst potential is often the initial step in metal deposition reactions.This monolayer formation not only represents an in- teresting case of chemisorption on metal surfaces but is also very important for the further growth of the deposit. Numerous electrochemical experiments have been performed in recent years to study adsorption isotherms adsorption-desorption kinetics and relative binding energies. More recently measurements on single crystal surfaces have revealed more detail in the adsorption i~otherms,~-~ which thus allow some conclusions to be drawn on the structure of the adsorbate layer and its depend- ence on the electrode surface struct~re.~?~ However none of these in-situ electro-chemical experiments give a direct insight at a molecular level such as the electronic properties of the adsorbate and its geometric arrangement.This information seems only to be accessible by photoemission and electron scattering experiments such as UPS XPS Auger LEED and RHEED. The severe drawback of these highly surface- sensitive methods for electrochemical systems is their need for a vacuum which means that the electrode surfaces cannot be looked at under real electrochemical operating conditions. On the other hand underpotentially formed metal monolayers are certainly among the most promising systems to be studied under vacuum conditions because their strong bonding to the substrate guarantees that the character of the adsorbate is not changed significantly by removal from the electrochemical environ- ment. First experimental results with XPS on the electronic structure of under- potential deposits seem to support this view.6* Up to now however the metal * To whom correspondence should be addressed.RHEED INVESTIGATIONS OF COPPER DEPOSITION ON GOLD adsorbates have not been investigated by structure sensitive methods like LEED or RHEED which also allow one to test the quality of single crystal surfaces used in electrochemical experiments and its influence on adsorbtion behaviour.8 One of the open problems in underpotential deposition of metal monolayers which still has to be solved is the question of whether or not the adsorbate forms regular arrays at certain coverages. To answer this question the adsorbate covered electrode has to be transferred from the electrochemical cell into a high vacuum chamber and investigated by electron scattering techniques.Although LEED seemed to be the obvious choice we considered RHEED as more promising for the following reason. Since LEED requires an ultra-high vacuum system the experimental efforts would be substantially higher than with RHEED which can be performed at Torr. For LEED the cleaning of the electrode surface plays a crucial role and usually no LEED pattern is observed before the surface is ion-bombarded or heated. Such a treatment however would inevitably destroy the monolayer. No such problems are usually encountered with RHEED because of the much higher electron energy used while this technique is still highly surface sensitive by virtue of working at grazing angles of incidence. EXPERIMENTAL Gold single crystal discs were cut by spark erosion from melt-grown single crystal rods after orientation by Laue back scattering.The discs of -2 mm thickness and 10 mm in diameter with (111) or (100) surfaces were mechanically polished with abrasives of succes- sively finer grades electrochemically polished in a cyanide bath9 for 10-50 min at current densities up to 2 A cm-2 and annealed at 850 "Cfor 4 11in ahelium atmosphere. The quality of the single crystal surface was finally tested by RHEED. The electrochemical experiments were performed in a standard type electrochemical cell with separated compartments for the calomel reference and the Pt counter electrode. For measurements with single crystal electrodes the dipping technique described by Schultze et aL4 was used.The crystals were glued with conducting silver paste onto a special holder which also fitted into the RHEED apparatus. The electrode holder was lowered until the electrode dipped into the electrolyte and then partially withdrawn so that the electrode was above the electrolyte level with only the desired single crystal surface in contact with the electrolyte because of surface tension. The base electrolyte was either 0.5 mol dm-3 HzS04 or 1 mol dm-3 HC104 and Cu2+-ions were added from or 1 mol dm-3 stock solutions of CuS04. All chemicals were of p.a. grade and dissolved in triply distilled water. All potentials are quoted against the saturated calomel electrode (SCE). Reflected electron diffraction experiments'O were conducted in a conventional diffraction camera under ordinary high vacuum conditions of Torr.The crystal was mounted on a special specimen stagell allowing arotation of 360"about an axis perpendicular to the crystal surface and a second rotation of -& 12" about an axis in the crystal surface to tilt the crystal with respect to the direction of the incident electron beam. In order to reduce contamination effects the specimen was surrounded by an anticontamination shield which was cooled down to liquid nitrogen temperature. The diameter of the electron beam was w 70pm at the speci- men. Under these conditions the crystal area contributing to the diffraction pattern was at grazing incidence conditions (angle between crystal surface and incident electron beam in the order of 2") x 70 x 2000 pm.The diffraction pattern was recorded photographically. RESULTS Fig. 1 shows cyclic current potential curves for Au(l11) and Au(100) electrodes in 1 mol dm-3 HClO, containing 5 x low4mol dm-3 CuSO,. The crystallographic orientation of the electrode surfaces and their quality have been tested by RHEED H. 0. BECKMANN H. GERISCHER D. M. KOLB AND G. LEHMPFUHL 53 after surface preparation. In the potential region between 0.0 and 0.6 V the Cu mono- layer is formed or stripped depending on the direction of the potential scan while beyond +1.O V oxygen adsorption on gold takes place the adsorbate being reduced again on the cathodic scan around +0.95 V. With a few minor exceptions these curves resemble closely those reported by Schultze et L~Z.,~ demonstrating the marked influence of the substrate structure on oxygen adsorption and the metal deposition re- action.Tn fig. 2 the potential scale for the Cu monolayer adsorption and desorption 100 l~ I -80 -60 ht -& 40 a 3 + 20 -0 0.5 1 .o 1.5 USCE /v FIG. 1.-Cyclic current-potential curves for Au(l11) (-) and Au(100) (--) in 1 in01 dmP3 HC104+ 5 x mol dm-3 CuS04. Scan rate = 10 mV s-'. has been expanded to reveal more clearly the details in the adsorption/desorption isotherms. Moreover a lower scan rate had been chosen. From the result shown in fig. 2 it is noted that the current against potential curves for adsorption and desorption of Cu on Au(100) indicate a slow but rather reversible process while deposition and stripping of the Cu monolayer on Au(ll1) clearly occurs at somewhat different peak potentials suggesting some type of phase transition.It is interesting to note by com- parison of fig. 1 and 2 that the adsorption peak for Cu on Au(100) is split into two when increasing the scan rate from 1mV s-l to 10 or even 5 mV s-l. Further increase of the scan rate shifts the second peak still more cathodic while the first one remains unaffected at least up to a sweep speed of 100 mV s-l. The charge connected with the various desorption peaks is in good agreement with data reported by Schultze et aL4 The charge for a complete monolayer was found to be 360 ,uC cm-2 for Cu on Au(100) and 440 ,uC cm-2 for Cu on Au(ll1). Both num- bers agree very nicely with those for a (1 x 1) structure on Au and sustain the assump- tion of an epitaxial monolayer.The charges corresponding to the four peaks in the RHEED INVESTIGATIONS OF COPPER DEPOSITION ON GOLD desorption spectrum of Cu on Au(ll1) are 50,220 and 170 pC cmV2 for peak No. 1 2 and 3 and 4together respectively (fig. 2). This means that at a desorption poten- tial close to peak No. 3 the surface is covered roughly by 2/3 of a monolayer. It is also found that the half width of the most cathodic desorption peak for Cu on Au( 1 1 1) (peak No. 4 in fig. 2) is markedly dependent on the scan rate increasing from S112= 8 6 4 e4 '2 5 4 3 Go -2 -2 -6 0 0.2 0.4'' 0.6 0.8 'SCE FIG.2.-Cyclic current-potential curves for Au(l11) (-) and Au(100) (--) in 1 mol dm-3 HC104+ 5 x mol dm-3 CuS04.Scanrate = 1 mV s-l. The desorption peaks for Cu on Au( 11 1) are numbered. 10 mV at 1 mV s-l to close to 100 mV at 200 mV s-l whereas the more anodic de- sorption peak (No. 2 in fig. 2) has a half width NN 30-40 mV nearly independent of the scan rate (fig. 3). Although in the beginning the main effort of this work was focused on the study of the bare Au surface before and after Cu deposition to look for " finger prints " which the deposit had left on the surface we also tried to investigate adsorbate covered surfaces. Therefore before transferring the electrode from the electro- chemical cell into the vacuum chamber several experiments were performed to find out how much of a deposited layer would remain on the surface during the transfer process.The electrode was dipped into a cell with a Cu2+ containing electrolyte the potential held at a value close to E (~0.0 V against SCE) to allow monolayer deposition then the electrode was removed from the cell with potentiostatic control operating. The electrode was rinsed carefully with deaerated triply distilled FIG.4.-RHEED pattern from a clean Au(ll1) surface for the [211] azimuth (60 keV). The indices of the reflections for this azimuth are shown in fig. 5(6). [Toface page 55 H. 0. BECKMANN H. GERISCHER D. M. KOLB AND G. LEHMPFUHL 55 water dried in a N2stream and dipped into a copper-free solution in a second electro- chemical cell at the very same potential.The subsequently recorded stripping curve revealed that at least half of a monolayer had still been present on the surface. We assume that diffusion of Cu into Au is one of the main reasons for the observed loss. Similar experiments with Cu and Ag on Pt showed that under carefully chosen con- ditions nearly a complete monolayer could be transferred from one cell to the other. A small cathodic current was observed in all cases when the electrodes were dipped into the second cell at the deposition potential indicating that a minor fraction of the adsorbate had been oxidized during the transfer. > E \ N 50 I '0 25 1 1 10 100 1000 scan rate / mV s-1 FIG.3.