Electrochemical Phase Formation and Growth

E. Budevski, G. Staikov W. J. Lorenz

Electrochemical Phase Fomation and Growth

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E. Budevski, G. Staikov, W J. Lorenz

Electrochemical Phase Formation and Growth An Introduction to the Initial Stages of Metal Deposition

VCH

Weinheim New York Base1 - Cambridge - Tokyo a

Prof. Dr. E. Budevski Central Laboratory for Electrochemical Power Sources Bulgarian Academy of Sciences Sofia 1113 Bulgaria

Prof. Dr. E. Staikov Prof. Dr. W. J. Lorenz Institute for Physical Chemistry and Electrochemistry University of Karlsruhe KaiserstralJe 12 D-76131 Karlsruhc Germany

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Die Deutsche Bibliothck - CIP-Einheitsaufiialime Budevski, Evgeni B.: Electrochemical phasc formation and growth : an introduction to the initial stagcs of mctal deposition I E. Budevski ; G . Staikov ; W. J. Imrenz. Wcinhcini ; New York : Basel ; Camhridge ;Tokyo : VCH, 1996 ISBN 3-527-29422-8 NE: Stajkov, Georgi T.:: Lorenz, Wolfgang J.:

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Preface

This book is a result of a collaboration by the authors over a long period of time. It is devoted to fundamental problems of electrochemical metal deposition. The first part gives an introduction to electrocrystallization. The second part describes structure, morphology, and reconstruction of solid metal surfaces treated as crystalline s u b strates including the dynamic behavior of surface atoms. The third part treats surface modification by underpotential deposition (UPD) of metals. Physical nature, thermodynamics, structural aspects, kinetics, as well as surface alloy formation are discussed. Experimental support is given based on classical electrochemical investigations as well as on some recent results from modern in situ surface analytical studies including atomic imaging by in situ STM and AFM. In the fourth part of the book the problem of three-dimensional phase formation and growth by overpotential deposition (OPD) is presented. Thermodynamic and kinetic aspects are considered. The atomistic approach is discussed and illustrated on bare and UPD modified substrates. The f&h part deals with growth mechanisms of single crystal faces. The growth by 2D nucleation of quasi-perfect faces as well as the spiral growth mechanism of real crystal faces are discussed. Experimental verification is presented for the case of silver electrocrystallization. The transition from the initial nucleation stages of metal deposition to 3D compact bulk deposits is described in the sixth part. Nanoscale structuring and modification of solid state surfaces by in situ STM and AFM are also considered. At the end of the book, an outlook is given in which future research and some practical aspects of metal thin films and bulk deposits are discussed. The book is directed to advanced students and scientists working in the fields of electrochemistry, phase formation and crystal growth, surface chemistry and physics, ultrathin film formation, and structuring and modification of solid state surfaces. The authors gratefully acknowledge scientific cooperation with the following colleagues: R Kaischew and the coworkers V. Bostanov, D. Kashchiev, I. Markov, A. Milchev, W. Obretenov, A. Popov, S. Stoyanov, T. Vitanov, all working at the Bulgarian Academy of Sciences, Sofia, Bulgaria, as well as H. Fischer and the coworkers H. Bort,

v7

Preface

K. Engelsmann, A. Froese, H.-D. Herrmann, R Hopfner, K. Juttner, R Potzschke, U. Schmidt, S. Vinzelberg, N. Wiithrich, all working at the Institute of Physical Chemistry and Electrochemistry of the University of Karlsruhe, Germany. The authors also gratefully acknowledge international cooperation with the following colleagues: H. Rohrer (IBM Rlischlikon, Switzerland), E. Schmidt and H. Siegenthaler (University of Bern, Switzerland), B. Mutaftschiev (CNRS, Paris, France), D. Kolb (University of Ulm, Germany), J. van der Eerden (University of Nijmegen, The Netherlands), R Barradas (University of Ottawa, Canada), M. Fleischmann (University of Southampton, England), D. Roe (University of Portland, USA), J. Harrison (University of Newcastle upon Tyne, England), C. Mayer, S. Garcia and D. Salinas (Universidad Nacional del Sur, Bahia Blanca, Argentina), M. Froment (CNRS, Paris, France), R Wiart (CNRS, Paris, France), P. Allongue (CNRS,Paris, France) and W. Paatsch (Bundesanstalt fiir Materialforschung und -priifung, Berlin, Germany). For helpful and critical discussions during preparation of this book the authors are indebted to E. Schmidt, D. Kolb, and W. Schmickler (University of Ulm, Germany) and V. Bostanov (Bulgarian Academy of Sciences, Sofia). The authors would also like to thank I. Mackiw, K. Richter, A. Froese and R T. Potzschke for technical assistance preparing this book. Special gratitude should be expressed to the following associations for making possible long-time projects by financial support: Bulgarian Academy of Sciences (BAS), Deutsche Forschungsgemeinschaft (DFG), Arbeitsgemeinschaft Industrieller Forschungsgemeinschaften (AIF), Bundesministerium f i r Bildung und Forschung (BMBF), Deutsche Gesellschaft fur Chemisches Apparatewesen und Biotechnologie e.V. (DECHEMA), Fonds der Chemischen Industrie, and Volkswagen-Stiftung, T h e STM images obtained by the Karlsruhe electrochemistry group and presented in this book were taken with commercial NanoScope I1 and I11 instruments produced by Digital Instruments, Santa Barbara, USA. The authors gratefully acknowledge successful cooperation with this company in respect to R&D. Extended exchange of scientists between Sofia and Karlsruhe over a period of more than two decades was supported by BAS and DFG, Alexander von Humboldt Stiftung, Deutscher Akademischer Austauschdienst (DAAD), and International Seminar for Science and Teaching in Chemical Engineering, Technical and Physical Chemistry at the University of Karlsruhe, to all of whom we express our thanks. Finally, the authors gratefully acknowledge the cooperation with the publisher VCH, Weinheim. Evgeni Budevski Georgi Staikov Wolfgang J. Lorenz

Contents

1

Fundamentals of Electrocrystallization of Metals .....................

1

1.1

Thermodynamic and Kinetic Aspects ...............................................................................

1

1.2

Metal Deposition Mechanisms .........................................................................................

4

1.3

Topics of this Book ...........................................................................................................

-7

2

Crystalline Metal Surfaces ...........................................................

9

2.1

Structural Aspects ..............................................................................................................

9

Close-packed 2D and 3D crystal structures .................................................................... Crystal imperfections and surface inhomogeneities ......................................................

9

.................................................................................................... Surface roughness and the kink position ........................................................................ Step roughness ................................................................................................................ Atomic Dynamics .............................................................................................................

20

Atom exchange frequencies ............................................................................................

20

Local. partial. and overall current densities ....................................................................

23

Kink atoms and the Nernst equilibrium potential ..........................................................

24

....................................................................... Concentration of adatoms................................................................................................

25

Surface reconstruction

2.2

Exchange current density of kink atoms

2.4

13 16 19

26

.......................................................................... Mean residence time and surface displacement of adatoms ........................................

-28

Surface Profile Mobility ...................................................................................................

29

Surface diffusion and mean displacement of adatoms....................................................

30

Surface diffusion.The exact solution ..............................................................................

30

Direct transfer ..................................................................................................................

36

Current density on a stepped crystal face.......................................................................

37

Conclusions ......................................................................................................................

39

Exchange current density of adatoms 2.3

12

29

WZI

Contents

3

Underpotential Deposition of Metals . 2D Phases ...............41

3.1

Historical Background..................................................................................................... 41

3.2

Phenomenology ............................................................................................................... 43

3.3

Thermodynamics.............................................................................................................

52

Thermodynamic formalism.............................................................................................

52

Adsorption isotherm models ........................................................................................... 55 3.4

3.5

3.6

Experimental results ........................................................................................................

58

Structures of 2D Meads Phases ......................................................................................

63

Degree of registry ............................................................................................................

63

Internal strain ...................................................................................................................

68

Electrochemical results ...................................................................................................

71

Comparative and ex situ UHV results.............................................................................

74

In situ surface analytical results ......................................................................................

75

Kinetics ..........................................................................................................................

101

Quasi-homogeneous substrate surface approach........................................................

102

Inhomogeneous substrate surface approach ................................................................

107

Phase transitions............................................................................................................

111

2D and 3D Me-S Alloy Formation ................................................................................ Phenomenology .............................................................................................................

128

Thermodynamics...........................................................................................................

129

Structures of 2D and 3D Me alloys ...............................................................................

134

Kinetics ..........................................................................................................................

140

128

3.7

Conclusion ..................................................................................................................... 146

4

Initial Stages of Bulk Phase Formation

4.1

Equilibrium Form of Crystals and Forms of Growth ...................................................

................................

.. form............................................................................................................ Equilibrium ....................................................................................... Gibbs-Wulff-Kaishew theorem .................................................................................... "kdimensional crystal ............................................................................................... Forms of growth ............................................................................................................ Crystal-substrate interaction

149 149 149 150 152 154 156

Lx

Contents

Energy of cluster formation...........................................................................................

157

3D nucleation .................................................................................................................

157

2D nucleation .................................................................................................................

160

Gibbs-Thomson equation .............................................................................................

161

Nucleation Rate ..............................................................................................................

163

Classical approach (Volmer and Weber) ......................................................................

163

Kinetic approach (Becker and Doering) .......................................................................

165

Binding energies and energy of nucleation ..................................................................

166

Atomistic model .............................................................................................................

168

Nucleation rate equation ................................................................................................

171

Small cluster model .......................................................................................................

173

Experimental results......................................................................................................

174

3D Phase Formation on UPD Modified Foreign Substrate Surfaces ..........................

180

UPD-OPD transitions ...................................................................................................

181

Nucleation and growth ..................................................................................................

182

Epitaxy............................................................................................................................

184

Experimental results ......................................................................................................

185

4.4

Conclusions....................................................................................................................

199

5

Growth of Crystalline Faces .....................................................

5.1

Dislocation-Free Crystal Faces .................................................................................... 201

4.2

4.3

201

Preparation of single crystal faces by electrodeposition ..............................................

203

Double pulse technique .................................................................................................

207

Nucleation rate-overvoltage dependence .....................................................................

210

Time distribution of the nucleation events ...................................................................

213

Form of growth of monatomic layers ............................................................................

214

Propagation rate of monatomic steps ............................................................................

216

Space distribution of nucleation events.........................................................................

221

Propagation rate of polyatomic steps ............................................................................

223

........................................

225

Mechanism of metal deposition and adatom concentration

X

Contents Growth Kinetics of Perfect Faces .................................................................................

226

Mononuclear layer-by-layer growth ............................................................................

227

Multinuclear monolayer formation ...............................................................................

227

Deposition kinetics on quasi-perfect crystal faces.......................................................

231

Real Crystal Faces .........................................................................................................

235

Dislocations....................................................................................................................

235

Spiral growth mechanism..............................................................................................

237

Theory of spiral growth .................................................................................................

239

Growth morphology ......................................................................................................

245

Steady state and transient current densities.................................................................

252

Impedance behavior ......................................................................................................

257

5.4

Conclusions....................................................................................................................

260

6

Metal Deposits and Surface Structuring and Modification .263

6.1

Formation of Compact Me Deposits.............................................................................

263

Phenomenological classification of 3D Me deposits ....................................................

263

Texture. epitaxy and morphology of 3D Me deposits ..................................................

264

Impedance studies of 3D Me deposition ......................................................................

270

Metal deposition by pulse techniques...........................................................................

271

Laser-induced metal deposition....................................................................................

275

Electrodeposition of 3D Me alloys ................................................................................

280

6.2

Theoretical Considerations...........................................................................................

280

6.3

Ultrathin Metal Films and Heterostructures................................................................

283

Ultrathin metal films on foreign metal substrates ........................................................

286

Heterostructures on foreign metal substrates ..............................................................

288

Ultrathin metal films on semiconductor substrates .....................................................

294

Surface Structuring and Modification...........................................................................

299

Metal single crystal surfaces .........................................................................................

300

HOPG surfaces ..............................................................................................................

304

HTSC thin film surfaces ................................................................................................

308

5.2

5.3

6.4

Semiconductor single crystal surfaces.......................................................................... 311 6.5

Conclusions....................................................................................................................

312

XI

Contents

7

Outlook.......................................................................................

8

Appendices

8.1

Compilation of Experimentally Studied Me-S(hk0 UPD Systems ...............................

317

References to Appendix 8.1 ...........................................................................................

322

8.2

Thermodynamics of an Ideally Polarizable Electrode.,................................................

327

8.3

Mean Field Theory and Adsorption Isotherms ............................................................

333

8.4

Monte Carlo Simulation of l/n Adsorption ..................................................................

335

8.5

Transfer Function of Me UPD on Inhomogeneous Substrate Surfaces

337

8.6

Thermodynamics of 3D Me-S

...................... Bulk Alloy Electrode ...................................................

339

8.7

Instantaneous and Progressive Nucleation ..................................................................

342

9

References .................................................................................

9.1

Chapter 1........................................................................................................................

343

9.2

Chapter 2 ........................................................................................................................

344

9.3

Chapter 3........................................................................................................................

346

9.4

Chapter 4 ........................................................................................................................

362

9.5

Chapter 5........................................................................................................................

366

9.6

Chapter 6........................................................................................................................ 371

9.8

Chapter 8 ........................................................................................................................

10

Abbreviations and Symbols

10.1

Abbreviations.................................................................................................................

381

10.2

Symbols ..........................................................................................................................

383

................................................................................

.....................................................

315

317

343

380

381

.......................................................................................

393

Subject Index........................................................................................

405

Author Index

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

1 Fundamentals of Electrocrystallization of Metals

1.1

Thermodynamic and Kinetic Aspects

Electrocrystallization denotes nucleation and crystal growth in electrochemical systems under the influence of an electric field i1.1-1.211. Electrocrystallization of metals takes place at an electronic conducting substrate / ionic conducting electrolyte interface including, in general, three stages: i)

Formation of metal adatoms, Meads, on native metal substrates, Me, or on foreign substrates, S, via adsorption,

ii) Two-dimensional (2D) and three-dimensional (3D) Me phase formation via phase transitions (nucleation) and cluster growth, and iii) Crystal growth of the 3D Me bulk phase.

A foreign substrate, S, is a solid with a different composition from that of Me, and is considered as electrochemically inactive in a certain potential range which is considered in this book. A 2D Me phase is considered as a specific Me adsorbate located in the inner Helmholtz plane of the electrochemical double layer existing at a substrate/electrolyte interface. A 3D Me phase can be either a bulk phase or a small atomic cluster of Me, where bulk has the meaning of infinitely large. There are two major factors which have to be considered in the process of electrochemical metal deposition. First, thermodynamics and growth properties of 2D Me and 3D Me phases can be treated in a similar manner to that for Me deposition from vapor or electrolyte phases. Second, the properties of the electrolyte phase strongly affect the structure of the substrate/electrolyte interface, the kinetics of the mass and charge transfer across it, and the kinetics of chemical reactions which can precede or follow the charge transfer. In this book the problems connected with the formation and growth of 2D and 3D Me phases are discussed more closely, while the problems arising from the ionic

1 Fundamentals of Electroclystallization of Metals

2

conducting electrolyte phase are treated as simply as possible. In the last chapter of the book, the implications arising from the character and the properties of the electrolyte phase are considered briefly, treating the electrocrystallization process as a whole. The stability ranges of 2D Me and 3D Me phases on S are characterized by the Nernst equation describing the thermodynamic equilibrium for Me deposition and dissolution on native and foreign substrates. For 3D Me bulk phase formation and growth on native substrate Me and dissolution of the 3D Me phase, the overall reaction of the Me/MeZt electrode is

where Me:& are solvated metal ions in the electrolyte phase. The Nernst equilibrium of the Me/MeZt electrode is given by:

EMeIMeZ+ is the Nernst equilibrium potential of the Me/MeZt metal ion electrode, E0 denotes the standard potential of the Me/Mezt metal ion electrode, and Me/MeZ+ aMeZtis the activity of Me:, ions in the electrolyte. For a pure 3D Me bulk phase, a M e is equal to unity. The actual electrode potential, E, determines the direction of reaction (1.1). 3D Me bulk phase can be deposited cathodically at E < EMe/MeZ+. On the other hand, 3D Me and dissolves anodically. Therefore, the bulk phase is unstable at E > EMe,Mez+ , represents the upper limit of the stability Nernst equilibrium potential, EMe/MeZ+ range of a 3D Me bulk phase. The crystallization overpotential (overvoltage), vc, of the Me/Me” electrode was defined by Vetter [1.8, 1.9]*thus:

and ~ u~ ~ ~ , Mdenote ~ ~ ~ the ~ ~ activities of Meads at E # EMelMeZ+ and E = EMe/Mez+, respectively. This definition supposes that all additional steps involved in reaction (1.1)such as charge transfer, diffusion, and chemical reactions are fast, so that they can be considered to be in thermodynamic equilibrium. Then, as their contribution to the overpotential can be neglected qtotal = qc . Me deposition happens

where

U

M

*Theterm “crystalliiation overvoltage“ was first introduced by Fischer [1.1,1.10]and Lorenz [1.111 in conjunction with the term “adatoms“.

1.1 l7aermodynamic and Kinetic Aspects

3

at cathodic overpotentials, qc < 0, i.e., at supersaturation, Ap > 0, while Me dissolution takes place at anodic overpotentials, qc > 0, i.e., at undersaturation, Ap < 0. Supersaturation or undersaturation, Ap, is defined by

using the chemical potential p i = + (RT)In ai where py denotes the standard chemical potential of component i. Deposition of Me on a 3D native bulk phase proceeds by incorporation of atoms in “kink site“ positions as a final step of the overall reaction (1.1) (cf. Section 2.1). In contrast, Me dissolution can also take place at all sites where lattice atoms are more loosely bound to the crystal than kink atoms. Usually dissolution starts, in addition to the kink sites, at crystal edges and corners, or at surface defects and inhomogeneities. Therefore, the Me deposition-dissolution processes are not necessarily symmetric. At the Nernstian equilibrium potential, E,,,zt the equality

holds (cf. Sections 2.2 and 3.2). Needless to say, the second part of equation (1.5) holds in all cases for 3D Me bulk phases. In the case of Me phase formation on foreign substrate S, the overall reaction of the S/MeZ+electrode is

For a 3D Me bulk phase on top of S, the thermodynamic equilibrium is again given by the Nernst equation (1.2). The actual electrode potential, E, determines the direction of reaction (1.1).This statement is valid, however, for 3D Me bulk phases only, while small 3D Me cluster phases have a more negative potential of stability, E < (cf. Section 4.1). Under certain conditions, 2D Me phases are stable at E > EMe/MeZ+ and Ap < 0 (undersaturation) on a foreign substrate S. Therefore, in this case the potential difference E -EM,,,,,+ is defined by convention as [1.22-1.261: def - EMvle/Mez+

-

AE (underpotential)

1q

> 0

(overpotential)
EMeIMez+ for^ < E

~

~

/

~

~

~

,

1 Fundamentals of Electrocrystallization of Metals

4

In this case, the Nernst equilibrium potential, EMe,Mez+, represents the limit of the stability ranges of both 2D and 3D Me phases. At E = EMelMez+, 2D and 3D Me phases coexist. Consequently, underpotential deposition (UPD) and overpotential deposition (OPD)of Me on S are connected with the formation of 2D and 3D Me phases, respectively. In the case of Me UPD at E > EMelMeZ+ in eq. (1.3), vC must be replaced by hE according to eq. (L’7). The process of Me OPD on S becomes identical with that of Me OPD on Me if the deposited Me film on S exceeds a certain thickness and behaves like a 3D Me bulk phase. Then, eq. (1.6) becomes identical with eq. (1.1).Usually, the critical thickness ranges between one and about twenty Me monolayers on S. If UPD and OPD processes of 2D and 3D Me phase formation are investigated under non-equilibrium conditions, then Ap and, therefore, 17 and AE can be influenced by the reaction kinetics. For example, the charge transfer itself, mass transport, and chemical reaction steps which precede or follow the charge transfer can be kinetically hindered. Then, Ap, 17, and AE are determined not only by crystallization overvoltage and underpotential as defined in eq. (1.3), but also contain charge transfer, diffusion, and/or chemical reaction contributions.

Metal Deposition Mechanisms

1.2

The most important parameters determining the mechanism of UPD and OPD of Me on a foreign substrate are the Meads-S binding energy and the crystallographic misfit between S and a 3D Me bulk deposit. Considering the deposition process at nearly equilibrium conditions, i.e., small supersaturation and negligible kinetic influences, and disregarding M e 4 alloy formation, two different growth modes can be distinguished as schematically illustrated in Fig. 1.1 (cf. also Section 3.3) [1.20, 1.21, 1.27-1 301. I

i)

In the first case (Fig. l.la), the binding energy of Meads on foreign substrates S, ! P M ~ , ~is ~ -lower s , than that of Meads on native substrate Me, Y‘M~,~,-M~. Consequently, the surface concentration of Meads at EMelMeZ+ is small, and OPD of a 3D Me bulk phase takes place on an unmodified substrate surface according to the “Volmer-Weber” or 3D island growth mode independent of crystallographic Me-S misfit.

1.2Me Deposition Mechanisms

5

ii) In the second case (Figs. l . l b and l.lc), the binding energy of Meads on the foreign substrate S, Y M ~ ~ is~ higher ~ - s ,than that of Meads on native M ~ . 2D Meads phases can be formed in the substrate Me, Y M ~ , ~ , -Then, UPD range and the surface concentration of Meads at EMe,MeZ+canreach one or more Meads monolayers depending on Y M ~ , ~ , -Two s . different subcases can be distinguished: iil) In systems with negligibly small crystallographic Me-S misfit (Fig. Llb), 2D Me UPD overlayers and 3D Me OPD crystallites are epitaxially oriented following the “Frank-van der Merwe” or layer-by-layer growth mode up to the disappearance of the strong Me-S attraction. Further Me growth continues in a layer growth fashion as on native Me substrate (cf. Chapter 5). iid In systems with significant crystallographic Me-S misfit (Fig. l.lc), the 2D Meads phase formed in the UPD range has a different structure compared to that of the 3D Me bulk phase, and contains considerable internal strain. The formation and growth of unstrained 3D Me crystallites (islands) on top of strained 2D Me overlayers is energetically favored following the “Stranski-Krastanov” growth mode. The misfit between the 2D Meads phase and the 3D Me bulk phase is mainly removed by misfit dislocations [1.28-1.31]. Generally, in Me UPD systems with non-vanishing solubility of Me in S, the formation of a 2D Me-S surface alloy and/or a 3D Me-S bulk alloy becomes energetically possible even in the UPD range. A 2D Me-S surface alloy is considered as site a exchange processes between Me and S across a limited number of surface layers. 2D and 3D Me-S alloy formation processes are often kinetically hindered and difficult to study. However, in some Me UPD systems, clear evidence was found experimentally for such 2D and 3D Me-S alloy formation processes, complicating Me UPD phenomena. 2D Meads overlayers, 2D Me-S surface alloys, and 3D Me-S bulk alloys, if present in the UPD range, can act as precursors for the nucleation and growth of the 3D Me bulk phase in the OPD range (cf. Chapter 4).

1 Fundamentals of Electroctystallizatwn of Metals

6

IGgure 1.1 Schematic representation of different growth modes in metal (Me) deposition on foreign substrate (S) depending on the binding energy of Meads on S, !?'M~,~~-S, compared to that of Meads on native substrate Me,!PMeads-Me, and on the crystallographic misfit characterized by the interatomic distances d o , ~and c do,s of 3D Me and S bulk phases, respectively. (a) "Vohner-Weber" growth mode (3D Me island formation) for Y M ~ ~~! -Vs M ~ ~ ~and - Mratio ~ (do,& - do,s)/do,s PS 0. (c) "Stranski-Krastanov" growth mode (3D Me island formation on top of predeposited 2D Meads overlayers on s for Y M ~ ~>>~yMeads-Me ~ - s and ( d o , ~-edo,s)/dos> 0 (positive misfit) or (do,Me - do,s)/d0sc 0 (negative misfit).

-

1.3 Topics of this Book

1.3

7

Topics of this Book

Texture and the surface morphology of metal deposits are strongly affected by crystal properties of the depositing metal as well as by mass and charge transfer across the interface boundary. The incorporation of metal atoms into a crystal lattice, i.e., the growth process of a crystal, depends on the crystallographic character of the growing surface and is mainly affected by the surface structure itself. The surface of a solid metal substrate has a complex character. Areas occupied by crystallites on the surface with different crystallographic orientations and intergrain boundary regions can be differentiated. In addition, crystal defects (atomic disorder, monatomic steps with atoms in kink site positions, dislocations, etc.), adsorbed molecules, oxide layers, etc., complicate the state of substrate surface. The simplest conditions can be expected when single crystals are considered. Therefore, the structural and dynamic aspects of crystalline metal surfaces are dealt with in Chapter 2. Chapter 3 describes the 2D Me phase formation in UPD systems. Chapter 4 deals with Me nucleation and 3D phase formation. In Chapter 5, the growth of perfect and real crystal faces is reviewed. Finally, in Chapter 6, the transition from initial stages to compact 3D Me deposits as well as nanoscale structuring and modification of electron conducting solid state surfaces by UPD and OPD of metals using in situ STM and AFM are discussed.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

2 Crystalline Metal Surfaces

2.1

Structural Aspects

The surface of a crystalline solid is strongly correlated to its bulk structure. The atoms of a crystal are arranged in a periodical sequence forming the crystal lattice. Most frequently metals and metal alloys tend to form close-packed sphere (cps) arrangements reflecting the isotropy of the forces of atomic interaction.

Close-packed 2D and 3D crystal structures There are two possible cps arrang&ments,the hexagonal close-packed (hcp) and the face centered cubic (fcc) crystal lattice. In both cases the planes of highest atomic density, (0001) and (lll), respectively, have the same two-dimensional (2D) hexagonal close-packed (2D hcp) structure, Fig. 2.1. The sequence of consecutive planes forming the bulk cps structure, however, are different : In the first case the atoms of every second layer (i.e., every even layer) occupy one of the three (every second out of six) concavities, e.g., B in Fig. 2.1, around each

Figure 2.1 Two-dimensional hexagonal close-packed structure.

* The term "2D hcp" is used in the following to describe the 2D structure at the surface and should not be confused with the common term for the packing of a 3D crystal lattice.

10

2 Crystalline Metal Sugaces

Figure 2.2 Three-dimensional hexagonal close-packed crystal lattice structure. The atoms of the third layer are positioned above those of the first layer. The atoms of all following layers repeat the positions of every second preceding layer. The structure is denoted as an ABlzB . . . structure. The basal face, (OOOl), has a 2D hcp structure. The layered structure of the prismatic faces is also clearly seen. The unit cell of a hcp crystal containing 17 atoms is given on the right-hand side.

sphere, A, while the atoms of every consecutive odd layer are positioned exactly above the atoms of the first, giving rise to an ABAB. . . sequence of planes and to a hexagonal close-packed (3D hcp) bulk structure, Fig. 2.2. In the second case every third consecutive layer occupies a concavity lying above a concavity of the first layer. Therefore, an ABCABC . . . sequence of planes results, forming a face-centered cubic (fcc) 3D Me bulk lattice, Fig. 2.3. The unit cells of both crystal lattice structures are also given in Figs. 2.2 and 2.3.

Figure 2.3 Three-dimensional face-centered cubic crystal lattice structure. The atoms of every third and all consecutive third layers are positioned above an empty B or C place of the first layer. A crystal with cubic and octahedral faces results. The structure of the octahedral (111) faces is a hcp structure. The smooth quadratic structure of the cubic (100) faces is also clearly seen. The unit cell containing 14 atoms is shown on the right-hand side. The (111) plane is given by the hatched surface.

2.1 Structural Aspects

11

A deviation from the normal stacking in both hcp and fcc bulk structures leads to the so-called stacking faults. For example, in the fcc bulk structure a stacking fault of the type . . . ABCABABCA . . . causes a thin layer across the lattice to have a hcp bulk lattice sequence . . . ABAB . . .. Stacking faults are related to so-called twin crystals, particularly contact twins. Contact twins have a common contact plane with the same crystallographic indices, and in the hcp or fcc structures are rotated by 60' with respect to each other. A fcc contact twin is characterized by a sequence . . , ABCABCABACBACB . . . across the twin boundary layer. As seen, the stacking fault changes the sequence from ABC to ACB across the twin boundary layer.

Figure 2.4 A hemispherical silver single crystal develops during electrochemical growth flat faces belonging to the equilibrium form. The front cubic face, (loo), is surrounded by four triangular octahedral faces (111) and four round rhombododecahedral (110) faces. The flat regions around the (111) faces are kinetically stabilized vicinal (311) faces and belong to the so-called form of growth l2.41.

