Electrochemical kinetics of formation of monolayers of solid phases

Electrochlmlca

Acta,

1964, Vol

9, pp

757 to 771

Pergamon

Press

Ltd

hinted

m Northern

Ireland

ELECTROCHEMICAL KINETICS OF FORMATION OF MONOLAYERS OF SOLID PHASES* Department

M FLEISCHMANN and H R. THIRSK of Physical Chenustry, Umverslty of Newcastle-upon-Tyne,

England

Abstract-The mechamsms of crystal growth on electrodes are still mainly a matter for speculation, prnnardy because of madequate expenmental data In a few cases m which centres could be shown to grow m two or three dnnenslons it has been possible to charactenze the nature of the nucleation and growth processes of the crystals and to follow the concentration and potential dependence of In some examples, the formatlon of the lattice from adsorbed species can be the rate constants shown to be rate-determmmg In most cases of crystal growth the relative roles of electrochemical deposItIon, surface dlffuslon and lattice formation (and the formation of lattice growth sites) 1s uncertam, however, and it 1s of value to exploit procedures that seem hkely to produce such data Earlier work by the authors on the electrochemical growth of calomel m chlonde solutions under potentlostatlc condltlons mdlcated that the study of the growth of sohds on hqmd surfaces appeared hkely to gve data of this kmd The successive deposition of monomolecular layers of calomel was observed, the kmetlcs being shown to be controlled by the formatlon, growth and subsequent overlap of two-dlmenslonal centres This mechamsm IS sm-nlar to the classical mechanism of crystal growth except that lattice formatlon 1s the rate-determmmg step and that the formatlon of a large number of two-dlmenslonal growth centres IS observed Work has been extended to the formation of cadmium hydroxide on c&-mum amalgam and thallous chlonde on thallium amalgam A slrmlar pattern of behavlour can also be observed m the electrodeposltlon of metals, m addltlon to other oxide and hahde systems A general account 1s presented of the results of these mvestlgatlons, winch have combmed lcmetlc and structural studies The concentratatlon and potential dependence of the rate constants 1s discussed, together with some conslderatlon of the kmetlcs of the specific adsorptlon of ions, which precedes the crystal-growth process R&m&-Faute de don&s expenmentales suffisantes, le mkamsme de la crolssance cnstalhne sur Dans quelques cas cependant, la crmssance bi ou tndlmenles 6lectrodes demeure assez sphulatlf tlonnelle de germes ldentlfiables a pu i%re observk et nuse en relation avec la concentration et la tension apphquQ, pour certams systkmes, la formatlon du r&au B partlr des esp&es adsorb&s Dans la plupart des cas, malheureusement, les apparalt l’btape r6gulatnce du processus anttlque r8les respectlfs de l’&ctro-d6posltlon, de la dlffuslon en surface, de la formatlon du r&eau sont encore tres mcertams et l’acqmsitlon de nouvelles don&es expenmentales est done souhaltable Les auteurs rappellent leurs p&&dents travaux sur la crmssance 6lectrochlrnlque du calomel en solution de chlorures, dans des condltlons potentlostatlques 11semble que l’&ude de la crolssance Ce travail des sohdes g l’mterface d’un hqmde pourralt fourmr des renselgnements appropr& est lc16tendu aux formations de Cd(OH), sur (Cd, Hg) et de TlCl sur (Tl, Hg), des comportements analogues sont observables lors de l’tlectro-d&posltlon d’un m&al De l’ensemble de ces r&sultats, ISSUSconlomtement d’6tudes cm&ques et structurales, paralssent se dtgager les influences de la concentration et de la tensIon apphquQ sur la constante de vltesse, en tenant compte de la cmetlque de l’adsorptlon des ions, qm p&&de la crolssance cristalhne Zusammenfassung-Der Mechamsmus des Knstallwachstums an Elektroden 1st IIllfner noch em Nur m Geblet der Spekulatlon, hauptsachhch mfolge der unzulanghchen expenmentellen Daten emlgen wemgen Fallen, wo (m zwel oder drew DimensIonen wachsende) Zentren nachgewlesen werden konnten, war es moghch, die Natur des Kelmbddungs-und Wachstumsprozesses zu charaktensleren und die Konzentratlons-und Potentlalabhanglgkelt der Geschwmdlgkeltskonstanten zu verfolgen * Presented October 1963