-Half width &12 of the desorption peaks in the current-potential curves for Cu on Au(111) peak No.2; (-0-0-0-)peak No. 4. as a function of scan rate. (-O-O-O-) The RHEED experiments were performed mainly with Au(1 1 1) surfaces which were prepared as described in the experimental section. Kikuchi lines in the diffrac- tion patterns showed the good single crystallinity of the electrodes.10 A reflection diffraction pattern in the [?ill] azimuth with Bragg reflections and Kikuchi lines is shown in fig. 4 for a clean (1 11) surface of an electropolished and annealed crystal. The Bragg reflections are elongated into streaks perpendicular to the shadow edge [see also fig. 5(6)]indicating a smooth crystal surface. Due to the mean inner poten- tial of the crystal the streaks are shifted towards the shadow edge.The sharp spots in fig. 4 are produced by electrons which passed through steps on the surface. The same diffraction pattern was observed after dipping the electrode into the electro- chemical cell containing the metal ion free base electrolyte and cycling the electrode potential in the double layer region. Even when the potential was driven a few times into the oxygen adsorption region the diffraction pattern did not change. The same was true for an Au(1 11) electrode in Cu2+ ion containing electrolyte provided that Cu deposition was carefully avoided during the potential cycling. Subsequently the potential was scanned into the region where the Cu monolayer is formed carefully avoiding the bulk Cu deposition and after reversal of the potential scan at various points the electrode was removed from the cell while the potential RHEED INVESTIGATIONS OF COPPER DEPOSITION ON GOLD was held in the double layer region at -+0.9 V.When the scan had been reversed after about half monolayer coverage a faint superstructure was seen. The same superstructure became more pronounced when the electrode was removed from the cell just at the potential corresponding to 2/3 of a monolayer (at No. 3 in fig. 2). This diffraction pattern is shown in fig. 5. The horizontal distance between the super- structure streaks is 1/3 of the distance between 000 and 022 as indicated in fig. 5(b). These additional streaks correspond to a (43 x 4%R30 superstructure arising from a 1/3 or 2/3 coverage at the ~urface.~ The fact that the superstructure is visible even after stripping the Cu adsorbate indicates that the deposited Cu leaves a rearranged surface.The superstructure always disappears during the observation with an in- tense electron beam obviously because of local annealing by the beam. Reversal of the potential after completion of the monolayer caused the same superstructure described above to appear regardless of whether the surface is bare of Cu or still covered with the full Cu monolayer. When the potential was cycled into the bulk Cu deposition region to record the usual current against potential curves for bulk and monolayer formation of Cu a drastic effect was observed on the Au(ll1) surface after removal from the electrolyte at a potential positive enough to guarantee a Cu free surface.Besides the (djx 4% R30 superstructure a (2 x 2) structure and sometimes a more complicated not yet identified superstructure was observed together with a Debye-Scherrer ring pattern. This is shown in fig. 6. (The superstructures after bulk Cu deposition were visible with and without a Cu monolayer on the surface. However since their contrast was better with the Cu monolayer we show these diffraction patterns.) It may be interesting to note that the superstructures could be changed but not removed by electropolishing which only made the Debye-Scherrer rings disappear. Annealing removed the superstructures and restored the initial state of the surface. DISCUSSION The RHEED iiivestigations have shown that the deposition of Cu onto Au(ll1) re- arranges the gold surface even in the underpotential region.The adsorbate covered substrate shows a (d3x 16)R30 superstructure when 2/3 of a monolayer is de- posited underpotentially. A possible model explaining such a superstructure is shown in fig. 7. The electrochemically determined coverage 9 = 2/3 allows us to de-cide which atoms are Cu atoms in this geometric arrangement (fig. 7). This seems to be the first direct evidence for the occurrence of ordered arrays in electrolytically formed metal deposits. Surprisingly the superstructure is also seen although it is very weak when the adsorbate is stripped and the bare Au surface is investigated by RHEED. This means that the adsorption process rearranges the Au surface e.g. by place exchange between CLKand Au leaving a finger print of the adsorbate geo- metry at.the surface after removal. This also explains the high kinetic barrier often found for underpotential deposition which would not be understandable if a mere adsorption process took place. The fact that an Au(ll1) surface either covered with one monolayer of Cu or after stripping still shows the 1/3 streaks in the RHEED pattern rather than a (I x 1) structure is more difficult to explain. Obviously completing the monolayer after deposition of the 2/3 coverage is just a filling up of vacant surface sites without further rearrangement. However it is not yet clear whether this is only observed after at least some potential cycling into the bulk deposition regime which definitively re- arranges the Au surface.Further experiments are necessary to substantiate this find-ing. suDer structure (444 1462 1 -d -a shadow edge ii3 111 131 e022 0 e022 000 lbl FIG. S(a).-RHEED pattern with superstructure streaks from a Au(ll1) surface covered with approximately2/3 of a Cu monolayer. [21I] azimuth. (b) Indices of the Bragg reflections for the [Zl I] azimuth. Streaks due to a (djx dgR30 superstructure are indicated. [Toface page 56 FIG.6.-RHEED patterns from a Au(ll1) surface covered with a Cu monolayer after repetitive bulk Cu deposition and stripping. Besides the clear (43x 2/3R30 superstructure as shown in fig. 6(a), Debye-Scherrer rings are visible. Fig. 6(6) shows a (2 x 2) superstructure. [Tofuce page 57 H.0. BECKMANN H. GERISCHER D. M. KOLB AND G. LEHMPFUHL 57 FIG.7.-Model of the Au(ll1) surface leading to a (45x 47)R 30 superstructurein the diffraction pattern. The surface layer is composed of two different kinds of atoms. The experimental results also show that deposition of bulk Cu at potentials nega- tive of E and subsequent stripping rearranges the surface strongly. The bare Au( 11 1) surface after such a treatment shows an additional (2 x 2) superstructure which could be assigned to the formation of ordered domains of an Au,Cu alloy. Dissolving the Cu from this alloy should leave vacant sites in the surface corresponding to 1/4 of a monolayer coverage. In addition removal of Cu from the alloy causes a breakdown of the gold lattice leading to the formation of small randomly oriented Au crystallites on the surface.From the width of the resulting Debye-Scherrer rings an average size of ~30 to 50A in diameter can be estimated depending on the number of preceding cycles. Since the amount of bulk Cu deposited and stripped during each potential cycle is only of the order of a few monolayers the observed clustering shows that the Au atoms which are left on the surface after decomposition of the alloy are rather mobile. It is an interesting phenomenon that electropolishing could not re- move these superstructures despite a substantial etching while the Au crystallites did dissolve. All the above results indicate that the structure of the initially perfect Au(ll1) surface is altered during the very first potential cycle especially when allowing bulk deposition to occur.The recorded current against potential cycles therefore represent curves from reconstructed surfaces. Such a reconstruction seems also to occur at the Au(100) surface which so far we have found more difficult to prepare well enough for RHEED. CONCLUSION RHEED measurements very conveniently allow one to study the geometric struc- ture of metal adsorbate layers. This can be done either by investigating the bare substrate surface and looking for “ finger prints ” which the adsorbate layer has left or by studying directly the adsorbate covered surface. In the latter case problems arising from the transfer of the electrode from the electrochemical cell into the vacuum chamber have to be overcome.For Cu on Au(ll1) the more anodic of the two pro- nounced peaks in the desorption spectrum can be attributed to the desorption of an ordered array with a (43x dgR30 structure and a coverage of 213 of a monolayer. Stripping the Cu adsorbate obviously leaves a rearranged Au surface which indicates a more complicated deposition process for the monolayer than simple adsorption. RHEED INVESTIGATIONS OF COPPER DEPOSITION ON GOLD Presumably a place exchange occurs which would also explain the high kinetic barrier often found in underpotential deposition. Bulk Cu deposition immediately leads to alloying probably to the formation of Au,Cu and dissolution of Cu leaves a strongly rearranged surface together with small randomly oriented Au crystals.This observa- tion has an interesting consequence for surface preparation since monolayer and bulk metal deposition on gold obviously may be used to "prepare '' various rearranged surfaces. See e.g. D. M. Kolb in Advances of Electrochemistry and Electrochemical Engineering ed. H. Gerischer and Ch. Tobias (Wiley-Interscience New York 1978) vol. 1 I. A. Bewick and B. Thomas J. Electroanalyt. Chem. 1975 65 911. 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. K. Juttner G. Staikov W. J. Lorenz and E. Schmidt J. Electroanalyt. Chem. 1977 SO 67. J. S. Hammond and N. Winograd J. Electroanalyt. Chem. 1977,80 123. J. S. Hammond and N. Winograd J.Elecfrochem. SOC.,1977,124,826. W. E. O'Grady M. Y. C. Woo P. L. Hagans and E. Yeager J. Vacuum Sci. Technol. 1977 14 365. W J. McG. Tegart The Electrolytic and Chemical Polishiizg of Metals in Industry and Research (Pergamon New York 1959). lo H Raether in Handbuch der Physik (Springer Berlin 1957) vol. 32 p. 443. R.Didszuhn 2.angew. Phys. 1970 30 226.