12

2 Crystalline Metal .%$aces

At equilibrium the surface of a crystal is surrounded by flat, atomically smooth, low-index, high atomic density faces lying parallel to corresponding planes of the bulk. In Frank’s classification, these faces are denoted as singular faces, because they correspond to the singular points, where the polar diagram of the specific surface energy shows a cusp with a minimum for cs [2.1], but see also [2.2]. Burton and Cabrera [2.3] classified the crystal faces with respect to their capability to grow into close-packed and step#ed surfaces. In the case of a fcc crystal the close-packed singular faces are the cubic, (loo), and the octahedral, ( l l l ) , faces. T h e rhombododecahedral face, (110), can also be considered as a singular non-stepped face, Fig. 2.4. All other faces can be derived as composed of the two, (111) and (loo), basic types of faces showing equidistant monatomic steps lying parallel to each other. These faces are known as vicinal faces and have higher Miller indices. In the case of a hcp crystal only the basal plane (0001) is atomically smooth. The two prismatic faces (1001) and (1100) are also singular faces, but, although atomically stepped, they can be considered as smooth surfaces, similar to the rhombododecahedral face of a fcc crystal. The equilibrium form faces are defined by the Gibbs-Curie theorem [2.5, 2.61 requiring a minimum surface energy, @, of the crystal at constant temperature and volume (cf. Section 4.1). Having the lowest specific surface energy, 0,singular faces belong always to the equilibrium form faces. Depending on growth conditions, crystals can be confined also by kinetically stabilized faces with higher indices. Thus, the growth form of a crystal can be different from the equilibrium form.

Crystal imperfections and surface inhomogeneities Generally the following imperfections of a 3D crystal lattice can be distinguished: OD: point defects, such as atomic disorder, vacancies, interstitials, 1D: edge and screw dislocations, 2D: grain boundaries, stacking faults, 3D: crystal domains with different chemical or physical properties, which lead to the following surface inhomogeneities: OD: point inhomogeneities, such as atomic disorder, vacancies, interstitials, emergence points of edge and screw dislocations, 1D: monatomic steps generated by screw dislocations, intersection lines of grain boundaries, and/or stacking faults,

2.1 Structural Aspects

13

2D: surface domains (grains) with different chemical and physical properties, macrosteps. Further surface inhomogeneities such as reconstruction, adatoms, kink sites, and cluster formation are induced thermally or by the electrode potential as discussed in the following. Surface reconstruction

The surface top layer of a 3D crystal lattice often deviates from the corresponding bulk lattice plane with respect to atomic distances and structure [2.7, 2.81. If only the interatomic distances between surface atoms and underlying bulk atoms are different compared to these within the bulk crystal, the phenomenon is called su&ce relaxation. In this case the structure of the surface remains unchanged [2.7]. However, when as well as the interatomic distances between surface atoms and underlying bulk atoms, the surface structure, and the lateral distances in the top layer are changed, the phenomenon is called surfdce reconstruction. This phenomenon is observed under UHV as well as under in situ electrochemical conditions [2.7-2.111. The reason for surface relaxation and surface reconstruction is the minimization of the specific surface energy of the system. Surface reconstruction can be induced either thermally or by the electrode potential. As a typical example, the surface of Au(100) and Au(ll1) under UHV and electrochemical conditions is normally reconstructed as shown schematically in Fig. 2.5. Note that the top layer of Au(100) exhibits not a quadratic, but quasi-hexagonal Au(100)-(5 x 20) Au 2D surface structure. However, this surface structure has an extended corrugation due to the misfit between top layer and the underlying (100) bulk planes. In the case of Au(ll1) surface, a Au(ll1)-(1 x 23) Au 2D surface layer is observed which is compressed by about 4 percent in the (110) direction causing every 23rd atom to be in registry with the underlying bulk atoms [2.10]. Different findings show a A u ( l l 1 ) - ( a x 23) Au 2D surface layer [2.11]. Experimental results obtained under in situ electrochemical conditions are shown in Fig. 2.6 [2.101. Surface relaxation and surface reconstruction phenomena can be lifted thermally, by adsorption of foreign species, or by changing the electrode potential in the case of electrochemical systems [2.10]. In the case of Au(hkl) surfaces, the influence of the electrode potential on the structure of the surface top layer is illustrated in Fig. 2.7. The transition from the reconstructed to the unreconstructed surface top layer represents a first order phase transition process in many cases.

2 CrystallineMetal Su&ces

14

Au(100) - (5 x 2 0 ) A ~

Au(ll1)- (1 x 1)Au

Figure 2.5 Reconstructed Au top layer on an Au(100) face (Au(100)-(5 x 20)Au) (a), and compressed top layer of Au on anAu(ll1) face (Au(ll1)-(1 x 23)Au) @).

It is clear that surface reconstruction phenomena play an important role in electrochemical 2 D and 3D phase formation processes. Lindsay [2.11] has shown that in the underpotential range (cf. Chapter 3) 2D Pb monolayer domains are formed preferentially along the stripes of reconstructed Au(ll1) surfaces. In many cases the electrochemical formation of 2 D and 3D Me phases on foreign substrates S occurs in such potential ranges where surface reconstruction phenomena can be disregarded.

2.1 StructuralAspects

15

168 nm x 168 nm

275

0 nm

Figure 2.6 In situ STM images of a freshly prepared Au(ll1) substrate showing the initial thermally induced reconstruction rows (visible as stripes) for different surface areas I2.101. System Au(lll)/ 10" M H2SO4 at E = - 150 mV vs. SCE and T = 298 K (a): top view of an atomically smooth surface, and (b): 3D representation of a face with a monatomic step. Reprinted by permission of Kluwer Academic Publishers.

16

2 Cqstallhe Metal Su&ces

4.8 nm x 4.8 nm

4.8 nm x 4.8 nm

Figure 2.7 In situ 5TM images illustrating the influence of the electrode potential on the surface structure of a Au(100) substrate IZ.10). System Au(lOO)/lO-l M H2S04 at T = 298 K. (a) and (c): E = - 200 mV vs. SCE; (b) and (d): E = 300 mV. Images (a) and (b) show atomic resolution of reconstructed (rows) and unreconstructed surfaces; (c) and (d) represent larger scans emphasizing reconstruction rows and monoatomically thick islands, respectively. Reprinted by permission of Kluwer Academic Publishers.

Surface roughness and the kink position Due to thermal fluctuations, singular faces show at elevated temperatures a degree of surface roughness manifested by the presence of single adsorbed atoms (udatoms) and/or by the absence of atoms in the surface lattice structure, known as vacancies, Fig. 2.8. In addition di- and poly-atomic clusters of adatoms or vacancies can be formed. On steps, if present, kink site positions can be distinguished. The density of kink sites gives an additional degree of surface roughness, the step roughness.

2.1 Structural Aspects

17

Figure 2.8 The structure of a singular face of a crystal with a simple cubic lattice at lower temperatures.

T h e surface roughness is a function of temperature and becomes appreciable above a critical roughening temperature, Tr, only. The theoretical value of Tr for a crystal with a simple cubic lattice is Tr = 0.6r,q/k [2.1], where v/1 denotes the bond energy between two first neighbor atoms. This relation gives critical temperatures of surface roughening lying around or above the melting point. In reality the critical temperature is lower but not substantially lower than the melting point. At room temperatures singular faces of metal crystals show a relatively low degree of roughening and exhibit only single adatoms and monatomic vacancies, as well as kink sites on steps, if present. Among the different surface atom positions illustrated on Fig. 2.8, the kink site position, or the half crystal position, as introduced independently by Kossel [2.121 and Stranski [2.13], has a special significance for the definition of the equilibrium conditions (vapor pressure, equilibrium concentration, equilibrium electrode potential, etc.) of the infinitely large (bulk) crystal. The salient feature of the kink position is the fact that if an atom is removed from such a position, the next atom, in the row of the step edge atoms, will find itself in the same position. The removal of a kink atom from the step edge does not change the structure of the surface and is, hence, a repeatable step. A sufficiently large crystal can be disintegrated (evaporated or dissolved) by consecutive removal steps (detachment

18

2 CrystallineMetal Sugaces

steps) of kink atoms, so that the energy of disintegration can be calculated by summation of the separation work of all crystal atoms assumed as kink atoms. The deviations caused by other types of atoms, as found for instance in the case of atoms at the beginning or the end of a row, which have a different energy of detachment, would be insignificant. The second remarkable feature of an atom in a kink position is that it is bonded to the crystal with exactly one half of the bonds of one bulk atom. This is schematically illustrated in Fig. 2.9 for a crystal with a simple cubic lattice. The parts A, B, and C represent exactly the missing half of the infinitely large crystal. After adding A, B, and C, the half crystal position is changed to a bulk position. For a crystal with a hcp or fcc (bulk) lattice, a kink atom or an atom in a half crystal position has 6 first neighbors, that is, half of the coordination number of a bulk atom. The third very important feature of a kink atom is the fact that it represents the final stage of the transfer of an atom from the ambient phase to the crystal. Only after integration of an atom in a kink position can the atom be considered as belonging to the bulk crystal. Therefore, a kink site can be considered as the site of growth or dissolution of the crystal.

Figure 2.9 The half crystal (or kink) position. The figure shows the binding energy of an atom in a kink position and how the name “hulfcrystu2position“ has been derived. A represents the missing part of the bulk crystal above the surface plane, B the missing half of the surface plane, and C the missing half of the atomic row along the step in front of the kink atom. They all together add the half crystal to a bulk crystal.

2.1 Structural Aspects

19

According to Volmer t2.141 the chemical potential, & & k , of kink atoms is related to the separation work of an atom from a kink position, &ink, by the equation

where Ehk is the mean vibrational volume of kink atoms. NA &ink and RT In EM represent the enthalpic and entropic contributions, respectively. The separation work of an atom from a kink site position into a vacuum is equal to the sublimation enthalpy, ASu& of the crystal assumed as infinitely large:

Considering a crystal with hcp or fcc lattice and first neighbor interactions only, &ink is given by

Here lyl is the work of separation of two neighbor atoms in the crystal lattice or the binding energy between two first neighbors. Usually only differences of chemical potentials A,U;,~= f i - ,q of atoms in various crystal positions i, j are theoretically considered and because the mean vibrational volumes u”;, E j are roughly equal, A,u;,~ can be given, according to eq. (2.1), by the respective separation works 4 :

Step roughness

From viewpoint of the process of deposition or growth, it would be of interest to make an assessment of the step roughness as defined by the density of kink atoms per unit step length, because it would give an important kinetic parameter of growth. The step roughness can be given as the reciprocal of a normalized mean distance parameter &ink /do,Me, where &ink is the mean distance between kink atoms and do,Me is the atomic diameter. For the most dense step [110] on a cubic (100) face of a fcc crystal, the mean distance parameter is i2.1, 2.151

(2.5)

2 Crystalline Metal Surfaces

20

With a typical value of the sublimation enthalpy of metals, A , , d = 150 kJ mof', the detachment enthalpy (work of separation) per atom in a kink position is calculated to be &ink = 250 x J and the binding energy of two next neighbor atoms to be t,q = 41.7 x J per atom. With that value of ty1 every 75th atom on a step would be in a kink position at room temperatures. This calculation may be roughly valid for a metal crystal face in a vacuum. In presence of condensed phases, however, as in the case of electrochemistry, the specific surface energy, a, may be decreased significantly, decreasing at the same time the effective value of the bond energy iy1 compared to that estimated from the desorption energy of a kink atom in a vacuum. A more reasonable value for the aims of eq. (2.5) can be found from the specific surface energy a, or the related specific edge energy E, as given, e.g., by Chernov L2.151:

The value of ~1 calculated in this way obviously includes a part of the hydration energy of the surface atoms, as considered by Conway and Bockris [2.16, 2.171, For the case of silver in 6M &NO3 at T = 318 K, a value of E = 2.1 x J cm" has been found (cf. Chapter 5), giving, with do,& = 2.88 x l o a cm, v/1= 1.52 x J per bond. With this value of ~ 1eq. , (2.5) shows that every fourth atom is in a kink position [2.15].

2.2

Atomic Dynamics

Atom exchange frequencies It has been mentioned already that the exchange of kink atoms with the ambient phase can be used for the definition of the equilibrium. This statement is based on the fact that the separation of kink atoms requires the same Gibbs energy as the average disintegration energy per atom of an infinitely large crystal, which is related to the chemical potential of the atoms in the bulk phase. According to Kaischew [2.18], the definition of the equilibrium conditions involves the frequencies of attachment and detachment. In the case of attachment-detachment processes of atoms of a crystal from/into a gas phase, the conditions are relatively clear: The attachment frequency is simply proportional to the impingement rate of atoms, i.e., proportional to the partial pressure of the atoms of the gas phase. It has roughly the same value for all surface sites.

2.2 Atomic Dynamics

21

The detachment frequency is proportional to the exponent of the work of separation (or bond energy) of the particular atom at the particular site. For a kink atom, as already discussed, the work of separation is equal to the sublimation enthalpy per atom (cf. eq. (2.2)). In the case of electrodeposition of metals, however, the charge transfer across the electric field of the double layer, as well the ion-solvent interaction, have also to be considered. According to Kaischew [2.18], the attachment (deposition),Wdepr , or the detachment (dissolution), Wdiss,x*, frequencies [s-l] of atoms to or from a site x of a crystal surface, respectively, can be given for this case by

where E is the electrode potential measured vs. a reference electrode (cf. Appendix 9.1). The AG""' values are the activation energies for the ion transfer from the solution is the to the crystal, or vice versa, at E = 0. a is the charge transfer coefficient, aMeZ+ activity of metal ions in the electrolyte, and kdep,x and kdiss;rf are rate constants for the deposition and the dissolution reaction at site x and x*, respectively. These equations can be applied for any site x. One should remember, however, that any unoccupied site x is changed to an occupied site x* after an ion transfer to that particular site: diss (-1)

u

X

*u

A 7

dep (+I)

"X"

(2.9)

For instance, an adatom site "ads" on the surface is transferred to an unoccupied or "free" adsorption site after dissolution. A "surface atom" site is changed to a vacant site "vac" on the surface, accordingly. In both cases each single ion transfer changes the number of sites on the surface by unity: "ads"

"surface atom"

diss (-1) A

7

dep (+I)

"free"

(2.10)

"vac"

(2.11)

2 Cgstalline Metal Suflaces

22

Discussing the exchange of atoms on a site x or x * (both can be arbitrarily used for x“ must always be the description of the site), the conjugated reaction “x* considered. It should be noted that the conjugated reactions are asymmetric because x, representing a non-occupied site x *, is not identical to x* and the numbers of sites per unit area n, and n,p are also not necessarily equal. Even more, after an ion transfer event these numbers change by unity, f 1. This should all be carefully taken into account when considering the equilibrium. The only (exceptional) site that remains unchanged after deposition or dissolution is the kink site (“kink). Any deposition or dissolution event just shifts the kink site by one atom along the step, but does not change the number of kink sites on the step or the surface, nor changes the character of the site. “kink

diss (-1) A

7

dep (+1)

“kink

(2.12)

9 nm x 9nm

Figure 2.10 In situ STM image showing the frazzled appearance of a monatomic step on Ag(ll1) substrate [2.22].SystemAg(lll)/ld4MCuSO4+5x 10-2MH2SO4atE=60 mVvs.SCEandT=298 K. Reprinted from Surface Science Letters, Vol. 327, M. Dietterle, T. Will, D.M. Kolb, Step dynamics at the Ag(lll)-electrolyte interface, p. U95,1995, with kind permission of Elsevier Science.

2.2Atomic Dynamics

23

Recently, monatomic steps, which look frazzled in STM images, were observed by several authors [2.19-2.221. An example for a monatomic step on Ag(ll1) is shown in Fig. 2.10. This phenomenon was attributed to a mobility of kink sites on step edges.

Local, partial, and overall current densities With the charge, ze, transferred by deposition or dissolution of one single atom, a formal local current density, or , for each site of type x or x*, respectively, can be defined, taking into account the conjugated pair of reactions (eq. 2.9):

ig$ ik:$,

local = idep,x

-

qmon Wdep,x

(2.13 a)

(2.13 b) where R is the area occupied by one atom on the surface of the respective face and qmon = z e / R [C cmV2]is the charge needed for the deposition of one monolayer per unit surface area. Note, that for any different atomic surface arrangement, R, and consequently qmOn,have different values. For the 2D hcp surface arrangement of a hcp or fcc crystal and for the (100) face arrangement of a fcc crystal, R has the values :

The local current densities are imaginary quantities derived for an imaginary surface where all sites N = 0-lare occupied by one single type of surface atom. With the exception of these, corresponding to the kink sites, the conjugated local current densities are not equal even at equilibrium. One can introduce also partial current densities, idqJand idissr*,of the sites type x and x* as averaged current densities for the whole face, given by the product of the local current densities, and idissJx*, local and the coverages n,/N and n p / N of the surface by sites x and x*:

ik$

(2.14 a)

(2.14 b)

2 CrystallineMetal Su$aces

24

At equilibrium all conjugated, "x*

x", partial current densities are equal

(2.15) forming partial exchange current densities ioJand iOJ*,characteristic for the sites x or, arbitrarily, x* [2.23]. Obviously, the partial exchange current densities represent a part of the overall exchange current density given by 2

o,Me/MeZ+

.

= Ci0,i I

With (eq. 2.14) follows also

The detachment frequency WdiSS,X* is characteristic for the particular site x". It depends on the structure of the site but not on the general structure of the surface. The detachment frequency is, obviously, a system property. Being generally different from the deposition frequency Wdep,x, it cannot be used for the definition of the equilibrium of the crystal with its ambient phase. The equality (eq. 2-16), however, involving nx and nx* can be used for the definition of the equilibrium coverages as a function of the potential. The restriction discussed above does not apply to the kink sites, however, where the numbers of sites of deposition and dissolution are always equal (nx= n,.), so that, at equilibrium, the equality (2.17) holds for the kink sites uniquely, offering a possibility for the definition of the equilibrium of the crystal as a whole, regardless of its surface structure.

Kink atoms and the Nernst equilibrium potential Using the equilibrium condition for kink sites given by eq. (2.17) and eqs. (2.7) and (2.8) it follows

2.2Atomic Dynamics

25

which is the Nernst equation:

EMe/Mez+ = E0

Me/Mez+

+-RT fl

lna

(2.19)

Me"

i

Neglecting the entropy terms*, the difference A G $ ; ~ -~~ ~~ t t ( s o s =l NAq&k,$ ~~~) represents the dissolution energy of kink atoms involving &ink (cf. eq. 2.2) arid additional energy contributions connected to the presence of the electrolyte solution. This is denoted by the subscript "s". The first two terms in the first equality give a constant as required by the Nernst equation. Note, however, that &ink,s is related to the chemical potential of the bulk Me atoms. Equation (2.19) is, therefore, strongly valid for sufficiently large crystals (cf. Section 4.2). The equilibrium potential of a crystal is unambiguously determined by the exchange frequency of kink atoms. The concentration of kink sites has no effect on the potential, but the presence of kink atoms is essential for the establishment of the equilibrium potential.

Exchange current density of kink atoms The equilibrium condition for kink atoms requires an equality between the rates of deposition and dissolution, thus forming an exchange current density of kink atoms. follows: From (2.14) for E = EMeIMeZ+

(2.20) or from eqs. (2.14 a) and (2.7)

nki& [kinks ern-'] is proportional to step density, i.e., to the total step length per unit surface area, Ls [cm ern-'], and to the number of kinks per unit step length, Skik (cf. Section 2.1): nkmk = Ls / 6 k i n k .

* This approximation is allowed as far as differences of

4 are used (cf. Section 2.1).

26

2 CrystallineMetal Sut$aces

(2.22)

Then ko,kink is a Constant including &ink, the kinetic Constant kdep,kbk, as Well as the activation energy term of eq.(2.21) According to eq. (2.21), the exchange current density of kink atoms, io,kjnk, depends on the concentration of kink atoms nkink. As long as the surface profile of a crystal face, which depends on the pretreatment and includes an arbitrary number of steps populated by kinks, the exchange current density of kink atoms is not a constant quantity, but depends on step density Ls or on the s u ~ a c etopography. It cannot be considered as a system property. This is because io,kink is an averaged quantity, extended to the whole surface involving an arbitrary number of kink sites. Owing to the symmetry of the attachment-detachment process on a kink site from eq. (2.21), a local exchange current density (cf. eq. (2.14 a)) may be defined (2.23) This quantity is independent of the surface profile and directly connected to the exchange frequencies @dep,kmk or @diss,kmk and can be considered as a system property giving a key to the kinetics of the metal ion transfer reaction. The local exchange current density as defined by eq. (2.23) is an imaginary quantity assuming a surface fully covered by kink sites. Needless to say, the number of kink sites per unit surface area must be known for the determination of i:& from io,kink or vice versa. Concentration of adatoms

The adatom concentration at equilibrium, no,& [atoms cmm2],is determined by the Gibbs energy AGdispl W mol-'1 of the displacement reaction of atoms from kink positions to "free" adsorption sites on the surface, where it can form an adatom [2.11: (2.24) The preexponential term is equal to the number of free sites per unit surface area nfree. As already discussed, at room temperature the number of occupied adsorption sites is very small, so that nfree o N. The displacement energy AGdispl can be obtained as the

2.2Atomic Dynamics

27

difference of the chemical potentiaIs of kink atoms and adatoms, and is approximately given by AGdispl FZ NA(&ink- +a&). The separation work of an atom from an kink site position, &ink = ASua/N~, is a constant characteristic for the crystal, while depends on the crystallographic character of the face and contains the difference of the enthalpies of free and occupied adsorption sites. AGdispl and accordingly no,ads depend on the crystallographic character of the face. The equilibrium adatom concentration is a well-defined thermodynamic quantity characteristic for the respective crystal face. It does not depend on the profile of the su@ace, particularly on the presence of steps as long as %free = N. The equilibrium condition for adatoms with the ambient phase is, in accordance with eq. (2.16) : Wdiss,ads no,ads = Wdep,free nfree

at

E

=

EMe/Mez+

(2.25)

Hence, with eqs. (2.7) and (2.8), and nfree = N = f2-I one obtains

and

] . constant kads includes the where Co,ads is the adatom concentration in [mol ~ m - ~The difference AG!L;kee - AG!{::ads, representing the dissolution energy of one adatom at E = 0. It includes also the ratio of the kinetic constants kdep,freeand kdiss,ads,as well as f2 and NA. At equilibrium, the electrode potential is equal to the equilibrium potential E = EMe/Mez+ , and is a function of activity aMez+of the metal ions in the solution. The activity term aMeZ+in eq. (2.27) can be eliminated using the Nernst equation (2.19), so that (2.28)

2 Crystalline Metal Sulfaces

28

where EGelMez+ is the standard potential. The equilibrium adatom concentration Co,ads, as expected from eq. (2.24), is independent of the ion activity aMeZ+and the actual value of the equilibrium potential EMe/Mez+

*

Lf, however, for any reason, the electrode potential deviates from the equilibrium potential and the balancing equilibrium with kink atoms is blocked, as, e.g., in the absence of steps and kink sites (cf. also Section 2.3), the adatom concentration may change until a dynamic equilibrium between deposition and dissolution is reached: Wdiss,free nads = w dep,free nkee. The adatom concentration, flads, or Cads, becomes a , so that function of electrode potential, E, or overpotential q = E - EMelMeZ+

(2.29)

At more negative potentials, i.e., at higher (negative) overpotentials q, the adatom concentration increases because the flux of ions from the solution increases accordingly. Exchange current density of adatoms

One can also ascribe an exchange current density to the adatoms. The partial deposition and dissolution current densities of adatoms, idep,free and idiss,ads respectively, can be evaluated from eq. (2.14), giving with nkee x N = 0 -1 (2.30 a) Idiss,ads =

ze wdiss,ads nads

(2.30 b)

At the equilibrium potential both partial current densities are equal forming the exchange current density of adatoms: io,ads = I idep,freeI = idiss,+ds. From eq. (2.30 b), replacing f l a d s by Co& at E =EMeIMeZ+ and e by F, one obtains with eq. (2.8) (2. 31)

The exchange current density of adatoms is a thermodynamically well defined quantity. It depends on the Nernst potential or on the respective ion activity, and is, in general, as long as flfree x N holds, independent of the surface topography.

2.3 S u ~ a c eProfile Mobility

29

Mean residence time and surface displacement of adatoms The mean residence time of adatoms on a crystallographic face is given by the dissolution frequency I / Z r = wdiss,ads, and using eq. (2.8) l2.171: r..=

1

-

1

(2. 32)

The mean residence time is potential-dependent and is related to the anodic (dissolution) current density of the adatoms. Multiplying eq. (2.32) with eq. (2.31) and by 71 one obtains replacing E - EMe,MeZ+ zr =

(2.33)

7

where

.

(2.34)

To,r = flco,ads zo,ads

is the residence time of adatoms at the Nernst equilibrium potential. zu,ris a function of or the Nernst electrode potential EMe,MeZ+ via io,ads. the ion activity aMeZ+ During their stay on the surface, adatoms are subject to thermal drift making an average random surface displacement &d (2.35)

where D s d is the surface diffusion coefficient of adatoms. The average displacement of adatoms during their life on the surface is a function of overpotential 7.

2.3

Surface Profile

Mobility

If the potential of an atomically smooth (non-stepped) singular face is changed, e.g., to a value more negative than the reversible potential, the enhanced deposition rate will increase the adatom concentration above its equilibrium value Co,ads until the opposite reaction of dissolution idiss,ads reestablishes the balance. The adatom concentration Cads(7) increases and becomes a function of overpotential as given by eq. (2.29). idep,free

30

2 Crysfalline Metal Su~aces

Surface diffusion and mean displacement of adatoms In the presence of steps, in the close vicinity of the step edge, the kink-adatom exchange reaction will keep the adatom concentration at its equilibrium value Co,ads, At a distance from the step greater than the mean displacement Ad (cf. eq. (2.35)), however, adatoms deposited on the face cannot reach the step edge during their lifetime on the surface, so that the adatom concentration will remain unaffected by the presence of the step and equal to Cads( q). This causes a diffusion flux, Dsd(Cads - Co,ads) /Ad, of adatoms towards the step edge, where the adatoms are rapidly incorporated into kink positions. Therefore, the adatom concentration at the step edge is kept at the equilibrium value Co&. At room temperatures, where the average kink distance, &ink (cf. eq. (2.5)), is low and smaller than the mean displacement of adatoms, diffusion along the steps can be neglected and the diffusion process can be treated as linear. The incorporation of atoms in the step results in a step propagation with a rate Vsd [cm s'l] determined by the flux Dsd Ac,ds/&d [mol cm*'S1] and the area .RQR[)NAoccupied by one mole. Atads vsd = - O ( h k l ) NA Dsd _ _ sd

a

ZF Dsd

With eq. (2.35) for Ad and eq. (2.29) for

Atads ___

co,ads

(2.36)

~

a sd

qmon

-

cads -Co,ads co,ads

one gets*:

The factor 2 accounts for the two equivalent fluxes from both sides of the step. For zFIqI/RT > Sstep, Le., the surface diffusion penetration depth is much larger

than the average step distance. This is equivalent to a high surface diffusion rate or a very rough surface profile. With tanh(i&P/&,d) = &tep/$d

38

2 Crystalline Metal Suflaces

for &d > IOSStep, equation (2.51) yields a Butler-Volmer relation i = io,ads v(q). For instance, Fig. 2.13b shows that the current is distributed uniformly over the surface and the concentration profile is also flat and uniform (Fig. 2.12b), for $d > 3.1Sstep In this case the charge transfer is the rate-determining step and the current density is unaffected by the surface morphology. Deposition and dissolution proceed as on a liquid surface. (ii)

asstep, i.e., a flat face with large terrace

regions, or a very low surface diffusion coefficient. The tanh term in eq. (2.51) becomes equal to unity, &d 5 0.3&ep would be sufficient, so that $d


Ssteprespectively are dependent on the step density. Being linearly dependent on step density both equations are homomorphous. Experimentally they are indistinguishable from each other unless other quantitative identitication criteria are found. A high-indexed surface zone with a high density of steps or growth sites (kink positions) would follow the same growth law as liquid metals, i.e., the Butler-Volmer relation. Vicinal faces, characterized by low-index surface zones separated by uniformly distributed monatomic steps show an intermediate behavior. Consequently, non-singular faces are faceted and transformed into vicinal faces during growth. Subsequently, vicinal faces are transformed into singular faces because of step propagation and growth. Thus, in a later stage of growth, a perfect crystal will be bound by low-index singular faces. For a perfect, defect-free crystal bound by singular faces, the only way for further growth is the formation of 2D clusters of Me

2.4 Conclusions

39

atoms giving birth to a new lattice net. Then the peripheral steps of 2D islands make possible atom incorporation into the crystal lattice. This mechanism is known as the 2D nucleation mechanism of growth, and will be discussed in Chapter 5. Defect-free crystals are, however, rarely found or produced. Real crystals show defects that make the nucleation process not indispensable, and create conditions for growth at lower supersaturations or overpotentials. Among the defects making the process of growth easier, the defect known as a screw dislocation has a special significance. The step emanating from the emergence point of a screw dislocation cannot disappear during growth and winds into a spiral giving rise to the so called spiral growth mechanism. The spiral growth mechanism was predicted by Frank in 1949 [2.35], and will be treated in detail in Chapter 5.