at the 14th meeting of CITCE,

Moscow,

August

1963, manuscript

received 23

758

M FLEISCHMANN and H R THIRSK

In den melstcn Fallen von elektrochemlschem Knstallwachstum 1st Jedoch das Verhaltms des gegensatlgen Zusammenwu-kens der elektrochenuschen Abschadung der Obcrflachendlffuslon und des Gttteraufbaus (der Bddung von Gltterwachstumsstellen) ungewss, und es 1st wertvoll, die Methoden auszunutzen, welche zur Gewrnnungderartrger Informationen errmttelt werden konnen Fruhere Arbelten der Autoren uber die elektrochenusche Bddung von Kalomel m Chlondlosungen unter potentlostatlschen Bedmgungen deuteten darauf hm, dass das Studmm des Wachstums von Festkorpem auf flusslgen Obertlachen geqnet sem konnte, solche Informationen zu hefem Es wurde die sukzesslve Abscheldung von monomolekularen Schichten von Kalomel untersucht, wobel gezelgt werden kann, dass die Kmetlk des Vorgangs durch die Bddung, das Wachstrum und das nachfolgende uberlappen von zweldlmenslonalen Zentren beherrscht wlrd. Dleser Mechamsmus 1st dem klasslschen Mechamsmus des Knstallwachstums ahnhch nut Ausnahme der Tatsache, dass der Gltteraufbau geschwmdlgkeltsbestlmmend 1st und eme grosse Zahl zweldlmenslonaler Wachstumszentren beobachtet werden kann Die Untersuchung wurde auf die Bddung von Cadmmmhydroxyd an Cadmmmamalgam und von Thallochlond an Thalhumamalgam ausgedehnt Em glelches Verhalten kann lrn weitem such be1 Metallabschadungen me such be1 andem Oxyd- und Halogemdsystemen festgestellt werden Es urlrd umfassend uber die Resultate dleser Untersuchungen benchtet, welche kmetlsche und strukturelle Untersuchungen bemhalten Die Konzentratlonsund Potentlalabhanggkelt der Geschwmdlgkeltskonstanten wrd dlskutlert zusammen rmt emlgen Betrachtungen uber die Kmetlk der spezdischen Ionen-Adsorption, welche dem Knstallwachstum vorausgeht INTRODUCTION

THE mechanisms of crystal growth on electrodes have been mvestigated by several methods m recent years and, although much useful mformatton has been obtained, many details of the processes mvolved are still a matter for speculation In several cases the growth of discrete centres of the phase concerned has been observed to take place m two or three dimensions. 1-4 In these examples it has been possible to analyse the current/ttme transients observed at constant potential, to deduce the appropriate nucleation law and the rate constants governing nucleation and crystal growth. The concentration and potential dependence of these constants has indicated the mechanism of lattice formation. In several mstances the slow stage of crystal growth is m fact the formation of the lattice from adsorbed species formed by electrochemical preeqmhbna, and m two examples the hmlting behavtour of growth from a saturated monolayer has been observed.2ps These examples have naturally given no direct mformation about the relative roles of deposttton and surface diffusion prior to lattice formation. It has been claimed, however, that surface dtffuslon of adsorbed species to lattice growth sites can be demonstrated, by ac impedance measurements, m the electrocrystalhzation of metals 6 It has also been claimed that this can be demonstrated by measurements of potential/time curves at constant currents %’ although this view has been cnt1azed.s None of these experiments, however, gives any mformatlon about the kmetlcs of the formation of lattice growth sites The views on thts aspect of the model of the process rest entirely on theoretical speculation. The classical postulate m crystal growth has been that perfect crystal planes continue to grow because of the nucleation of twodimensional nuclei of the appropriate lattice plane D Crystal growth takes place at kmk sites m the steps of the two-dimensional patches.lO In view of the disparity between the theoretical supersaturatton or overpotenttal required to mltrate this nucleation and the actual values at which growth can still be observed, it has more recently been suggested that the lattice is formed instead at kmk sites m a self-perpetuating step such as that generated by screw dislocations meeting the surface.4v5J1p12 Evidence for this view has been drawn almost entirely from the morphology of crystals, although it has been suggested4 that the electrocrystalhzatlon of cadmium and tm13