ISSN:0301-5696    

DOI:10.1039/FS9771200051

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Simulation of 2D Nucleation and Crystal Growth BY GEORGE H. GILMER Bell Laboratories Murray Hill New Jersey 07974 U.S.A. Received 1st September 1977 The kinetic Ising model of a crystal-fluid interface is investigated by the Monte Carlo method. The growth rate transient is calculated in the case of a perfect crystal and good agreement with experi- mental data is obtained for the first time. The steady-state growth rates are compared with values calculated using nucleation theory. Large growth rates at high temperatures are related to the small step free energies. The effect of surface mobility is considered. The growth rates obtained for low-index faces of the simple cubic (s.c.) and face centred cubic (f.c.c.) lattice correlate well with the a-factors for these faces.Computer models have been applied to crystal growth and dissolution processes for a number of years. Complex situations that proved difficult to treat analytically could often be modelled by numerical techniques. Early applications included the dynamics of ledge formation by a one-dimensional array of parallel steps.l Two-dimensional (2D) arrays were used to represent the complex surface structures that arise from the nucleation and spreading of 2D clusters on a growing crystal.2 Later lattice models were developed that included the atomic processes of con-densation evaporation and migrati~n.~-~ These models include the long range correlations that are basic to such phenomena as nucleation and second order phase transtions. Here a lattice model is applied to the deposition of atoms of a single component onto a low-index face of a crystal.THE MODEL The Ising (or lattice gas) model provides an atomic-scale representation of the growing crystal yet it is simple enough to permit rapid computation. A fixed array of lattice sites is assumed; each site may either be occupied by a single atom or be vacant. Surface configurations are represented by a square array of integers which specifies the numbers of atoms in columns of sites perpendicular to the plane of the interface. Vacancies and overhanging atomic configurations are not permitted; hence this is a restricted version of the Ising model. Crystal growth kinetics are simulated through the exchange of atoms between the crystal and the adjacent fluid.Atoms impinge at randomly selected sites in the square array at a rate k+ = v exp up) where v is the frequency factor is the reci- procal of Boltzmann’s factor multiplied by the absolute temperature and ,u is the chemical potential. The dissolution (or evaporation) of surface atoms occurs at a rate that depends on the coordination k; = v exp (-Pnp) where n is the number of nearest neighbours and q is the energy of the bond between a pair of such neigh- bours. The frequency factor v includes any retardation due to the formation of ac- tivated complexes during the transfer of atoms between the fluid and sites on the crystal surface. Equilibrium is achieved with ,u = -2q/2 where z is the coordination num- ber of the lattice; this assures that impingement and evaporation at a kink site occur SIMULATION OF 2D NUCLEATION AND CRYSTAL GROWTH at equal rates.The simulation proceeds by the generation of a chain of deposition and evaporation events with the calculated frequencies. Surface migration can also be included; an atom on the surface is then allowed the additional option of a move to an adjacent lattice site. The model is capable of exhibiting a large number of differ- ent growth mechanisms since the fundamental nature of its operation affords con- siderable flexibility. However the model does have some important limitations. For example the lattice structure must be chosen apriori; hence this model can not be used to investigate the formation of dislocations or extended lattice defects.However if a lattice containing defects is chosen initially their effect on the kinetics can be measured. INITIAL TRANSIENT Low index faces of perfect crystals are often quite flat and smooth with only iso- lated adatoms and vacancies. This structure is expected at temperatures well below the melting point if the crystal is in equilibrium with the surrounding fluid. If a crystal bounded by low-index surfaces is subjected to a large driving force for crystal- lization rapid changes in the surface structures occur. The adatom concentration rises very quickly to a new level and on a somewhat slower time scale stable clusters of atoms are nucleated. These clusters expand and eventually entire layers are deposited. This process is illustrated in fig. 1.Fig. l(a) shows a typical structure after the deposition of a quarter of a monolayer. Even at this early stage some stable clusters have nucleated in the second layer. Fig. l(b) is a drawing of the same system after several monolayers have been deposited. Holes are present as a result of the incomplete mergers of large clusters at the lower levels and small clusters predominate at the upper levels. Fig. l(c) illustrates the effect of a larger driving force. The rate of nucleation generally increases more rapidly with driving force than does the edge velocity of a stable cluster and this causes the higher cluster density and rougher appearance of this surface. Fig. 2 is a plot of the average growth rates measured on ninety different 60 x 60 sections of S.C.(100) faces. Each section was subjected to a sudden application of the driving force. The open triangles represent the growth rates simulated without surface migration; the temperature and driving force correspond to those of fig. l(c). The open squares represent growth rates obtained in the presence of surface migration where the migration rate to sites of equal coordination is 7.4 times the evaporation rate. At the instant the driving force is applied there is a very large surge that persists only until the new adatom concentration is established. This surge is reflected in the first data point of fig. 2 which appears somewhat higher than anticipated. (The corre- sponding relaxation time is the adatom evaporation rate ki = 4.1 x 10-3k+ whereas the deposition rates are averaged over the interval At between data points; At = 0.34k+ for the upper curve.) The growth rates exhibit damped oscillations around the asymptotic rate R repre-sented by the dashed lines.The thickness of the deposit in monolayers is indicated above the curves. The minima correspond roughly to the points where a layer is complete and only small clusters occupy the next level. The amplitude of the oscillations is a measure of the correlation in the surface heights at different sites in the array. At the beginning the majority of the sites are at the same level but later they are distributed over a range of levels as a result of statistical variations in the nucleation rates at the various locations. Sites in close proximity remain highly corre- GEORGE H.GILMER FIG.1.-Computer drawings of the surfaces of perfect crystals during growth by the Monte Carlo method. (a)was calculated with v = 4/pand Ap = 2/p. (b) illustrates the same crystal at a later stage of growth. In (c) cp = 4/p and Ap = 2.51b. SIMULATION OF 2D NUCLEATION AND CRYSTAL GROWTH lated in height since a cluster which nucleates near one site quickly spreads to the other. But sites that are widely separated in the lateral dimension may eventually have large differences in height7 In this case there should be little variation in the growth rate since the different portions of the surface are experiencing the fast and slow growth at different times. When the transient decays and the growth rate approaches R,the mean squared height deviations between such sites should be large and probably exceed one layer spacing.k‘t 3.15 -. =% =L 0.10 I I I 20 40 60 k‘t FIG.2.-The transient growth rates normalized by the impingement rate multiplied by the layer spacing. The squares represent data calculated with mobile surface atoms and the figures at the left and above apply to this case. The triangles represent growth with immobile atoms and the figures on the right and below apply here. Note that the growth rate scale does not extend to zero in this case. As in fig. 1 p = 4/p Ay = 2.5IP. 0kJk-= 7.4 A k,lk-= 0. Note the larger amplitude and greater persistence of the oscillations in the presence of mobile surface atoms. This is a consequence of the increase in the capture region near the cluster edges.Atonis that impinge within a distance of -3 atomic diameters of the edge of a cluster have a good chance of migrating to the edge and of being cap- tured. The adatom concentration in this region is depleted. The surface heights of different sites remain correlated even after several layers have been deposited since nucleation is suppressed on top of the smaller clusters. Many of the atonis that impinge on top of a cluster migrate to the edge and are captured at the lower level. The nucleation of clusters in the second layer for example generally occurs at a much higher coverage than was observed without surface migration [fig. 1(a)]. Bertocci calculated transients with oscillations of large amplitude using a simulation model in which nucleation is excluded near the edges of cl~isters.~ Surface migration also causes a more rapid increase in the deposition rate at the start of the process The average rate during the deposition of the first monolayer is (0.69 & 0.02)R without migration and (0.81 & 0.02)R with migration.The transients of fig. 2 are consistent with experimental observations. Darbing-haus and Meyer observed large amplitude oscillations in the flux of atoms evaporat- ing from a KCI crystal when an impinging beam was suddenly removed.8 (Evapora-tion or dissolution should display phenomena similar to those observed during growth since the nucleation of negative clusters or holes is necessary for the removal of suc-cessive layers of the crystal.) Surface mobility is expected to be quite large in this GEORGE H.GILMER case. Rather large amplitudes were observed in electrochemical systems although a slightly smaller mobility would be expected because of the dense fluid pha~e.~.~ The data of ref. (9) were obtained with crystals free of screw dislocations; these should be directly comparable with the simulations. The growth rates in fig. 2 approach the asymptotic values quite rapidly. For example the average growth rate during the deposition of the third monolayer is -0.97R without migration and -0.99R with migration. The maxima located at about seven-tenths of a monolayer are greater than the asymptotic rate. This is in agreement with the experimental measurements mentioned above.The more gradual increase derived froin previous model^^*^^ is probably a consequence of the idealized cluster shapes that were assumed. The clusters of fig. 1 have a much longer periphery than the squares or circles of the earlier models. As a result a uniform coverage of the surface with cluster edges is accomplished with fewer clusters and a shorter transi- ent. Finally it should be mentioned that a rough initial crystal surface does not exhibit the oscillatory transient. Later we consider certain crystal faces that have weak bond networks within the surface layer of atoms. These surfaces may have a disordered multi-level structure even while they are in equilibrium with the fluid. In fact faces with strong bond networks may also disorder in this way provided the surface roughening temperature can be exceeded.ll Non-oscillatory transients were com- puted above the roughening point of the S.C.(100) face using a pair approximation of the Ising rnode1.l2 STEADY-STATE GROWTH RATES The growth rates during the transient period can provide valuable information about the basic crystal growth process but these measurements are often not feasible. More commonly available in the literature are growth rates averaged over a large number of layers and measured at different values of the driving force. The functional relation between these two variables can also yield useful information. Computer simulation measurements of the asymptotic rate R are shown in fig. 3.13 The effect of the transient was minimized by depositing ten to twenty layers at each value of Ap and omitting the first two layers from the average.The numbers ad- jacent to the curves are the values of L/kT where L = zy/2 is the binding energy of the crystal. The normalized growth rates R/k+d were calculated without surface migration. The product k+dis the rate of growth that would occur if every impinging atom remained with the growing crystal and therefore R/k+d is also the condensa- tion coefficient and has a maximum value of unity. According to the data of fig. 3 the normalized growth rate increases rapidly with temperature. The absolute rate R should be even more sensitive to temperature since the parameter k+ includes a temperature dependent exponential in most cases.Two different growth mechanisms are evident in fig. 3. The roughening transition occurs at L/kT = 5.0 and only the data with L/kT= 4.5 depict the normal growth pro- cess. This surface is disordered and is distributed over a large number of levels even in equilibrium. Impinging atoms can easily be incorporated at the edges of existing clusters. Only in this case does the growth rate increase linearly with Ap at the origin. At the lower temperatures a coherent surface is present in equilibrium and new layers must be initiated by a nucleation event. The transition from normal growth to nucleation kinetics can be shown to take place over a very small range of ternperat~res.