2.4

Conclusions

The surface structure as well as the nature, density, and distribution of surface inhomogeneities determine the thermodynamic and dynamic properties of a crystalline substrate/electrolyte interface. Surface structure and surface inhomogeneities are mainly affected by the 3D crystal structure and crystal imperfections as well as by temperature, electrode potential, and electrolyte composition. Different surface inhomogeneities such as point defects, adatoms, kink sites (OD), monatomic steps, surface grain boundaries (lD), surface domains with different chemical or physical properties, macrosteps, clusters, pits and islands (2D), and surface roughness (3D) strongly influence the initial steps of electrochemical 2D Me phase formation on foreign substrates in the UPD range (cf. eq. (1.7)) and those of electrochemical 3D Me phase formation and growth in the OPD range (cf. eq. (1.3)) as described in the following Chapters.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

3 Underpotential Deposition of Metals - 2D Phases

3.1

Historical Background

Formation of Meads on polycrystalline inert metals (Pt, Au) as foreign substrates S was initially studied using radiotracer measurements by Haissinski et al. [3.1-3.41, Voicu [3.5], Rogers et al. [3.6-3.151, Haenny et al. [3.16, 3.171, Bowles [3.18-3.233, and Frumkin et al. [3.24]. Electroanalytical experiments gave additional evidence for the formation of Meads in the underpotential range. Mills and Willis [3.25] investigated amperostatically the cathodic reduction of Tl’,Pb2’, Bi3’, and Sb3’ on polycrystalline silver and gold electrodes. They found that a part of the measured charge amount must be related to an adsorption of metal ions in the underpotential range. Nicholson [3.26, 3.271 and Nisbet and Bard [3.28, 3.291 studied chronoamperometrically the anodic dissolution of copper, silver, and lead deposits from polycrystalline platinum substrates. The stripping of metal deposits was found to be extended into the underpotential range. Similar results were obtained by various authors in different Me UPD systems L3.30-3.431, In the sixties and early seventies, detailed electrochemical studies were carried out by Schmidt et al. [3.44-3.681 in different Me UPD systems using polycrystalline substrates and introducing different electrochemical thin-layer techniques: “singleelectrode thin-layer” (STL) [3.48], “twin-electrode thin-layer” (?TI,) L3.551, and “flow-through thin-layer” (ITIT) i3.67, 3.681 techniques. These thin-layer techniques were successfully applied to study quantitatively the charge-coverage stoichiometry of 2D Meads overlayer formation on polycrystalline substrates in the underpotential range. Similar experiments were carried out by Bruckenstein et al. [3.69-3.811 using the “rotating ring-disc electrode” W E ) technique. Some authors combined electrochemical investigations with optical and UHV studies L3.82-3.861. In the seventies, Me UPD experiments on metal single crystal faces as foreign substrates were started by Lorenz, Juttner, Schmidt, Siegenthaler, Staikov, and Budevski et al. [3.87-3.1091, Yeager et al. I3.83, 3.841, Bewick et al. [3.110-3.1141,

3 UnderpotentialDeposition ofMetak - 20 Phases

42

Schultze et al. t3.115-3.1201, and Kolb et al. [3.121-3.1281. The experimental results gave evidence of the formation of well-ordered 2D Meads overlayers in the underpotential range depending on the crystallographic orientation and the crystal imperfection density of S. Electrochemical results were first hypothetically interpreted in terms of "2D Meads superlattice structures" [3.87-3.89, 3.93, 3.981, which were also observed in comparative f3.121, 3.122, 3.129-3.1331 and ex situ t3.123-3.1281 UHV studies. In the last decade, important information on the structure of 2D Meads overlayers, the mechanisms of 2D Meads overlayer formation, and UPD-OPD transition processes was obtained by in situ application of surface analytical methods such as X-ray scattering (GMS, EXAFS), second harmonic generation (SHG) , and local probe techniques which give lateral atomic resolution (STM, AFM), Gordon, Abruna, Toney, Melroy, and Ross et al. [3.134-3.1451 determined structures and interatomic distances of 2D Meads overlayers on vapor-deposited (111) oriented single crystal substrates as a function of the Meads coverage using in situ GMS and EXAFS. Richmond and Koos [3.146, 3.1471 obtained structural information from SHG measurements. Hansma et al. [3.148, 3.1491, Bard et al. [3.150, 3.1511, Kolb and Behm et al. [3.152-3.1551, Gewirth et al. [3.156-3.1621, Itaya et al. [3.163-3.1671, Lindsay et al. [3.168], Siegenthaler et al. [3.169-3.1791, Lorenz, Staikov, Budevski et al. [3.171-3.174, 3,180-3.1921, Green et al. [3.193-3.1951, and Siradzki et al. [3.196, 3.1971 investigated the structure of monocrystalline substrate surfaces and 2D Meads overlayers on an atomic level as well as the mobility of surface profiles by in situ STM and AFM. Different authors studied substrate surface reconstruction phenomena and their influence on Me UPD [3.1983.2081. First theoretical interpretations of Me UPD by Rogers L3.7, 3.121, Nicholson L3.209, 3.2101, and Schmidt 13.451 were based on an idealized adsorption model already developed by Herzfeld [3.211]. Later, Schmidt [3.54] used Guggenheim's "interphase concept" [3.212, 3.2131 to describe the thermodynamics of Me UPD processes. Schmidt, Lorenz, Staikov et al. [3.48, 3.57, 3.89-3.94, 3.100, 3.214, 3.2151 and Schultze et al. [3.116-3.120, 3.2161 used classical concepts to explain the kinetics of Me UPD and UPD-OPD transition processes including charge transfer, Me:& bulk diffusion, and nucleation and growth phenomena. First and higher order phase transitions, which can participate in 2D Meads phase formation processes, were discussed controversially by various authors [3.36, 3.83, 3.84, 3.92-3.94, 3.98, 3.101, 3.110-3.114, 3.117-3.120, 3.217-3.2251 I

3.2 Phenomenology

43

Different theoretical models were proposed by Schultze et al. r3.120, 3.226-3.2281, Kolb and Gerischer et al. [3.229, 3.2301 and Trassati [3.231, 3.2321 to explain the physical nature of Me UPD phenomena. Quantum-mechanical approaches, which were recently started by Schmickler and Leiva [3.233-3.2391 as well as by Neckel t3.240, 3.2411, give a better insight into the complicated Me UPD phenomena. A current compilation of investigations on Me UPD systems using monocrystalline substrates and different electrolytes is presented in Section 8.1 with a special reference list. Typical examples of Me UPD systems are discussed in the following sections.

3.2

Phenomenology

Me UPD processes involving formation of 2D Meads phases, 2D Me-S surface alloy phases and 3D Me-S bulk alloy phases in the underpotential range (cf. eq. (1.7)) are due to a strong Me-S interaction and represent the initial step of metal electrocrystallization. The formation of 2D Meads phases on a foreign substrate, S, in the underpotential range can be well described considering the substrate-electrolyte interface as an ideally polarizable electrode as shown in Section 8.2. In this case, only sorption processes of electrolyte constituents, but no Faradaic redox reactions or Me-S alloy formation processes are allowed to occur, The electrochemical double layer at the interface can be thermodynamically considered as a separate interphase L3.54, 3.212, 3.2131. This interphase comprises regions of the substrate and of the electrolyte with gradients of intensive system parameters such as chemical potentials of ions and electrons, electric potentials, etc., and contains all adsorbates and all surface energy. is a definite function of Furthermore, it is assumed that the chemical potential pMeads the Meads surface concentration, & and the electrode potential, E, at constant temperature and pressure: = pMeads (CE). Such a model system can only be realized within a restricted potential range using inert noble metals as foreign substrates in contact with electrolytes containing solvated MeZ' ions. The formation of Meadson S corresponds to a transfer of solvated Met&, ions from the electrolyte phase (El) to the interphase (IP) forming specifically adsorbed metal adions, Me::s, which are partially desolvated and located in the inner part of the electrochemical double layer:

3 Undeeotential Deposition ofMetals - 20 Phases

44

Simultaneously, the adsorbed species Me:, (IP) can interact with electrons of the interphase which can lead to a partial or complete discharge of MeSs (IP): Met;,(IP)

+ A t . e-(IP)

+

Me;$-')+(IP)

with 0 I R I 1

(3.2)

where R is defined as the partial charge transfer coefficient [3.226, 3.227, 3.242-3.2441. The partial charge number, z(1-A), of Meads depends on the character of the adatomsubstrate bond: 1 is zero for a completely ionic bond and approaches 1 for a covalent bond where the Me-Me bond is the limiting case. However, localization of charge in the adatom-substrate bond occurring within the interphase according to eq. (3.2) is thermodynamically irrelevant and cannot be determined by electrochemical equilibrium measurements according to the interphase concept used [3.54, 3.212, 3.2131. Theoretical considerations show that R should be close or equal to unity for the formation of Meads on native Me substrate or in systems with relatively small differences of electronegativities of Me and S [3.228]. It should be noted that an electronic interaction between Me::, UP) and other constituents of the interphase forming complex bonds can also lead to a localization of charge which can be expressed in terms of R using an equation similar to eq. (3.2). Let us consider the electrochemical equilibrium conditions for an electrochemical system shown in Fig. 3.1.

Figure 3.1 Phase scheme of an electrochemical system containing substrate (S) in contact with metal @lei), electrolyte (El) with Me;,", and metal (Me2) to derive the electrochemical equilibrium conditions for 2D Meads phases and the 3D Me bulk phase on S. Me1 and Me2 are chemically identical metals Me.

3.2 Phenomenology

45

The equilibrium condition for the formation of Meads on S, assuming A = 1, at an electrode potential E according to eqs. (3.1) and (3.2) is (cf. Section 8.2, eqs. (8.14) and (8.15)):

pg

where defines the chemical potential of a completely discharged Meads in the ads interphase. On the other hand, the equilibrium for a 3D Me bulk phase in contact with an electrolyte containing Me:&, at the equilibrium potential EMeIMeZ+ is described by (cf. Chapter 2)

Mekink (Me)

.+ Mel&,(El)

+ ze-(Me)

(3.4)

The corresponding Nernst equilibrium condition is given by

Eliminating

Em')

from eqs. (3.3) and ( 3 9 , one obtains:

Me::Iv

where Ap corresponds to the super- or undersaturation (cf. eq. (1.4)). The actual are measured vs. a electrode potential, E, and the equilibrium potential, EMelMez+, reference electrode (cf. Section 8.2, eq.(8.17b)). For E = EMeIMeZ+

which corresponds with eq. (1.5). Me UPD phenomena were observed in many S/Me:iIv systems using poly- or monocrystalline metals as foreign substrates, S, and aqueous solutions, non-aqueous solutions, and ionic liquids (melts) as electrolytes. Me UPD systems with single crystal substrates are summarized in Section 8.1. Me UPD on S is reflected in well-pronounced cathodic and anodic peaks at different AE in cyclic voltammograms. Using defined single crystal surfaces as substrates, the peak structure is found to depend strongly on the crystallographic

46

3 UnderpotentialDeposition ofMetals - 20 Phases

orientation of S(hkl) and the density of crystal imperfections (monatomic steps, dislocations, grain and subgrain boundaries, atomic disorder, etc.) at the substrate surface. As examples of the influence of the crystallographic orientation of S(hkl) on the UPD peak structure, cyclic voltammograms of Pb and T1 UPD on Ag(hkl) with (hkl) = ( l l l ) , (loo), and (110) are illustrated in Figs. 3.2 and 3.3 L3.97, 3.98, 3.1051. The different cathodic and anodic peaks are caused exclusively by adsorption and desorption of Meadsrrespectively. Cosorption and competitive sorption phenomena can be neglected for the components of the electrolyte used (cf. Section 3.3)- In the case of Pb UPD (Fig. 3.2), one monolayer is formed, whereas Tl UPD (Fig. 3.3) leads to two monolayers at AE + 0. ' 1

conditions) in systems Ag(hkl)/5 x M Pb(C104)~+ Figure 3.2 Cyclic voltammograms 5 x 1O-I M NaC104 + 5 x M HC104 with (hkl) = (111) (a); (100) (b); (110) (c), and IdE/dtl = 0.42 mV s-l at T = 298 K [3.93,3.97,3.981.An and Dn with n = 1, 2 ,3 ,4 denote cathodic adsorption and anodic desorption peaks, respectively.

3.2 Phenomenology

47

100

50 D3

25

50 9-

9E

0

9 .-

6

a

0

0

._

-25

-50 A2

-50

-1 00

0

200

400

LIE [mvl

600

0

200

400

600

AE [mvl

Figure 3.3 Cyclic voltammograms (semiinfinite-linear diffusion conditions) in systems Ag(hkl)/ 1.5 x lo3 M TIC104 + 5 x 10-1M NaC104 + lo2 M HClO4 with (hkl) = (111) (a); (100) (b) and IdE/dtl = 10 mV s-l at T = 298 K i3.1051. An and Dfl with n = 1, 2, 3, 4 denote cathodic adsorption and anodic desorption peaks, respectively.

The influence of the density of crystal imperfections on the UPD peak structure is illustrated in Fig. 3.4 for real and electrochemically grown silver single crystal surfaces with different densities of monatomic steps L3.93-3.95, 3.1091. Electrochemically grown silver single crystal faces have an extremely low crystal imperfection density and are prepared by electrochemical growth using the well-known capillary technique. This preparation technique was developed by Budevski and Bostanov [3.245-3.2481 and will be described in more detail in Chapter 5. Cyclic voltammograms in Fig. 3.4 show that the adsorption/desorption peaks A1/D1 are more pronounced at the real silver single crystal surfaces and, therefore, can be related to a preferential decoration process of monatomic steps and other surface inhomogeneities. The UPD peak structure on polycrystalline substrates is not as well pronounced in cyclic voltammograms. Obviously, this structure is determined not only by the contributions of different crystallographically oriented substrate domains, but also by the higher density of crystal imperfections at the substrate surface. This is demonstrated in Fig. 3.5 for the system Ag(polycrystalline)/Pb2'.

3 UnderpotentialDeposition ofMetals - 20 Phases

48

?-

5 5 .-

800

800

600

600

400

400

200

200

0

0

- 200

- 200

- 400

~

- 600

400

- 600

- 800

- 800 0

100

200

AEI mV

300

0

100

200

300

AEImV

Figure 3.4 Cyclic voltammograms (semiinfinite-linear diffusion conditions) in systems Ag(lll)/ 5x M Pb(C104)2 + 5 x 10-1 M NaC104 + 5 x l o 3 M HClO4 with IdE/dtl = 10 mV s-l at T = 298 K [3.93, 3.953. A,, and Dn with n = 1, 2, 3 denote cathodic adsorption and anodic desorption peaks, respectively. (a): Chemically polished and cleaned Ag(ll1) substrate surface, (b) : Electrochemically grown quasi-perfect Ag*(111) substrate surface according to the capillary method [3.245-3.2481.

Contributions of different crystallographically oriented domains are clearly indicated in the system Ag(cubooctahedron)/Tl+ using an electrochemically grown silver single crystal with (111) and (100) faces as substrate as shown in Fig. 3.6 [3.95]. Me UPD is caused by a stronger binding energy of Me-adatoms on a foreign substrate, yMeads-s [J per atom], compared to the binding energy of Meads on native ~ ~section - M 3.3 ~ and Fig. 1.1). Me substrate, Y M ~ ~ (cf. 2D Meads phases formed in the UPD range are not necessarily Meads overlayers with a monatomic thickness. The Meads overlayer thickness is a function of the MeadsS binding energy, YM~,~,-s , the lateral Meads-Meads interaction energy, v / M ~ ~ ~ ~and - M the~ underpotential, ~ ~ ~ , hE. At the equilibrium potential (AE = 0), a 2D Meadsphase with a finite number of Meads overlayers can coexist with the 3D Me bulk phase (cf. Fig. 1.1). The binding energy, ! P M ~ , ~as ~ -as microscopic , quantity, can be related to the adhesion energy, p W ~ m - ~as] a, macroscopic quantity (cf. Section 4.1) [3.247-3.2501. Thus, Me UPD can be expected in systems with an adhesion energy, p, higher than the cohesion energy, 2q, of the crystal plane i of an infinite 3D Me crystal. In the opposite case, 2D Meads phases in the UPD range are unstable, and stable 30 Me islands can only be formed in the OPD range according to the Volmer-Weber growth mechanism (cf. Fig. 1,la).

3.2 Phenomenology

49

0

100

200

300

AE Imvl

Figure 3.5 Cyclic voltammogram (semiinfinite-linear diffusion conditions) in the system Ag(poly)/ M HClO4 with IdE/dtl= 10 mV sal at T =298 K. 5 x lo2M Pb(C104)2 + 5 x 10-1M NaC104 + 5 x

An attempt was made by Gerischer, Kolb, and Przasnyski [3.122,3.229, 3.2301 to empirically correlate the difference of work functions of 3 D S and 3 D Me phases, A@ = - me, with a characteristic underpotential shift, AEp, corresponding to the most positive Meads desorption peak in an anodic stripping curve (cf. Figs. 3.2-3.6). A linear relation

AE, = 0.5A 0

(3.8)

was found for a number of Me UPD systems with polycrystalline substrates S as indicated in Fig. 3.7.However, AEp can only be considered as a qualitative measure for A Y = YMeads-S - Y M ~ , ~ , as - Mdiscussed ~ below (cf. eq. (3.21)).

3 Undeeotential Deposition of Metals - 20 Phases

50

0.3 0.2 0.1

T-

5

9 ._

0 -0.1

-0.2

-0.4

I

0

I

I

I

I

100

200

300

400

500

AE [mvl Figure 3.6 Cyclic voltammogram (semiinfinite-linear diffusion conditions) in the system Ag(cubooctahedron)/7.5x l W 4 M fl2so4 + 5 x l W 1 M Na2S04 + M HClO4 with IdE/dtl= 10 mV s-l at T = 298 K [3.95].4tOhl= 3 x cm2,A(100)= 2.1 x crn2,A(111)= 0.9 x 10-3 cm2.

0

0.5

10

1.5

2.0

25

A@ [evl

Figure 3.7 Underpotential shift, AJip, in different S(poly)/Mezt systems as a function of the difference of electron work functions of polycrystalline S and Me, A# = @, - we[3.122,3.229,3.230].

3.2Phenomenology

51

Different physical models were developed to explain the correlation between dE, and A@ [3.231-3.2391. Trasatti assumed an ionic bond Me:& - S (cf. eq. [3.2] with A = 0) and considered the underpotential value for the deposition of the first single Mez&ion at vanishing surface coverage [3.231, 3.2321. From this model, a linear relationship between this underpotential value and A@ with a slope of unity was derived. Schmickler and Leiva proposed a jellium model representing both the 2D Meads phase and S [3.233-3.2391. This model can explain the experimental results obtained by Gerischer, Kolb, and Przasnyski [3.122, 3.229, 3.2301 on polycrystalline S in terms of the difference of the surface energies of the two metals involved and the dipole moment which is formed when two metals with different work functions make contact. However, experimental UPD data obtained on defined monocrystalline substrate surfaces by various authors [3.93-3.95, 3.97-3.99, 3.105, 3.109-3.1201 do not agree with the relationship in eq. (3.8) as demonstrated in Fig. 3.8 L3.2511.

0.8 06 04

02 0

06 0.4

02 0 06

04

02 0

0

0.4

08

A Q [eW

F i r e 3.8 Underpotential shift, AEp, in different S(hkl)/MeZ' systems as a function of the difference of electron work functions of polycrystalline S and Me, A @ = - me[3.251].

a

3 Underpotential Deposition ofMetals - 20 Phases

52

Structural properties of the 2D Meads phase and S as well as the lateral interaction energy between Me adatoms, Y M ~ ~ ~ and ~ - other M ~ parameters ~ ~ ~ , have to be taken into account in order to quantitatively explain UPD phenomena (cf. Section 3.3). However, a complete physical Me UPD model does not yet exist. Recently, calculations based on a jellium model with lattices of pseudopotentials for the 2D Meads phase and S were started by Schmickler and k i v a [3.234-3.2391. In addition, local density full potential linearized augmented plane wave calculations were carried out by Neckel [3.240,3.2411. Both approaches are important for a better understanding of Me UPD phenomena on single crystal surfaces taking into account structural aspects. Me UPD on foreign substrates is comparable to sorption phenomena and 2D phase formation occurring at solid/gas and solid/liquid interfaces at undersaturation conditions. For example, adsorption of hydrogen, oxygen, and rare gases on graphite or noble metals are typical undersaturation sorption phenomena.

3.3

Thermodynamics

Thermodynamicformalism The thermodynamics of 2D Meads overlayers on ideally polarizable foreign substrates can be relatively simply described following the interphase concept proposed by Guggenheim [3.212, 3.2131 and later applied on Me UPD systems by Schmidt [3.54] as shown in Section 8.2. A phase scheme of the electrode-electrolyte interface is given in Fig. 8.1. Thermodynamically, the chemical potential of Meads is given by eq. (8.14) as a result of a formal equilibrium between Meads and its ionized form Me:& in the interphase UP). The interphase equilibrium is quantitatively described by the Gibbs adsorption isotherm, eq. (8.18). In the presence of an excess of supporting electrolyte KX, i.e., dEDdED>> dE1) the chemical potential p g D is constant and K + ' XMeZ+ ' (ED = 0 . Then, the Gibbs isotherm can be simplified to (cf. eq. (8.17 a))

"+MeZ+

where the relative surface excess Concentration, rM,Z+m, approaches the absolute surface concentration in the compact double layer: rMez+oy) m rMez+o (compact) def = r . The charge isotherm is given by = r ~ ~ , ~ ~ (3.10)

3.3 l7aemodynamics

where qo = F

53

[r(w) dW) K+ 1 denotes the charge in absence of MeZ+(El), -

X-

The q-I--E relation was first introduced by Schmidt [3.54] as the charge coverage coefficient, and later described as the electrosorption valency by Vetter and Schultze [3.226, 3.2271:

(=-)

y def = F - 1 84

= E

(

z + F -1 % ar)

(3.11)

E

Using Jacobian transformation and the Maxwell relation [8.201 in Section 8.2, one obtains (3.12)

where p = p MeZ+' In general, the electrosorption valency yis a function of E and r: y = Y(E,

n

(3.13)

In the absence of specific adsorption, qo is relatively small, and it can be assumed that

and y -+ z. On the contrary, if cosorption or competitive sorption processes occur in parallel with Me UPD in the interphase (dN(IP) # 0), then Iq,l is relatively large and itMeZf

Consequently, y # z gives information about the coupling of q,, with but not to any partial charge of Me;$-')+(IP) in eq. (3.2). In contrast to this thermodynamic interpretation of y, an attempt was made by Vetter and Schultze l3.226, 3.2271 to obtain information on the location and the partial charge of Me;i-')+(IP) in the compact double layer from the electrosorption valency. Starting from the thermodynamic definition of y in eq. (3.11), using the total differential of eq. (3.13), setting r=constant and introducing the definition of the double layer capacitance' * Note that the minus sign is connected with the definition of q given by eq. (8.17d) in Section 8.2 and by eq. (3.10).

3 Underpotential Deposition ofMetals - 20 Phases

54

(3.14) the authors correctly obtained by integration:

(3.15) The integration constant y~ denotes the electrosorption valency of a hypothetical Me UPD state at the "potential of zero charge", EN.However, this potential is defined def by E N = E ( r = 0, 40 = 0), and can only be measured in electrolytes free of Me" ions. The value y~ was arbitrarily split into the following terms by Vetter and Schultze [3.226, 3.2271: Y N = gz-A'(l-g)+Ka&-

VKW

(3.16)

where the geometric factor, g, describes the location of the adsorbed species within the compact double layer. A' is correlated to the partial charge transfer coefficient A introduced in eq. (3.2) by the relation A' = z(1-A) - z = - zA. Kads and ICWrepresent dipole terms of the adsorbate and of v desorbed solvent molecules, W, respectively. It should be noticed that the model assumption in eq. (3.16) is rather arbitrary. Tne true state of charge of any adsorbed species is unknown from a thermodynamic point of view since a localization of electronic charge within the interphase would not change the total surface excess concentration, G o ,of the species i involved. According to the thermodynamic interphase concept presented here [3.54], experimentally observed deviations y # z have only to be explained in terms of cosorption or competitive sorption phenomena, i.e., y

-z =

t3E*

czi -

The relative surface excess concentration r i s a function of E and p (cf. Section 8.2, eq. (8.19)) which can be expressed by p ( E , r )= p o + RT haMel+

The last term on the right hand side can be arbitrarily split into a coverage and an electric term according to Delahay L3.2521: In uMez+= In f ( r ) + In p ( E , r ) Defining

3.3 Thermodynamics

55

one obtains

(3.17) This means that the Me UPD adsorbate follows a quasi-Nernst equation [3.54]. Compatibility with the electrosorption valency

requires

whence

Me/MeZ+


1 adsorption sites [3.87-3.89, 3.98, 3.122, 3.191, 3.214, 3.2611. Such a multisite or l / n adsorption can be caused by a crystallographic Me-S misfit, i.e., the adatom diameter exceeds the distance between two neighboring adsorption sites, and/or by a partial charge of adatoms (A c 1 in eq. (3.2)), i.e., a partly ionic character of the Mead& bond. The theoretical treatment of a l / n adsorption differs from the description of the 1/1 adsorption by a simple Ising model. It implies the so-called hard-core lattice gas models with different approximations [3.214, 3,262-3.2661. Generally, these theoretical approaches can only be applied far away from the critical conditions for a first order phase transition. In addition, Monte Carlo simulations are a reliable tool for obtaining valuable information on both the shape of isotherms and the critical conditions of a 1/12 adsorption L3.214, 3.265-3.2671. As an example of a 1/1 adsorption in Me UPD systems, the “Fowler-Frumkin” isotherm, which is derived using the so-called mean field approximation (Section 8.3), is given by f3.257,3.258, 3.2681:

3.3 Thewtodynamics

57

(3.19) The degree of coverage, 0, is related to the surface excess concentration, l-, by B = T/T'L where TML denotes the surface excess concentration of a Meads monolayer. The parameter c represents the number of first nearest neighbors in the compact Meads monolayer. The lateral interaction parameter, w, is related to the lateral interaction energy, w ~ ~ ~ by~ w =~ yMeads-Meads - M ~ /kT. ~ ~The~ electrode , potentials E and E* ( 0 = 0.5) are measured vs. an arbitrary reference electrode. Using the Nernst equilibrium potential of a Me/MeZ+electrode (cf. eqs. (1.2)) as a reference potential, eq. (3.19) can be rewritten: (3.20) The underpotential AE* corresponds to a reference state at B= 0.5 and is given by

In this equation, Aad& corresponds to the enthalpy difference between occupied and unoccupied adsorption sites and contains YMe,ds-S and the difference of the solvation enthalpies of Meads and S. A S u a is the sublimation enthalpy, which is related - ~ ~ , as v/1 in the case of to the interaction enthalpy per Me bond, t p ~ ~approximated first nearest neighbors (cf. eqs. 2.2 and 2.3). The terms i&hk and Gads represent the mean vibrational volumes of an atom in a kink site position or in an adatom position, respectively [3.269]. They are related to the mean atomic vibration frequencies in the 3D Me bulk lattice and in the Meads overlayer, respectively. For localized 1/1 adsorption, AE* is related to the inflection point of a r(E3 isotherm at p = constant, corresponding to the potential of the most positive peak, Up, in cyclic or linear sweep voltammograms under quasi-equilibrium conditions (slow sweep rates). This peak potential corresponds to the formation of a first Meads overlayer on S. The formation of a second Meads overlayer on top of the first one can be considered as Me adsorption on an UPD modified substrate. Determination of the excess binding energy, ALY = Y M ~ , ~-~ Y - s M ~ ~from ~ ~ - M ~ eq. (3.21) requires additional knowledge of the following parameters: the differences of solvation energies of Meads, Me, and S, the structures of the substrate S and of the Meadsoverlayer reflected in c, the interaction energy within the adlayer, I , v / M ~ ~ ~, ~ - M ~ ~ ~ ~ and that within the 3D Me bulk phase, ~ M ~ - M as ~well , the vibrational volumes ck,, and cads. Therefore, previous attempts to correlate directly AEp with physical

58

3 Underpotential Deposition ofMetals - 20 Phases

parameters characterizing the Mead& bond such as the difference of electronegativities or work functions are more or less of qualitative character (cf. eq.(3.8)). The shape of the adsorption isotherm given in eq. (3.20) is symmetric with respect to the reference point 8 = 0.5, i.e., AE = AE*.For the limiting case w 4 0, the Langmuir isotherm is obtained representing the exact solution of a 1/1 adsorption independent of the geometry of the 2D lattice of adsorption sites. The influence of this geometry is reflected in the coordination number c in the second term of the Fowler-Frumkin isotherm (eq. (3.20)). At w > 4/c the isotherm becomes s-shaped and the criteria for intrinsic stability are not satisfied at every point of the isotherm. As a consequence, a first order phase transition will happen, expressed by a discontinuity in the corresponding extensive system parameter, 6 which is related to 8. The critical value of the interaction parameter, w, = 4/c, is determined by the geometry of the 2D lattice of adsorption sites of the substrate. In the case of a localized l/n adsorption, which is observed in many Me UPD systems at relatively high AE or low r (formation of expanded Meads superlattice structures, cf. Section 3.4), the adsorption process can be described by the so-called hard-core lattice gas models using different analytical approximations or Monte Carlo simulations [3.214, 3.262-3.2641, Monte Carlo simulation for 1/2 adsorption on a square lattice is dealt in Section 8.4. Adsorption isotherms become asymmetrical with respect to AE* and are affected by the structures of the Meads overlayer and S even in the absence of lateral Meads interactions [3.214, 3.262-3.2641. Furthermore, the critical interaction parameter for a first order phase transition, w,, which is related to the critical temperature, T,, increases in comparison to the 1/1 adsorption. In the case of a first order phase transition, the equilibrium underpotential of a 2D Meads phase, a*, is given by eq. (3.21). It is related to the binding energy of Meads in a kink-like position which includes one half of the lateral bonds c of an atom in a condensed 2D Meadsphase.