Electrochemical kinetics of formation of monolayers of solid phases

159

m the steady state at low overpotentlals might be consistent with this model. Nonetheless there 1s no direct mformatlon on the kmetlcs of formation of lattice growth sites It 1spossible, however, to study the kmetlcs of crystal growth under such condltlons that the rate of formatlon of lattice growth sites (which on either view would be an edge whose height IS of atomic dlmenaons) becomes important m the overall process This sltuatlon would always be expected to apply for the formation of a new phase on a foreign substrate The kmetlcs are most easily formulated for a variant of the classical mechanism U-M If the new phase IS formed by the growth of two-dlmennonal centres then the current at constant potential due to a single circular centre is 2zFnMhk2t

1=

(1)

’

P

weight, h the height m cm, p the den&y m g/cm3 and k the rate constant of crystal growth m mole/cm2/s In contrast to the classlcal theory it 1s assumed that the slow stage IS the formation of the lattice at the periphery of the growmg centres, rather than surface dlffuslon with local quasi-equlhbrmm at the step In the classical theory it 1s also assumed that the formation of a single nucleus can lead to the deposition of one layer. Such a model 1s unlikely, however 4 If a single layer 1s formed from a large number of nuclei and nucleation 1s progressive with time, the number of nuclei 1s N = A’t, (2) where M IS the g-molecular

where A’ 1s m nuclel/cm2/s. Combmatlon of (1) and (2) gives zEnMhk2A’t2 1=

(3)

P

for the mltlal stages of growth Provided nucleation 1s completely random over the surface It 1s possible to derive the whole current/time curve for the deposltlon of a smgle layer takmg mto account all possible over1ap.4,14p15J7One obtains I=

.zFrMhk2A’t2

exp

nWk2A’t3

-

3p2

f

P

1 ’

(4)

while for the instantaneous formation of N, randomly distributed nuclei 1=

2zFrMhNa2t

(5)

P

l/3 1

The equation (4) predicts an m&al rise m current, reachmg a maxlmum current

I,=

4z3F%rh3pk2A exp t-2)

M

at a time t,=

2P2 [ ,rrM2k2A -

1

(6)

l/3

(7)

760

M FLEJXHMANN and H R THIIUK

in the case of progressive nucleation The current then decreases asymptotically to zero. An essential requisite for observmg the transient (4) 1sthat the nucleation should be truly random over the whole surface For this reason we have recently mvestlgated crystal growth on mercury and hquld amalgam substrates U-M It 1s likely that m the case of solid substrates the mteractlon of growth centres with boundaries and the lack of synchromzatlon between different regions on the metal would obscure the maxlmum and m the hmlt give rise to a current plateau, a pattern that 1s indeed frequently observed with sohd metals. Other factors which can obscure the transient

I 50

150

loci

Growthstep FIG 1 Sunulatlon of the growth of successive layers of calomel on mercury by the nucleation and growth of two-dnnenslonal nuclei , a fallmg nucleation rate with time with an mltlal rate of two nuclei per growth step

are chiefly the superposition at short times of the current transient due to specific adsorption whch has been shown to be relatively slow (time scale ~100 ,us)~~~~~J~J~ and the superposltIon of the transients due to succeeding monolayers or multlmolecular layers at long times.,, In fawourable cases mdlvldual peaks are well separated on the time axls and the posltlon of separate maxima can be observed The problem can be simulated m a dlgltal computer and 1s illustrated m Fig 1 l4 Patches are grown by the logical manipulation of dlglts, the co-ordinates of the nuclei being selected with pseudo-random numbers Expenmental transients can be fitted to such nmulatlons. Alternatively the data for a single peak can be tested m a number of ways For example from (4) ln;=ln

zF?rMhk2A’

p

.rr@k2A’tS

-

3p2

’

(8)

while a Taylor series expansion around t, for small displacements u gives I, f I_., M 21,

-

3 exp ($)M2z,3~2 2z2Fh2p2

’

(9)

Electrochemxal

kmetlcs of formatlon of monolayers

of solid phases

761

An alternatlve method, which IS useful, 1s to rewrite (4) m terms of t, and I,,,,