~~ This transition is a manifestation of surface roughening. Crystal growth kinetics at low temperature should be described by the theory of SIMULATION OF 2D NUCLEATION AND CRYSTAL GROWTH growth by the 2D nucleation and spreading of clusters.In every case a number of different nuclei are formed in each layer and the “large-crystal ” model is ~a1id.l~ Then the growth rate is related to the nucleation rate J (per unit area) and the edge velocity u of stable R = d(~J~~/3)~1~. (1) Here 21 is assumed to be independent of the cluster size. The nucleation rate J may be evaluated over most of the range of Ap by means of an atomistic expression,16 since the numbers of atoms in the critical clusters are small at these relatively high driving forces. For simplicity we include only the lowest energy clusters in each size class.We calculate the rate of formation of adatoms dimers trimers etc. from the rate equations governing the addition and removal of 3.4 P -t \ Q 0.2 4/kT FIG.3.-Normalized growth rates of perfect S.C. (100) faces. The dashed lines represent theatomistic nucleation model. single atoms from these clusters. [See ref. (13) for a list of the clusters and their con- centrations in equilibrium.] Since k+ and k; are exactly known for each simulation all parameters necessary for a calculation of J are available. The dashed lines in fig. 3 are the growth rates predicted by eqn (1) with the values of J obtained from the atomistic calculation outlined above,13 and v calculated from an expression derived by Temkin.17 The simulation results are in good agreement with the theory at LIKT = 12 but at the higher temperatures the theory exaggerates the nucleation depression.This theory does not predict a finite slope at the origin at any temperature. Clusters other than the lowest energy configurations are present in significant numbers at the higher temperatures ; apparently these must be included in the nucleation theory. Instead of attempting to enumerate all of the different cluster configurations we take a different approach. The rapid nucleation and growth at high temperature can be qualitatively explained using classical nucleation theory. The nucleation rate is related to the edge free energy of clusters by an expression of the form J = k+(Ap/kT)’i’exp (-4F2/kTAji) (2) GEORGE H. GILMER <001> step free energy 1.2 '" 021 0 1IIII \\\ /R -I '---.-! -.0 0.4 0.8 1.2 1.6 2.0 2.4 2. k7/j FIG.4.-The excess free energy of a (001 > step on a S.C. (100) face calculated by the mean field and pair approximation methods. Onsager's expression for the free energy of the 2D Ising model inter- face is included. where F is the free energy of a segment of the edge equal to an atomic diameter.18 Normal growth kinetics can only occur when the edge free energy of the clusters is zero. The excess free energy associated with an isolated (001) step on a S.C. (100) face can be calculated using the mean field and pair approximations.19 The step excess F is defined as the difference between the free energy of a surface containing a single step and that of a (100) surface.The results are shown in fig. 4 where Fis plotted as a function of the temperature. Both are normalized by the energy of a broken bond j = q/2. For comparison the free energy of a (001) interface between the phases in a 2D Ising model is also displayed.20 The edge free energy is approximately equal to the <OW step free energy kT/ j FIG.S.-The excess free energy of a 45" step. The free energy of the interface in the 2D Ising model at this angle was obtained in ref. (21). 66 SIMULATION OF 2D NUCLEATION AND CRYSTAL GROWTH zero Kelvin value (F -j)over a finite range of low temperatures. The kinetic data of fig. 3 at L/kT = 12 (kT = 0.5j) correspond to the upper limit of this range and here F -0.9j.At intermediate temperatures kink sites and other defects appear in significant quantities and cause a drastic reduction in the free energy. This accounts for the fast simulated rates at small values of the driving force in fig. 3 for LIkT = 9 and L/kT = 6. In the regime where kT >1.2j the calculated edge free energy is small but finite. The more accurate pair approximation yields much smaller free energies than the mean field method. This suggests that higher order approximations may converge to zero above T, in agreement with the kinetic data of fig. 3. A cluster may be bounded by step segments of different orientations; variations in the edge free energy are expected. Fig. 5 illustrates the free energy of a step at a 45" angle to the close-packed (001) direction.The free energy at low temperatures is appreciably higher than that of the (001) step since kink sites are present even at T = 0. However when the edge begins to disorder the difference between the two orientations diminishes and at high temperatures the free energy is essentially isotropic. Again these results indicate that the exact Ising model has a unique roughening temperature where the free energy of any step on the (100) face vanishes. GROWTH RATES OF AN F.C.C. MODEL The sensitivity of growth kinetics to the free energy of steps also implies that differ- ent faces of the same crystal may have very different growth rates. A weak bond net- work connecting atoms in a surface layer implies low free energies of steps formed on this surface.Jackson 22 has suggested that corresponding states of different faces may scale with the dimensionless temperature parameter a =c(L/kT),where 6 is the fraction of the zbulk nearest neighbours that are in the same layer as the atom. Here we apply this criterion to low-index faces of the f.c.c. lattice. The lattice model of the f.c.c. crystal is similar to the S.C. model described above. Only nearest neighbour interactions are included and the transition probabilities are given by the same equations. The solid-on-solid restriction is applied to columns oriented along the (1 10) direction.23 The calculated growth rates are shown in fig. 6. A very large anisotropy is pre- dicted at small values of Ap/kT,where the nucleation rates are most sensitive to the edge free energy.The faces with the larger a factors grow more slowly as expected. The kinetics on the (110) face are typical of a normal growth law. Nucleation of 2D clusters is not necessary on this face since the atoms in a (1 10) layer are in isolated rows which are equivalent to the edges of steps on the (100) face. The growth rates of different faces of the f.c.c. and S.C. lattice are compared in fig. 7.23924 The open circles and triangles are the S.C. (100)growth rates at the indicated values of LlkT. The closed circles are f.c.c. (111) growth rates and the closed triangles are f.c.c. (100) rates both with L/kT = 12. The circles represent faces with a = 6 in both cases and the triangles a = 4. The agreement is very good; the slightly lower growth rates in the case of the two f.c.c.faces is probably a result of the larger bulk coordination and binding energy of that lattice. The logarithmic plot in fig. 7 also helps to delineate the region where the growth rate is determined by a nucleation process. If we assume that v cc Ap then from eqn (1) and (2) we have R = A(Ap/kT)516exp (-4F2/3kTAp) (3) where A is a constant. A plot of the logarithm of R from eqn (3)against (Ap/kT)-' is approximately linear and the slope is roughly equal to -4F2/3(lcT)2. The S.C. data at GEORGE H. GILMER A,u/kT FIG.6.-Crystal growth rates on three faces of an f.c.c. model. The growth rates are normalized by the product of k+ and the lattice constant a. A (Ill) 0(loo) 0(1 10). L/kT = 20. L/kT = 6 in fig.7 are approximately linear for kT'/A,u > 2 and the slope in this region affords an estimate of F. A value of F is chosen such that the slope of a plot of eqn (3) is in accord with that of the data. This yields the value F/j = 0.40 5 0.05 and the pair approximation gives F/j = 0.47 at this temperature. A similar procedure with L/kT = 9 yields F/j = 0.90 &-0.05 and the pair method gives F/j = 0.78. The small discrepancies here are partly a result of the pair approximation but apparently the values of F calculated by eqn (1 3) are too large. kl/A/ FIG.7.-Logarithm of the normalized growth rates on several S.C. and f.c.c. faces (see text). Here all growth rates are normalized by the product of kf and the corresponding layer spacing. Open triangles LIkT = 6; open circles L/kT = 9.SIMULATION OF 2D NUCLEATION AND CRYSTAL GROWTH SURFACE MIGRATION The inclusion of surface migration may increase the growth rate dramatically as already observed in the transient calculations of fig. 2. The steady-state growth rates with a migration to evaporation ratio of 7.4 and 54.6 are shown in fig. 8 for L/kT = 12. For comparison the data of fig. 3 without surface mobility are also included. The effect of mobility is accentuated at small values of Ap where the nucleation rate is small A) 1kT FIG.8.-Normalized growth rates on the S.C. (100) face at L/kT = 12. The values of the surface mobility are indicated by the ratios k,/k-next to the curves. The curves were calculated using eqn (3) with Flj equal to 1.2,O.g and 0.75 for k,/k-equal to 0 7.4 and 54.6 respectively.clusters are far apart and the competition for the adatom flux is not important. This preferential enhancement at small driving force causes a reduction in the slope of a plot of the logarithm of the rate and hence calculations of F yield erroneous values when the surface atoms are mobile. CONCLUSlONS Realistic models of crystal growth are essential for a detailed understanding of the process. Crystal growth kinetics are directly related to the structure of the crystal surface and accurate representations of this surface are required. The Ising model simulation of the growth rate transient is in much better accord with measurements than were the previous models. Cooperative interactions among large groups of atoms are accurately represented in this model.A qualitative change in the kinetics is observed at a critical roughening temperature. Above this point the normal growth law obtains but at lower temperatures the perfect crystal grows by a nucleation mechanism. A reduction in the free energy of a close packed step is observed at temperatures as low as half of the roughening point and this tends to increase the growth rate. Some low index faces may roughen at very low temperatures if the atoms in the surface layer are not connected by a strong network of bond chains. These temperatures can be calculated from the a factors of the crystal faces. GEORGE H. GILMER The author thanks J. D. Weeks and IS.A. Jackson for helpful discussions and V.Bostanov for suggesting a calculation of the transient. L. D. Hulett and F. W. Young J. Electrochem. Soc. 1966,113,410. ’A. Bewick M. Fleischmann and H. R. Thirsk Trans. Farday Soc. 1962,58,2200. U. Bertocci J. Electrochem. SOC.,1972 119 822. F. F. Abraham and G. H. White J. Appl. Phys. 1970,41 1841. V. V. Solovev and V. T. Borisov Sou. Phys. Crystallography 1973,17 814. G. H. Gilmer and P. Bennema J. Appl. Phys. 1972,43,1347. J. D. Weeks G. H. Gilmer and K. A. Jackson J. Chem. Phys. 1976,65,712. H. Darbinghaus and H. J. Meyer J. Crystal Growth 1972 16 31. V. Bostanov R. Roussinova and E. Budevski J.Electrochem. Soc. 1972,119,1346. lo L. A. Borovinskii and A. N. Tsindergozen,Sou. Phys. Crystallography 1969,13,1191. J. D. Weeks G.H. Gilmer and H. J. Leamy Phys. Rev. Letfers 1973,31 549; also see H. J. Leamy G. H. Gilmer and K. A. Jackson in Surface Physics of Materials I ed. J. M. Blakeley (Academic Press New York 1975) p. 121. J. P. van der Eerden R. L. Kalf and C. van Leeuwen J. Crystal Growth 1976,35,241. l3 G. H. Gilmer in Computer Simulation.for Materials Applications (National Bureau of Standards Gaithersburg 1976) p. 964. l4 S. W. H. de Haan V. J. A. Meeussen B. P. Veltman P. Bennema C. van Leeuwen and G. H. Gilmer J. Crystal Growth 1974,24/25,491. l5 A. E. Nielsen Kinetics of Prec@itation (Pergamon Oxford 1964). l6 D. Walton J. Chem. Phys. 1962,37,2182. l7 D. E. Temkin Sou. Phys. Crystallography 1969 14 179. l8 G. H. Gilmer J. Crystal Growth 1976 35 15; B. Lewis J. Crystal Growth 1974,21,29.l9 J. D. Weeks and G. H. Gilmer J. Crystal Growth 1977 in press; G. H. Gilmer and J. D. Weeks J. Chem. Phys. 1978 in press. 2o L. Onsager Phys. Rev. 1944,65 117. *’ M. E. Fisher and A. E. Ferdinand Phys. Rev. Letters 1967,19 169. ”K. A. Jackson in Liquid Metals and Solidification (American Society for Metals Metals Park Ohio 1958) p. 174. 23 G. H. Gilmer and K. A. Jackson in Crystal Growth and Materials (North-Holland Amsterdam 1976) p. 79. ”U. Bertocci J. Crystal Growth 1974 26 219.