Experimental results As examples, experimental r(E) isotherms at p = constant for Pb and T1 UPD in acidic perchlorate electrolyte on Ag(hkZ) single crystal faces with (hkZ) = (111) and (100) are shown in Figs. 3.9 and 3.10, respectively [3.97, 3.1051. These isotherms were measured stepwise, waiting for equilibrium conditions according to polarization routines illustrated in Fig. 3.11 using the "twin-electrode thin-layer technique" (TM,) for Pb UPD and the "flow-through thin-layer technique" (E;rrz) for TI UPD.

59

3.3 Thermodpamics

400

0

50

100

150

200

2 I

Figure 3.9 r(E) isotherms measured under 'IT'L conditions in systems Ag(hkE)/x x M Pb(C104)2 + 5 x lo-' M NaC104 + 5 x lo9 M HC104 with (hkl) = (111) (a); (100) (b); (110) (c), and lo4II l o 3 at T = 298 K [3.93,3.97,3.98].Different symbols denote experimental .$rand AE values at different z.Polarization routine: loop technique (Fig. 3.11a).

Both thin-layer techniques were developed by Schmidt, Siegenthaler et al. [3.55, 3.67, 3.681 and allow an independent and precise measurement of q(E,p) and IXE,p) isotherms. From the q-rplot, the electrosorption valency can be directly determined as illustrated in Fig. 3.12 f3.97, 3.1051. The electrosorption valency was found to be y = z in both UPD systems indicating the absence of cosorption and competitive sorption processes in the systems studied.

3 Underpotential Deposition ofMetals - 20 Phases

60

200

100 9-

5

s c Y

ci

'c, 300

200

too

C

0

100

200

300

400

500

AIE [mvl

Figure 3.10 I@) isotherms measured at m L conditions in systems Ag(h&l)/1.5x lom4 M TlClO4 + 5 x 10.' M NaC104 + M HClO4 with (hkl) = (111) (a); (100) (b), and adsorption (A)and desorption (A) measurements at T =298 K I3.1051. Polarization routine: loop technique (Fig. 3.11a).

. . t

t

Figure 3.11 h o p (a) and step (b) techniques as quasi-static polarization routines for coverage isotherm measurements (4= initial potential, Efwith f = 1,2,... = final potential).

3.3 7Jaermodynamics

61

400 400 ..

c

300

200

100

0

0

100

200

300

400

m- [pCcm12] 300

~

0

100

200 ZIT

300

[pCmi2]

Figure 3.12 Determination of the electrosorption valency, 5 from independent Aq and r measurements (Aq = q - qo) according to eqs. (3.10) and (3.11). (a): System: Ag(lOO)/.r x M Pb(ClO4)2 + 5 x 10-l M NaC104 + 5 x M HClO4 with lo45 x 5 [3.97,3.98]. 772 measurements at T = 298 K. Different symbols denote experimental Aq and radsorption and desorption values at different x and E. (b): System: Ag(lOO)/1.5 x M TIC104 + 5 x 10-1 M NaC104 + M HClO4 [3.105]. F " L measurements at T = 298 K. Different symbols denote experimental Aq and radsorption (B)and desorption (0) values at different E.

3 UnderpotentialDeposition ofMetals - 20 Phases

62

The isotherms in Figs. 3.9 and 3.10 are continuous, reversible, and without hysteresis. Therefore, they were previously interpreted as a Meads adsorption/ desorption process excluding 2D nucleation and growth under the given experimental conditions [3.97, 3.1051. 2D nucleation and growth as a first order phase transition would require a discontinuity in the corresponding extensive system parameter f l E , p ) f3.92-3.94, 3.98, 3.1011. A discontinuity of the q(p,E) isotherm was observed in the system Cu(111)/Pb2+, H', CIOi, acetate by Bewick et al. [3.2701 as shown in Fig. 3.13. However, the electrosorption valency and the steepness of the q(p,E) isotherm step were found to be significantly affected by the pH and the prepolarization conditions of this system [3.1081. Therefore, it was suggested that the discontinuity in the q(,u,E) isotherm in Fig. 3.13 is most probably not related to a 2D nucleation process of Meads, but should rather be explained by a pit nucleation within a preformed specifically adsorbed monolayer of an oxygen-containing species on Cu(ll1). At this point, it should be mentioned that experimental Z-(E,p) isotherms obtained by electrochemical measurements provide only integral information on the thermodynamic properties of Me UPD overlayers. Therefore, the interpretation of flE,p) isotherms without any direct structural information is relatively uncertain.

cu-

300

200

100

130

140

AE

150

160

[mv]

Figure 3.13 Aq(E) isotherm (semiinfinite-linear diffusion conditions) in the system Cu(lll)/lO~z M Pb(CH3COO)z + 5 x 10-1 M NaC104 + M HClO4 at T =298 K [3.270].

3.4 Stmctures of 20 Meah Phases

63

Recent in situ applications of different surface analytical techniques such as EXAFS, GIXS, STM, AFM,etc., opened a new window to get direct information on the structure of Me UPD adlayers at an atomic level. Structural aspects of UPD adlayers based on both electrochemical and modern surface analytical results will be discussed in detail in the next section.

3.4

structures of 2D Meads Phases

Degree of registry Adsorption processes on crystallographically well-defined substrate surfaces lead to the formation of 2D Meads phases with well-ordered structures denoted as "overlayers". Generally, three different types of overlayers, depending on the degree of registry between overlayer and substrate, can be distinguished: commensurate, higher-order commensurate or incommensurate overlayers, as illustrated schematically in Fig. 3.14. The term "superlattice structure" is frequently used for commensurate overlayers which can be characterized by either the Wood o r the matrix notation [3.271-3.2741.

Figure 3.14 1D schematic representation of the degree of commensurability of Meads overlayers on single crystal substrates. Commensurate overlayers (a) and (b) , higher order commensurate overlayer (c), and incommensurateoverlayer (d) .

3 Underpotential Deposition of Metals - 2D Phases

64

S(ll1)

E

- (Gx 6)R 30"Me

S(lOO)-c(2x2)Me S(lO0) (-&x R 45" M e

-

a)

-

s(110) (1 x 2) Me

Figure 3.15 Different expanded commensurate Meads overlayer (superlattice) structures. (a): S(111)- (& x &) K 30' Me in different domains occupying d ~ e r e n types t of adsorption sites, (b): S(100)- c(2 x 2) Me which is equivalentto S(lO0)-(& x &) R 45' Me, (c):S(110)-(1 x 2) Me.

3.4 Structures of 20 Meah Phases

65

The commensurability of overlayers is characterized by the coincidence of reciprocal lattice vectors of adsorbate and substrate. Low or higher order coincidence leads to commensurate or higher order commensurate overlayer structures (Figs. 3.14a, b, c). If the reciprocal lattice vectors do not coincide, the overlayer is incommensurate (Fig. 3.14d). The formation of expanded commensurate overlayer structures requires a localized l / n adsorption with n > 1 (cf. Section 3.3) at relatively high AE or low r (Figs. 3.14a and 3.15). In UPD systems with negligible crystallographic Me-S misfit, (do,Me-do,s) / dos = 0, the formation of unstrained commensurate overlayer structures with n = 1 remains also at low AE or high r (Figs. 3.14b and 3.16). On the contrary, in f 0, higher order the presence of significant Me-S misfit, (do,Me-do,S)/d~,s commensurate (Figs. 3 . 1 4 ~and 3.17) or even incommensurate (Figs. 3.14d and 3.18) overlayer structures are formed at low AE or high r: In this case, S can induce considerable strain in the 2D Meads overlayer, and first or higher order phase transitions can occur depending on AE (commensurate t)higher order commensurate or commensurate t) incommensurate transitions). Furthermore, in the case of different 2D lattice geometries of Meads overlayer and S, higher order commensurate Meads structures may arise caused by S-induced anisotropic internal strain as schematically shown for a row-matching structure in Fig. 3.19.

-

S(100) (1 x 1) Me

Figure 3.16 Condensed commensurate Meads overlayer (superlattice) structure S(lOO)-(l x 1) Me.

3 Underpotential Deposition ofMetals - 2D Phases

66

Me-S interactions leading to higher order commensurate and under certain conditions to incommensurate Meads overlayer structures give "superstructures" and "moirC pattern" which can also be described by the Wood or matrix notation (cf. Figs. 3.17, 3.19).

-

S(111) ( c 8 x 4%) R 40.9" MeMdfi

s(w) - ( 6 7 x 6 7 ) R 34.7" Me,, Figure 3.17 Higher order commensurate ZD hcp Meads overlayers in presence of significant Me-S misfit, ( d o , ~ e - d o , S ) / d o ,z~ 0, leading to superstructures with moirk pattern S(111)x &)R 40.9' MeMoirC (a) a d S(lll)-(& x R 34.7' MeMoirC (b).

(6

6)

67

3.4 Structures of 20 Meah Phases

l-.

a = 4.5"

---r-

Figure 3.18 Rotated incommensurate 2D hcp Meads overlayer in presence of signifcant Me-S misfit, (do,Me-do,S)/do,S > 0.

s (1101

S( 100) - c (6x 2)M e,,

Figure 3 . 1 9 Anisotropically compressed 2D hcp Meads overlayer in presence of significant Me-S misfit, (do.~e-do,s)/do,s > 0, forming a row-matching superstructure With moirC pattern

68

3 Underpotential Deposition of Metals - 20 Phases

Internal strain There are different reasons for the appearance of S induced internal strain in 2D Me overlayers. The first one is the ordering field of the periodic S lattice, forcing Meads to occupy energetically favored adsorption sites, i.e., trying to form a commensurate 2D Meads overlayer as described in the “coincident site lattice“ concept l3.275, 3.2761. In this case, the S-induced internal strain is more or less homogeneous and the strain energy must be overcompensated by the energy gain due to a proper relative orientation of both the 2D Meads lattices and S. If the homogeneous internal strain becomes too high to fulfill this condition, incommensurate overlayers are formed. In this case, the periodic field of S can induce inhomogeneous strain and static distortion waves (SDW) in the 2D adlayer according to the theory of Novaco and McTague [3.277, 3.2781. SDW describe the static displacement of adatoms from their regular positions in a 2D adlayer lattice. The corresponding strain energy depends on the orientation (rotation) of the overlayer with respect to S, and is minimized at a given rotation angle. In the SDW model of Novaco and McTague [3.277, 3.2781, the adlayer on a rigid substrate is treated in the harmonic approximation at T = 0. For small displacements, the mean interaction energy per adatom, FMe,ds-$, between a rigid substrate with reciprocal lattice vectors, G , and a non-rigid overlayer with reciprocal lattice vectors, g; is given by 13.277, 3.2781:

(3.22)

where yo represents the mean adatom-substrate interaction energy in the case of a laterally averaged substrate field, Y’c are the Fourier coefticients of the periodical substrate potential, 6 ~ and, 6 ~ ~ , are ~ + the~Kronecker deltas, q = G -g are the wave vectors of the SDW, A is related to the Planck constant by A = h / 27c, u(q) are the Fourier components of the static displacement pattern, and w ( q ) denote the phonon frequencies of the overlayer. The second term in eq. (3.22) is related to the direct orientational effect of the periodical substrate field, whereas the last two terms represent the orientation-dependent contribution of SDW. For an incommensurate adlayer (G # g),i.e., if no vectors from the set { A coincide with vectors belonging to the set {GI, it follows that 6~~ = 0, and the second term in

3.4 Structures of 20 Meah Phases

69

eq. (3.22) vanishes. In this case, the relative orientation of the overlayer and substrate lattices is determined by a compromise between the remaining last terms in eq. (3.22), which produce a strong variation of the energy with the orientational angle, a. The energetically favored orientational angle corresponds to a given SDW vector qmin = G-g.

Internal strain of 2D UPD overlayers is generally induced by a strong adatom~-s is ,not necessarily related to the periodicity of the substrate attraction, Y M ~ , ~ but substrate lattice. Incorporation of excess Meads into a preformed unstrained and undistorted monolayer becomes energetically more favorable than the adsorption of Meads on top of the first Me overlayer. Such an incorporation also leads to a compression of the 2D UPD monolayer. This process obviously depends on AE,and proceeds as long as the adatom-substrate binding energy exceeds the induced strain energy. Assuming that the 2D adlayer behaves as an isotropic elastic medium, the strain energy E U atom-'] can be expressed by [3.276,3.279-3.2811:

(3.23) In this equation, A' and p' are the 2D Lame coefficients,R is the area of Meads in an undistorted 2D Meads overlayer, and Ad/do = (do - d)/do denotes the relative compression of the adlayer where do and d are the atomic nearest-neighbor distances in the uncompressed and compressed overlayer, respectively. Equation (3.23) can be regarded as a first approximation for a hexagonal close-packed (hcp) Meads overlayer with a 2D hcp lattice'. However, it is a very rough approximation for more expanded overlayer structures such as quadratic or rectangular superlattices and cannot be used for anisotropically compressed and strained Meads overlayers. The dependence of d on hE was derived [3.174, 3.2821 starting from the definition of the specific surface energy at constant temperature and pressure (cf. Section 8.2):

(3.24)

Via stepwise differentiation of

*

See footnote on p. 9.

CTone

obtains

3 Underpotential Deposition of Metals - 20 Phases

70

(3.25) In this equation, the term ( d T / a q ) E can be replaced by (F9-l according to eq. (3.12). Then, using the definition r;: = - ( a a / a , u J E , p F t (cf. Section 8.2, eq.(8.19)) and the Maxwell relation (d q/ a f i )E , = ~ ( a~C /~a (cf. Section 8.2, eq. (8.20)) one gets:

ar

=

(*)E

FYI-($)

P

(3.26)

In an ordered monolayer, both the surface area, A, and the surface adatom concentration, r,may be expressed in terms of a characteristic lattice parameter, r, as a common independent variable. Therefore

and (3.28)

In a close-packed overlayer consisting of N& particles, r is the nearest neighbor distance, d ~

=

(3.29)

d

whence

A = Nadsad2

(3.30)

r=

(3.31)

and

( N A ad2)-'

where a is a geometric coefficient and ad2 = R is the area per adatom in the overlayer. Assuming that, as a consequence of a 2D isotropic compression of the overlayer, the corresponding increase of the specific surface energy is given by the elastic strain energy according to eq. (3.23), one gets: ( d ) = G g i d , ( d o ) + NadsE

=

G(d,)

GM%ds

Combining eqs. (3.24) through (3.30) gives

+ Nads2 ( A f + p ' )R (d - dJ2 do2

(3.32)

3.4 Structures of 20 Meah Phases

71

which by integration with y = z and p = constant leads to (3.33)

In this equation AEo and AE denote the underpotential values for the uncompressed

and compressed UPD monolayers at do and d, respectively. The 2D Lam6 coefficients A' and p' are related to the 2D compressibility, QD, by IQD = (A'+ pU')-l. Notice that in eq. (3.31) no distinction is made between the relative surface excess of Meads and its absolute surface concentration in the compact double layer: rMeZfm def = r M e Z + ( w ) (compact) = r (cf. eqs. (3.9) and (3.10)). Assuming that the 2D Lam6 coefficients, A' and p', are related to the 3D ones, A and p, by A' = A - ~ M and L p' = ,u- ~ M L where , ~ M denotes L the thickness of the Meads overlayer, eq. (3.33) can be rewritten as (3.34) where v [cm3 atom-'] is the volume of Meads in an uncompressed Meads overlayer. It is interesting to note that the term zFAEo is related to the relative compression (do - d)/do = Ad/& of the monolayer coexisting with the 3D Me bulk phase at E = EMe,MeZ+ (AE = 0). Assuming that the interatomic interactions as well as the atomic frequencies of vibration are equal in the close-packed monolayers on foreign and native substrates, the relative compression at AE = 0 can be expressed by (3.35) This equation allows one to estimate the compression of the UPD adlayer at hE = 0. For many Me UPD systems, the excess binding energy A Y= !FMe,ds-S - YMeadSpMe is in the order of J (corresponding to about lo4J mole-'), so that eq. (3.35) predicts a substantial compression of several percent since the 3D Lame' coefficients are usually 10" Pa I (A+ p) < 10" Pa [3.283, 3.2841.

Electrochemical results

In early Me UPD studies on single crystal substrates S 13.89, 3.98, 3.1221, classical electrochemical techniques such as cyclic voltammetry, f i E , p ) isotherm measurements using thin-layer techniques FITL), transient techniques in the time domain, and electrochemical impedance spectroscopy @IS) in the frequency

3 UndeQotential Deposition of Metals - 20 Phases

72

domain as well as optical measurements such as in situ reflectance spectroscopy were applied to indirectly obtain structural information on Meads overlayers. As a major disadvantage, these classical methods provide only integral information on the entire surface studied. Therefore, all structural interpretations at this early stage of Me UPD investigations have had a more or less hypothetical character. Charge and surface coverage isotherms exhibiting a continuous course (cf. Section 3.3) as well as monotonously decreasing current transients in the UPD range have usually been explained in terms of localized Meads adsorption taking into account lateral interaction between the adsorbed Meads species r3.97-3.99,3.101,3.105, 3.1741, As an example, the system Ag(hkl)/Pbzt, H+, C1Oi ( y = z) with significant Me-S lattice misfit ( d o , ~>ed,,~)will be discussed in the following. I@') data at p = constant and the corresponding charge equivalents Aq = q - qo = zFT (cf. eq. (3.10)) are presented in Table 3.1 [3.97-3.99, 3.1741. Initially, these values were hypothetically related to a localized adsorption and a stepwise formation of different commensurate Me superlattice structures depending on the crystallographic substrate orientation and AE [3.87, 3.89, 3.93-3.95, 3.97, 3.98, 3.105, 3.122, 3.1741. Table 3.1 Pb surface concentrations, charge equivalents, Aq = q - qo, and superlattice structures as a function of underpotential, AE,in the system Ag(hkt)/Pb2+, II', ClO4- [3.87, 3.93, 3.97, 3.981. (Electrosorptionvalency y = z)

Substrate S

AE [mvl

I Aq I

= zFT

[PC c m - 2 ~

Exu.

Superlattice Structure of Pbads

Remarks

Theor.

Ag(ll1) Ag(ll1) Ag(W

175 140 0

110+10 204+10 340 + 10

112 224 336

- (2x2) Pb - 2 ( 2 ~ 2 Pb ) - 3 ( 2 ~ 2 Pb )

Ag(100) Ag(100)

140 0

1 8 2 t 10 372 t 10

193 386

- ~(2x2)-~(2x2)Pb

Bilayer structure

302

- hcp Pb(ll1)

Incommensurate and uncornpressed hcp monolayer do.pb = 0.35 nm)

'I'he charge and coverage values at respectively.

Honeycombs Filled honeycombs

-c(2x2) Pb

hE = 0 mV correspond to saturation values A4s and

rs,

3.4 Structures of 20 Meah Phases

73

A comparison between cyclic voltammograms using electrochemically grown and real silver single crystal substrates showed a significant influence of the density of monatomic steps on r at the adsorption peak A1 in Fig. 3.4 [3.93-3.95, 3.1091. Therefore, the assumption of an expanded superlattice structure Ag(ll1)-(2 x 2) Pb at low T o r high AE Cable 3.1) is unrealistic. New experimental results have shown that a better approach is to assume a step decoration at low T i n the potential range of the adsorption peak Al. The charge equivalent values in column 3 of Table 3.1 show that the experimental saturation coverage values, Ts, of Pbads on &(loo) and Ag(ll1) faces are significantly higher than the theoretical value for an uncompressed hexagonal close-packed Pb monolayer. Therefore, on the cubic silver face, the formation of a bilayer structure Ag(lOO)-c(2 x 2) Pb-c(2 x 2) Pb was proposed to explain the excess surface coverage. On the octahedral silver face, the excess surface coverage was interpreted by suggesting a filled honeycomb structure Ag(ll1)-3(2 x 2) Pb. This commensurate hexagonal superlattice structure, however, requires a higher atomic density than the Pb(ll1) plane. Therefore, an internal strain was assumed within the Pb adlayer. In addition, every third Pb atom is placed on top of an underlying silver atom instead of an adsorption site leading to a higher corrugation of the Pb adlayer. Later, first attempts were made to correlate cyclic voltammetric, coulometric, transient, and reflectance data in terms of first or higher order phase transitions, taking into account the formation of commensurate and incommensurate Meads overlayer structures [3.92-3.94, 3.101, 3.110-3.114, 3.118-3.120, 3.2701. For example, the formation of a close-packed hexagonal Pbads overlayer at relatively high r; independent of the crystallographic orientation of S, was assumed, taking into account first and higher order phase transitions from expanded Pbad, superlattice structures at low r to condensed and compressed hcp Pbads overlayers at saturation coverages [3.111-3.114, 3.2701, A first order phase transformation was proposed for Pb UPD on &(lll), whereas higher order phase transitions were assumed to be involved for Pb UPD on Ag(100) and Ag(ll0) [3.111-3.1131. Analogous results found in the system Ag(hkZ)/TI+, H', C1Oi were interpreted in the same way [3.110]. 2D nucleation and growth as a first order phase transition should exhibit a discontinuity in the r ( E , p ) isotherm of Me UPD processes (cf. Section 3.3). Such a discontinuity could not be found experimentally in Me UPD systems in the absence of specific cosorption phenomena [3.93, 3.94, 3.97, 3.981. However, kinetic effects may mask a discontinuity of a f i E , p ) isotherm: first, a slow Mead& site exchange (cf. Section 3.6), and second, a nucleation process at surface inhomogeneities with a limited growth of Meads islands,

3 UnderpotentialDeposition ofMetals - 20 Phases

74

as discussed below. Therefore, 2D nucleation and growth processes in Me UPD systems cannot be determined unambiguously from classical electrochemical and optical measurements only (cf. Sections 3.4 and 3.5). Comparative and ex situ UHV results

In the seventies, different UHV surface analytical techniques (electron diffraction methods, ion and atom scattering methods, XPS, UPS, AES, XSW, etc. [3.254, 3.273, 3.274, 3.285, 3.2861) were applied to study structural and chemical aspects of clean single crystal substrate surfaces and Me deposition processes. First, comparative UHV experiments were carried out in parallel to electrochemical measurements in order to compare Me deposition from the vapor phase with Me deposition from an electrolyte. Later, electrochemical and UHV measurements were combined to give the so-called ex situ UHV technique, using appropriate transfer devices to switch the electrode from contact with the electrolyte to UHV conditions and vice versa. Under UHV conditions, the substrate can be precleaned and crystallographically well characterized. After transferring the substrate into the electrochemical cell, the electrode is immersed in the electrolyte and electrochemical processes such as UPD of Me can be studied under exact potential control. After retransferring the electrode, the resulting electrochemical surface modifications can be studied under UHV conditions. A great disadvantage of this ex situ UHV technique is the lack of exact knowledge of how the electrochemical double layer is changed from the potentially controlled state in the electrolyte to vacuum conditions. As an example, Pb and T l vapor deposition on Ag(ll1) under UHV conditions was first studied using RHEED by Newman L3.1291, Gruenbaum l3.1301, and using RHEED, B E D , and AES by Rawlings i3.1311. Later, Pb deposition on Ag(ll1) was investigated electrochemically and under UHV conditions in parallel by Takayanagi et al. I3.123, 3.132, 3.1331. Cyclic voltammetry and optical measurements were carried out in parallel with LEED,AES, TEM, and electron work function measurements. The most important result of UHV investigations concerns the formation of a R 30' Pb overlayer structure (cf. Fig. 3.15a) at low & and a slightly Ag(ll1)-(A x compressed and rotated (3.8' 5 R < 4.7") hcp Pb overlayer structure at high (cf. Figs. 3.17 and 3.18). Both overlayer structures were found to coexist at medium coverages in UHV experiments [3.123, 3.132, 3.1331, indicating a first order phase transition. However, a clear indication of a first order phase transition was not found under electrochemical conditions since a discontinuity of the flE,p) isotherm was not observed (cf. Fig. 3.9a).

a)

3.4 Structures of 20 Meah Phases

75

The system Au(lll)/Cu2', H', SO-:, as a typical example of ex situ UHV measurements, has been extensively studied L3.121, 3.124-3.1281. This system exhibits a negative Me-S lattice misfit (do,cu= 0.2556 nm, &A,, = 0.2884 nm) and a 1/2 Cu adsorption is expected *. Indeed, an Au(ll1)-(1 x 1) Cu overlayer structure was found at high K However, at medium an Au(111)-(& x R 30' structure was suggested from RHEED and LEED experiments. This structure corresponds to a R 30' copper coverage of kU= 1/3 of a (1 x 1) Cu monolayer. The Au(lll)-(& x structure was originally explained by the formation of an Au-Cu surface alloy [3.121] and later by the formation of a Cu honeycomb structure being adsorbed on top of underlying Au atoms (not on adsorption sites), since electrochemical Aq measurements indicated a much higher copper coverage of kU'Y 2/3 [3.128, 3.2871, It was assumed that the anions play an important role in the formation of such expanded overlayer structures [3.128]. However, the electrosorption valency (eq. (3.12)) was not measured. It should be noted that such an expanded overlayer structure could not be observed in UHV experiments studying the vapor deposition of Cu on Au(ll1) [3.125]. This fact was explained by a surface reconstruction of Au(ll1) under UHV conditions, whereas the Au(ll1) surface was assumed to be unreconstructed under electrochemical conditions. This example demonstrates that clear relations between ex situ UHV measurements, vapor deposition studies in UHV, and electrochemical investigations are sometimes dSicult.

a)

a)

In sib surface analytical results The development of in situ surface analytical techniques represents a revolution in studying structural and electrochemical properties of electrified solid/liquid interfaces. This development was initiated by applying in situ ellipsometry and surface enhanced Raman spectroscopy (SERS) . Fourier transform infrared spectroscopy (FTIR) and second harmonic generation (SHG) were introduced later in the eighties. These methods give only indirect structural information. At the same time, the application of synchrotron radiation opened a new window for in situ X-ray scattering methods such as extended X-ray absorption fine structure ( E M S ) and grazing incidence X-ray scattering (GMS) , These methods give direct, but integral structural surface information in reciprocal space. On the other hand, "local probe methods" such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) were * A (111) face of a fcc crystal exhibits two types of threefold adsorption sites as shown in Fig. 3.14a. Thus, the number of adsorption sites is twice the number of surface atoms.

76

3 UnderpotentialDeposition of Metals - 20 Phases

developed by Rohrer and Binnig in the eighties L3.288-3.2961. Related local scanning probe microscopy (SPM) methods have followed in the nineties [3.291-3.2961. Local probe methods represent the most powerful tool for acquiring direct information on surface properties. In the case of STM, the surface electron density of states at the Fermi level is measured via an electronic tunneling current between a tip and an electron conducting substrate. In the case of AFM, atomic or molecular forces between a cantilever and the substrate surface are registered which are determined by the integral electronic density of states. Both methods give local real space information on the substrate structure and morphology of electron conducting substrates such as metals, superconductors and semiconductors (STM, AFM) and insulators (AFM). However, the interpretation of STM and AFM images in terms of Meads surface structures is not straightforward, as discussed below. Local probe methods were first applied under UHV conditions, later under a gas atmosphere, and in 1986 for the first time at the solid/liquid interface, however, without potential control of the substrate [3.148-3.1501. In 1983, Rohrer and Siegenthaler had already started in situ STM investigations at solid/liquid interfaces under defined electrochemical conditions, i.e., independent potential control of tip and substrate. This measurement technique requires the development of an appropriate electronic device (bipotentiostat). Under defined conditions, electrochemical studies using four probe technique (substrate as the working electrode, counterelectrode, reference electrode, and tip) became possible in the late eighties [3.151, 3.169, 3.1701. At this time, electrochemical in situ STM and AFM imaging with lateral atomic resolution was achieved by Kolb and Behm et al. i3.152-3.1551, Gewirth et al. L3.1563.1623, Itaya et al. [3.163-3.16'71, Lindsay et al. [3.168] Siegenthaler et al. [3.1713.1791, and Lorenz et al. [3.171-3.174, 3.182-3.1911, Today, both STM and AFM .equipment for electrochemical measurements is commercially available. Lateral atomic resolution under defined electrochemical conditions is necessary to interpret quantitatively structural aspects of Me UPD phenomena. Local probe information from in situ STM and AFM imaging are complementary to integral information obtained from X-ray surface scattering methods which, however, are more precise. In addition, in situ STM provides structural and chemical information of substrate surfaces via tunneling spectroscopic methods such as distance tunneling spectroscopy (DTS) and voltage tunneling spectroscopy (VTS) [3.297]. In the following, structural aspects of substrate surfaces and Me UPD overlayers obtained by in situ GES, STM and AFM are discussed. UPD systems without and with different crystallographic Me-S lattice misfit are presented.