-=“exp[-;(-gl)]. 1

bn

L2

(10)

EXPERIMENTAL

Measurements of the kmetlcs of formation of the solid phases on hquld substrates have been carried out m cells of the type Illustrated m Fig 2 14-16 The electrode takes

Y-

FIG 2 Cell for the mvestlgatlon of the kmetxs of formatlon of thm films on mercury and amalgams

form of a segment of a sphere, the mercury or amalgam being extruded by means of a syrmge actuated with a micrometer The capillary on wluch the drops are formed and the Luggm capillary leading to the reference electrode are narrowed only at the end so as to mmmuze electrical resistance, and are also chamfered so as to reduce screenmg to a mmlmum. The subsldlary electrode IS m the form of a platinum hehx placed symmetncally around the workmg electrode After the extrusion of a drop at a chosen potential negative to the reversible potential of the phase to be formed, a sultable potential IS apphed usmg a potentlostat m conJunction with a pulse generator the

762

M Furs-

NandH

R.THIRSK

The potential IS raised to a value posrttve to the reversible potential either m one step or alternatively m two steps, the first to the appropriate reversible potential and the second to the chosen positive overpotential. The second procedure allows the effects of the specific adsorption of anions preceding crystal growth to be largely removed. In all cases current/time transients have been measured osclllograpmcally. Samples of the films to be examined by electron microscopy and diffraction have been prepared m cells of the type illustrated m Fig 3 The solid IS formed on a pool Diagram

of cell

electrode

FIG. 3. Cell for the preparation of thm fdms for electron mlcroscopy and electron dlffractlon

electrode again fed by a syringe A suitable potential pulse can be apphed by means of the potentrostat m conjunction with a pulse generator, and the workmg electrode can be isolated by swrtchmg a polarized relay usmg the fallmg edge of the pulse. Alternatively, a second working electrode at a lower level m the solution can be used together with a movable reference electrode mounted on a syrmge Joint. The deposit IS formed with a step pulse of chosen height and the Luggm capillary is then placed opposite the second workmg electrode. Usmg either method the solution level is then lowered and the deposit is washed with water (or, for example, alcohol). After drymg, a thm layer of Formvar IS applied which IS backed by a thrcker layer of collodlon These operatrons can be carried out under mtrogen m cases where oxidation by air rmght take place. The deposit 1s then separated, the collodron drssolved off and the sample examined by transmission microscopy and diffraction.

763

Electrochemrcalkmetrcsof form&on of monolayersof solid phases

0

I

I

I

I

I

4 Time,

FIG

I

I

2

6

ms

4 The rate of formatlon of calomel on mercury m M/10 HCl at an overpotentlal of 36mV

Examples of current/trme transients are illustrated m Figs. 4-8. For the formatron of calomel on mercury, Fig 4, the first system mvestrgated m thrs way,14 up to seven peaks can be drfferentrated under favourable conditrons, and these have been assigned

0

I

IO

I 20

I 30

I 40 Time,

FIG. 5 The form&on

I 50

I 60

I m

I 80

I

90

ms

of cuprous oxide on 0 4% copper amalgam m 1 M sodmm hydroxide at an overpotentlal of 9 mV

to the successrve deposmon of monomolecular layers. The formatron of the hexagonal cadmium hydroxide was subsequently shown= to be hmrted to the successrve depositron of three layers of monomolecular herght, the first two layers grvmg nse to drstinct maxlma. Another example studred IS the case of thallous chloride, where the formatron of a layer, consrstmg of several monolayers, by the mechamsm expressed m equatron (4) has been shown to succeed the deposmon of one monolayer at low and

M FLEBCHMANNand H R THIRSK

764

0

I

I

I

I

I

Time,

I

I

40

20

I

so

80

tns

FIG 6 The oxldatlon of cuprous oxide to cupnc hydroxide m 1 M sodmm hydroxide The cuprous oxtde was formed for 5 s at an overpotentlal of 180 mV and the oxldatlon camed out at an overpotentlal of 280 mV

