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.