3.4 Structures of 20 Meah Phases

77

System Au (hkl)/Ag' UPD of silver on gold single crystal substrates has been studied by various authors using differently prepared single crystal substrates and different electrolyte solutions [3.157, 3.159, 3.165, 3.167 ,3.183-3.186, 3.188, 3.189, 3.191, 3.196, 3.1971. The system Au(hkZ)/Ag' is chosen as a typical example for UPD systems with negligibly small Me-S lattice misfit (do,& = 0.2890 nm, d o , ~=u 0.2884 nm). It is well known that single crystal surfaces of gold can undergo surface reconstructions (cf. Section 2.1) which may influence the initial stages of Ag UPD [3.185, 3.198-3.2081. Indeed, in situ STM imaging with lateral atomic resolution of a flame-annealed Au(100) substrate in deaerated perchloric or sulphuric acid solutions free of Ag' ions shows the existence of a potential-induced surface reconstruction with an undulated quasi-hexagonal ("quasi-hex") structure at EH I 240 mV (cf. Figs. 2.5 and 2.7). Reconstructed domains were not observed at higher AE, which indicates that the quasi-hex reconstruction of the Au(100) surface is lifted by the applied positive electrode potential. In deaerated perchloric or sulphuric acid solutions containing Ag' ions, Ag UPD is clearly indicated in cyclic voltammograms (Fig. 3.20a) as well as in q(E) or r(E) isotherms at ,u = constant in the underpotential range 0 mV I AE < 600 mV (Fig. 3.20b). Electrosorption valency measurements under 'ITL conditions indicated that cosorption or competitive sorption of HSOY or SO?- can be neglected at medium AE [3.298, 3.2991. At higher underpotentials (AE2 650 mV), in situ STM imaging with lateral atomic resolution shows a quadratic structure of the topmost surface layer with a regular first neighbor interatomic distance (Fig. 3.21a). This structure can be related to a mainly bare Au(100) surface, despite the fact that the onset of oxygen adsorption may interfere in this underpotential range. In the range 200 I AE I 550 mV, stable domains of an expanded quasi-hex Ag-induced overlayer structure are imaged by in situ STM (Fig. 3.21b). This "quasi-hex" overlayer structure does not appear in electrolytes free of Ag' ions. In the underpotential range 100 mV I AE I 200 mV, coexisting domains with a quasi-hex and a quadratic overlayer structure with a regular first neighbor interatomic distance are observed [3.298, 3.3001. At AE 5 100 mV, only a commensurate quadratic (1 x 1) structure is observed (Fig. 3 . 2 1 ~ )which can be related either to 2D UPD Au(100)-(1 x l)Ag domains or to Au-Ag surface alloy domains (cf. Section 3.6).

3 Underpotential Deposition ofMetals - 20 Phases

78

-

(a)

12 -

T E

4-

5.-

0

0

-4

Dl

-

-12 -

4

A2

-

-20

160

cYn

E

I

I

I

I

1

0

100

200

300

400

I

I

I

600

700

-

120-

0

Y kIu Y

80 -

40

-

0 500

Figure 3.20 Cyclic voltammogram (a), measured under serniinfhite-linear diffusion conditions with IdE/dtl = 7 mV s-l in the system Au(100)/5 x los M AgzSO4 + 5 x lo1M H2SO4, and r(E) isotherm (b), measured under’ITL conditions in the system Au(100)/4.2 x lo4M Ag2SO4 + 5 x 1O-I M H2SO4, at T = 298 K [3.298,3.299].An and Dnwith n = 1,2,3denote cathodic adsorption and anodic desorption peaks, respectively.

3.4 Structures of 20 Meah Phases

79

Figure 3.21 In situ STM images in the system: Au(100)/5 x lV3 M Ag2SO4 + 10.' M at T = 298 K [3.299,3.3001. (a): ffi= 650 mv, IT= 20 d, (b): ffi = 400 mv,IT = 3 nA, (c):ffi = 100 mv, ZT = 5 nA, Pt-Ir tip.

Similar Ag UPD phenomena were found on the Au(ll1) substrate [3.157, 3.159, 3.1651. In sulphuric acid solution containing Ag' ions, an expanded Au(ll1)(& x&) R 30' overlayer structure (cf. Figs. 3.14a and 3.15a) was observed at medium underpotentials (G= 500 mV) as shown in Fig. 3.22 [3.165]. This overlayer structure was attributed to Ag UPD on the basis of q measurements. It was concluded that SO;- ions are specifically cosorbed to the same extent on both the Au(ll1) substrate and the expanded Ag overlayer [3.165, 3.1671. However, in situ AFM studies in the same system combined with ex situ UHV measurements indicated an expanded Au(ll1)-(3 x 3) - 4Ag overlayer structure at AE = 420 mV as illustrated in Fig. 3.23 [3.157]. The composition of the surface coverage was estimated from a comparison of

80

3 Underpotential Deposition ofMeta2s - ZD Phases

electrochemical q values with in situ AFM images and ex situ UHV results. Cosorption or competitive sorption of sulphate or bisulphate ions can be neglected at medium A,? as found by electrosorption valency measurements using the ’ITL technique t3.298, 3.2991. At low AE,an Au(ll1)-(1 x 1) Ag overlayer structure was suggested, but the possibility of surface alloy formation was not taken into account (cf, Section 3.6). EXAFS 13.135, 3.1401 and SHG l3.146, 3.1471 measurements confirm the formation of commensurate Ag UPD overlayers. In some papers, the formation of a second Ag monolayer on Au(ll1) at very low AE is assumed [3.162, 3.196, 3.197). In this UPD range, however, there is clear evidence of the formation of an Ag-Au surface alloy even at room temperature (cf. Section 3.6).

Figure 3.22 In situ STM images in the system: Au(111)/10f3 M Ag2SO4 + 5 x 10.’ M H2SQ at 7’= 298 K 13.1651.ffi/mV = GOO (a); 500 (b); 35 (c), Fr = 10 nA, Pt-Ir tip.

3.4 Structures of 20 MeadsPhases

81

Figure 3.23 In situ AFM images (5nm x 5nm) of the first Ag UPD monolayer on Au(ll1) in different systems at T = 298 K 13.1571. (a): Au(111)/7.7 x M H2SO4 in the range M AgzSO4 240 mV 5 AE 5 500 mV, (b): Au(111)/10-3 M &NO3 + lo1 M HNO3, negative of adsorption peak A1, (c): A ~ ( l l l ) / l O -M~ k c 1 0 4 + lo1 M HC104, negative of adsorption peak A1, (d): Au(lll)/lOs M CH3COOAg + 10-l M CHJCOONa + 1O-l M CHQCOOH,negative of adsorption peak A1.

Morphological in situ STM studies showed 2D Ag island formation and limited growth on Au(hk0 with (hk0 = (100) and (111) in the UPD range 0 mV I AE I 250 mV depending on AE and the polarization time, as illustrated in Fig. 3.24, for Au(100) [3.196, 3.2981, The islands dissolve during subsequent anodic stripping. The analysis of DTS results obtained in the system Au(lOO)/Ag', H', Clod at AE = 100 mV revealed a higher effective barrier height on top of islands than on terraces in their neighborhood [3.300]. This indicates that the Ag overlayer structure may be locally dserent. The appearance of growing 2D Ag UPD islands on Au(100) may be explained in terms of a first order phase transition. However, surface inhomogeneities and surface alloy formation may influence the thermodynamics and kinetics of 2D nucleation and growth (cf. Section 3.6).

3 Underpotential Deposition ofMetals - 20 Phases

82

-80.0

-60.0

-40.0

-20.0

0

20.0

40.0

60'.0

80.0

-0

-

Figure 3.24 In situ STM images of 2D island formation and limited growth in the system Au(lOO)/ 5 x 1K3 M AgClO4 t 5 x 10-1 M HClO4 at T = 298 K [3.298, 3.2991. (a): AE = 500 mV, no island formation, (b): AE = 200 mV, island formation and growth. IT = 20 nA,Pt-Ir tip.

System Au (hkl)/Cu2'

This system is chosen as a typical example for UPD systems with a significant negative Me-S lattice misfit (do,cu= 0.2556 nm, doAu= 0.2884 nm). The structural aspects of Cu UPD on Au(ll1) were investigated by in situ GMS and EXAFS [3.134, 3.136, 3.1441, STM [3.152-3.154, 3.1651, AFM [3.1561, cyclic voltammetry and rotating ring-disc electrode O E ) experiments [3.3011, chrono-coulometry [3.302, 3.3031, and theoretical considerations [3.221-3.223]. Au(ll1) films on mica, deposited from the vapor phase, were used in GIXS, EXAFS and AFM studies, flame-annealed Au(ll1) single crystal faces in STM and chronocoulometric measurements, and electropolished and precleaned Au(ll1) surfaces in voltammetric and RRDE studies. A cyclic voltammogram of the system Au(111)/Cu2', H', Clod is characterized by two wellseparated adsorption/desorption peaks, Al/D1 and A2/D2 as shown in Fig. 3.25 [3.3011. In situ investigations were mainly carried out in the system Au(111)/Cu2', H', SOL in order to clarify the discrepancies remaining from ex situ UHV and electrochemical R 30' overlayer measurements described above. The expanded A u ( l l 1 ) - ( a x structure in the U W studies was found also by GMS, EXAFS, STM, and AFM in situ investigations at medium r L3.134, 3.136, 3.144, 3.152-3.154, 3.156, 3.1651.

a)

3.4 Structures of 20 Meah Phases

83

70

D2 60

50

40

30 7-

6

20

4

u

.-

lo 0

i,

-10

-20

-30

-40 0

200

400

600

800

A E [mvl

Figure 3.25 Cyclic voltammogram measured under semiinfinite-linear diffusion conditions in the system Au(111)/5 x M CuSO4 + 9 x lo2M H2SO4 with IdE/dtl = 10 mV at T = 298 K l3.3011. A,, and D,,with n = 1,2 denote cathodic adsorptionand anodic desorption peaks, respectively.

Measurements of the electrosorption valency, AM, 0, yield y = z = 2 only at high r or low AE,but y = 1 t z at low r or high AE [3.301, 3.3041. The deviation y # z indicates a cosorption of SO?- or HSOL ions' , which are obviously imaged by in situ STM and AFM as an A u ( l l 1 ) - ( a x A) R 30" SO -: structure. Consequently, the Cu coverage at medium r or AE is characterized by a honeycomb structure Au(ll1)2(& x &) R 30' Cu on adsorption sites (&, = 2/3), and the coadsorbed SO-: or * The equilibrium S042-+ Hf + HSO4- is shifted to the right-hand side in acidic aqueous solutions, but may be changed in the case of specific adsorption.

-

84

3 UnderpotentialDeposition ofMetals 20 Phases

HSOd ions fill the honeycomb centers on adsorption sites, stabilizing this structure (Fig. 3.26).

7 nm

7 nm

3.26 Cyclic voltammogram measured under semiinfinite-lineardiffusion conditions and in situ STM imag-es depending on AE in the system Au(l1 I)/lO-’ M CuSO4 + 5 x M H2SO4 with laE/dtl= 5 mV s’l at T = 298 K 13.1541. (a): bare Au(ll1) substrate, 300 mV I: hE < 500 mV, = 45 nA. (b): Au(lll)-(J3 x&) K 30’ SO;’. overlayer structure stabilizing the Au(111)-2(43 xJ3) R 30’ Cu honeycomb structure which is not detectable by in situ STM, 100 mV 5 AE 5 220 mV (peak A1). IT = 15 nA, (c): Au(111)-(1 x 1)Cu, 0 mV 5 AE 5 20 mV (peak Ad, IT = 15 nA, Pt-lr or W tips. Reprinted by permission of Kluwer Academic Publishers. Figure

3.4 Structures of 20 Meah Phases

85

It is interesting to note that such an expanded Au(ll1)-(& x&) R 30' S04" overlayer structure in the case of Cu UPD on Au(ll1) was theoretically predicted by Blum on the basis of a statistical mechanical model for a l / n adsorption of SO:[3.221-3.2231. In this model, the Me UPD overlayer formation takes place as a sequence of first order phase transitions. Cu UPD on Au(100) is less studied. In situ STM studies showed that Cu UPD adlayers on Au(100) are less ordered than on Au(ll1) substrates. A relatively stable and expanded quasi-hexagonal Cu overlayer structure was observed from medium to low AE.This structure was also attributed to a cosorption of SO:- anions [3.152]. System Ag(hkl)/Pb2+

This system is a typical example of UPD systems with a significant positive Me-S misfit (do,pb = 0.3500 nm, do& = 0.2890 nm). Cyclic voltammograms and r(E) isotherms of the system Ag(hkl)/Pb2+, H', ClOi, measured with the 'ITL technique 13.55, 3.971, are presented in Figs. 3.2 and 3.9, respectively. A great advantage of the system Ag(hkI)/Pb2+, H', C10i is the knowledge of the electrosorption valency, which was found to be y = z = 2 in the entire UPD range (Fig. 3.12a). This means that cosorption or competitive adsorption processes of anions can be excluded. A further advantage is that real and electrochemically grown Ag(ll1) and Ag(100) faces can be comparatively studied (cf, Section 3.3, Fig. 3.4). The atomic surface structures of real and electrochemically grown Ag(hkl) substrates with (hkl) = ( l l l ) , (100) were studied by in situ STM at AE = 250 mV and found to be unreconstructed with small surface corrugations L3.172, 3.184,3.186-3.1911. These system-specific advantages facilitate the analysis and interpretation of experimental results obtained by different in situ surface analytical techniques. Therefore, most experimental data has been collected in the Pb UPD system. In the case of Pb UPD on Ag(lll), in situ E M S and GIXS measurements in systems Ag(lll)/Pb2', H', CH3COO- and Ag(111)/Pb2+, H', Clod yield an incommensurate and internally strained Pb overlayer rotated by 4.5' with respect to the Ag(ll1) substrate at high T o r low AE L3.137-3.139, 3.141, 3.1431. The interatomic distance d decreases linearly with decreasing AE (Fig. 3.27) in accordance to the theoretical considerations mentioned above (eqs. (3.33) and (3.34)). Theoretical considerations on the basis of a jellium model with a lattice of pseudopotentials gave evidence that the interatomic distance, d o , ~ ein, the 3D Me lattice is larger than the interatomic distance, do, in a 2D Me monolayer separated from the Me bulk [3.2391. In the case of a 2D Pb monolayer a value of do = 0.3432 nm was calculated. Using this value for do and eq.

3 Underpotential Deposition ofMetals - 20 Phases

86

(3.33), A& = 100 mV and IQD = (A' + p')-' = 1.2 A'(eV)-' = 7.5 x lU4 Pa-' cm-' were estimated from the experimental data in Fig. 3.27. The experimental value of 2D compressibility IQD corresponds relatively well to the theoretical value IQD = 0,44 A'(eV)-' = 2.75 - lo4Pa-' cm-' calculated on the basis of a 2D free electron gas model [3.141]. On the other hand, from the experimental value of IQD using eq. (3.34) and ~ M L= 0.286 nm, a value of (A + p) = 4.66 x 10'' Pa for the 3D Lam4 coefficients was derived in good agreement with the literature data L3.283, 3.2841. Fig. 3.28 shows an in situ STM image with lateral atomic resolution of a nearly complete Pb monolayer at AE = 15 mV on Ag(ll1) [3.173-3.1751. The image shows a compressed hcp Pb overlayer with d = 0.34 f 0.01 nm. Additionally, a superstructure with a moirC pattern is observed. The mean distance between the moire spots is &'ire = 1.65 r 0.07 nm. This overlayer is rotated by a = 4.5 2 0.2' with respect to the Ag(ll1) substrate. These results are in good agreement to those obtained from GMS and EXAFS measurements l3.137-3.139,3.140, 3.141, 3.143, 3.1451. 3.46

3.44

3 38

0

25

50

75

100

125

150

AE [mvl

Figure 3.27 Interatomic distance, d , in a 21) Pb overlayer as a function of AE in the system Ag(111)/5 x M Pb(CIO4)' + 10' M NaC104 + 10' M HClO4 from in situ GMS measurements at T =298 K [3.143].

3.4 Structures of 20 Me,& Phases

87

0 0

15

nm

Figure 3.28 In situ STM image of a compressed 2D hcp Pbads overlayer showing a superstructure with moirk pattern in the system Ag(111)/5 x M Pb(ClO4)2 + lo2 M HClO4 at AE = 30 mV and T =298 K with ZT = 20 nA and Pt -1r tip [3.173-3.175].

However, the experimental results do not allow one to decide whether the rotation of the Pb UPD overlayer (cf. eq. (3.22)) can be explained by the “coincident site lattice“ concept (involving higher order commensurate overlayers, Fig. 3.17) or the “static distortion waves“ (SDW) concept (dealing with incommensurate overlayers, Fig. 3.18). The estimation of d as a function of AE from a statistical analysis of in situ STM images coincides with GIXS results illustrated in Fig. 3.27 [3.176]. Expanded Pb overlayer structures on Ag(ll1) substrates at AE > 100 mV could not be detected by in situ GIXS and STM. A possible reason for this lack may be a dynamic instability of expanded overlayer structures such as Ag(ll1)-( xa R 30’ Pb (cf. Fig. 3.15a) in the absence of appropriate coadsorbed anions which can stabilize less dense overlayers (cf. system Au(111)/Cu2+). Morphological in situ STM investigations show that the initial step of Pb UPD on Ag(ll1) at low T o r high AE is a decoration of monatomic steps I3.175, 3.177-3.179, 3.3021. This observation is in good agreement with cyclic voltammetric results

a)

88

3 Underpotential Deposition of Metals - 20 Phases

(concerning peak A1 with hE, = 170 mV) obtained on real and electrochemically grown Ag(ll1) substrates (Fig, 3.4). At higher Tin the range 140 mV 2 AE 5 170 mV, the uncompleted first Pb monolayer is relatively unstable in the time scale of minutes due to surface alloy formation (cf. Section 3.6). On the other hand, the structure of an expanded Pb overlayer on Ag(100) could be atomically resolved by in situ STM in the range 150 mV < AE < 200 mV after decorating monatomic steps at lower r o r higher AE (Fig. 3.29b) [3.187, 3.1901. For comparison, Fig. 3.29a shows the same surface area of the bare Ag(100) substrate at AE = 300 mV. In Fig. 3.29b, two coexisting domains are seen: on the right hand side a small domain with a quadratic structure representing a part of the uncovered Ag(100) substrate, and on the left hand side a larger domain with an expanded and rotated quadratic structure which corresponds to a Pb overlayer. The interatomic distance of first nearest Pb neighbors is dl = 0.40 2 0.01 nm and of second nearest Pb neighbors 4 = 0.59 2 0.01 nm. The most dense atomic rows of the Pb adlayer are rotated by an angle of 45' with respect to the A g [ l l O ] and Ag[liO] directions of the substrate. This adlayer structure corresponds to an Ag(lOO)-(& x &) R 45' Pb or Ag(lOO)-c(2 x 2) Pb superlattice structure. Consequently, the formation of the Pb adlayer in this underpotential range can be considered as an 1/2 localized adsorption on a square lattice. In this case each adatom in the compact monolayer covers effectively two adsorption sites. Thus, domains with an Ag(lOO)-c(2 x 2) Pb structure located on different substrate sublattices (like white and black fields of a chessboard) separated by mismatch boundaries are obtained as shown, for example, by Monte Carlo simulation (cf. Section 8.4) of 1/2 adsorption on a square lattice [3.214]. The fit of experimental coverage data of the first Pb adsorption step on Ag(100) (cf. Fig. 3.9) by Monte Carlo simulation is illustrated in Fig. 3.30. From this fit, a lateral attraction energy between the Pb adatoms of 1/1pbads-pb,ds 2.5 x 1021J (corresponding to 1.5 x lo3J mole-') can be estimated [3.184, 3.190, 3.191, 3.2141. Preferential Me adsorption on surface heterogeneities like monatomic steps was disregarded in the fit procedure. Adlayer domains with an Ag(lOO)-c(2 x 2) Pb superlattice structure were also observed in the UPD range 40 mV < AE < 100 mV [3.172, 3.174, 3.182, 3.184, 3.186, 3.188, 3.1911. However, more detailed STM investigations show that hcp Pb adlayer domains are also present in this potential range as seen in Fig. 3 . 2 9 ~[3.187, 3.1901. The azimuthal orientation of the Ag(lOO)-hcp Pb overlayer in Fig. 3 . 2 9 ~ is characterized by a parallelism of one of its most dense atomic rows with the Ag[llOl direction of the Ag(100) substrate.

89

3.4 Structures of 20 Meah Phases

4.00

L

~ gii[n]

(4

3'00 2.00

Ag[l 101

1.00

n 0

1.00

2.00

3.00

4.00

,1111

~

4.00

L

Ag[liO]

3 000 2 0

Asll101 1.00

" 0

1.00

2.00

3.00

4.00

~

~~

-4.00

3.00

Ag[liO]

-2.00

~1.00

-0

nm

Figure 3.29 In situ STM images in the system Ag(100)/5 x M Pb(C104)2 + M HClO4 at T = 298 K [3.187]. (a): AE = 300 mV, bare substrate, (b): AE = 175 mV, Ag(lOO)-c(2 x 2) Pb domain besides bare substrate, (c): AE = 80 mV, slightly distorted 2D hcp Pba& overlayer structure. ZT = 5 nA, Pt -1r tip.

3 UnderpotentialDeposition ofMetals - 20 Phases

90 1.o

a 0.5

0

-3

-2

-1

0

1

2

3

a Figure 3.30 r(E) isotherm for 1/2 adsorption on a square lattice expressed as 0 vs. p plot according to Sections 8.3 and 8.4. (0):Monte Carlo simulation data at Y M ~ , ~ ~/kT - M = 0.6 ~ ~(cf.~ Fig. ~ 8.4), (0):Experimental data for Pb TJPD on Ag(lO0) (system of Fig. 3.9b) in the range 125 mV < hE'I 225 mV [3.214].

The interatomic distance of nearest Pb neighbors in this STM image is d = 0.35 0.01 nm. It can be assumed that in this UPD range the overlayer most probably consists of coexisting domains of Ag(lOO)-hcp Pb and Ag(lOO)-c(2 x 2)Pb overlayer structures. The structural transformation from a com-mensurate quadratic Ag(100)c(2 x 2) Pb overlayer to an Ag(100)-hcp Pb monolayer, which most probably starts at mismatch boundaries between adlayer domains and/or monatomic steps of the substrate, is completed at relatively low AE.In the UPD range 0 mV 5 AE < 30 mV, only the hcp Pb overlayer structure could be observed by in situ STM. More detailed information about the Ag(lOO)-hcp Pb UPD overlayer structure in the potential range 0 mV 5 AE < 100 mV were obtained from different moire patterns which could be observed by STM images with a larger scan size (Fig. 3.31) l3.187, 3.190,3.302]. In Fig. 3.31a the distance between the nearest moirC spots in Ag[llOl direction is di,$L = 1.70 +- 0.05 nm, and in the A g [ l i O ] direction dg!gi= 0.59 0.05 nm. The angle between the most dense moire spot rows and the Ag[llO]

3.4 Structures of 20 MeahPhases

91

dkgi

direction is p = 9' ? 2' (Fig. 3.19). The moire spot distance corresponds well to 2d, which indicates a matching of every close packed Pb atomic row with every close packed substrate A g [ l l O l atomic row. This matching is confirmed by the large extension of the moire superstructure in the Ag[liOl direction. A significant deviation from the matching would lead to a vanishing of the moire spots after a few nm. The matching of the close packed Pb and Ag atomic rows in the A g [ l i O l direction requires a certain compression of the 2D Pb adlayer.

.8.00

-6.00

-4.00

.2.00

n

0

2.00

4.00

6.00

8.00

nm

-8.00

-6.00

-4.00

.2.00

.n

0

2.00

4.00

6.00

8.00

IIM

Figure 3.31 In situ 5TM images with differently orientated domains (a) and (b) of an anisotropically compressed 2D hcp Pb,& overlayer showing a superstructure with moire pattern (cf. Fig. 3.19) in the M HClO4 at T = 298 K [3.87]. (a): A E = 80 mV, M Pb(ClO4)g + system Ag(100)/5 x (b): hE = 20 mV. IT = 40 nA, Pt-Ir tip.

92

3 Underpotential Deposition ofMetals - 20 Phases

In order to explain the moire structure, one can consider the following two cases: (i) isotropic compression or (ii) anisotropic compression of the Pb overlayer. In case (i), the overlayer has a perfect hexagonal symmetry. However, the assumption of row by row matching in the Ag[liO] direction requires an interatomic Pb distance of d = 0.334 nm, corresponding to a relatively high compression of about 5 percent. In case (ii), the overlayer structure is in higher order registry with the Ag(100) substrate in the two directions Ag[llO] and Ag[liO] (Fig. 3.19). The distances of the nearest moire spots in this Pb adlayer superstructure are d$Aii = 6 do,& = 5 d = 1.73 nm in the Ag[llO] direction and di::k= 2 do,& = 0.58 nm in the Ag[llOl direction. The angle between the most dense moire spot rows and the close packed Pb atomic rows, which are parallel to Ag[llO], is p = 9-05' (Fig. 3.19). This Ag(lOO)-c(2 x 6) moire superstructure leads to an interatomic Pb distance of d'""] = 0.347 nm (dl in Fig. 3.19) corresponding to a compression of 0.8 percent, and a distance of d = 0.337 nm (d2 in Fig. 3.19) in the other two close packed Pb atomic row directions corresponding to a compression of 3.7 percent. The average compression of this Pb adlayer is close to the compression found for the hcp Pb adlayer on Ag(ll1) [3.137-3.139, 3.141, 3.143, 3.1451. Fig. 3.31b shows the structure of an overlayer domain with the same superstructure, but rotated by an angle of 90' with respect to that in Fig. 3.31a. The appearence of these two types of domains is expected from the symmetry of the Ag(100) substrate. In summary, UPD of Pb on Ag(100) leads to the formation of internally anisotropically strained hcp Pb overlayers at high T o r low AE. The results of the structural properties of 2D UPD Pb overlayers and their dependencies on the substrate orientation and AE, which were obtained by in situ scanning probe microscopy, were supported by in situ DTS measurements [3.184, 3.186, 3.190, 3.3031. The effective tunneling barrier height, &.ef, was measured on bare and UPD Pb-modified Ag(ll1) and Ag(100) substrates as well as on Pb(ll1) surfaces prepared by epitaxial growth of 3D Pb on Ag(hkl) in the OPD range L3.93, 3.98, 3.174, 3.183, 3.184, 3.186, 3.188, 3.1911 as described in Chapter 4. The results showed that &eff of bare Ag substrate depends on the crystallographic orientation f3.273, 3.274, 3.2841. Recent results show that no clear correlation exists between &eff and the vacuum work function in corresponding systems [3.300]. On the other hand, the hcp Pb overlayer structures formed in the UPD range 0 mV < AE 5 100 mV on Ag(ll1) and Ag(100)

3.4 Structures of 2D Meah Phases

93

gave similar &-values as Pb(ll1). However, a clear interpretation of DTS results is not yet possible due to influences of coadsorbates and contaminations on the effective barrier height and the tunneling mechanism. In situ STM results of Pb UPD on Ag(hkl) substrates show that Me superlattice structures on S based on localized adsorption may exist, however, only at low r or relatively high AE in the case of l / n adsorption. Therefore, the previously proposed hypothetical superlattice structures in Table 3.1 must be critically reconsidered. The stepwise formation of Pbads overlayers in the systems Ag(hltl)/Pb2+, H', Cloy depending on AE is summarized in Table 3.2. Morphological in situ STM studies in the system Ag(100)/Pb2+, H', Cloy at AE 5 100 mV showed 2D Pb island formation and growth on top of a predeposited hcp Pb overlayer as illustrated in Fig. 3.32 [3.187]. Table 3.2. Stepwise formation of Pbads overlayers in the System Ag(hkl)/Pb2', on a.

Substrate

ffi

ImVl

(3 150 < f f i < 250

Peaks in cyclic voltammograms

A1

H', ClO4' depending

Stepwise formation of Pbads overlayers

Step decoration and formation of expanded 2D Pbads phase at terraces Formation of a condensed 2D hcp Pbads phase from an expanded 2D Pbads phase via 1st order phase transition starting at steps

O 0, condensed Meads overlayer

(3.63)

Analogously to 3D nucleation processes, a supersaturated state of an expanded structure is formed first which is characterized by actual Cp(t) and qep(t) values kinetically controlled by Me:$" bulk diffusion and charge transfer. 2D nucleation and growth start from a supersaturated expanded 2D Meads phase and lead to a condensed 2D Meads phase which is characterized, in a first approximation, by time-independent equilibrium values of Tcd(AEf)and qcd(AEf). The part of the substrate surface covered by the condensed 2D Meacls phase will be denoted by S(t). The charge balance of Me:$" is given by

where i(t) is the overall cathodic current density and qCp(t= 0) denotes the initial charge amount of the expanded overlayer. The symbol * represents the convolution product.

3.5 Kinetics

113

S(t) can be described by the well-known Avrami theorem [3.317], supposing multiple nucleation on a quasi-homogeneous substrate surface with a sufficient density of nuclei, statistically local distribution of nuclei, and overlapping of growing 2D islands:

[

S ( t ) = 1 - exp - 1 * ___ i;:t)]

(3.65)

The flux term jfree describes the "extended" growth of islands without overlapping [3.318] and is related to the growth rate of a single nucleus, Jl(t), and the nucleation rate, dZnUc/dt: (3.66) J1

(t) represents the flux of Me:& to an isolated nucleus.'