I 4

I

I

I

8

12

16

Ttme,

ms

FIG 7 The deposltlon of mckel on mercury at -1300 mV with respect to a saturated calomel electrode Solution composltlon 0 01 M NICI~, 1 M NH,OH, 0 4 M NH&l, 0 4 M KC1

two monolayers at high overpotentlals lQ The deposltlon of one or successively of several layers can m fact be observed m a large number of systems ranging from salts to senuconductmg oxldes and metals. The behavlour IS illustrated m Fig 5 by the deposltlon of cuprous oxide on copper amalgam,80 m Fig 6 by the oxldatlon of cup rous oxide to cupric hydroxldeaO and m Fig 7 by the electrodeposltlon of nickel on

Electrochermcalkmetlcsof formatlon of monolayersof solid phases

765

mercury.21 Attention has also been drawn to the fact that the reduction of layers can proceed by the nucleation and two-dlmenslonal growth of “holes” 16S22This IS lllustrated m Fig 8 by the reduction of a monolayer of mdlum oxide 23 Thu oxide has a cubic lattice with a large unit cell. The reduction m 1 M potassmm hydroxide takes place m two stages, the first being the removal of a section of the layer by a rapld potential-dependent process, the second the removal of the remamder by a potentlalindependent reaction. In ddute hydroxide solutions the whole layer 1s removed m one stage With a few exceptions of this kind, the formation and removal of layers IS

I

I

4

8

Time,

FIG 8

I2

ms

The reduction of a monolayer of mdmm oxide at - 1300 mV with resp& to a

mercury/mercuric-oxide electrode The oxide was formed for 0 2 s at a potential of -4.00 mV 0 05 M KOH, 0 95 M KNO,

Solution 6omposltlon

found to be potentlal-sensltlve, the currents increasing and the ttme scale contracting with increasing magnitude of the overpotential The fact that thin layers of well-defined phases are formed has been confirmed by electron dlffractlon and these measurements have also shown that the layers are frequently highly orientated The form and size of the crystalhtes can be investigated simultaneously by electron microscopy The structural characterlstlcs of the anodlcally formed solids which we have studied, to date, differ in certain important ways which are relevant to the stencallydefined arrangement predominant In certain cases and absent m others, the observations of the growth habit 1s an essential part of the data determined m the course of the kinetic studies The unique arrangement of calomel formed on the surface of mercury has been examined m great detail m our laboratories (we have summarized relevant references elsewherel3, and we consider that the preferred manner of growth 1sthat most hkely, of all the systems studled, to give rise to two-dimensional growth centres This 1s substantiated by the results exemplified by Fig 4 The single crystal areas finally 6

766

M. FLEIBCHMAW and M. a. TWRSK

formed may sometimes be quite large, 10 ,u (Fig. 9), where the diffraction pattern arises from a layer of several umts of the crystal vector parallel to the electron beam, but showing very closely the umque onentatlon for the deposits with the (a&,) face diagonal and the c, axes of the tetragonal cell lying parallel to the mercury surface. Cd(OH),, with a layer lattice structure of the Cd& type, is clearly a compound that might favour two-dimensional growth with the c,, axis perpendicular to the substrate That this IS so will be mentioned briefly below, it has been discussed m detail elsewhere l5 Two oxide systems with large differences m their crystalline complexity have recently been mvestigated, In,4 and HgO. In,O, has the Tl,O, structure, this has cubic symmetry but a very large unit cell contammg 16 molecules. The metal atoms may be pictured on a face centred cubic lattice as m ZnS, m the idealized lattice there are 6 oxygens to place m the eight corners of the cube enclosed by the f.c c metal, so that there IS considerable distortion m the structure. Figure 10 shows a diffraction pattern of mdmm oxide due to random crystalhtes m the film with some secondary crystals oriented with respect to the substrate plane, We have noted that this system is exceptional m its extreme sensmvity to the electronbeam intensity, with these thm mdmm oxide films recrystallization readily takes place. The structure of HgO, on the other hand, is remarkably simple, conslstmg of zig-zag Hg-0-Hg chains lying along the b,, axes and m a parallel position through the centre of an orthorhombic umt cell of symmetry Imm The Hg-0-Hg chains all he m planes parallel to the (100) face and thus the structure consists of planar layers perpendicular to the long (C,> side of the unit cell The tetrahedral angle of the covalently bonded Hg-0-Hg chams arises from sp3 hybridization of electrons promoted from the 5d level of mercury, between the chains the distances are such as to indicate non-bonded van der Waals mteractlon A diffraction pattern from a typical thm film anodically formed on mercury is shown m Fig. 11; the evidence of the orientation indicates that the planes of the Hg-0-Hg chains are parallel to the substrate. Figure 12 is a diffraction pattern from a film of nickel electrodeposited on mercury. The presence of {1IO} irrational diffractions is only explicable if we assume that considerable relaxation m the conditions for diffraction is developmg due to the extreme thinness of the deposit DISCUSSION