ISSN:0301-5696    

DOI:10.1039/FS9771200059

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Simulation Studies in Electrocrystallisation JEFFREY AND SARRIKHAI K. RANGARAJAN A. HARRISON School of Chemistry University of Newcastle upon Tyne Newcastle upon Tyne NE1 7RU Received 10th August 1977 The properties of a simple “chess board” type computer simulation of electrocrystallization are investigated. The importance of the “discrete effect” and the “ingestion effect” is evaluated for the formation of a single layer. A quantitative investigation of the Avrami equation for square nuclei is carried out. Some comments are made about multilayer formation. The results suggest that this method can be used to make quantitative predictions in cases where analytical mathematical solutions are difficult. The importance of simulation studies in electrocrystallisation lies in bridging the gap between the naive idealisation of theoretical models and the complex response of an actual experimental ~ystem.~ A similar philosophy is also used in other prob- lems where information is sought on a molecular level for example by (molecular dynamics) computer experiments in studies on radial correlation functions computer studies of nucleation and crystal growth etc.In real problems of electrocrystallisa-tion there will be interactions which can only be understood by setting up simulation models. The purpose of the present paper is to present some of the elementary pro- perties of a simulation and to suggest their relation to real events. The parameters of the simulation are no doubt related to molecular processes for example lattice incorporation and electron transfer but it is not necessary that the scales of distance and time involved are those of the elemental processes.More specifically consider the activation-growth model. The familiar Avrami equations are expected to follow but should they? After all the kernel of this approach is the introduction of the concept of an extended area S and the relation of this to the true area accounting for overlap by S = 1 -exp (-Sx). (1) S itself is then evaluated by simple addition or convolution according to conditions of instantaneous or progressive nucleation. Several questions can be asked (a) Does eqn (1) correctly evaluate the overlap effects especially for a geometry other than a circular one e.g. square or hexagonal? (b) Is it possible that eqn (1) has to be replaced by a more general law S =f(S,)? (c) Is eqn (1) reliable for both instantaneous and progressive nucleation conditions.This is not so obvious because there are two types of randomness involved namely spatial and temporal. (d)Even if eqn (1) holds does eqn (2) hold and if so what are the values of p and n? S = 1 -exp (-PI”). (2) 7 Permanent address :Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012 India. JEFFREY A. HARRISON AND SARRIKHAI K. RANGARAJAN Obviously there must be limitations to eqn (1) and it will be interesting to obtain indications of these by simulation studies. An even more specific question which this paper can answer is how important is the ingestion effect.Under conditions of progressive nucleation the rate of successful nucleus activation is governed not only by the rate of nucleation but also by the availability of free surface for nucleation. This introduces into the calculation of S a new factor e-Sx and consequently results in a non-linear differential equation for S,. It will be interesting to know the significance of this as no new parameter is involved in the model. A simulation study can naturally incorporate this phenomenon and hence provide an interesting ground for discussion of this aspect. Problems become even more intriguing when these ideas are extended to multi- layer growth. The problem can be treated as a cascade process and visualises a linear relation between the n + 1 layer and the layer n namely wheref is the rate of monolayer formation on the nth layer.Eqn (3) and (1) constitute the simple but fundamental relations in most theories. Any relaxation of simplicity e.g.,fn+l #fn can make the solutions very difficult to derive but simulation can incorporate such realistic features more conveniently. THE SIMULATION A square matrix L x L (nominally 40 x 40 or 100 x 100)was chosen to represent the ~urface.~,~ Nucleation sites N per time step were chosen by random number generator. If a coordinate chosen for monolayer growth fell on an already occupied portion of the surface this was ignored. Each nucleus was then grown by advancing the periphery by G length units per time step. The nuclei were squares.The bound- aries were cyclical in that nuclei moving over a boundary were reintroduced at the 240 --190-0 -0 X -+ 150 E -.--_w 97 -+ -X0 48 - - +9 0 I I 1 I I I I I I 1 1.o 2.8 4.6 6.4 8.2 10 "1 FIG.1.-Example of a simulation result N = 5 G = 1 L = 39 showing successive averages (+)second;(O)fourth;( x)fifth. SIMULATION STUDIES IN ELECTROCRYSTALLISATION opposite edge. This procedure generates cylindrical boundaries in the two directions. The program was organised as a series of subroutines for setting the nuclei growing the nuclei and dealing with the boundaries. Monolayer or multilayer growth could be carried out. In the case of multilayers the same subroutine for nucleation was used except that nuclei falling on an occupied surface adopted the identity of the next layer.The scan subroutines scanned for periphery (isim)or for area covered (Ssim). The scans for isimor Ssim as a function of nT* were accumulated in separate runs and the average values plotted by computer so that the standard deviation at each value of nT could be reported. However averaging was very effective in all the runs reported here and the final result which was then independent of further averaging was reached in 3 or 4 runs. A typical simulation result is shown in fig. 1. GROWTH PARAMETERS Since simulation experiments only involve numbers it is worthwhile showing how to make contact with " real situations ". For example the L x L grid with N square centres introduced in a stepwise fashion can map a real situation as follows.If a unit spacing in the grid corresponds to a real distance E cm say and the unit of time is then At s table 1 shows the correspondence rules in terms of the thus-far unknown E and At. TABLE 1.-RELATION BETWEEN REAL AND SIMULATION PARAMETERS real system simulation correspondence number of nuclei nucleation rate growth rate N" dN m AN* $= zFyk dt No N G N* = Nol(L2e2) AN* =I-N/(At * L2e2) zFyk = GEfAt time t nT t = nT * At In the case of instantaneous nucleation the extended area S becomes S = (4NoG2nT2/L2) (4) a non-dimensional form independent of E and At. If the nucleation is progressive again independent of E and At. As an example if N* = 1OI2 cm-2 in the real system and No = 100 and L = 100 in the simulation it follows that E -lo-' cm i.e.,if the values of No and L are used in the simulation for No* -10l2cm'2 each unit in the grid then corresponds to lo-' cm.In addition if the progressive nucleation rate A in the real system is known to be -10-1 s and N = 10 in the simulation the unit of time is then fixed and At -1 s. With these values if G is assumed to be 5 then it follows that the characteristic time constant for the growth in the real system becomes accessible in -5 time steps in the simulation Le. when nT = 5 the coverage is nearly unity. * See table 1 for definition. JEFFREY A. HARRISON AND SARRIKHAI K. RANGARAJAN EQUATIONS FOR S AND i On the basis of the last section and the Avrami eqn (I) then the appropriate equa- tions for S and i in real parameters are' S = 1 -exp (-PIt2) (6) l=qm-2PIt * exp (7) where P = 4N*(zFyk)*,(see table I) for instantaneous nucleation and S = I -exp (-ppt3) (8) i = 3ql,,ppt exp ( -ppt3) (9) where Pp= 4/3AN*(~Fyk)~ for progressive nucleation.The corresponding simulation equations are Ssim= L2[l -exp (-Ti)] isim= 4LNo*GT exp (-Ti) where Ti = 4NoGnT2/L2 for instantaneous nucleation and isim= 4(3/4)2/3L2( $2)'Tp2e-Tp3 NG2 where Tp3= (413)-n-r3 L2 for progressive nucleation. RESULTS MONOLAYER SIMULATION The first question is whether the Avrami eqn (1) is valid for the 2D instantaneous nucleation model. In this model there is only spatial randomness and no further complications are expected.The test which has been applied to the simulation is two-fold (1) to confirm that S is in fact given by 1 -exp (S,) and (2) to confirm that the extended area S is the sum of the individual centres and = 4No(ykt)2. In the above formulae the geometrical factor x appropriate for circular centres' has been replaced by 4. Since there is no continuum in the simulation studies S is written as 4NOG2nT2/L2.Fig. 2 in which the non-dimensional current iND in the form In (isim/4LGNo*TI) is plotted against the non-dimensional time T clearly demonstrates how satisfactory both Avrami's equation and the expression for S are. The case of progressive nucleation is probed in a similar way in fig. 3 and 4; here the non-dimensional current iND in the form In (isi,/[4(~)3L2(NG2/L2)~~~2)~ is plotted against the non-dimensional time Tp3.In graphs 2-4 the circles give the Avrami result i.e. a 45" line. Any deviation in view of the agreement between simulation and the Avrami equation for instantaneous nucleation could be attributed to S,. Possible sources of deviation lie in the stochastic nature of the activation process the discrete nature of time imposed by the simulation and the ingestion effect. SIMULATION STUDIES IN ELECTROCRYSTALLISATION -0202 W -0.95 - m a ;f -1.9 .,= cl 5 -2.8- 0 + 0 -4- - 3.7 - 0 + 0 f -4.7 1 L-LU FIG.2.-Ln (4L&'& for instantaneous nucleation of a monolayer, plotted against 'v No = 8 G = 1 L = 39 after 8 averages.In order to eliminate the stochastic effects in this paper all the figures refer to averaged data so that only an averaged activation process is considered. This leaves only time discretisation or ingestion to be considered. Fig. 3 and 4 show how deviations from the Avrami result can be seen in simula-tions. However it is somewhat more convenient to consider the behaviour of Ssim and this will be used in the subsequent discussion. + 0 i 0 -3.1 t -4.0) I I I I + 0.0033 0.67 1.3 20 2.7 3.3 FIG.3.-Ln (4(~)2,3L2(Nc2,L2>',3Tpzplotted against F2 nT3for progressive nucleation of a mono-) layer (+)N = 4 G = 1 L = 39 after 8 averages. JEFFREY A. HARRISON AND SARRIKHAI K.RANGARAJAN If the extended area Sx,in the case of progressive nucleation is evaluated taking into account the discrete nature of the time steps then sx(nT) becomes 0 4--2.6 c 0 T; FIG.4.-Plot as fig. 3 for N = 1 G = 1 L = 39 after 6 averages. Note that when nT = 0 Sx(nT) = 0. Also when nT -co,s behaves as predicted by continuum theory. It seems likely that this effect must play a significant role. Fig. 5(a) and (b) verify this by plotting for the various cases Ssim against Tp3and In (1 -Ssim/L2) Because the graphs are from a computer printout a against (Tp3)disc. square represents where two or more points cross. The agreement is satisfactory and shows a strong correlation with the discrete effect. Thus the Avrami equation and the parameter S are being employed correctly.Even a geometric " fudge " factor in addition to the factor 4 is not necessary. However it is still necessary to evaluate the extent of the ingestion effect. This can be evaluated in the continuum case by solving the non-linear differential equation for S S = T2IoTexp [-S,(z)]dz z exp [-S,(z)]dz -I-loT z2 exp [ -Sx(z2)]dz where T3/3= Tp3.Note that as T-0 S +T3/3,as expected in the classical version. The fact that progressive rates of nucleation become proportional to the available " free " area is responsible for the coefficient e-sx in the analysis. An inter- esting limit is predicted as T+co,namely S cccT2,but the effect per se does not seem SIMULATION STUDIES IN ELECTROCRYSTALLISATION H X + X f .:I 0.60 0 0 .LoL m H B OS2Ot+ 0.00088 m I I I I 0.00088 0.18 0.35 0.53 0.70 0.88 u -0-0'3" -1.0 i3 4- -2.0 - 0 I -3.0 - C -4.1 - 0 + -5.1 1 I I I d -4.1 51 ( Tg disc (6) FIG.5.-(a) Ss1,/L2against Tp3,N = 5 G = 1 L = 39 4 averages (+).( x ) is the discrete result, (0) N Avrami and (a) due to ingestion.(b)Ln (1 -Ssi,/L2) against (Tp3)disc= 5 G = 1 L = 39 4 averages (+). (0) is a 45"line. JEFFREY A. HARRISON AND SARRIKHAI K. RANGARAJAN + I- X 0.60L 0.40 0.0035 I 1 1 1 1 0.0035 0.70 1.4 2.1 2. a 3.5 0 + 0 -0.1 1 I I 1 1 9 0.021 1.6 3.3 4.9 6.5 8.1 (~p3 disc (b) FIG.6.4~) Ssim/L2 against Tp3,N =2 G =2 L =39; 5 averages (t).(x)is the discrete result Avrami and (0)due to ingestion.(b)Ln (1 -Ssim/L2)against (TP3)disc, (0) N =2 G =2 L = 39 5 averages (+). (0) is a 45" line. SIMULATION STUDIES IN ELECTROCRYSTALLISATION 0.98-+ + 8 ? X f X 0.78-+8 X +$ E 0.59 -k 8 (4 .GI4 0.39-5 8 N f 8 0.20-D a $ -0.74- ? 0 -1.5-*.:I- t 0 + 0 + -2.2 - 0 c- + 0 -3.0- + 0 -3.7 I I I I + JEFFREY A. HARRISON AND SARRIKHAI K. RANGARAJAN 1.0- + + v m w X . 0.80- + 8 X 0.61 - 8 + -x 0.41 il 0.21 -0 0 0 0 0 161 I I I I 9 0.042 3.3 6.5 9.7 13.0 16.0 FIG.8.-(a) Ssi,/L2 against Tp3,N = 1 G =4,L = 39 3 averages (-I-).(x ) is the discrete result (0)Avrami (a)due to ingestion. (6) Ln (1 -Ssi,,,/L2)against (Tp3)disc N = 1 G =4 L = 39 3 averages (+). 80 SIMULATION STUDIES IN ELECTROCRYSTALLISATION to be important except at larger times where the coverage is large. The equation for S has been solved in this work by both numerical and perturbation methods. Fig. 6(a)is a typical curve which demonstrates the magnitude of the ingestion effect com- pared with the discrepancy between the simulation and classical Avrami theory. It seems likely that a discrete version of the ingestion effect however would make the agreement between the simulation and the discrete version of the Avrami equation even better. Fig. 7(a) reflects the same analysis for a different choice of N and G.MULTILAYER SIMULATION Similar investigations have been made to verify eqn (3) used in multilayer analysis. Only one aspect will be reported here uiz. the dependence of the steady state multi- layer current i on the growth parameters. It has been shown7 that an exact solution of this problem leads to i =qm/imexp (-S,)dz in particular for 2D progressive nucleation Approximate versions of the above result are also available by numerical lointegration of eqn (3) and by simulation.ll Fig. 9 indicates that the simulation results support the dependence on pP1l3, where -I 8 -h .--.+ -1r 0 -!! lo-’ I I I I I Ill1 I I I Ill Ill I I I I I Ill log-NG L2 NG2 FIG.9.-Log (isim)m/L2) against log 7for multilayer growth each point is the average of approxi-L mately 10 runs.a simulation equivalent of Pp i.e. NG2/Lis actually plotted. The coefficient (-1.82) seems to differ from the theoretically predicted one (1.12) (fig. 10). An analysis for ingestion effect on multilayer form has been made by evaluating the integral in eqn (17) but the correction is not sufficient to explain the difference in coefficient. Pre-liminary studies by using eqn (14) to evaluate the integral in eqn (17) however indicate that the discrete effect is probably largely responsible. JEFFREY A. HARRISON AND SARRIKHAI K. RANGARAJAN / OeSr ~:~~ 0 .1 0.1 0.2 0.3 0.4 0.50.6 0.7 0.8 against (f 9)' FIG. lO.-(is,&/L2 for inultilayer growth.The full Iine has slope 1.82. CONCLUSION This paper has considered some of the features of simulation which must be talcen into account if these are to be used to investigate more realistic models of nucleation and growth processes. We believe that the discrete and ingestion efkcts also have their physical counterparts in real systems. Unfortunately not many experiments are available in simple and well-characterised systems. However the form of some recent experiments12on "dislocation " free Ag surfaces indicate that some of the effects discussed in this paper may operate. On the other hand experiments on real metal5 systems are also available. In order to make substantial progress in understanding these processes in necessarily more complex models it will be essential to set up models and identify the key parameters.Simulation is a convenient way of achieving this and we are embarking on a programme to investigate some of the obvious effects. In the field of monolayer formation we are investigating the effect on the kinetics of growth of the geometry and arrangement of centres the nature of the growth process fluctua- tions in space and the effect of interactions among centres also the influence of the ingestion effect for more complicated growth profiles (other than for example deter- mined by constant potential conditions). For multilayer growth we are using simula- tion to investigate the transients the effect of different growth and nucleation rates for successive layers and the influence of fluctuations and correlations in the activation process.We hope to present some of these results shortly. M. Fleischmann and H. R. Thirsk in Advances in Electrochemistry and Electrochemical Eng-ineering ed. P. Delahay (Interscience New York 1963) vol. 3 p. 123. J. A. Harrison and H. R. Thirsk in Electroanalytical Chemistry ed. A. J. Bard (Marcel Dekker New York 1971) vol. 5 p. 67. E. Budevski in Progress in Surface and Membrane Science ed. D. A. Cadenhead and J. F. Danielli (Academic Press New York 1976) vol. 11 p. 71. SIMULATION STUDIES IN ELECTROCRYSTALLISATION J. A. Harrison S. K. Rangarajan and H. R. Thirsk J. Electrocherit. SOC.,1966 113 1120. W. Davisoii J. A. Harrison and J. Thompson Faraday Disc. Chem. SOC.,1973 56 171. M. Avrami J. Chem.Phys. 1939,7,1103; 1940,8,212; 1941,9,177. S. K. Rangarajan J. Electroarmlyt. Chenz. 1973 46 119 125. M. M. Clark J. A. Harrison and H. R. Thirsk 2.phys. CIzem. N.F. 1975 98 153. J. A. Harrison and W. J. Lorenz J. Electroanalyt. Chenz. 1977 76,375. lo R. D. Armstrong and J. A. Harrison J. Electrochem. Sac. 1969 116 328. l1 U. Bertocci Surface Sci. 1969 15 286. l2 E. Budevski personal communication.