From eqs. (3.64) and (3.65) one gets after differentiation and elimination of S(t) for the overall current density:

The Faradaic current for the formation of a condensed 2D Meads phase without adsorption, inuc(t), is given by

Combining eqs. (3.67) and (3.68), one obtains: (3.69) Consequently, the polarization current i(t) consists of nucleative and sorption components which depend on each other and, therefore, cannot be clearly separated. However, it can be assumed that after a critical time, t,, qep(t) is approaching a steady state final value qep(t + a)) which is of the order of magnitude of the metastable equilibrium charge amount qep at A& This means, dqep(t)/dt tends to zero for t >> tc. On the other hand, in& tends to zero for t -+ 0 and t -+ co in conventional 2D ~~~

~~~

~

'Jl(t) is assumed to depend on the growth time t of an isolated nucleus only, but not on the time of its generation. Therefore, eq. (3.66) is only valid for negligible or constant diffusion polarization and at AE = const. The considerations cannot be applied to potentiodynamic or galvanostatic polarization conditions.

3 Underpotential Deposition of Metals - 20 Phases

114

nucleation and growth models f3.318, 3.3193. Therefore, i(t) has the following properties: for t -+ 0

i(t)=

(3.70)

l o

fort-,

00

Eq. 3.64 shows that short-time pulse polarization experiments or EIS measurements at high frequencies carried out at A& give information on dqep(t)/dt, i.e., on the kinetics of the adsorption process forming the expanded 2D Meads overlayer. On the other hand, i(t) measurements can only provide information on in& in a time domain t >> to This condition corresponds to medium and low frequencies in EIS experiments. The critical time, t,, can be estimated for a purely bulk diffusion and D L3.941. controlled adsorption process taking into account c" Mez+ Information on the model-specific flux jkee(t) can be obtained from eq. (3.69, which can be written after rearrangement:

(3.71) where (3.72) Since dqe,(t)/dt

-+ 0 for t >> tc,one obtains (3.73)

In an 1 i(t)/(l - 8)I vs. t plot, the normalized function I i(t)/(l- 6) I approaches asymptotically jkee at relatively high t. Then, information on the 2D nucleation and growth model is available using an appropriate analysis [3.318, 3.3191. Furthermore, integration of the I i(t)/(l-&) I vs. t plot gives information on qep:

3.5 Kinetics

115

On the contrary, if for t >> tc

(3.75)

2D nucleation and growth can be excluded. This is a necessary but not sufticient criterion for a nucleation-free Meads overlayer formation process on quasihomogeneous substrate surfaces. The surfaces of real substrates are inhomogeneous and exhibit surface defects such as steps, kinks, pits etc. These defects do significantly influence not only the energetics of 2D nucleation i3.2491, but also the overlapping of growing 2D islands. Thus, the assumptions of the Avrami equation (3.65) are not fulfilled in this case. In the following, the influence of surface inhomogeneities such as monatomic steps on the kinetics of 2D Meadsphase formation is briefly discussed. According to the classical nucleation theory, the Gibbs energy for the formation of a critical 2D nucleus of a 2D Meadsphase on an atomically flat terrace 0 ,AGcrit,T, is given by [3.249] (cf. eq. (4.25a)): (3.76) where b is a geometric factor depending on the shape of the critical nucleus, R represents the area of an adatom in a condensed Meads overlayer, E denotes the specific edge energy, and ZFIAE - AE*l corresponds to supersaturation with respect to the condensed 2D Meads phase. AE* represents the equilibrium underpotential of a condensed 20 Meah phase and is defined in eqs. (3.20) and (3.21). It is related to a kink-like position of Meads in a condensed 2D Meads phase which is characterized by c/2. At AE < a*, a condensed infinite 2D Meads phase is thermodynamically stable, whereas, at AE > AE*,the condensed 2D Meadsphase dissolves and only expanded 2D Meads overlayers can exist. Thus, AE < AE* and AE > AE* correspond to supersaturation and undersaturation ranges, respectively, with respect to the condensed 2D Meadsphase. However, the Gibbs energy for the formation of a critical 2D Me cluster at a monatomic step (S), AGcrit,s, is reduced by an additional term including the lateral interaction energy between Meads and a step, Y M ~ ~ ~ For , - sa ~nucleus ~ ~ . of a 2D Meads phase with a square lattice structure (b = 4, c = 4 ) , assuming only first nearest neighbor ~ ~for-AGc,it,s ~ ~ t3.2491: ~ ~ ~ interactions ( i , v ~ ), ~one~obtains

3 Underpotential Deposition of Metals - 20 Phases

116

AGcrit,S = AGcrit,T

yh'fc?ad,-Step Meads-Meads

I

(3.77)

If yMeads-Step > W M ~ ~ , ~the~formation - M ~of a~ 1D ~ Meads ~ phase along monatomic steps (Fig. 3.42~) becomes possible in the undersaturation range A,? > AE* with respect to the condensed 2D Meads phase. The width of such a 1D Meadsphase at monatomic steps is not necessarily restricted to a monatomic dimension, but depends on the step activity. These effects play an important role in step decoration processes of Me UPD at relatively high AE as found experimentally in the systems Ag(lll)/Tlt and Ag(hkZ)/Pb2+ by in situ STM studies i3.177-3.179, 3.1871.

Figure 3.42 Formation of 2D and 1D Meads phases on stepped foreign substrates. (a) 2D nucleation on atomically flat terraces; (b) 2D nucleation at monatomic steps; (c) 1D Meads phase formation along monatomic steps at hE > hE* for weads-Step>> meads-ads.

3.5 Kinetics

117

The influence of monatomic steps on AGcrit,i with i = T, S (eq. (3.77)) is also reflected in the nucleation rate,Ji, per nucleation site by C1.16, 1.18, 1.191: (3.78)

where the preexponential factor Ki and AGcrit,i depend on the supersaturation zFIAE - M*l.However, the supersaturation dependence of Ki is relatively weak and can be disregarded. According to eq. (3.78), a detectable 2D nucleation rate Ji is obtained after passing a critical value, IAE - AE*lcrit. A schematic representation of Js andJT as a function of the supersaturation zFlAE - M*l is shown in Fig. 3.43. It is seen that the critical threshold value IAE - AE*lcrit is strongly reduced for a 2D nucleation process at monatomic steps in comparison to that on flat terraces. Monatomic steps at real surfaces do significantly influence not only the nucleation act, but also the spreading and overlapping of 2D islands, which determine the shape of potentiostatic current transients. Neglecting the adsorptive contribution in eq. (3.64), i.e., qep 0) ambient phase to the crystal phase. The second is mainly connected to the surfaces created by the emergence of the new crystal. The first part is proportional to the transferred number of atoms, or in other words to the crystal volume: the second is related to the created new surface. Keeping the volume constant, the form of the crystal can be changed until the surface contribution part is minimized. This, obviously, would correspond to the energetically most favorable, or equilibrium form of the crystal, as defined by Gibbs [4.21 and Curie

4 Initial Stages of Bulk Phase Fomation

150

L4.31. Hence, the equilibrium form of a crystal is defined as that having the lowest total surface energy, Q, = C cr jAi , at constant volume, It 1

cli = C o i A i = min.

at

V =const.

(4.1)

2

Here crj and Ai denote the specific surface energies and the surface areas of the respective crystallographic faces i confining the crystal form. Crystal-substrate interaction

In electrodeposition, crystallites are formed on an electron conductive substrate, so that any growing crystal always stays with at least one of its faces in contact with the surface of the substrate. Let us assume that the contact face j * of the crystal is parallel to the crystal plane j and has an area Ap and a specific interface energy 9%(Fig. 4.1). The surface energy contribution of that face is then given by the product of the area of the contact face and the specific interface energy, op, diminished by the specific energy of the substrate-solution interface, Osub, i.e., A p ( 9 * - crsub), since, with the creation of the contact interface, an equivalent surface area of the substrate (with interface energy as,d disappears. Then, for a crystal staying in contact with a substrate

The Gibbs-Curie condition including the crystal-substrate interaction can be rewritten in the form 6@ = Ccri€iAj = 0

at

6V= 0

(4.3)

i ,j *

The interaction of the crystal with the substrate can be described in a more perceivable way by the specific adhesion energy, p. According to Kaischew [4.4, 4.51, the adhesion energy can be defined by the detachment energy, @jet, of the crystallite from the substrate per unit contact surface area

p

= - -o d e t

Ai

(4.4)

As shown in Fig. 4.1, the relation of p to the conventional specific surface energies cr can be found taking into account the fact that, with the detachment of a crystal from

4.1 Equilibrium Form of Crystals and Forms ofgrowth

151

the substrate, the contact interface disappears. At the same time, two new surfaces are created, the first on the substrate-electrolyte interface and the second on the crystallite itself. All three surfaces have the same area, A?. The specific surface energies of these and 9,where 9 is the specific surface energy of a face parallel to faces are: cp, the plane j*. In the summation of the surface energies for the estimation of p according to eq. (4.4) the areas Aj* cancel, leaving for p the sum of the specific surface energies taken with their signs, "c" for the appearing and "-"for the disappearing surfaces. Hence,

This equation corresponds to the well-known DuprC equation [4.6] for the adhesion energy of two different crystals staying in contact with each other. It should be clearly stated that, using surface energies, the adhesion energy, p, is defined as a macroscopic quantity. Its use is restricted, therefore, to interactions between 3D phases only, where surfaces and surface energies have a physical meaning. Introducing the adhesion energy p into eq. (4.2), the total surface energy of a crystallite staying in contact with a substrate is given by @J =

CajAj + A j * ( ~ j - p ) i+ j *

Figure 4.1 Schematic representation of the detachment of a crystal from a substrate showing the transformation of the contact interface (left) into two new interfaces (right): (i) crystal/ambient phase and (ii) substrate/ambient phase. The detachment energy is the sum of the surface energies for creation of the new surfaces and annihilationof the old one.

4 Initial Stages of Bulk Phase Formation

152

Gibbs-Wum-Kaischew theorem The form of a crystal can be described by the distances hhkl)of the respective (hkl) faces from an arbitrary central point, Fig. 4.2 [4.2, 4-71. According to Kaischew [4.44-61, the relation between these distances and the specific surface energies can be found in the following way. The volume of a crystal, thought of as the sum of the pyramids formed on the crystal faces with a common apex in the WuKf point, is related to hi and Ai by (4.7) This relation corresponds to the Euler equation, and the following treatment is similar to that familiar from thermodynamics. The variation of the volume 6V with an infinitesimal change of hi, 6hi, can be obtained, on one hand, from 6V= CAiGhi . i

For the infinitesimal variation of the distances hi, the variation of the areas of the surface elements Ai is neglected in this relation. On the other hand, from (4.7) it follows that 6V= 1/3 CAiGhi + 1/3 Chi&& , giving, with 6V= CAi6h; i

1

5

Now the Gibbs-Curie equilibrium condition (4.3) can be rewritten as

Ca;GA; i ,j *

=

0

at

Ch;6Ai = 0

(4.9)

i,j *

Wulff PO

Figure 4.2 The white arrows represent the normal distances hhkl) of the Wulff point, located in the center of the crystal, from the respective faces.

4.1 Equilibrium Form of Crystals and Forms ofgrowth

153

According to Lagrange, the first equation is multiplied by a constant, A, and is then added to the second equation. The variables 6Ai can now be treated as independent and all but one made zero. Then A o ~= hi, or (4.10)

This is the Gibbs-Wulff theorem as generalized by Kaischew for a crystal in contact with a substrate, i.e., for the case of heterogeneous nucleation and growth. Relation (4.10) allows the construction of the equilibrium form of a crystal: (i) Vectors normal to all crystallographic planes Ihkl} are drawn with a modulus proportional to the specific surface energy q h k 0 . (ii) Planes normal to these vectors are then drawn. (iii) The polyhedron confined by the most inner planes represents the equilibrium shape of the crystal. Fig. 4.3 shows a 2D representation of the procedure. The contact face is drawn, as p). All faces having a higher avalue lie shown, at the distance hj", proportional to (9.outside this polyhedron and do not belong to the equilibrium form.

F i r e 4.3 A two-dimensional representationof the construction of the equilibriumform of a crystal.

154

4 Initial Stages of Bulk Phase Formation

As seen, the influence of the substrate is restricted to the thickness of the crystal only. A higher value of /? only makes the crystal flatter, leaving all distances except the distance hp unchanged. With increasing /?,the distance of the contact face to the Wulff point decreases, taking negative values at /? > q. "wwdimensional crystal The contact face p usually lies parallel to one of the faces belonging to the equilibrium form, so that the top face of the crystal very often lies parallel to the substrate surface, as illustrated in Fig. 4.4. A thickness d can be ascribed to the crystal in this case: d = hj + hp, where hj is the distance of the top face from the Wulff point and hp is that to the crystal-substrate interface. With eq. (4.10) one obtains for the thickness of a crystal lying with its contact face parallel to the plane j on a substrate: (4.11) 29, can be treated as a cohesion energy, in analogy to the adhesion energy /?, because it represents the adhesion between two crystals of the same composition staying in contact with faces of the same orientation. It should be noted that for /?+ 2q,as in the case of a crystal on a native metal substrate, d tends to zero, where the definition based on surface energies is no longer valid. /?can still be formally used, however, but its definition must be based on atomic forces of interaction. the thickness of the crystal decreases. For /? With increasing adhesion energy /I, approaching the cohesion energy 2 9 , the thickness reaches its minimum value, that of a monatomic layer*.The side faces confining the top face degenerate to edges. The top face remains unchanged in form and dimensions (see Fig. 4.4). The contact interface becomes equal in dimensions to the top face, i.e., Aj* = Aj, so that in eq. (4.6) the term q A j of the top face can be extracted from the sum and added to the second term: (4.12)

The second term in (4.12) vanishes for /? + 2 9 leaving for the surface energy of the 2D crystal the contribution of the side faces from the first term only. With decreasing height, however, the specific surface energies of the side faces become a The limit 2 9 applied to 2D layers is also rather formal. It gives only the margin of p, where the 2D layer becomes monatomic. For a rigorous definition of this limit, atomic forces of interaction should be used instead of surface energies, in the same way as in the case of p.

4.1 Equilibrium Form of Crystals and Forms ofgrowth

155

function of the crystal thickness. Therefore, they can be better introduced as specific ~ Li are the side lengths of the 2D edge energies, ~i D ern-']. Then, @ = C E ~ G ,Lwhere 1 crystal.

h(oiy

Figure 4.4 Influence of the adhesion energy P on the shape and thickness d of a crystal staying in contact with a substrate. The distances of the side faces from the WuKf point remain unaffected by the presence of the substrate. The top face also remains unaffected in shape and dimensions.

156

4 Initial Stages of Bulk Phase Formation

The specific edge energies Ej are related to the respective surface energies q ( h ) by: ~i (h) = h crj (h).The equilibrium form of the 2D crystal is defined in full analogy to the 3D case (cf. eq. (4.2)) by 0 =

C E ~=Lmin. ~

at

A = const.

(4.13)

i

With a constant thickness of the 2D crystal, the last requirement is equivalent to V =const. Using eq. (4.13), a Gibbs-Wulff relation can also be derived for the 2D case: hi

= A

(4.14)

Ei

In general, clusters of atoms on a native metal substrate are formed with epitaxial orientation. For this case, the contact interface energy, q* in eq. (4.5) vanishes, and the surface of the substrate has the same composition and atomic structure as the deposited cluster, so that ussub= q.Hence,

With eq. (4.11), crystalline clusters formed on the native metal substrate are expected to be always two-dimensional. ] to the adsorption energy IJ rnol~'],and The adhesion energy p IJ ~ m -is~related depends on the structure of the 2D phase staying in contact with the substrate. When the adhesion energy becomes larger than twice the specific surface energy of a closepacked 2D structure, i.e., that of the cohesion energy, an appreciable adsorption and nucleation of compact monatomic layers can begin even at more positive potentials than the reversible potential of the depositing metal, thus leading to underpotential deposition of metals(cf. Chapter 3). The formation of 2D phases on foreign crystalline singular faces in the absence of steps can be treated as a quasi-homogeneous nucleation process, in full analogy to the 3D case. Using the same formalism as in the 3D case [4.5], in the presence of monatomic steps the 2D nucleation can be treated as heterogeneous process considering the step edge as a substrate (cf. Section 3.5).

Forms of growth The problem of growth forms is much more complicated. Theoretically, the growth form is confined by the faces having the lowest normal growth rate. Under idealized

4.1 Equilibrium Form of Crystals and Forms ofgrowth

157

conditions these are the faces having a close-packed structure (singular faces), which are restricted to growing by 2D nucleation. Crystal defects, particularly screw dislocations, can enhance the growth rate of singular faces, while adsorption of inhibitors, predominantly taking place on non-singular faces, decreases their growth rate. In electrodeposition diffusion and electric field effects can also influence the growth forms of crystals, making the prediction of the growth forms a difficult task at this stage of knowledge.

Energy of cluster formation

If the ambient phase is supersaturated (Ap > 0), a new crystal may be formed which, after reaching a critical dimension, will begin to grow. In electrodeposition, the supersaturation Ap of the ambient phase is given by a cathodic (negative) deviation of the actual electrode potential from the equilibrium potential, I?, = E - EMe/MeZ+ < 0, as defined in eq. (1.7).The transfer of ions from the solution to the electrode across the electrochemical double layer, under the influence of the overpotential, is accompanied by a decrease in the Gibbs energy of the system, AG(N) = - Nzelql, and usually proceeds spontaneously. With the formation of a new cluster of the depositing phase, however, a part of the transfer energy, @(N),is consumed for the formation of the new interface boundaries: cluster/solution and cluster/substrate. As introduced, @(N) is an excess energy term connected with the formation of the interface boundaries of the cluster. It may, however, contain additional energy terms connected with the deviation of the atomic arrangement of the initially small cluster from that of a 3D bulk crystal, including internal strains inherited from the substrate. This excess energy, @(N), increases the Gibbs energy of the system correspondingly. The total Gibbs energy change of the system associated with the formation of a cluster of N atoms (4.16) is known as Gibbs energy of cluster formation, Depending on the value of Nzelq1 with respect to that of @(N),the energy of formation of a cluster, AG(N), can obtain positive or negative values, making metal deposition not necessarily a spontaneous process even in the presence of a cathodic overpotential.

3D nucleation In eq. (4.16), both terms are functions of the size N of the cluster. The first term increases linearly with N and, being negative, makes the process of deposition possible. The second term, connected with the creation of the new surface, is

4 Initial Stages ofBulk Phase Formation

158

proportional to the surface of the cluster as a first approach, i.e., to the power 2/3 of the volume, or N2’3, respectively. An illustration of the dependence of the cluster formation energy components on number of atoms is given for the 2D case in Fig. 5.1. For small clusters, @(N),being a parabolic function of N, dominates in eq. (4.16). The formation of clusters, in this case, is connected with an increase of the Gibbs energy and can proceed as an energy fluctuation process only. For larger clusters, the first term increases faster than the second with increasing N, and the AG(N) function obtains a negative slope. Therefore, if by an energy fluctuation a crystal of N atoms is formed for which the AG(N) function obtains a falling (negative) slope, that crystal can begin to grow spontaneously. The cluster with size Ncrit, where the function AG(N) has a maximum, is called the critical cluster or the nucleus of the new phase. With the maximum condition, dAG(N)/dN = 0, the probability for further growth of the nucleus is equal to that for its dissolution. Let us now consider a crystalline cluster of size N formed on a substrate. The excess energy term is connected mainly to the new interfaces. This is strictly valid for macroscopic crystals only as discussed later in Section 4.2. From eq. (4.16) with eq. (4.6) one obtains: AG(N) = -Nze(q1 + C a i A i

+ Ai’

(aj- p )

(4.17)

itj

A differentiation of eq. (4.17) with respect to N is only possible if a relation between Ai, A,.*, and N exists. This is the case when a given arbitrary geometrical form is considered. The surface area of any given 3D geometrical form is related to its volume by A3 = BV2, where B is a constant depending on the geometry. For a sphere, evidently, B = 36n and for a cube B = 63. With A3 = BV2and V = VJV, the maximum of AG(N) is found at

8BV&r Ncrit

=

27(ze17

(4.18)

and with that value of Ncrit (4.19a) (4.19b) (4.19~)

4.1 Equilibrium Form of Crystals and Forms ofgrowth

159

where Vm is the volume occupied by one atom in the crystal lattice. The subscript “crit“ refers to parameters of the critical cluster and

is the average specific surface energy. Note that, for any given arbitrary geometrical form, (T does not depend on the size of the crystal. As seen from eqs. (4.18) and (4.19), the size and energy of formation of the nucleus is a function of the overvoltage, but depends also on the geometrical form of the cluster. This is accounted for by the geometrical factor B and is implemented in the average surface energy O. The second equality (4.19b) follows immediately from (4.18), with &it, the total surface of the critical cluster, calculated from Ncrit: Acrit = B1l3(Vm Ncri32/3* The relation AGcrit = 0Acrit/3 is general and valid in all cases where the surface of the cluster is related to its size N to the power 2/3, i.e., in all 3D cases with preservation of the crystal form. As seen from eq.(4.20) applied to the critical cluster, where A =&it, PAcrit represents the total surface energy of the critical cluster, i. e., (4.21) The sum in this equation includes the areas Acrit,i of all faces of the critically sized cluster with their respective surface energies. Eq. (4.21) shows also that the formation energy of the critical cluster has a minimum at the Gibbs-Curie equilibrium crystalline form, where the surface energy C ai Acrit,i has a minimum. i

Eq. (4.19~)follows directly from eqs. (4.18) and (4.19a) and gives the relation between the size of the nucleus and its formation energy. A very useful relation can be derived from this equation connecting Ncrit, AGcrit and 171 [4.8, 4.91 by differentiation of AGcrit with respect to I 71*: (4.22) It has been shown in [4.8]that this equation is very general and useful, and is is a weak applicable with sufficient accuracy in all cases of nucleation where Note that, in differentiating ACcrit,the number of atoms (4.18).

*

is also a function of 171 as given by eq.

4 Initial Stages of Bulk Phase Fomation

160

function of 7, including 2D nucleation (cf. eqs. (4.24) and (4.25)), as well as the case of small clusters (Section 4.2).

2D nucleation In the absence of growth sites on crystalline singular faces of the native metal (cf. Section 2.1) or on a foreign substrate with strong metal/substrate interaction (cf. Chapter 3), metal deposition proceeds by formation of 2D monatomic layers. The energy of formation of a 2D cluster on a native substrate can be given by an equation similar to equation (4.16). In the case of deposition on the native metal, the excess energy @(N) is connected to the formation of the step edges: cD= C ~ i 6 L (cf. i eq. i (4.13)). For any given conservative geometrical form, the length of the peripheral sites Li of a 2D cluster, i.e., the perimeter P = C Li , is related to its area A by P2 = 4bA. As an i

example, b = R: for a circular and b = 4 for a quadratic form of the cluster. The surface area A, on the other hand, is related to N by A = R N , with R the area occupied by one atom on the surface of the cluster, so that CLi = P = 2m. I

If ~i is constant for all sides considered, or if an averaged value, specific edge energy,

E,

is taken for the

(4.23)

@(N) can be calculated from the perimeter P and given as a function of N: @(N) = E P = 2 ~ J b n NWith . this relation, differentiation of eq. (4.16) gives: (4.24)

(4.25a) (4.25b) (4.25~) = zel

lNc,it

(4.25d)

4.1Equilibrium Form of Crystals and Forms ofgrowth

161

As in the 3D case, eq. (4.25b) follows from (4.24) with Pcrit, the perimeter of the critical cluster, calculated from Ncrit: Pcrit= 2 J b n N , , . This relation is general and valid in all cases where the perimeter of a 2D cluster is related to its size N to the power 1/2, i.e., in all 2D cases with preservation of the form. EPcrit represents the total surface energy of the critical cluster, showing that the formation energy A G c a of a critical 2D cluster has a minimum at the Gibbs-Curie equilibrium form where the surface energy has a minimum. Noting that in the 2D case AGcrit = zelq INcrit, it can easily be seen that eq. (4.22) is valid also for 2D nucleation. Gibbs-Thomson equation For the equilibrium form, the Gibbs-Wulff-Kaischew theorem can be applied. It states that the normal distances hi of all faces from the Wulff point, including the top face j and the contact facep, are proportional to the specific surface energies (cf. eq. (4.10)). Hence, the specific surface energies in eq. (4.21b) can be replaced by the respective distances, hi/A = cq, so that (4.26)

1 C hiAcrit,i is the volume of the critical cluster. Replacing Vcrit with 3 i, j* V, Ncrit and AGcrit with ZeNcrit 17 1/2 from eq. (4.19~)in eq. (4.26b), one obtains with eq. (4.10) Here

Vcrit =

-

This is a general form of the well-known Gibbs-Thomson (Lord Kelvin) equation applied to the case of electrochemical metal deposition. It gives the size of the critical nucleus and its equilibrium form in terms of the normal distances of the equilibrium form faces from the Wulff point, hi, as a function of the overvoltage. When this form is a regular polyhedron (oj = const.), the size of the nucleus can be given by the radius of the inscribed sphere, Pcrit = h, SO that Pcrit =

~

2v,o zelq I

(4.28)

Substituting ei in eq. (4.25~)with hJA from eq.(4.14), having also in mind that Aj = LWcrit and AGcrit = Ncritzelq I, one obtains from eq. (4.14) similar relations for the 2D case:

4 hitial Stages of Bulk Phase Fornation

162

A

=

-

~i

R

(4.29a)

zelq I

and for the inscribed circle of a regular polygon the 2D nucleus:

(Ej

= const.) representing the form of

(4.29b) Under the acting overpotential, the probabilities for growth and dissolution of a critically sized cluster are equal. In other words, the nucleus of the new phase stays in equilibrium with the ambient phase at a more negative potential than the equilibrium potential of the bulk crystal. It has to be emphasized, however, that this equilibrium is metastable, and the smallest change of the cluster dimensions will result in either further growth or complete dissolution. It is of significance for the electrochemist to note that, according to this relation, a small cluster has a more negative (cathodic) equilibrium potential than a large one. As an example, a cubic crystal of size p = cm being the radius of the inscribed cm3 and D = 500 x 1U7 J ern-', shows a shift of circle in the cube), with Vm = 2 x the equilibrium potential of -0.1 mV. According to eqs. (4.26a and b), the energy of formation of the critical cluster is also given by its volume Ilcrit. This equation holds for both homgeneous and heterogeneous nucleation. If, according to Kaischew i4.4, 4.51, AG& and V& are introduced as formation energy and volume of the nucleus in the case of a homogeneous nucleation one can write: AGcrit = AGgrit ___ Vcrit

(4.30)

‘,“,it

This equation is quite general, but can be rigorously applied for nuclei having the equilibrium form only. The linear dimensions of the critical cluster are defined by eq. (4.27) as a function of the overpotential. As discussed already, the presence of the substrate affects the thickness of the cluster via hi’ only. The larger the adhesion energy p, the smaller is the thickness and, hence, the volume Vcrit of the critical cluster. If different orientations of the cluster with respect to the substrate are considered, the cluster having the highest adhesion energy would give the smallest volume and hence the lowest formation energy. When the substrate is non-crystalline and/or does not exert orientational effects (epitaxy) on the nucleus, the face with the most close-packed surface structure would be expected to have the highest adhesion energy. From the

4.2 Nucleation Rate

163

viewpoint of the energetics of the nucleation process, the most favorable orientation would then be the most close-packed face staying in parallel to the surface of the substrate. As a matter of fact, for energetical reasons only, no change of the nucleus orientation can be expected with increasing overpotential, as is sometimes suggested in the literature [4.10].

4.2 Nucleation Rate Classical approach (Volmer and Weber) The rate of nucleationjis a probability process connected with the energy of formation of the critical cluster, AGcrit, which owing to the creation of the new crystal/solution and crystal/substrate interfaces, is always positive. The probability of a fluctuation connected with an increase of the Gibbs energy AG of a system is given in the case of nucleation, with AG = AGcrit, by

(4.31) where the preexponential factor A only slightly depends on the supersaturation. Eq. (4.31) is known as the Volmer-Weber equation, and was derived as early as 1926 [4.11].It can be applied to 3D or 2D nucleation processes. Using eqs. (4.19) for the 3D case and (4.25) for the 2D case, one obtains

J

=

A3DeXP(-

4BV2a3 2

for 3D nucleation

(4.32)

27(zelq I) kT

and