The transients m Figs. 4-8 can frequently be shown to correspond to the deposition of monolayers of the expected chemical phase by the fact that the integrals under each peak agree with the quantity of electricity predicted for a single lattice plane m the cases where oriented deposits are formed, eg m calomel (Fig 9), where 100 ,uC/ cm2 are required for a one-electron transfer process In general we have found that the repeat unit m the direction perpendicular to the electrode is an appropriate vector of the unit cell. The general shape of the transrents resembles that predicted by (4), that the mechanism outlmed m the Introduction applies is also shown by the constancy of the product z,t,, (6) and (7) More detailed tests of the kmetics of formation can be based on eq (8), (9) and (10) The first can be shown to apply m cases where the current peak due to the deposition of the first layer does not overlap with current/ time transients due to any other electrochemical processes 15v18This is illustrated m

Electrochemical

L

kmetlcs of formatlon

dl’ monolayers of solrd phases

I

I

I 6

4

2

t?

767

J

8 x10-7

53

FIG 13 Test of the kmetlcs of reduction of a layer of mdmm oxide accordmg to (8) Expenmental condltlons as for Fig 8

..t/t, FIG 14 Test of the kinetics of reduction of a layer of mdmm oxide according to (10) Experimental condltlons as for Fig 8, with the oxide formed for 0 0 02 s, 0 0 2 s, 020s The full lme IS that predlcted by (10)

Fig 13 for the first step m the reduction of mdmm oxlde,23 whde Fig. 14 gives an lllustratlon m the dlmenslonless form (10) In cases where the mdlvldual peaks are not well isolated on the time axis, equation (9) can be applied, since the current due to the form&on of a single layer wdl be most nearly independent of all other layers m the vlcmlty of the maximum. The equation has been deduced for the growth of circular pitches, but 1s actually independent of their shapes provided that they are

768

M FLEISCHMANN and H R THIR~K

randomly dlstrlbuted and orlented A strmgent tesP4*151s to plot the slopes of the parabohc plots (9) agamst the cube of the current at the maximum. This 1s illustrated m Fig 15 by the formation of the first two layers of cadmium hydroxlde,16 the posltlon of the full lme bemg calculated from (9) usmg the crystallographic lattice spacing. These observations have several important consequences. The first 1s that monomolecular layers of a defined phase are formed at a very low overpotentlal which m some cases 1s of the order 5 mV This clearly demands that the deficit m lattice energy due to the absence of the three-dlmenslonal extension of the lattice 1s compensated by onentatlon polanzatlon of the solvent and the adsorption of countenons The final form of the deposit also consists of a few or, m some cases, even of one

A3/

cm6

FIG 15 Test of the kmetlcs of formation of a layer of cadmmm hydroxide on 1% cadmmm amalgam, accordmg to (9) 0 first layer m 5 M sodmm hydroxide 0 second layer m 5 M sodmm hydroxide 0 iirst layer m 1 M sodmm hydroxide n second layer m 1 M sodmm hydroxide The full lme IS drawn with the crystallographic values of It and p

monomolecular layer of the defined phase. This can be regarded as a Iimltmg form of adsorption, a view that was held at the begmnmg of this century The second major consequence 1s that a modlficatlon of the classical mechamsm of crystal growth can lead to the rapid formation of lattice planes. The modlficatlons he m the fact that a single layer 1s formed from a large number of nuclei rather than from one nucleus and that the slow stage 1sthe formation of the lattice at the periphery of the growing centres. Tlus slow step at the edge 1s clearly demanded by the fit to (9) m the vlcmlty of the maximum I,, t, In this region the growing centres overlap,