ISSN:0301-5696    

DOI:10.1039/FS9771200070

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Role of Screw Dislocations in Electrolytic Crystal Growth BY VESSELINBOSTANOV BUDEVSKI STAIKOV EVGENI AND GEORGI Central Laboratory of Electrochemical Power Sources Bulgarian Academy of Sciences Sofia 1000 Bulgaria Received 10th August 1977 The theory of form and interstep distance of spirals and the growth rate of crystals under spiral growth conditions are discussed and illustrated for the electrodeposition of silver. The overvoltage dependence of the slopes of pyramids can be used for the evaluation of the rate of propagation and the specific edge energy of the spiral steps the latter being also accessible from experimental current against overvoltage curves. The coincidence of these values with values obtained from other experi- ments (two-dimensional nucleation) is a good proof of the validity of the theory of spiral growth.The mechanism of growth of singular faces intersected by screw-dislocations is completely different from that of perfect faces where the growth mechanism is con- trolled by two-dimensional nucleation. Because of the structural defect a ledge eman- ates from the point where the dislocation line intersects the surface of the crystal face. The ledge being constrained to terminate at the dislocation emergence point will wind up into a spiral as it advances during growth and will never disappear from the face. This step ensures a sufficient number of growth sites so that growth can proceed at low overpotentials making the two-dimensional nucleation mechanism an unnecessary process. The theory of spiral growth has been developed by Frank' and Burton et aL2 The basic equation for calculation of the form of the spiral in the isotropic case is the dependence of the rate of propagation of a ledge on its radius of curvature assuming that for a region of the step p =pc (where pc = &/qmOnqc is the radius of the two-dimensional nucleus at the given overvoltage rc,equivalent to the supersaturation where E J cm-l is the specific periphery energy of the nucleus and qmonC is the amount of electricity needed for the deposition of one monoatomic layer on the crystal face) the propagation rate is zero and increases to vo3as the step becomes straight (P-+ 4.Burton Cabrera and Frank found two approximations of the solution r(8) de-scribing the form of a stationary rotating circular spiral.The first approximation yields an Archimedian spiral with a radius of curvature at the centre p =pc. The ledge spacing d is in this case uniform for the whole spiral d = 4zpC= 12.6~~. This result corresponds to a constant radial propagation rate except for ledges for which p. <pc. A second approximation is derived by the same authors combining the solu- tion for small Y values where the relation (1) is taken into account with the former solution valid for large r values. This solution yields 19.9 for the factor connecting d and pc which value has been later corrected to 19.0 by Cabrera and Le~ine.~ The case of polygonized spirals has been discussed by Cabre~a,~ by Kaischew el aZ.5 84 ROLE OF SCREW DISLOCATIONS IN ELECTROLYTIC CRYSTAL GROWTH and by Chapon and Bonissent.'j In all these treatments the ledge advancement rate is considered as constant equal to that of an infinitely long step except for steps shorter than the side length I of the two-dimensional nucleus i.e.v = urn for I I and ZI = 0 for I < I,. The step distance is calculated from the period Tof rotation (at steady state) and vco:d = Tv,. For a quadrangular spiral the period T is 4 times the time lapse z needed for a new step to reach the length I,. For a constant propagation rate u = urn r = Ic/vco and d = 41,; the ledge spacings are independent of the distance from the centre in this case. For a k-cornered spiral the ledge spacing is given by d = 4kp sin2(;n/k). The assumpton u = urn for I 2I and v = 0 for I < Ic is obviously incorrect.A modification of the BCF-equation v = v,(l-l$) (2) can be used here.7 It is obvious that the time lapse z and hence the period of rotation become larger because the step adjacent to the newly growing step propagates with less speed than urn. The calculation is complicated because the propagation speeds of all the adjacent steps are also I-dependent and hence the propagation rate of the spiral is given by a system of differential equations. A numerical calculation of this system was given by Budevski Staikov and Bo~tanov,~ who found that irrespective of the form of the spiral the period of rotation of a k-cornered spiral is T = 19pC/v (3) and hence d = 19pc= 19~/~,,,,,,,~,.(4) The situation becomes more complicated in the casz of two dislocations located at a distance comparable with I,. If the two dislocations have the same sign and their distance is close to I they are acting as one dislocation with a double step height the slope of the produced pyramid is increased. If L >Z, d remains unchanged as does the slope.z When the two dislocations have opposite signs (fig. 1) they produce only one step both ends of which terminate at the two emergence points of the dislocations. If the distance of the two dislocations is smaller than I this step becomes inactive. For larger distances the dislocation pair produce loops of steps. The period of pro- duction of loops was calculated by Nanev s using approximation methods. The results of the exact numerical solution calculated for the two cases represented in fig.1are given in fig. 2. It is seen that for low supersaturations where Zc approaches the value of the dislocation distance L the step distance becomes infinitely high (be- cause of the very low advancement rate in the initial stage) while with increasing super- saturation i. e. decreasing I,-value the period of loop production decreases rapidly bringing the d/I value below the 9.5 margin (note that I = 2p in this case of quad- rangular symmetry). With higher supersaturations the d/Z,-value increases to 9.5 because two non-interacting spirals are formed. The growth pattern becomes even more complicated if more than two dislocations are interacting and especially if the component of the Burgers vector normal to the face is higher than the height of a monoatomic step.From these considerations it follows that a uniform step density for all spirals of growth on a crystal face can only be expected when simple non-interacting spirals are produced. VESSELIN BOSTANOV EVGENI BUDEVSKI AND GEORGI STAIKOV phase 4 phase 3 phase 2 1 -phase ' 1 phase 0 (initiai) phase & = phase 4 (final) \J \I \ I I phase 4 1 I phaise 1 phase 0 .(initiat)'= b 'I FIG.1 .-Interaction of pairs of screw-dislocationswith opposite sign. (a)Dislocations situatedalong a line parallel to the direction of closest packing (Le. normal to that of lowest propagation rate); distance L = 21,. (b) Dislocationsalong a line at an angle of 45" to the directionof closest packing; L = I,.86 ROLE OF SCREW DISLOCATIONS IN ELECTROLYTIC CRYSTAL GROWTH 1 2 3 4 5 L /I FIG.2.-Relative step distance d/I,of the pyramid of growth of conjugated pairs of screw-dislocations as function of dislocation distance L/lc. 0-dislocations situated as shown in fig. l(a). O-dis-locations situated as shown in fig. l(b). (The transition from phase 3 to phase 4-the final phase. in the case fig. l(b) is assumed to proceed with a velocity of the concave angle steps equal to urn). GROWTH MORPHOLOGY OF IMPERFECT FACES On a face intersected by screw-dislocations a pyramidal growth pattern is observed. On a cubic face the pyramids are rectangular (fig. 3) while on an octahedral face they are triangular (e.g.fig 6). The pyramids of growth are obviously the macroscopic picture of the spirals of growth. There is much evidence for this statement (i) the slope of the pyramids depends on supersaturation. Changing the supersaturation the slope is also changed. (ii) The pyramids appear always on the same site of the face. At anodic dissolution an etch pit is produced at these sites. The regular pyramidal pattern of growth is observed on faces with a high degree of perfection intersected by only few dislocations. In some cases pyramids with differ- ent slopes are observed (fig. 4). The ratio of the slopes can be easily calculated from some geometrical parameters e.g.,the angle between the valley line of the two pyramids and the edge of the pyramid.A slope ratio of 1.26 was calculated in the case of fig. 4(u). For the three pyramids of fig. 4(b) all of them having different slopes ratios of 1:1.5 :2.25 have been found. In fig. 5 a variety of pyramids with different slopes are observed with typical slope ratios ranging between 1.3 to 1.5. The picture sequence in fig. 6 shows the develop- ment of a pyramid with higher slope than the basic one fig. 6 (u)-(d). The slope ratio here is -2. In later stages (e)-(A) the sequence shows a sudden flattening of the top of one of the pyramids and the appearance of a series of new pyramidal tops which have been overgrown by the basic pyramid and have become active as this pyramid dis- appears. These are few selected examples of the growth morphology in simple cases.The FIG.3-Pyramids of growth on a cubic silver single crystal face. a b FIG.4.-Pyramids of growth with different slopes. (a) Slope ratio of the two pyramids is 1 :1.26. (b)The slope ratio of the three pyramids is tan al:tan uz = 1.5 and tan q:tan a3 = 2.25. A pulsat-ing current of growth is used in case (b)to demonstrate direction and velocity of propagation of the spiral steps. FIG.5.-Pyramids of growth on cubic face. Slopes of the marked pyramids are tan u1:tan uz = 1.5 tan all:tan a4 = 1.3 and tan a5:tan a(;= 1.9. [Toface page 86 FIG.6.The development of the growth process of pyramids on an octahedral single crystal face. Slope ratio of the two upper pyramids in (d) 1 :2. A flattening of the top of the lower left pyramid is observed in (e) resulting in the appearance of a series of new pyramids.[Toface page 87 FIG.7.-Separated pyramids of growth obtained by injecting a certain amount of electricity on a previously levelled face. [Toface page 87 VESSELIN BOSTANOV EVGENI BUDEVSKI AND GEORGI STAIKOV 87 morphological pattern becomes more complicated and impossible to interpret in the general case. SLOPES OF PYRAMIDS OF GROWTH The slope of a pyramid of growth determined by the step height h and the step distance d tan C( = uh,/d = uq,,,h,q,/l9e (5) is proportional to the overvoltage qc. h is the height of a monoatomic layer and u the number of layers forming the ledge. This slope against overvoltage dependence can be easily investigated using the technique developed by Nanev Budevski and Kais~hew.~ On previously levelled face intersected by a small number of screw- dislocations a short current pulse is applied.As separated regular pyramids are formed (fig. 7) the amount of electricity injected can be assumed to be evenly dis- tributed among them. Thus the volumes of these pyramids are known their bases can be directly measured so that the slopes are easily calculated. Fig. 8 represents data obtained by this technique. The straight line is in agree- u) c g d -6 C (n 5 c -v 10% 01 -G. E u2 e 5' x u) -15 0 -0 I -2oz d' -302 3 ;L I I I 1 20 40 60 overvoltage / 10-3 v FIG.&-Slope of the pyramids (tan a) as function of overvoltage.The slope is given in step height units in the right ordinate. ment with eqn (5). The value of E calculated from these data assuming u = 1 is E = 0.98 x J cm-I in a fairly good agreement with previous results (E = 2 x from measurements on dislocation-free face^).^ RATE OF PROPAGATION OF SPIRAL LEDGES The propagation velocity of the spiral ledges is an important kinetic parameter. Being monoatomic the single steps of the pyramids are invisible. The following technique has been used10 to get information for this parameter it has been demon- strated that the slope of the pyramids of growth depends on overvoltage. If therefore 88 ROLE OF SCREW DISLOCATIONS IN ELECTROLYTIC CRYSTAL GROWTH during growth at constant overvoltage the overvoltage is changed for a short period a condensation of the spiral ledges at the centre results which begins to propagate with a constant speed from the top of the pyramid downwards as a stripe with a different slope (Le.with a different shade as observed by phase-contrast microscopy). A stripe produced by this technique is observed on the octahedral face represented in fig. 9. A linear relation between velocity and overpotential has been ObservedlO giving for the rate constant K = 0.92 cm s-l V-l in good agreement with values obtained from propagation rates of monoatomic layers.11 A linear relation between step velocity and overvoltage indicates a linear relation between current and step length. i = icLy (6) where K is connected to K by K = Kvqmon (7) The linear current-step length relation (6) has been experimentally verified in other experiments.ll CURRENT AGAINST OVERVOLTAGE RELATION At steady-state growth conditions the spirals of growth have uniform ledge spacings producing a uniformly stepped surfhce with a step density L = l/d or from eqn (4) Ls = 4mon TC/l9&* (8) For small yc values the current density is proportional to rc.With eqn (6) this equation yields i = ~q~~~~~~/19~ (9) = By:. 1 I I I 1 0.05 0.10 015 0.20 j-1/2/ (A cm-2) 1/2 FIG.10.-Steady-state current-overvoltage relation in a AEi-lj2 against Pplot for separation of the concentration polarization and the ohmic potential drop from the crystallization overpotential according to eqn (10).FIG,9.-Stripes produced by a short increase in the overpotential on a growing octahedral face. The photograph was taken about one second after the pulse application. [Toface page 88 VESSELIN BOSTANOV EVGENI BUDEVSKI AND GEORGI STAIKOV 89 To verify the theoretically expected square of overvoltage dependence of the cur- rent at steady-state conditions we have to separate the ohmic drop and the concentra- tion polarization terms from the overall voltage change AE of the cell. For this pur- pose we may assume that for the low potential changes observed in the discussed experiments both these terms depend linearly on current density while the part of the polarization which drives the ions across the double layer to the crystal lattice depends on the square root of the current [see eqn (9)].AE = i(Rc + RQ)+ (i/B)'I2 A straight line is obtained by plotting AEi-ll2 as function of the square root of i as seen in fig. 10. The ordinate intercept gives the value of the constant B in the i against qc2 relation. From this constant and knowledge of K the value of the specific edge energy E can be estimated IC can be taken either from monoatomic layer1' or more correctly from the spiral ledge propagation rate measurements which have been de- scribed.I0 The value of E is 2.4 x J crn-l in good agreement with the value of E from other experiment^.^ The experiments described are not only in accord with some basic deductions of the theory of spiral growth but represent a very good quantitative verification of the Burton Cabrera and Frank's theory for the case of electrocrystallization.F. C. Frank Disc. Faraday Soc. 1949 5,48,67. W. K. Burton N. Cabrera and F. C. Frank Phil. Trans. A 1951,243,299. N. Cabrera and M. M. Levine Phil. Mag. 1956,1,450. N. Cabrera Structure and Properties of Solid Surfaces (Chicago Univ. Press Chicago 1953) p. 295. R. Kaischew E. Budevski and J. Malinovski 2.phys. Chem. 1955,204,348. C. Chapon and A. Bonissent J. Cryst. Growth 1973,18 103. 'E. Budevski G. Staikov and V. Bostanov J. Cryst. Growth 1975,29 316. * C. N. Nanev KristaN und Technik 1977 12 587. R. Kaischew and E. Budevski Contemporary Phys. 1967 8,489. lo V. Bostanov R. Roussinova and E. Budevski Izuest. Otd. Khim. Nauk. Bulg. Acad. Nauk. 1969,2 885. '* V. Bostanov R Roussinova and E. Budevski Chem.-Ingr. Tech. 1973 45 179.