(4.33) where A ~ and D A ~ can D be treated roughly as constants. In general, the overpotential dependence of these constants (cf. next Paragraph) can be disregarded in a In J - 1/1qI2 or a l n j - 1/1q1 analysis of experimental results, as discussed later in this Section (cf. Section 5.1). The J - Iql dependence according to eq. (4.32) or (4.33) is characterized by an overvoltage threshold, known as a critical overvoltage Iqcritl. The nucleation rate is

4 Initial Stages of Bulk Phase Formation

164

practically zero below the critical overvoltage and rises steeply above this value'. An illustration for the 2D case is given in Fig. 5.2. From the slopes of the In J- 1/1VI2 or 1nJ- 1/1VI curves, the respective nucleation rate parameters involved in eqs. (4.32) and (4.33) can be obtained. This gives a possibility for the evaluation of the parameters Ncrit and AGcrit of the critical cluster from eqs. (4.18) and (4.19) for the 3D case and (4.24) and (4.25) for the 2D case, respectively. A In J- 1771 analysis is particularly useful for the estimation of the number of atoms Ncrit involved in the critical nucleus. Following Kashchiev [4.81, from eq. (4.22) the relation (4.34) valid for 3 and 2D nucleation, can easily be derived. Strictly speaking, the constants A ~ or D A ~ contain D overpotential-dependent factors as discussed later in this Section. These factors are (i) the Zeldovich factor 4 with an insignificant overpotential contribution to J, and (ii) the attachment probability watt,~critof one atom to the nucleus, converting the atomic assembly from a cluster in labile thermodynamic equilibrium to a cluster capable of spontaneous growth. Depending on the mechanism of attachment, (iia) direct transfer of solution ions with simultaneous discharge, or (iib) attachment of adatoms from the substrate, this constant is either proportional to the deposition frequency (cf. Section 2.2) or to the surface adatom concentration. In the first case, it is an exponential function of (l-a)lvl (cf. eq. (2.7)), and in the second case an exponential function of lql (cf. eq. (2.29)). The addition of a term having a value between 1and 0.5 to the right-hand side of eq. (4.34), however, has an insignificant effect on the estimation of Ncrit as long as this number is sufficiently large (cf. Paragraph "The small cluster model" this Section). From eqs. (4.19~)and (4.25d), i.e., AGcrit = zelVIN,rit/2 for the 3D case and AGCrit = zel ~ l Nfor~ the ~ 2D i ~case, the values of the respective Gibbs nucleation energies can be derived: kTIq1 dIn] for 3D nucleation (4.35) AGcrit = 2 dlV1 ~

AGcrit = KTIVI

~

dlnJ d1V I

for 2D nucleation

(4.36)

' As introduced, Ir]critl is a heuristic entity depending on the time scale of observation and on the size of the examined object, e.g.,on the substrate area in the heterogeneous nucleation case.

4.2 Nucleation Rate

165

Note, that equation (4.34) is general and not restricted by any assumptions about the size of the nucleus, while relations (4.35) and (4.36) require the validity of the treatment of the new phase as a continuum with bulk properties, known as the "classical approach".

Kinetic approach (Becker and Doering) The formation of nuclei of a new phase can be considered as a sequence of bimolecular reactions in which every cluster of one class (size N atoms) transforms into the next higher ( N + 1) or lower ( N - 1) class by attachment or detachment of one atom A1 [4.12]:

(4.37) At equilibrium, all attachment and detachment rates are equal : Watt,N-l

zi-1

= Wdet,N

for

N = 1, 2, 3 , . . .

(4.38)

where Watt,N-l and Wdet,N [Sl] are the probabilities (frequencies) of attachment or detachment of one atom to or from a cluster of N-1 or N atoms, respectively. Z& [clusters ~ m -are ~ lthe corresponding cluster concentrations at equilibrium. For N = 1, the number Z i - l can be introduced as the number of adsorption sites of the substrate per unit area, Z, [cm-2I, and watt,o as the probability for occupation of one free adsorption site, accordingly. The probability for occupation of a free adsorption site is, obviously, proportional to the impingement rate of atoms from the ambient (parent) phase per adsorption site. If all W , ~ , N and Wdet,N are known, the equilibrium cluster partition jknction Z& can easily be derived. If a supersaturation, or overpotential is applied, a net flux of clusters to higher classes is induced. In the steady state, the flux

as well as the concentrations Z, are constant with time. Needless to say, the ambient (parent) phase is tacitly considered as an infinitely large reservoir. The attachment probability watt,^ increases with size of the cluster, because more and more sites per cluster for attachment are offered. The detachment probability. Wdet,N, in contrast, decreases with increasing N, because the atoms get bound to the cluster more and more strongly. Hence, with increasing N, the transformation rate to lower classes decreases, so that for a sufficiently large value of N, e.g., S, the rate of

4 Initial Stages of Bulk Phase Formation

166

transformation to lower classes, w d e t , S Z S , can be neglected in comparison to the rate of transformation to higher classes. The flux rate J can be given then by the rate of transformation W,~,S-~Z~-, of clusters of class (S-1) to the higher class only: (4.40)

and represents the rate of formation of new crystals of the new phase, i.e., it is equivalent to the nucleation rate. Beginning with the second equation, each one of these S equations can be multiplied by the factor, (4.41)

where N varies from 1 to S -1, increasing by unity for every subsequent equation L4.121. If all equations are added, one can see that all right-hand terms cancel leaving the first one only: Watt,o Zo,while the last one, Wdet,S Z, can be neglected as stated above, so that

-

(4.42)

+ This is a quite general equation. It does not depend on type (two- or threedimensional), on state (solid or liquid), or on form (including non-equilibrium forms) or size of the cluster. If the clusters are crystalline, however, there are different ways of obtaining the final arbitrary shape with size S. Each one of these different paths is possible and, depending on the probabilities Wdet and watt , contribute independently to the overall flux rate. Binding energies and energy of nucleation Let us now scrutinize the products l 7 in the denominator of eq. (4.42) which can be rewritten in the form: watt.0 watt,N

fi(

wdet,n

1

(4.43)

watt,n-1

The detachment-attachment probability ratio Wdet,n,x* / for a given site x * of a crystalline cluster is independent of the cluster size characterized by n, but depends on the configuration of the site x (cf. Section 2.2). The product II(N),

4.2 Nucleation Rate

167

however, depends on both the size and the final configuration of the cluster, including all detachment-attachment steps leading to the final configuration. The ratio Wdet,n,x*/ w , ~ , can ~ , ~be then obtained from eqs. (2.7), (2.8), and (2.19):

This equation is obtained by multiplication of the ratio w diss,z* / w dep,z for an arbitrary potential, E, as obtained from (2.7) and (2.8), with the ratio #,a,kink/Wdet,khk for a kink site at the Nernst potential, EMe/MeZ+, where WaE,kink =wdet,khk. The entities # J ~ and ~ (bkink,s , ~ are the dissociation enthalpies of an atom from a site x * and from a kink site, respectively (cf. Section 2.2).

(AG!:;~

(4.45)

-

If, at an arbitrary site x * , the atom is in contact with the substrate, also includes the respective bond energy of this atom to the substrate. The subscript s in q & ) ~ * , denotes ~ that, in the calculation of the deposition-dissolution energies, the interaction of the metal ion with the solution should also be taken into account. The product in eq. (4.43) is given by & l ~ * , ~

where k N includes the product of the N pre-exponential constants coming from eq. (4.44). The sum C4x*,s gives the dissociation energy of the cluster, including its N

interaction with the substrate [4.13, 4.141. The term (N&ik,s-Cbx*,s ) represents the difference of the binding energies of N

N bulk atoms and of N atoms as arranged in the cluster. This excess energy is connected with the unsaturated bonds of the atoms on the surface of the cluster and can be identified as a surface energy. It may include, however, additional energy terms

168

4 Initial Stages of Bulk Phase Formation

connected to a possible different atomic arrangement from that of a regular crystal lattice. Internal strain in the cluster can be included in the calculations of the values for every atom individually, or can be extracted from the sum as a property of the ensemble of N atoms in the form EN,where E is the average strain energy per cluster atom of the cluster (cf. Section 4.3). A comparison with eq. (4.16) shows that the sum of the exponents of eq. (4.46) is equivalent to the formation energy of the cluster of size N: #xxf,s

AG(N) =

-

Nze(q1 + O(N)

(4.47a) (4.47b)

The second term in eq. (4.47b) is proportional to the excess energy contributed by the unsaturated bonds of the surface atoms. With increasing N, this excess energy becomes proportional to the surface area of the cluster. Therefore, as discussed already, AG(N), being positive at small values of N, rises initially, passes over a maximum, and becomes negative only at larger N values, The cluster of size NCrit at which AG(N) reaches its maximum value AGCrit is known as the critical cluster or the nucleus ofthe new phase, because its further growth is connected with a decrease of AG and proceeds spontaneously under the action of the supersaturation or overvoltage Iq1.

Atomistic model

If the bond energies between the crystal atoms themselves and those between them and the substrate are known, the value of AG(N) can be calculated as function of N for the assumed atomic arrangement. An example is given in Fig. 4.5 [4.14]. The atomic interaction is assumed to be confined to first nearest neighbors. The bond energies, me-~ and e me,ds-~e,ds for the Me-Me and Meads-Meads interactions and !&e,ds-~, for the Mea,& interaction, are considered equal to those in a vacuum, and are denoted by ~1 and !&, respectively. As seen from Fig. 4.5, the binding energy of the cluster atoms, given by the sum C@,* , is equal to t&b for a cluster of one atom, and increases for clusters of two N

atoms to q +2 !&,b, of three atoms to 3y4 + 3 !&b,

of four atoms to 6 ~ 1 3+!&,b, and so

on. For the calculation, the most stable configuration has been chosen in order to obtain a minimum value for (N$&i&- C#,*) = @(N), as required by the Gibbs-Curie N

condition for the equilibrium form.

4.2Nucleation Rate

169

Figure 4.5 Calculation of the binding energy of clusters of up to 7 atoms based on atomic bond energies in a vacuum [4.14]. y/1 denotes the bond energy between first neighbor Me atoms and YSub = me ads^ the bond energy of Meads atoms to the substrate. The next following atom in the process of attachment having the strongest binding energy to the cluster is indicated by a circle. The fivefold symmetry structure is clearly seen at N = 7 atoms.

The procedure would be complicated if a fured crystal lattice arrangement, e.g., an fcc or hcp structure of a bulk crystal, is considered [4.15]. This hardly has a physical meaning, however, because at room temperature small atomic aggregates have an increased mobility and can be treated as liquid-like. In the calculations of Fig. 4.5, only , this close-packed clusters are therefore considered. According to Stoyanov f4.141 leads initially to an icosahedral arrangement, clearly seen for N = 7 atoms in Fig. 4.5,

4 Initial Stages of Bulk Phase Formation

170

which only for larger clusters transforms to the normal bulk crystalline structure. The function AG(N) at different Ap values is shown in Fig. 4.6 assuming t,q = !&ub. In the calculation of the sum

C+,*, all deviations from the bulk atomic N

configuration can be obviously included. Additionally, substrate induced strains can be accounted for by introduction of the average strain energy per atom, E. Hence, a strained cluster of N atoms would give an energy contribution of ENto the formation energy of the cluster. In a real system, the solvent influence must also be accounted for. The excess energy term obtains, then, the form:

(4.48) N

5

10

15

Cluster size N [atoms]

Figure 4.6 Gibbs energy of cluster formation AC(N) as a function of size N at different supersaturations Ap 14.141.The binding energies q$ = h* and &ink = 6yq are calculated from bond energies limitcd to first neighbors in vacuum,yq. The bond energy Mead& is taken as Ysub =w. AC and Ap are given as multiples of ~1 [J]. Close-packed configurations with highest binding energies are considered only. Reprinted from S. Stojanov/Nucleation Theory for High and Low Supersaturations, 1978, Chap. 4, with kind permission from Elsevier Science.

4.2 Nucleation Rate

171

Being an integer, Ncrit changes with changing supersaturation taking discrete values only. Hence, to every discrete value of Ncrit a supersaturation interval of stability can be ascribed. This is clearly seen in Fig. 4.6. In the supersaturation interval between Ap = 2 and 2.5 NAW W marl], for instance, the critical cluster consists of 8 atoms. At a &atomic cluster forms higher supersaturations, e.g., between Ap = 2.5 and 3 NAV~, the nucleus, followed by a 2-atomic in the interval Ap = 3 and 4 N A ~For. Ap 2 4 N A Y ~ the nucleus is one atomic, showing that each adsorbed atom can be considered as the nucleus of the new phase. At lower overvoltages, with increasing Ncrit, the I TI intervals come closer, and the Nc,it(q)-function becomes smoother. The atomistic approach becomes cumbersome and can be reasonably replaced by the classical approach using bulk properties such as specific surface and edge energies as already discussed above.

Nucleation rate equation The interpretation of the nucleation rate equation in terms of its overpotential dependence is rather difficult to perceive as represented in the form of eq. (4.42). It has been shown already that the products in the denominator of this equation contain the formation energy AG(N of clusters of class N (cf. eq. (4.47)), and that, at a given overpotential, AG has a maximum determining the critically sized cluster, N = Ncrit. The Il terms in the sum of the denominator of eq. (4.42) show a maximum for the critically sized cluster. All terms other than that for this cluster can be neglected including the unity in the denominator [4.13, 4.141. Note that J is always much smaller than the impingement rate times the adsorption sites Z, and hence the denominator is much larger than unity. Then:

(4.49) In the derivation of equation (4.42), it has been tacitly assumed that the cluster partition function 2, remains unaffected by the flux of clusters to higher classes, i.e., 2, = 2;. A correction for the depletion of the cluster population due to this flux can be introduced by the factor known as the Zeldovich or non-equilibrium factor [4.161. Inserting eq. (4.46) into eq. (4.49), one obtains

172

4 Initial Stages of Bulk Phase Formation

where k * is the reciprocal of kN applied for the nucleus. Taking into account the discussion of eqs. (4.46) and (4.43, eq. (4.50) can be rewritten in the form (4.51) For lower overvoltages, where the critical cluster is sufficiently large, the Gibbs energy of nucleus formation AGc,it can be taken either from eq. (4.19) or eq. (4.25) for 3D or 2D clusters, respectively. Both equations are valid for larger clusters where thermodynamic bulk quantities can be reasonably applied. For higher overvoltages, however, where the nucleus consists of several atoms only, the classical approach is no longer valid, and eq. (4.47) of the atomistic approach should be used. The constant k * contains the ratio of the vibrational frequencies of cluster atoms in position x * and in the kink position, and can be assumed to be of the order of unity [4.13]. It has to be remembered, however, that if entropy terms are neglected (cf. Section 2.1), particularly when dissociation enthalpies are used for the calculation of AGCrit,the value of the pre-exponential term in the nucleation rate-overvoltage relation becomes largely uncertain. The Zeldovich factor rdepends on the geometrical form of the cluster [4.17, 4.181, and for liquid droplets has the value (4.52) The dimensionless Zeldovich factor is always less then unity, and has an order of magnitude of lo2.Via AGcrjt and Ncrit,this factor is a weak function of the overpotential and does not significantly affect the general J - I7 I relation. In the Becker and Doering theory, 2, [ ~ m -can ~ ] be defined as the number of adsorption sites per unit surface area at which a nucleation reaction sequence (4.37) can start. 2, is assumed to be inversely proportional to the surface occupied by one [ ~ m - ~This ] . is generally true for atom, Z,=1/12, i.e., roughly of the order of homogeneous surfaces. Real surfaces, however, are usually inhomogeneous, showing sites with increased adsorption and, consequently, nucleation activity. 2, can be defined, in such cases, as the number of active nucleation centers. Often, nucleation centers can be characterized by a range of activities. With increasing overpotential, they get progressively involved in the process of nucleation. A very instructive example of nucleation on active centers is the increased nucleation rate on monatomic steps of single crystal surfaces (cf. Section 3.5 and Fig. 4.20).

4.2 Nucleation Rate

173

The attachment probability, watt,Ncrit,of an atom to the critical cluster depends on the overpotential. It also depends on the form of the cluster and on the mechanism of attachment (direct transfer of ions from the solution and/or attachment of adatoms). In the first case, the attachment probability is proportional to the cathodic component of the exchange current density: kdep,&!Xp [(l-a)zFIr] IIRTI. In the second case it is proportional to the adatom concentration Cads, and hence to exp (&I v I/RT) [4.191. It has been emphasized already that atomic arrangements deviating from the bulk lattice, as well as crystals with non-equilibrium forms, can contribute to the overall nucleation rate. At low overvoltages, this contribution becomes appreciable [4.20]. The uncertainty of evaluation of k *, 2, and watt,NcAt,as well as the contribution ratio of non-equilibrium configurations, renders an attempt at a complete quantitative theoretical evaluation of the nucleation rate unsatisfactory. Nevertheless, significant progress toward a better understanding of the factors determining the pre-exponential term in eq. (4.51) has been achieved i4.18, 4.21, 4.221. From an experimental point of view, however, it seems that little progress has been made since the evaluation of the Volmer-Weber [4.111 equation in 1926. The experimentalist is bound to use eqs. (4.32) and (4.33), disregarding the small uninformative dependence of k* on r] derived from the Zeldovich factor T or the attachment probability watt,NCrit. More significant progress seems to have been made with the development of the small cluster model based on the atomistic approach of Becker and Doering. Small cluster model With increasing overvoltages, the number, NCrit, of atoms constituting the critical nucleus becomes dramatically reduced, attaining values of the order of several atoms or even a single atom. Macroscopic quantities such as volume, surface, surface energy, etc., lose their physical meaning, and the use of atomic forces of interaction becomes more reasonable. The atomistic approach for the calculation of the dependence of the nucleation rate on supersaturation was first suggested by Walton 14.23-4.251 and later developed by Stoyanov [4.14,4.26]to a general nucleation theory, based on the Becker and Doering model. Eq. (4.50) is directly applicable to small clusters. In terms of its overvoltage dependence, from a practical point of view, two factors have to be taken into account: (i) As already shown, the number of atoms in the nucleus remains constant for given intervals of lr] I, so that for each one of these intervals a J - I VI relation

4 Initial Stages of Bulk Phase Formation

174

can be written treating all pre-exponential terms, as well as the exponential term containing the bond energies, as constants. (ii) The overpotential contribution of zuatt,NClitcannot be disregarded in this case, however, so that an additional exponential term dependent on l y I is added to that given in eq. (4.50). Hence (4.53)

As already discussed, the factor p* depends on the mechanism of attachment of one atom to the critical cluster. This factor has either the value of unity for adatom attachments or (l-a) i3 0.5 for direct transfer. The pre-exponential term A(ZJV& of eq. (4.53) is obviously independent of 1y I as long as the number of atoms Ncrit is constant in the given overvoltage interval. In a logarithmic representation, In J is a linear function of 117 I with a slope containing Ncrit as the only unknown parameter. The contribution of p* makes the uncertainty of the determination of Ncrit by f 0.5 atoms insignificant. Because of the simplicity of the derivation of eq. (4.53) in the calculation of the binding energy of the cluster, a substrate-induced strain energy term may be added to the excess energy as given in eq. (4.48) (cf. Section 4.3). Experimental results Based on the specifics of the nucleation and growth kinetics, several techniques have been developed for the investigation of the rate of nucleation. In the following, some illustrative results will be discussed as measured on selected model systems. Earlier investigative techniques were based on galvanostatic methods. The first to use this technique were Samartzev and Evstropiev [4.27]. Later, the technique has been further developed and refined in experiments of Schottky [4.28] and Gutzov i4.291, but, because of the high sensitivity of the nucleation process to overpotential, the results were difficult to interpret. Potentiostatic techniques developed later gave more intelligible results. The simplest potential-pulse technique, first used by Kaischew, Scheludko, and Bliznakov [4.30] and by Scheludko and Bliinakov [4.31], is to apply an overpotential pulse to the electrode and to measure the time at which current is observed to flow. The technique allows an estimate to be made of the time lag q needed for the formation of the first

4.2 Nucleation Rate

175

nucleus. The identification of zl with the reciprocal of the nucleation rate J-' meets some difficulties connected with non-stationary processes discussed by Toshev [4.22]. The most straightforward test of the nucleation rate equation is to make a plot of the number of nuclei per unit area as a function of time at different overvoltages. The double-pulse technique developed by Scheludko and Todorova [4.32] has been successfully used in a wide range of experiments [4.33-4.361. The double pulse technique is based on the existence of a critical overvoltage in the nucleation rate-overvoltage relation, as already discussed earlier in this Section. Nucleation can start only above this critical value. Below lqcritl the nucleation rate is practically zero, but if for any reason nuclei of the new phase are present, they can grow further under the action of an imposed overvoltage. This mode of growth is known as instantaneous nucleation and growth. In the range above the critical overvoltage, nucleation and growth proceed simultaneously. This growth mode is known as progressive nucleation and growth (cf. Section 8.7). According to Sheludko and Todorova [4.32], the electrode is conditioned at the equilibrium potential of the metal to be deposited, and a short overpotential pulse is applied. The occasionally formed nuclei of the new phase are then grown with a second, growth pulse immediately following the first, nucleation pulse. The overpotential level of the growth pulse is chosen low enough, so that the formation probability of new nuclei is very small. At the same time, the pulse must be sufficiently high to ensure a further growth of the nuclei formed during the nucleation pulse. This procedure obviously simulates the instantaneous nucleation case. The growth pulse duration is chosen so that the nuclei formed during the nucleation pulse can be grown to a size visible under an ordinary microscope. An illustration of this technique for the 2D nucleation case is given in Fig. 5.6. Fig. 4.7 shows Hg droplets formed on a spherical Pt single-crystal electrode r4.371. The nuclei are formed with a cathodic pulse with a given amplitude and duration, and are then grown at a lower overvoltage until of a visible size. The density of nuclei [nuclei ~ r n . ~is] determined simply by counting the number of droplets on a given surface area of the electrode. The duration of the nucleation pulse at the given overpotential can be increased successively by equal increments until a linear relationship between number of nuclei and time is obtained. A second series of measurements is then performed at another overpotential. The technique, being based on visual counting, allows the determination of the nucleation rate on different crystallographic zones to be carried out. In other words, it enables differently active zones with respect to nucleation on the electrode surface to be distinguished i4.35, 4.361.

176

4 Initial Stages of Bulk Phase Formation

Figure 4.7 Mercury droplets formed on a spherical Pt single-crystal electrode. Nuclei are formed at qnuc = 88 mV, tnuc = 1.5 rns, and then grown at q g r o d = 20 mV,t g r o h = 3 s. [4.37]. Preferential nucleation is clearly seen on the (111) crystallographic zones.

A modification of the double-pulse technique is to record the current transient i(t) following the first pulse. In the case of diffusion-controlled growth, the current transient is analyzed using an i/t112 plot. From the slope, the number of the growing nuclei can be estimated. The nucleation rate is calculated from this number and the duration of the first nucleation pulse. This technique can be applied, however, in systems with high critical overvoltage and/or in cases with instantaneous nucleation. It has been successfully used by Gunawardena, Hills, and Montenegro [4.38-4.401 for calculation of the number of nuclei formed following a potentiostatic or galvanostatic pulse. From an experimental point of view, this modification is more easily performed, especially where large numbers of nuclei have to be counted. It has to be pointed out, however, that this method, being based on some additional assumptions, has to be carefully checked, whenever possible, by the visual counting technique described above [4.41]. In the case of progressive nucleation- and diffusion-controlled growth, the initial part of the current transient follows a t3'2 dependence and the nucleation rate can be estimated from the slope of the i vs. t312 plot. This technique has been successfully used in the systems Ag(hkl)/Pb2+,HOPG(OOO1)/Agt, and Au(lll)/Cu2+ [4.42-4.441. Fig, 4.8 shows experimental plots of the number of nuclei ZnUc vs. time (pulse duration) at different overvoltages (pulse amplitudes) in the electrodeposition of mercury on platinum t4.371, The steady state nucleation rate (dZnu,/dt = J = const.) is

4.2 Nucleation Rate

177

clearly attained only after an induction period. This nucleation time lag, observed very frequently in initializing the nucleation process, i.e., changing the overpotential from a non-nucleation level to a level where nucleation can proceed, has been successfully treated in terms of non-stationary effects connected with the adjustment of the surface cluster population, ZN in eq. (4.39) to the new overpotential conditions. A detailed mathematical analysis based on the Zeldovich-Frenkel formulation of nucleation kinetics has been given by Kashchiev [4.451 and Toshev [4.221. From the linear parts of the Znuc/tcurves of Fig. 4.8, the steady state nucleation rate, J, for different overvoltages can be evaluated. Fig. 4.9a represents a typical In Jvs. 1/lv l2 plot for the system of Fig. 4.8. The analysis of the data according to eq. (4.32) shows that, in the overpotential interval of 84 - 106 mV studied, the nucleation energy AGc,it varies between 8.4 and 5.3 x J, while the number of atoms forming the critical nucleus varies between 13 and 6, as calculated from eq. (4.19~). 1oc g2/ I 9 0 /

9-

E

0

' Y

0 3

50

0

100

9E Y

0 3

N '

50

0 0

0.1

0.2

Figure 4.8 Experimental plots of the number of nuclei vs. time in the electrodeposition of mercury on Pt at different overvoltages [4.37]. The time coordinate gives the length of the nucleation pulse in ms; its amplitude in mV is given by the numbers attached to the corresponding curves.

4 Initial Stages of Bulk Phase Formation

178

100

120

IT# [V2]

140

8 82

I

I

I

90

98

106

1111 [mV]

Figure 4.9 Experimental steady state nucleation rate values calculated from the data of Figure 4.8; (a) in a InJvs. 1/17 1’ plot and (b) in a Injvs. 17 I plot 14.461. The most probable straight line in Fig. 4.9a is represented as a dashed line in Fig. 4.9b.

The apparently straight line observed in Fig. 4.9a can be seen as an experimental verification of relation (4.32). The low number of atoms forming the critical nucleus, however, discredits calculations based on bulk concepts treating the new phase as a continuum, as in the classical approach. Therefore, the experimental results are better represented in Fig. 4.9b in a In J vs. I q I plot according to eq. (4.53), which represents the small cluster model of the atomistic approach. The drawn line having a cusp at 96 mV can be treated as experimental evidence of the validity of the small cluster model. The two slopes of the plot give 10 and 6 atoms for the size of the nucleus in the overvoltage intervals of 84-96 and 96-106 mV, respectively i4.14, 4.19, 4.46, 4.471, very close to the 13 to 6 atoms found by the classical treatment. The question is, which of the two treatments is the more reliable? How much can we trust the results on number of atoms forming the critical cluster? Is the Gibbs energy of nucleus formation acceptable? The comparison of a large number of experimental results obtained by different authors with the theory leads to the apparently important conclusion that the use of 1nJ vs. l / i V l 2 plots gives reasonable results with respect to the number of atoms and sometimes the Gibbs energy of nucleus formation, despite some objections connected

4.2 Nucleation Rate

179

with the size of the nucleus. Table 4.1, is based on data collected by Milchev and Stoyanov [4.14, 4.461 updated with current results, where a state-of-the art techniques have been used for a better control of the surface structure and its UPD-modification. The number of atoms of the critical cluster agrees well for both the classical and atomistic treatments, but is in all cases far to low to make the classical treatment acceptable. Table 4.1 Gibbs free energies of 3D nucleation and nucleus size in the deposition of different metals on Pt as estimated from the classical and atomistic treatment of the experimental results.

Classical model Exp.data

Ref.

Atomistic model

Overpot. interval ~qI [mv]

Energy of nucleation [J x 10201

Nucleus sue

[atoms]

Pt(lOO)/Ag+

4.36

200 - 280

3.7 - 1.9

2- 1

Pt(lll)/Ag+

4.36

200 - 250

4.8 - 3.1

3-2

Pt /Hg2' Pt /Hg2'

4.36 4.37

90 - 102 84-106

10.1 - 7.9 8.4-5.3

14 - 10 13-6

Pt/Ag+

4.48

170 - 210

8.0 - 5.2

6-3

pt/cu2+

4.49

47 - 80

2.7 - 0.9

7- 1

C/Ag+

4.47

25 - 90

2.4 - 0.6

7- 1

Pd/Cu2+