Electrcchemlcal

kmetlcs of formation

monolayers

of sohd phases

769

and, d any stages prror to lattrce formatron such as surface drffusron were m part ratedetermmmg, the rate of outward growth (determining k) would become time-dependent. This would lead to deviations from (9). The same conclusron 1s also demanded by the fact that the transients at a fixed overpotentral are independent of the amalgam concentratron m the case of growth on amalgams, so that transport of cations to the We have so far observed appreciable edges cannot be m any way rate-determining retardation due to discharge and surface dlffuslon only m the case of the crystal growth of metals The formation of the lattice at the edges of the growmg centres IS also likely to be the slow stage of crystal growth rf these edges are formed by a screw drslocation. It 1s of interest, however, that the rate of formatron of two-drmensronal nuclei can be extremely rapid at very low overpotentrals, particularly for the first layer This is presumably due to the high concentratron of adsorbed species that 1s already present at the reversible potential (analogous to the formation of monolayers below the saturation vapour pressure m the adsorption of gases), so that nucleatton takes place m a hrghly condensed layer The nucleation rate for the first layer 1s so high that rt 1s reasonable to assume the rate constant for this layer, Al’, to be nearly independent of overpotentral, nucleatron being ‘catalysed’ This catalysis 1s due to the reduction of the mterfacral free energy between substrate and solutron, a,, by the contact between the substrate and the monolayer, gS Classrcal nucleatron theory gives

, '3+(03 -(ul +u,)} Ii Nrrh201

RT

(11)

where a, 1s the surface energy between the nucleus and the solutron, k, the value of k at q = 0 and K a constant. The nucleation constant therefore remains finite as q -+ 0 On the other hand for the second and succeeding layers o3 - (cl + 02) 1s small and N?rha12M A,’ = Kk, exp (12) pzFqRT ’ It has been confirmed m a number of systems 1p16 that for the first two layers

(13) It is of interest that the so that the validity of (11) appears to be substantiated marked reduction m the two-drmennonal nucleation rate for the second and succeeding monolayers at low overpotentrals, (12), may support the hypotheses that continued growth under these condmons 1sdue to drslocatrons At hrgh overpotentrals the nucleation rates for all layers naturally become identical and constant (the value Kk,) so that the classical mechanism will again become dommatmg Thus 1s shown by the fact that the succeedmg peaks “catch up” on the first peak wrth mcreasmg overpotentral. If the nucleation rate constant for the first layer 1s taken to be virtually independent of overpotentral over the bulk of the potential range, the vanatron of the rate constant k with potentral and solutron and amalgam composrtron may be derrved from the

770

M. FLEBCHMANNand H R THIR~K

characteristics of the current/time curves such as z, or t,. The resulting composite rate constants kdA for three systems are illustrated m Fig 16 It has already been noted that the overall current/time curves are independent of the concentration metal m the amalgam and m consequence the constants kdA are also independent of this concentration The overall reaction leading to the formation of the lattice can be formulated m each case according to a number of possible schemes In the most

See legend Fkca 16 Vanatlon

of the rate constant kl/A with overpotenhal at low overpotentlals for the growth of the first monolayer of calomel, cadmmm hydroxide and thallous chlonde l Cadmmm

hydroxide kd/A osln

exp ‘$

- 1

@ Calomel kz/A us ln exp lSlF ~~ - 1 0 Thallous chlonde The full lmes are drawn with the theoretical slopes accordmg to the mechamsms suggested m the text

simple examples the mcorporatlon of one ion IS fast and the other slow, ze for a umumvalent lattice MX m simplest terms, either

%&my -M+ X,riphWy -=+

lattice

Xi&L?

04)

or X&lphery

-x-

lattice

Mp+enpherp -=+ M&m,

(15)

since the slow stages take place at the edges of the centres If these steps are formulated as normal slow electrochemical reactlons, the constants kdA would be expected to give Tafel hnes having defined slopes. The vanatron of the posltlon of these lines with solution composltlon has opposite signs for these two groups of mechanism