ISSN:0301-5696    

DOI:10.1039/FS9771200083

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Potentiostatic-Galvanostatic-Potentiostatic Study of the Deposition of Mercury on Graphite BY GAMINE GRAHAM MONTENEGRO A. GUNAWARDENA J. HILLSAND IRENE Chemistry Department The University Southampton SO9 5NH Received 23rd August 1977 A potentiostatic-galvanostatic-potentiostaticpulse train has been used to investigate the electro- chemical nucleation of mercury on graphite. The second potentiostatic pulse was used to evaluate the nuclear number density along the galvanostatic transient. The maximum in the galvanostatic- potential-time transient is seen to be related to the faradaic charge transfer reaction rate and can be made the basis of the determination of exchange currents. The kinetics of electrochemical nucleation are invariably investigated by the analy- sis of the time transients observed using single or double potentiostatic or galvanostatic pulse techniques.l-' The latter stages of such transients reflect the growth of estab- lished nuclei their geometry and the nature of the rate-controlling faradaic process.In the simple metal deposition process considered here namely the electrodeposition from aqueous solution of mercury onto vitreous carbon hemispherical nuclei are formed the growth of which is eventually entirely mass-transfer controlled. At the beginning of the transients however the faradaic current is controlled by the kinetics of the charge transfer reaction leading to the formation of clusters and nuclei. If the transients are appropriately recorded i.e. using equipment with suffi- ciently short response times the fine structure of the transient can be delineated and in principle at least deconvoluted into the various and varying contributions to the current or potential including that of the charge-transfer process whereby clusters of metal atoms are built up on the surface to a critical size formally defining the birth of stable nuclei under the prevailing conditions.There are basically two models of electrochemical nucleation onto a solid substrate. The first envisages favoured sites which trap and concentrate metal atoms by the direct deposition of single atoms and/or surface diffusion of neighbouring ad-atoms. The second model is of a more general character and envisages an initial build-up of a two-dimensional array of directly deposited ad-atoms which by surface diffusion and/ or by direct discharge onto ad-atoms and other clusters form a statistical distribution of differently sized clusters.Again a fraction of the clusters reach their critical size and will then grow irreversibly and spontaneously to macroscopic proportions. The two models are not very different. Short of a complete molecular description of the clustering process (and such calculations are in progress) it is necessary to assume (i) that at each stage during cluster formation there is instantaneous equilibrium between ad-atoms and clusters and (ii) that the properties of clusters can be described in macroscopic terms. The rate of their formation and disappearance can then be described in terms of the kinetics of charge transfer (a) to form isolated ad-atoms localised at the electrode surface and (b) to add metal atoms to existing two-dimen- sional or three-dimensional groups or clusters already adsorbed on the surface.Such varied processes are likely to be characterised by a range of transfer rate constants or C. A. GUNAWARDENA G. J. HILLS AND 1. MONTENEGRO exchange currents depending on the size of the cluster to be formed and for large clusters approximating to the standard equilibrium rate constant for the bulk metal =+= metal ion reaction. Whether these clustering rate constants can properly be interrelated through the Gibbs-Kelvin correction for excess free energy and other macroscopic relationships has yet to be established. Even if this could be done there remains the unknown rate constant for ad-atom formation.The evaluation of all these parameters is a lengthy and complex procedure not yet completed for any one system. Here we report some attempts to define certain parts of the problem and in particular to use the recently established relationship between overpotential and nuclear density to evaluate the nuclear current density and hence the apparent charge-transfer rate constant for the metal +metal ion deposition reaction. The experimental basis for the work is the so-called PGP pulse train in ref. (4) in which successions of potentiostatic galvanostatic and potentiostatic pulses are used respectively (a) to stabilise the electrode surface (b) to initiate a forced growth of nuclei and to grow the established nuclei to a countable and even visible size.The pulse train and corresponding responses are shown diagrammatically in fig. I n I 1 1 t FIG.1.-Schematic representation of the PGP method. and in fig. 2 is shown a set of the middle galvanostatic transients recorded for a range of current densities. The first potentiostatic pulse serves only to maintain the electrode surface at a convenient anodic potential i.e. in a controlled state of readiness for the subsequent electrodeposition process. By means of a mercury wetted relay this is followed in <10 ,us by the galvanostatic pulse which throughout its existence will be a convolution of (i) the faradaic process attending ad-atom formation cluster formation and nuclear growth and (ii) the non-faradaic process of charging the interfacial capacity.Although it is not yet proved that they can be totally separated there is no reason to suppose that such a separation involves great uncertainty. It may be noted that throughout the process of nucleation the electrode substrate surface remains essentially graphite. The electroactive area is relatively small and will therefore not contribute significantly to the " common " capacity'O except through the pseudo-capacitance which is part of PO TEN TI0 S TA TI C-GA L V A N 0STAT I C-P OT EN TI0STAT I C S T UDY 0 1 2 10 tls FIG.2.-Early stages of the overpotential transients during single galvanostatic pulsing for deposition of mercy onto viteous carbon. Hgg+ concentration = 5 x lo-’ mol CM-~, area of electrode = 0.32 cm’.The values of each curve refer to 1041/A. the faradaic process under investigation. At the beginning of the transient all of the current is non-faradaic in character and is given by I=.@) . t+O The double layer capacitance C,can therefore be determined from the initial slope of the overpotential-time transient n =f(t). In fact the slope was linear over 20 mV or so and gave a value for the integral capacity which was not only of expected magnitude but also sensibly independent of Z (cf. table 1). Using this value the non-faradaic current throughout the transient was evaluated from a computer fit of the variation of the overpotential with time. A typical deconvolution is shown TABLE INTEGRAL CAPACITY AT DIFFERENT GALVANOSTATIC CURRENT DENSITIES 1 .-CALCULATED 103 x I 106 x c A cm-2 farad.cm-2 7.03 57.7 9.38 57.8 11.22 56.3 24.11 53.1 18.63 53.4 in fig. 3 and for each total current density the faradaic component was evaluated as a function of time (and subsequently used to determine the average nuclear size in terms of the faradaic charge passed in a particular elapsed time). It is interesting to note that throughout the region of interest the galvanostatic method is not even approxi- mately a constant current procedure so far as the faradaic process is concerned. It may also be remarked that even if the capacity were not accurately defined by this method the charging current at the potential maximum will certainly be zero.The faradaic current at this point is therefore well established. The faradaic current flowing to the electrode is of course flowing to a large num- G. A. GUNAWARDENA G. J. HILLS AND 1. MONTENEGRO I I 2 4 103tis FIG. 3.-Deconvolution of total applied constant into charging and faradaic components. ber of small nuclei and for the faradaic current density to be determined the number density of nuclei must be known. In principle the nuclei can be grown under galvano- static conditions to visibly countable size but in practice to determine the nuclear density in this way is not so easy. First the visual method is tedious. Secondly it is subject to error because of the inhomogeneous distribution of nuclei on a sheathed and bounded electrode surface of the type used here.Thirdly under galvanostatic conditions it is easy to flood the surface with nuclei which further aggravates the preceding two difficulties. Here we preferred to determine the nuclear density by means of a succeeding potentiostatic pulse of appropriate magnitude which was switched in again by means of a mercury wetted relay. The relation between the potentiostatic current- time transient and the nuclear density has recently been well established.ll Thus the middle sections of a typical set of potentiostatic transients (fig. 4) show an exact Iversus t* relationship (fig. 5) corresponding to mass transfer controlled growth the slope of which is directly proportional to the number of nuclei. The precise description of the faradaic current to a growing microscopic hemisphere is not easily obtained.In terms of spherical diffusion to an electrode of stationary radius but of growing area (a slight contradiction in terms) a reasonably good value of the nuclear density N,can be found from the equation1 -Z~F(~DC)~~~M% *N rfaradaic -pk 3 where Mis the inolecular weight and p the density of the electrodeposited metal and where the other terms have their usual meaning. P OTEN TI 0S T A TI C-G A L V AN 0S T' A TI C-P 0TEN TI 0ST A TI C STUDY _................... ,.a. ...-.... .I.. -__.... ........ ......_.... ................. L.",.. I 1 I 1 2 tls FIG.4.-Family of potentiostatic single pulse transients for the deposition of mercury onto vitreous carbon Hg$+ concentration = 1 x mol crnp3,area of electrode = 0.32 cmz.I 2 4 6 8 10 11 12 14 16 10t2/s2 FJG.5.-Linear dependence between current and t* for the middle rising sections of the transients in fig. 5. q values are shown on curves in mV. G. A. GUNAWARDENA G. J. HILLS AND I. MONTENEGRO A more exact calculation of the current density to a growing hemisphere can be made by using numerical methods and computer simulation. The use of implicit numerical procedures for this purpose is described elsewhere in a series of papers con- cerned with the application of numerical analysis to electrochemical problems in general.lZ They all involve Crank-Nicolson or other such algorithms and matrices rather than iterative algebraic procedures.Such calculations allow the current to a single nucleus at any instant of time to be accurately expressed simply in terms of ionic concentration and diffusion coefficient. From the observed total current or its linear dependence on t3 the corresponding nuclear density can be derived and was found to be only slightly higher than that predicted by eqn (2) in generally good agreement with values established by visual counting. Suffice to say here that all of the succeeding potentiostatic transients exhibited the required I versus t* relationship from the slopes of which Nwas found from the relationship I= 1cND3/2c3/2t* (3) where k is a constant equal for mercury to 9.82 x lo6C cm* mol-3 established by the computer simulation of the growth of a single isolated nucleus for known experimental values of the concentration and diffusion coefficients of Hgg+ in aqueous KN03 soIution.The number of established nuclei can therefore be calculated from any rising potentiostatic transient including those recorded by interrupting the galvanostatic transient and fast switching to the potentiostatic mode. For comparison purposes they can be recorded at a fixed lower overpotential or better still at the overpotential at the point of interruption. Either way the number density of stable nuclei was found to increase progressively up to the potential maximum and then to remain constant. This is evident in fig. 6 which shows the slopes of a number of current-time 130 102t/s FIG.6.