Electroehermcal

kmetms of formauon

of monolayers

of sohd phases

771

The full hnes m Fig. 16 have been drawn respectively m accord with a slow mcorporation of H&f mto the lattice m the case of calomel, the slow rearrangement of two OHions mto the lattice of cadmium hydroxide and two successive and independent firstorder steps leading to the formation of the thallous chloride lattice This mechamsm is demanded by the form of the kinetic expression k=k,(expg-1)‘. It is of Interest that the experimental pomts follow lmes of the theoretical slope at low overpotentials; the assignment of mechanism IS to a large extent based on this fit together with the concentration dependence It is also possible to make order-of-magnitude estimates of the rate constant k by deriving values of A either from a detailed fit of current/time curves to simulation results, by countmg the number of nuclei on micrographs or by countmg the number of dtiraction spots on selected area electron-diffraction patterns. These rate constants are large, of the order k, N 5 x 1O-3mole/cm2/s m the case of calomel and k, - 8 x le4 mole/cm2/s m the case of thallous chloride Such large values of k,, which are probably the highest values of electrochemical rate constants so far observed, can be determined only because reaction is confined to a few monolayers of the material. It is of interest that although the reaction at the periphery is fast, nevertheless it still represents the slowest stage of the overall process It appears likely that this ~111 prove to be a feature common to many electrocrystalhzation reactions. REFERENCES 1 M FLEJ.XHMANNand H R THIRSK, Trans Faraday Sot 51,71 (1955) 2 M FLEIXHMANN and M LILER, Trans Faraaizy Sot 54, 1370 (1958), M FLE~SCHMANN and H R THIRSK, Electrochzm Actu 1, 146 (1959) I DUODALE, M FLEI~CHMANNand W F K WYNNE-JONES, Electrochzm Actu 5,229 (1961) 3 M FLEISCHMANN,H R THIRSK and I TORDESILLAS,Tram Faraday Sot 58,1865 (1962) 4 M FLEJXHMANN and H R THIR~K m Advances zn Electrochemzstry, Vol III, ed P DELAHAY Intersclence, New York (1963) 5 W hRENZ, Z Naturf 9A, 716 (1954), Z phys Chem, NF 17, 136 (1958), Z phys Chem N F 19. 377 (1959) H GER&HE~, Z ,&lectrochem 62,259 (1958) J O’M Bocm and W MEHL, Canud -J Chem 37,190 (1959) M FLEISCHMANNand H R THIRSK. Electrochzm Acta 2.22 (1960) I N STIUNSKI, Z phys Chem 136; 259 (1928), I N STIZA&KI and R KAIsHEw,Phys Z 36, 393 (1935), M VOLMER,Dze Kzhetzk der Phasenbzldung Stemkopf, Dresden and Lelpzlg (1939) 10 R BECKER and W DORING, Ann Phys 24,719 (1935) 11 W K BURTON, N CAEIRERAand C F FRANK, Phzl Trans AlW, 299 (1951) 12 D A VERMILYEAJ Chem Phys 25, 1254 (1956) 13 R PIONTELLI,G POLI and G SERRAVALLE,Transactzons of the Symposzum on Electrode Processes, ed E YEAGER, p 67 John Wiley, New York (1961), R PIONTELLI, G POLI and L PAGANINI, Rend 1st Lombard0 Scz 93, 42 (1959), R PIONTELLI, G POLI and B RNOLTA, Rend Accad

Naz Lzncez 26,431 (1959) 14 A BEWICK, M FLEIXHMANN and H R THIRSK, Tram Faraday Sot 58,220O (1962) 15 M FLEJXHMANN, K S RAJAGOPALANand H R THIRSK, Tram Faradq Sot 59, 741 (1963) 16 M FLEISXMANN and H R T~RSK, J Electrochem Sot 110,688 (1963) 17 M AVRAMI,J Chem Phys 7, 1103 (1939), 8,212 (1940), 9, 177 (1941) 18 A BEWICK, M FLEI~CHMANNand H R THIRSK, to be published 19 M FLEISCHMANN,J PATTISONand H R THIRSK, to be ubhshed 20 M FLEISCXMANN,T MEAD and H R THIRSK, to be pu 1 hshed 21 M FLEISCHMANN,J HARRIESN and H R THIRSK, to be pubhshed 22 M FLEIXHMANN, K S RAJAG~PALANand H R THIRSK, to be published 23 A H Em, M FLEIXHMANN and H R THIRSK, to be pubhshed 24 S J BONE and C CARRILES,to be pubhshed