-Nuclear number density as a function of time along the galvanostatic transient.q2 values are shown on curves in mV. transients and hence the nuclear number density at times up to and beyond the gal- vanostatic potential maximum. The number of nuclei evidently reaches a limiting value from which a number of conclusions can be drawn. (1) The galvanostatic potential maximum corresponds closely to a potential of nuclear arrest i.e. no further nuclei are formed beyond it. (2) Above a critical potential and up to the maximum nuclei are formed continu- POT E N TI 0S TA TI C-G A L VAN 0STAT I C-POT E N TI 0STATIC S T U D Y ously and most if not all of these continue to grow thereafter simply because there was never any indication of any relaxation of the number density of nuclei.The slope of the potentiostatic transients following the potential maximum was never less than the limiting value. (3) At the galvanostatic maximum there will be a distribution of nuclear sizes. The range of this distribution is not easy to assess and will require for its delineation a more detailed application of the PGP method to the rising part of the maximum. However there will be an average nucleus size and it is to the determination of this we next turn our attention. It was found simply from a knowledge of the faradaic charge passed up to the time of the potential maximum i.e. from the relation where fmax is the average nucleus size at the potential maximum. From the average nuclear area 27rt?2max the faradaic current density was calculated for each value of the overpotential maximum; these values are given in table 2 to-TABLE2.-cHARACTERISTICS OF THE MAXIMA IN GALVANOSTATIC POTENTIAL AGAINST TIME TRANSIENTSOBSERVED AT A VITREOUS CARBON ELECTRODE OF AREA 0.32 cm2IN A 50 mmol dm-3 AQUEOUS SOLUTION OF Hg2(N03)2IN mol dm-3 KN03.nuclear current 209 2.25 2.31 4.31 3.40 2.8 206.2 0.72 215 2.57 2.12 4.53 3.25 2.9 212.1 0.86 226 3.00 2.02 5.65 2.97 3.2 222.9 0.96 232 3.60 1.90 6.18 2.82 3.3 228.7 1.17 243 4.50 1.so 8.30 2.51 3.7 239.3 1.37 262 6.77 1.53 11.6 2.13 4.4 257.6 2.05 277 9.00 1.46 16.0 1.88 4.9 272.1 2.59 287 11.3 1.36 18.6 1.71 5.3 281.7 3.30 296 12.9 1.28 20.9 1.65 5.6 290.4 3.61 306 15.0 1.25 22.7 1.59 5.8 300.2 4.16 319 18.0 1.12 27.0 1.45 6.4 3 10.6 5.06 gether with the corresponding values of N and fmax.The table also includes the excess interfacial energy term 3aM/Jmaxp, the Gibbs-Kelvin term which is part of the nuclea- tion overpotential and which must be subtracted from the total overpotential before the correct dependence of faradaic current density on reaction overpotential can be delineated. The interfacial free energy term 0,is a complex function of the three interfacial tensions between the metal the substrate and the solution. In this case it will be close to the surface tension of mercury. is given in fig 7. ~t is linear over its entire length and although it might be argued that the range of overpotentials is not large its conformity to the simplest irreversible form of the Tafel relation is striking.The slope of the line leads to a value of the transfer coefficient u = 0.24 G. A. GUNAWARDENA G. J. HILLS AND I. MONTENEGRO which is in good agreement with previously published ~a1ues.I~ The intercept how- ever leads to a value for the exchange current density of 2 x A cm2. Since the solution under study was a 50 mmol dm-3 solution of Hg2(N03)2 (in 1 mol dm-3 KN03),this corresponds to a standard rate constant of -2 x cm s-l. Bindra et a1.I3have recently published a table of the best of such values determined by a wide variety of methods; the value obtained here is well below the value of 2.0 x lo-' cm s-l obtained by them the value of 2.1 x low2cm s-I obtained by Weir and Enke14 250 300 350 OlmV FIG.7.-Logarithmic behaviour between nuclear current density and the corrected overpotential at the maximum.and the value of 1.9 & 0.2 x cm s-l obtained by Matsuda Oda and Delahay." Although the present procedure therefore seems to be another quasi-stationary method for the determination of metal-deposition exchange currents it is evidently in need of refinement. The principal criticism of the method is that it is a high-over- potential method and that in " driving " this already fast charge-transfer reaction even faster there is likely to be interference from mass transfer effects even though the nuclei represent individual hemispherical micro-electrodes of very small radii. It is well known that the rate of mass transfer to such small electrodes is very high. Thus under potentiostatic conditions the diffusive flux to a stationary hemisphere of radius r is equivalent to a current density of I= zFD"c ZFDC + 7.~ 713t+ (5) Using rounded values of the coefficients (D= cm2s-l c =5 x mol ~m-~) it follows that when t = s and Y = lo-' cm then the first term is negligibly small and the second equal to 10 A cm2.This is a minimum value because of course the nuclei are not stationary but growing. This is a well known " moving-boundary '' or Stefan problem which has not been solved analytically12 but which was solved numerically in order to evaluate the constant in eqn (3). It need only be noted here that depending on the starting radius the mass transfer controlled faradaic current to a growing hemispherical nucleus can be an order of magnitude greater than that pre- dicted by eqn (5) i.e.-100 A cmw2. It was a comparison between this value and those POT E N TI 0STAT I C-GA L V A N 0STATI C-POT E N T 10s TA TI C S T U D Y in table 2 which supported the initial belief that the potential at the galvanostatic maximum was charge-transfer controlled. On the other hand a closer examination of the early stages of separate potentiostatic experiments carried out on the same system reveals a rapid transition to mass transfer control. This fig. 8 shows a log-log plot of the current-time dependence. There is an evident break from a t9 to a t3 time-dependence i.e. from conditions of progressive nucleation to those of 0.d c 0 0 d 0. 0.5 1.0 log t FIG.8.-Log-log plot of the early part of the potentiostatic current-time transient under conditions similar to those obtaining in fig.4. instantaneous nucleation. For an overpotential of -200 mV this is seen to occur at t z 50 ms and at an average nucleus radius of cm i.e. close to the values ob-taining at the galvanostatic maximum. It is therefore evident that the potential-time profile at the beginning of the galvano- static transient is the result of the build up of both activation and concentration overpotentials and their subsequent relaxation as the electro-active area grows suffi- cient to relax the current density. At a constant current density I this area is given by A = 2N,~nr'f (6) G. A. GUNAWARDENA G. J. HILLS AND I. MONTENEGRO 99 where ft is the average nuclear radius at time t i.e.3Mli *. = (w) (7) As the area increases so the current density decreases monotonically with time. However if at the same time the faradaic current increases from zero in the non- linear manner shown in fig. 3 the overpotential must pass through a maximum deter- mined largely by the applied current density and the exchange current density for the metal ---L metal ion reaction. The response of an electrode reaction to a non-linear current-time waveform has been considered by Rao and Rangarajan16 in the context of electrode processes in general. Even for a " homogeneous '' (non-nucleating) reaction a potential-time maximum can be observed and in principle at least made the basis for the deter- mination of the exchange current and the energy transfer coefficient.The involve- ment of the kinetics of nucleation and of the non-faradaic current were not con- sidered and it seems probable that the extent of their involvement and hence the description of the galvanostatic transient will require more extensive experimental examination e.g. of the density and of the size distribution of nuclei along the whole transient. Kashchiev has also considered the galvanostatic potential-time maximum and in the present context i.e. in the study of electrochemical nucleation under galvano- static conditions. His description of the maximum is in broad agreement with that presented here with however a few exceptions. Thus he identifies a critical over- potential yc below which nucleation will not take place and he allows nuclei to form along all of the crest of the transient above rc.The evidence here is that it is not so for the nucleation process is seen to terminate at the maximum not after simply because the onset of mass-transfer control has already begun to attenuate the activa- tion overpotential or " phase boundary transition control " (PBTC) overpotential as it is referred to in Kashchiev's comprehensive treatment.lo It is true that he sought only to describe the effects of the separate effects of ohmic volume diffusion (mass transfer) or PBTC control and that he recognised the likelihood of mixed control. On the other hand the equations describing even the separate effects are complex and in the main not subject to analytical solutions.It might therefore be better at this stage not to attempt a single synthesis of the combined effects of capacitance mass-transfer and charge transfer in this way but rather to continue with the experimental delineation of the separable parts of the problem e.g. the direct determination of the nuclear density the direct determination of dN/dt along the transient and the direct determination of the activation and mass transfer components of the overpotential. The aim of the present work is to con- tinue with the application of multiple pulse methods to describe the complex features of nucleation transients. The authors are grateful to Dr. L. M. Peter for stimulating discussions. G. G. thanks the British Council and I. M. thanks the Instituto Nacional de Investigagao Cientifica (Portugal) for scholarships.G. J. Hills J. Thompson and D. J. Schiffrin Electrochiin. Acta 1974 19,657. S. Toschev and I. Markov J. Cryst. Growth 1965 3 436. M. Fleischmann J. R. Mansfield H. R. Think H. G. E. Wilson and Lord Wynne-Jones Electrochitti. Acta 1967 12 967. 'V. Klapka Coll. Czech. Cheiu. Conuii. 1969 34,1131. 100 POT EN T I0 S TA TI C-G A L V AN 0S T A TIC-P OTE N TI 0S T A TI C STUD Y V. M. Rudoi Soviet Electrochem. 1976 11 521. D. Kaschiev Thin Solid Films 1975 29 193. A. R. DespiC T. RakiC and V. JovanciceviC 25th Meeting oj’the interitntional Society for Electro-chemistry (Brighton 1974). * W. Meld and J. O’M. Bockris Canad. J. Chem. 1959,37,190. J. W. Gibbs Collected Works Thermodynamics (Yale University Press New Haven 1948) vol.1. lo D. Kashchiev and A. Milchev Thilr Solid Films 1975,28 189. G. A. Gunawardena G. J. Hills and I. Montenegro Electrochim. Acta 1977 in press. l2 G. A. Gunawardena G. J. Hills and S. McKee J. Electroanalyt. Chem. 1977 in press. l3 P. Bindra A. P. Brown M. Fleischmann and D. Pletcher J. Electroanalyt. Chem. 1975 58 39. l4 W. D. Weir and C. G. Enke J. Phys. Chem. 1967,71,280. l5 H. Matsuda S.Oka and P. Delahay J. Amer. Chem. SOC.,1959 81,5077. l6 G. Prabhakara Rao and S. K. Rangarajan J. Electroanalyt. Chem. 1973 41,473.

ISSN:0301-5696    

DOI:10.1039/FS9771200090

出版商:RSC    

年代:1977

数据来源: RSC