4.50

-

2.8 - 0.8' 0.8 - 0' 0

-

-

Ag(100)/Pb2' 4.42 Ag(lll)/Pb2+ 4.42

HOPG/A~+ 4.43 Au (111)/Cu2+ 4.44

-

-

-

0 -

-

-

-

71 - 82

3.8 - 2.9

3-2

Overpot. Nucleus interval sue Iql [mVl [atoms] 200 - 240 240 - 280 200 - 220 220 - 250 90 - 102 84-96 96 - 106 170 - 193 193 - 210 47 - 51 53 - 80

1 0 3 1 10 6 5 2 14 2

25 -51 51 - 90 40 - 54 54 - 82 2 82 13- 18 15 - 19

4 1 4 1 0 13 11

10 - 35 71 - 82

4 3

11

A comparison of the atomistic with the classical treatment is given in Fig. 4.9b. The most probable straight line in Fig. 4.9a is represented as a dashed line in Fig. 4.9b. The close proximity of both the full (experimental in the small cluster presentation) and the dashed (most probable according to the classical model) lines observed in most of the Calculated from eq. (4.35)

4 Initid Stages of Bulk Phase Fornation

180

cases suggests that both equations, the classical eq. (4.32) and the atomistic eq. (4.53), coincide in the high overpotential region, the atomistic treatment better representing the experimental results by the broken line required by eq. (4.53). Going to lower overvoltages, however, as the 1171 intervals of constant cluster size become narrower, the experimental results are expected to give a smooth curved line. A classical representation in a In J vs. 1/1qI2 plot is then more informative, because in this representation it gives a straight line. How far the values of AGcrit and the quantity G ~ V & ~ ~ / obtained V& from the classical plot at higher overvoltages can be trusted is still an open question. A detailed analysis of this problem has been made by Milchev and Vassileva l4.471. The coincidence of the number of atoms of the nucleus in both treatments is not surprising, bearing in mind the validity of eq. (4.34) in both the classical and atomistic approaches. The calculation of AGCrjt based on this number of atoms using eq. (4.35) gives results very near to those calculated based on the classical treatment. Although eq. (4.35) based on the classical model is to some extent disputable in its application to small clusters, it cannot give values very much different from reality. Apparently the experiment confirms the basic theoretical relations. It must be pointed however, that older nucleation rate measurement were performed on Pt, where oxide formation affects the general nucleation rate, indicating that nucleation proceeds on structural defects, e.g., holes in the oxide coverage, or on other active sites [4.33,4.51-4.531. In addition, the rate of nucleation has been found to be strongly affected by the formation and the structure of UPD layers. This problem will be discussed in the following Section.

4.3

3D Phase Formation on UPD Modified Foreign Substrate Surfaces

In contrast to the bulk metal stability range, which covers the supersaturation or OPD range, a metal deposit can exist on a foreign substrate even in the undersaturation or UPD range in systems with strong Me-S interaction. In this last case, however, the deposit consists of 2D Meads overlayers and/or 2D Me-S surface alloy phases (cf. Chapter 1and Chapter 3). The formation of 3D Me phase takes place under these conditions on a modified substrate surface. In this section, the influences of structure and properties of 2D Me UPD phases on the subsequent nucleation and growth processes of a 3D Me bulk phase are treated.

4.3 30 Phase Formation on UPD ModifiedForeign Substrate Su$aces

181

UPD-OPD transitions Information about the influence of 2D UPD phases on thermodynamics and kinetics of subsequent 3D Me nucleation and growth can be obtained by UPD-OPD transition experiments. In general, the experiment has two stages. In the initial stage i, a 2D Me UPD phase is formed and eventually equilibrated at a selected underpotential AEi. The final stage f of the system is characterized by an external potentiostatic pulse to q into the OPD range. There are two possibilities for pulse excitation techniques: potentiostatic or galvanostatic conditions. Potentiostatic pulse polarization is recommended for UPD-OPD transition experiments since both undersaturation and supersaturation are held constant in the initial and final states: E(t) =

AEi = const. q = const.

fort=O fort>0

(4.54)

The resulting cathodic current density transients, i(t), can be analyzed in terms of the kinetics of the following reaction steps occurring during such a UPD-OPD transition experiment: i)

charging of the electrochemical double layer,

ii)

Me adsorption,

iii) structural changes of 2D Meads phases and/or 2D Me-S alloy phases, iv) nucleation and growth of the 3D Me bulk phase. The steps i) and ii) usually produce falling i(t) transients, whereas nucleative steps iii) and iv) give non-monotonous falling or rising i(t) transients (cf. Sections 3.5 and 4.2). The analysis of i(t) transients in the time domain is not trivial because of the superposition of different steps i) - iv) within a UPD-OPD transition experiment. A quantitative analysis of the various step kinetics is only possible if the corresponding relaxation time constants are significantly different. Potentiostatic UPD-OPD transition experiments can be carried out either varying A& at q = const. or changing q at AEi = const. In the first case, the influence of a 2D Meadsphase and/or of a 2D Me-S alloy phase on the nucleation and growth kinetics of the 3D Me bulk phase can be analyzed. In the second case, the nucleation and/or growth kinetics as a function of the supersaturation at constant initial state in the UPD range can be studied.

4 Initial Stages of Bulk Phase Formation

182

Galvanostatic pulse polarization is less recommended for UPD-OPD transition experiments since only the undersaturation of the initial state can be held constant whereas the supersaturation of the final state becomes undefined:

i(t) =

for AEi = const. and t = 0 const. for t > 0

(4.55)

Galvanostatic pulse excitation technique requires a fast E - i conversion device to switch from potentiostatic to galvanostatic conditions. The analysis of E(t) transients is rather complex since the nucleation and growth kinetics of the 3D Me bulk phase are changed continuously by the varying supersaturation. Nucleation and growth The initial step of Me electrocrystalliiation on a foreign (S) or native (Me) substrate surface is the formation of Me adatoms (MeadA. In Me-S systems with a weak interaction energy between Meads and a foreign substrate S compared to that on native substrate, YMe,d,-S >~ ~ - s the formation of 2D Meads and/or 2D Me-S surface alloy phases takes place in the UPD range (cf. Chapters 1and

4.3 30 Phase Formation on UPD Modified Foreign Substrate Suflaces

183

3). Then, the 3D Me bulk phase is formed according either to the Frank-van der Merwe or to the Stranski-Krastanov nucleation and growth mechanism depending on the crystallographic lattice misfit between Me and S as illustrated in Figs. l . l b and l.l.c, respectively. In both cases, a significant influence of AEi on the nucleation and growth kinetics of the 3D Me bulk phase is expected. In systems with negligible Me-S misfit, nucleation and a layer-by-layer growth occurs up to the disappearance of the strong Me-S attraction. A further growth in the OPD range continues as described for Me deposition on native substrate (cf. Chapter 5). In quasi-ideal systems with screw dislocation-free substrate surfaces, the growth proceeds via “mononuclear layer-by-layer‘‘ or “multinuclear multilayer“ mechanisms depending on vf (cf. Section 5.1). In real systems, substrate surfaces exhibit emergence points of edge and screw dislocations and, therefore, have monatomic steps and kinks as growth sites. The screw dislocations of the foreign substrate S can be inherited by the epitaxially growing Me deposit, so that the Me growth on S occurs even at low overpotentials according to the spiral growth mechanism (cf. Section 5.3). In systems with significant Me-S lattice misfit, the 2D Meads overlayers and/or 2D Me-S surface alloys formed in the UPD range have a different structure in comparison with the 3D Me bulk phase, and contain considerable internal strain (cf. Section 3.4). Thus, the nucleation and growth kinetics in the OPD range will be strongly influenced by the internal strain energy of 2D Me UPD phases. For a small number of Me atoms in a critical cluster, the strain of a 2D UPD Meads overlayer can be inherited by the nucleus. Using the atomistic approach [4.13], the rate of nucleation on top of a strongly compressed and internally strained 2D UPD Meads overlayer can be expressed by [4.54-4.571(cf. Section 4.2):

1-

(4.57)

kT

where E is the internal strain energy and I(%) is given by eq. (4.56). Replacing E by eq.(3.23), the nucleation rate J(q,E) becomes a function of the relative compression Ad/do:

(4.58) J

where A’ and p‘ are the 2D Lam6 coefficients and R is the area of an atom in an uncompressed 2D Meads overlayer. As already shown (cf. eqs. (3.33) and (3.34)), the relative compression Ad/do depends linearly on AE. Consequently, the nucleation rate according to eq. (4.58) will also depend on the initial underpotential AE,if the relaxation

184

4 Initial Stages of Bulk Phase Formation

time Tads for establishing a new equilibrium state of the compressed 2D Meads overlayer at a selected overpotential qf sufficiently exceeds the mean nucleation time , ,z (q-& > z .)? ,, Assuming that this condition is fulfilled, and using the correlations between Ad/do and AE and between the 2D and 3D Lame coefficients (cf. eqs. (3.33) and (3.34)), eq. (4.58) can be rewritten: (4.59) As a result, the nucleation rateJ (qf,AEJ for q = const. approaches its maximum value J(q)for an uncompressed 2D Meads overlayer, i.e., d = do or AEi = AEo. Decreasing d or AEi leads to a decrease of the nucleation rate in potentiostatic UPD-OPD transition experiments with qf = const. On the other hand, a linear relationship between In J(rlf) and lqfl is derived from eqs. (4.56) and (4.59) for potentiostatic UPD-OPD transition experiments with Mi = const. The number of Me atoms within the cluster of critical size is obtained from the slope of a lnJ(q) vs. lqrl plot at Mi = const: (4.60) The pre-exponential factor A(N,,it, 2,) in eq. (4.56) can be determined from the ordinate section of a lnJ(qf) vs. lqfl plot if all other values are known. EPitW Structure and orientation of a Me deposit on S in the initial stage of 3D Me bulk phase formation can be either independent of or influenced by the surface structure of S, which can be modified by 2D Meads overlayer formation and/or 2D Me-S surface alloy phase formation in the UPD range. Epitaxial behavior of 2D and 3D Me phases exists if some or all of their lattice parameters coincide with those of the top layer of S. The epitaxy is determined by a minimum of the Gibbs function at constant temperature and pressure. In the case of a weak Me-S interaction, the orientation of 3D Me crystallites deposited in the OPD range on top of a bare foreign substrate S according to the Volmer-Weber mechanism (cf. Fig. l.la) only weakly depends on the surface structure of S. The misfit between the lattice parameters of Me and S is adjusted by misfit dislocations.

4.3 30 Phase Formation on UPD ModifiedForeign Substrate Sulfaces

185

In the case of a strong Me-S interaction, the structure and orientation of a Me deposit on top of Me UPD modified S according to the Frank-van der Merwe (cf. Fig. Llb) or Stranski-Krastanov mechanisms (cf. Fig. 1.1~)strongly depend on the substrate structure. Independently of crystallographic Me-S lattice misfit, distinct correlations between the epitaxy of a condensed 2D Meads phase and/or 2D Me-S surface alloy phase and the epitaxy of a 3D Me bulk phase can be expected. In absence of Me-S lattice misfit, the structure of growing 3D Me layers usually continues that of the condensed and commensurate 2D Meads overlayer and or 2D Me-S surface alloy formed in the UPD range at high T o r low mi. The structure of a 3D Me film is usually in complete registry with the structure of the modified substrate surface S(hkl) [hkll II Me(hkl) [hkll, where (hkl) and [hkll are the Miller indices and crystallographic directions, respectively. In presence of significant Me-S lattice misfit, the epitaxy of isolated 3D Me crystallites or compact 3D Me films is strongly determined by the structure of internally strained 2D Meads overlayer and/or 2D Me-S surface alloy formed in the UPD range at high T o r low mi. The misfit between the lattice parameters of the 2D Meads phase and/or 2D Me-S surface alloy phase and the 3D Me bulk phase is mainly removed by misfit dislocations. The initial strain disappears after depositing a certain thickness of the 3D Me bulk phase. Usually, a thickness of n Me monolayers where 2 I n I 20 is necessary to adjust the 3D Me bulk lattice parameters i4.58, 4.591. If an incommensurate structure of a 2D Meads overlayer is formed in the UPD range, this structure will also be reflected epitaxially in 3D Me crystallites and ultrathin 3D Me films. Experimental results

UPD-OPD transition experiments were carried out under potentiostatic conditions in different model systems in order to study the nucleation and growth kinetics of 3D Me bulk phase formation and the epitaxy between Me and S. System HOPG(OOOl)/Ag'

This system was chosen as a typical example of a weak Me-S interaction. Potentiostatic UPD-OPD transition experiments in the system HOPG(0001)/Ag+, C1Oi showed that the 3D Ag phase formation follows a Volmer-Weber island growth mode [4.43, 4.60-4.631. Decoration of steps and other surface imperfections by a 3D Ag phase was observed at relatively low lvf whereas 3D Me crystallites are also formed on atomically flat terraces at relatively high I vf I . The initial deposition kinetics

I,

4 Initial Stages of Bulk Phase Formation

186

were described by a model involving progressive nucleation on active sites and diffusion-controlled growth of the 3D Me bulk phase [4.43, 4.62, 4.631. From the analysis of i(2) transients, the overpotential dependence of the nucleation rate according to eq. (4.60) is demonstrated in Fig. 4.10. From the slope of the log J vs. I vf I relation, it follows that a 4-atomic Ag cluster represents the critical nucleus in the overpotential interval - 35 mV I qf c: - 10 mV.

System Au (hkl)/'Agi This system is characterized by a strong Me-S interaction and negligible Me-S lattice o do,&), Potentiostatic and in situ STM measurements in systems misfit Au(hkl)/Ag+, C1Oi and Au(hkl)/Ag', SO; with (hkl) = (100) and (111) have shown the formation of a 2D &ads overlayer and a 2D Ag-Au surface alloy with commensurate (1x 1) structures at low AEi (cf. Sections 3.4 and 3.6).

6

-

5-

7

v

cn

6

Y

'5

4-

0)

0

3-

2 0

I

I

I

I

0.01

0.02

0.03

0.04

Figure 4.10 Nucleation rate,-/, as a function of HClO4 at T = 298 K and A@ = 100 mV [4.43].

0.

lvfl in thc system HO€'G(OOOl)/lV2 M &$I04

+ 1M

4.3 30 Phase Formation on UPD Modijied Foreign Substrate Su~aces

200

600

400

800

187

1200

1000

1400

100 -E

75

9-

E 50

0

4 ._ 25

t

B

i1 3 D2

0

- -

-25 -4 3

I

I

I

I

I

I

-200

0

200

400

600

800

r [mVl

AE [mvl

Figure 4.11 Anodic stripping of an Ag film deposited in the OPD range at q = - 150 mV and tp = 2400 s in the system Au(lll)/lW5 M AgClO4 + 5 x 1O-I M HClO4 + M HClO4 at T = 298 K IdE/dtl= 10 mV s-l (4.661. B: dissolution of 3D Ag bulk; D1,DZ: desorption of 2D Ag UPD overlayer.

UPD-OPD transition experiments in the system Au(hkl)/Ag'CIOi were first carried out by a special potentiodynamic polarization routine, applying a distinct polarization time, tp, at potentials in the UPD and OPD ranges and subsequent anodic stripping [4.64-4.691. Using a relatively low silver ion concentration in the electrolyte (ck+ = lo5M), 2D Agads overlayers in the UPD range and 3D Ag bulk phase in the OPD range are formed at a low rate under diffusion control. The polarization time in the UPD or OPD ranges determines the amount of deposited Ag which can be measured by analyzing the subsequent anodic stripping curve, as shown, for example, in Fig. 4.11 14.661. The charge amounts, Aq, corresponding to the surface coverages as a function of the polarization time at AE = 2 mV (curve 1) and different 17 (curve 2) are shown in Fig. 4.12 L4.66-4.691, Curve 1 represents the formation of only one Ag monolayer in the UPD range under diffusion control, i.e., Aq t"2. In contrast to this behavior, the Ag surface coverage increases linearly with the polarization time at

-

188

4 Initial Stages of Bdk Phase Formation

relatively high lqfl in the limiting diffusion current region (curve 2). Under this condition, a 3D Ag bulk phase is formed at a relatively low rate in the OPD range following a layer-by-layer or Frank-van der Menve growth mechanism (cf. Fig, 1.lb). Scanning Auger Microprobe (SAM) investigations showed a homogeneous distribution of the Ag deposit on the Au substrate confirming this growth mechanism [4.65]. Furthermore, growing 3D Ag crystallites could not be detected by Nomarskiinterference contrast studies after deposition of Aq = 8 mC cm-2corresponding to about 40 Ag monolayers 14.671. The layer-by-layer growth can also be checked by subsequent UPD of Pb on the Au substrate modified by the Ag deposit. The adsorption-desorption spectra observed were characteristic for the system Ag(hkl)/Pb2+ if Aq exceeds two Ag monolayers. The 3D Ag film on Au(hkl) grows epitaxially as demonstrated by in situ STM images of the 2D &a& overlayer at low AE and a 3D Ag film formed in the OPD range in Fig. 4.13 . 700 I

I 3.0

I

/ (2)

Y Y

P

0d

0

01

0

I &

1000

I

I

2000

3000

lo 4000

tP [SI Figure 4.12 Experimental Aq vs. tp dependencies obtained in UPD and OPD ranges of the system Au(lll)/lW5 M AgC104 + 5 x 10-l M HC104 + M HClO4 at T = 298 K [4.66].a / m V = 2 (0); q /mV = - 100 (6;- 150 (0); - 300 (A).

4.3 30 Phase Formation on UPD Modijied Foreign Substrate Su$aces

189

3.00

2.00

1.00

0 0

1.00

2.00

3.00 nu

(4

0

1.00

2.00

3.00 nM

(b)

Figure 4.13 In situ STM images in the system Au(100)/5 x los M AgClO4 + 5 x 10-1 M HClO4 at T = 298 K 14.66-4.681. (a): 2D Agads overlayer deposited at A?2 = 5 mV; (b): 3D Ag film deposited at 7 = - 3 mv, ZT = 5 nA, Pt-Ir tip.

4 Initial Stages of Bulk Phase Formation

190

0.8 -

0.2 -

\ 0 0

I

I

I

I

I

25

50

75

100

125

t

150

[$I

Figure 4.14 Current density transients for the UPD-OPD transition in the system Au(lOO)/ 10-1 M AgClO4 + 5 x 10.l M HC104 at T = 298 K [4.62, 4.63, 4.67-4.691. A& /mV = 15; qf /mV = - 5.0 (1); - 8.9 (2); - 10.6 (3).

Potentiostatic UPD-OPD transient experiments in the system Au(hRZ) /Ag+ClOi were also carried out in electrolytes containing a much higher Ag' ion concentration (c&+ = lo-' M) in order to reduce the influence of Ag' bulk diffusion and to get more information on the generation of the growth layers [4.62,4.63, 4.67-4.691 The current density transients (Fig. 4.14) exhibit two time constants. The first corresponds to the falling part of the transients at relatively short time, and the second to the rising part of the transients at extended polarization time. The process at short times can be related to the deposition of a certain number of Ag monolayers on gold influenced by the strong Ag-Au(hk2) interaction. Integration of the first falling parts of the transients up to their minima yields dq w 2 mC cm-2corresponding to about 10 Ag monolayers. The initial Ag monolayers are deposited at relatively low overpotentials by a Frank-van der Menve or monolayer by monolayer growth mechanism in accordance with results obtained from UHV experiments [4.70-4.741. The rising part of the transients obtained at relatively high lqfl is obviously correlated to a transition from a monolayer by monolayer to a multilayer growth mode [4.62, 4.63, 4.68, 4.691. It can be assumed that Ag deposition occurs as on native substrate at this stage. The deposited Ag layers can be generated by either multilayer growth with 2D nucleation or spiral growth (cf.

4.3 30 Phase Formation on UPD Moda5ed Foreign Substrate Sulfaces

191

Chapter 5). The measured overpotential dependence of the steady state current density of the transients (c.f. Fig. 6.15) indicates a multilayer growth mode generated by screw dislocations [4.62, 4.63, 4.68, 4.691. It can be assumed that the screw dislocations of a real Au(hR0 substrate are inherited by the growing ultra-thin Ag film, determining the growth mechanism under these experimental conditions. UPD-OPD transition experiments applying long-time polarization in the UPD range would reflect the influence of the slow 2D Me-S surface alloy formation in this system on the mechanism of 3D Ag bulk deposition in the OPD range. However, such measurements have not yet been published.

System Ag (hkl)/Pb2" This system is characterized by a strong Me-S interaction and a significant positive Me-S lattice misfit (dQb > do&). Ag(100) and (111) substrates are modified by compressed 2D hcp Pb,d, overlayers, which are higher order commensurate or incommensurate, at relatively low AE (cf. Section 3.4).

6'o

I

0

0.02

004

006

0.08

0.10

0.12

AEi [VI

Figure 4.15 Nucleation rate as a function of Pb(C104)a + 5 x 10-1 M NaC104 + 5 x r7f /mV = - 15.1 (1); - 17.1 (2);

- 19.0 (3).

at different %values in the system Ag(111)/10-2 M M HClO4 at T = 298 K [4.42, 4.54-4.56, 4.693.

192

4 Initial Stages ofBulk Phase Formation

2 14

16

18

20

hfl [mVI

1

Figure 4.16 Nucleation rate as a function of 1?,q at different e, values in the system Ag(lll)/10-2 M Pb(C104)~+ 5 x 10-1M NaC104 + 5 x lW3 M HClO4 at T =298 K 14.421.m,/mV = 0 (1); 40 (2); 60 (3); 80 (4); 100 (5).

UPD-OPD transition experiments in the system Ag(hkl)/Pb2+,Clod show that the deposition kinetics can be described by a progressive nucleation process and growth of isolated 3D Pb clusters controlled by hemispherical diffusion [4.42]. The results indicate that the nucleation rate of the 3D Pb bulk phase formed in the OPD range is affected by both f f i i and q as shown in Figs. 4.15 and 4.16 [4.42, 4.54-4.56, 4.69, 4.75, 4.761. The Mi dependence of the nucleation rate in Fig. 4.15 is compatible with eq. (4.59). A value of ( A + p) = 3.9 x lo1' Pa has been obtained from the best fit in good agreement with literature data (cf. Section 3.4). The analysis of the results in Fig. 4.16 according eq. (4.60) leads to Ncrit = 11 for Ag(ll1) [4.42, 4.54-4.56, 4.691. In the case of &(loo), Ncrit = 13 was found [4.42]. Previous morphological studies of 3D Ag crystallite formation in the OPD range on electrochemically grown silver single crystal faces (100) and (111) showed an epitaxial growth of isolated 3D Pb crystallites as shown in Fig. 4.17 [4.54-4.56,4.69,4.75-4.771.

4.3 3 0 Phase Formation on UPD Modijied Foreign Substrate Sugaces

193

Figure 4.17Epitaxy of 3D Pb crystallites deposited in the systernAg(hkl)/10'2 M Pb(C104)~+ 5 x 10-1 M NaC104 + 5 x l o 3 M HClO4 at T =298 K [4.54,4.56].(a): Ag(ll1); (b): Ag(100).

194

4 Initial Stages of Bulk Phase Formation

A strong correlation between the close packed crystallographic directions [110] of substrate and 3D Pb,d, crystallites is detectable. In the case of &(loo), two different azimuthal orientations of the 3D Pb crystallites are seen. In the case of &(Ill), a rotation of about 4.5' of the 3D Pb crystallites can be detected. Consequently, the epitaxy of the 2D Pb,d, overlayer (cf. Section 3.4)

Ag(100) ill01 II compressed 2D hcp Pb [110] Ag(ll1) [1101 II compressed 2D hcp Pb [1101 R4.5' is reflected in the epitaxy of the 3D Pb crystallites:

Ag(100) [1101 II Ag(ll1) [I101 II

3D Pb (111) [110] 3D Pb (111) [110] R4.5'

This indicates that the UPD-OPD transition obviously proceeds via the StranskiKrastanov mechanism (cf. Fig. lc) involving the formation and growth of 3D Pb crystallites on top of the 2D internally strained Pb UPD adlayers which act as precursors for the nucleation and growth process in the OPD range. The unstrained 2D hcp surface structure of a 3D Pb(ll1) crystal face is reached after deposition of about 10 Pb monolayers as shown in Fig. 4.18.The interatomic distance corresponds to &pb.

0

1.00

2.00

3.00

Figure 4.18 In situ STM image of the surface of ca. 1 pn thick Pb epitaxial film deposited on Ag(100) in the system Ag(100)/5 x M Pb(ClO& + 1W2 M HClO4 at T = 298 K [4.56,4.66, 4.771.IT = 2 nA, Pt-lr tip.

4.3 30 Phase Formation on UPD Modijied Foreign Substrate Su$aces

195

Results on the influence of 2 0 Me-S surface alloy formation on the UPD-OPD transient behavior are not reported. System Ag(hkU/T1'

This system is also characterized by a strong Me-S interaction and a significant positive Me-S lattice misfit (do,n> do&. At low AE,Ag(100) and (111) substrates are modified by compressed 2D hcp g a d s overlayers, which are higher order commensurate and incommensurate, respectively (cf. Section 3.4). UPD-OPD transition experiments and morphological investigations in the system Ag(hkl)/Tl+, SO:- using real and electrochemically grown silver single crystal faces as substrates gave similar results to those in the system Ag(hrct>/Pb2', C104 14.54, 4.761. 2D n a d s overlayers formed at low A& in the UPD range also act as precursors for the subsequent 3D Tl bulk phase formation in the OPD range independently of the substrate orientation, as demonstrated for the epitaxy of 3D Tl crystallites on top of electrochemically grown Ag(100) and Ag(ll1) substrates (Fig. 4.19). System Pt (polfaced)/'+

This system is characterized by a small positive Me-S misfit ( d o h> do,&. Ag UPD on Pt(ll1) leads to the formation of a Pt(ll1)-(1 x l)Ag overlayer structure at low bE [4.78]. However, the oxidation of Pt surfaces plays an important role f4.791. Potentiostatic pulse polarization was used to study the nucleation and growth kinetics of silver on polyfaced monocrystalline platinum substrates. The experiments were carried out in the system Pt(polyfaced)/Ag+, Cloy [4.51-4-53]. The resulting i(t) transients as a function of q and temperature were explained using the atomistic nucleation theory and a model involving progressive nucleation at surface defects. Obviously, holes in an oxygen species containing monolayer present in the UPD range act as active sites for Ag UPD and OPD. System Au (hkl)/Cu2'

This system is characterized by a strong M e S interaction and a significant negative Me-S lattice misfit (dO,cu< do+&. Au(ll1) substrate is modified at low AE by a commensurate 2D CUads overlayer (cf. Section 3.4). The deposition of 3D Cu bulk phase follows a Stranski-Krastanov growth mechanism, i.e., formation of 3D islands on top of an internally strained 2D CUads overlayer [4.44, 4.80, 4.811.

196

4 Initial Stages ofBulk Phase Formation

I

Figure 4.19 Epitaxy of 3D T I crystallites deposited in the system Ag(hk1)/7.5 x 5 x 10' M Na2S04 t M €IC104 at T =298 K [4.54,4.76]. (a):Ag(ll1); (b):Ag(100).

M TlzSO4 t

4.3 30 Phase Formation on UPD Mod$ied Foreign Substrate Surfaces

197

In situ STM studies [4.44, 4.80, 4.811 show that the 3D Cu bulk phase is deposited preferentially at steps (Fig. 4.20). Nucleation and growth on atomically flat terraces need higher nucleation times or higher 1 ql.The results indicate that the 2D hcp surface structure of a 3D Cu(111) crystal face is reached after deposition of 2-3 monolayers. The analysis of i(t) transients gives Ncrlt = 3 in the OPD range - 82 mV I vf I - 71 mV [4.44]. Au(lO0) substrate showed a commensurate 2D Cu,ds overlayer at low AE. UPD-OPD transition experiments yielded epitaxial growing 3D Cu islands. The fcc Cu bulk spacing was reached after deposition of about 10 Cu monolayers. Different Cu spacing in between was explained by the formation of thermodynamically unstable bcc Cu within the first monolayers to adjust the crystallographic misfit [4.82].

M CuSO4 + 5 x Figure 4.20 In situ S r M images in the system Au(lll)/ 5 x M IIgSO4 at T = 298 K [4.80, 4 811. (a): m, = 40 mV; @): qy = - 20 mV. Reprinted by permission of Kluwer Academic Publishcrs.

198

4 Initial Stages of Bulk Phase Formation

However, it should be noted that generally different lattice parameters between the substrate S and the 3D Me bulk phase are usually adjusted by an appearance of misfit dislocations. System Ag(hkl)/Cu2'

This system is characterized by a relatively weak Me-S interaction and a significant negative Me-S lattice misfit (do,cu< d o h ) which is approximately equal to the system Au(hkZ)/Cu2'. UPD of Cu on Ag(hlzZ) is not well pronounced. The initial deposition in the OPD range follows a Frank-van der Merwe mechanism involving 2D nucleation and growth [4.81, 4.831. Cu islands formed in the OPD range were found to be in registry with the substrate up to thicknesses of about 2 and 8 monolayers for Ag(111) and Ag(100) substrates, respectively. In the case of Ag(100) substrate, the Cu spacing change was similarly explained as in the case of the system Au(1O0)/Cu2+ by a transition from bcc Cu to fcc Cu [4.82].

Figure 4.21 In situ STM images in the system Ag(111)/5 x lC5M CuSO4 + 5 x lo9 M H2SO4 at T = 298 K (4.811.hEi/mV = 150 qf/mV = - 7 0 t1Js = 0 (a); 29 (b); 85 (c); 142 (d). Reprinted by permission of Kluwer Academic Publishers.

4.4 Conclusions

199

In situ STM studies showed that at relatively low I 2D nucleation in the system Ag(hkl)/Cu2', SO:- exclusively occurs on atomically flat terraces and not at the step edges as shown in Fig. 4.21 [4.811. Obviously, under the given experimental conditions, steps are blocked by specifically adsorbed anions owing to a positive surface charge of the substrate determined by the potential of zero charge. This interpretation is supported by previous experimental results based on Cdl measurements on electrochemically grown silver single crystal faces with a defined step density [4.84]. However, nucleation and 3D Cu growth can also be observed at step edges at relatively high I q1,as expected.

4.4

Conclusions

The theory of heterogeneous phase formation is well developed from the viewpoint of classical thermodynamics. A significant turning point seems to be the introduction of the adhesion energy and an appreciation of its influence on the form and energy of formation of crystals on foreign substrates. The derivation of a simple relation connecting the Gibbs energy of nucleus formation to overpotential and nucleus size and its application for an analysis of the nucleation rate equation gives a powerful tool for the estimation of the number of atoms forming the critical cluster and the energetics of the phase formation process. This relation is general and is not restricted by any assumptions about the state of aggregation, form, or size of the nucleus, and can also be applied to small clusters outside the limits of validity of classical thermodynamic bulk phase concepts. Under the specific conditions of electrochemical metal deposition, the critically sized clusters of the new phase have been found to consist of only a few atoms, where classical thermodynamic bulk quantities cannot be applied. Therefore, the original kinetic theory of Becker and Doering was further developed to an atomistic theory of nucleation. The atomistic theory becomes of additional significance for the transition from 2D Me phase formation in the UPD range to 3D Me phase formation in the OPD range. Experimental results obtained using modern in situ techniques with lateral atomic resolution showed that the transition phenomena can only be interpreted on the basis of atomistic approaches. The UPD surface modification turns out to be a more general phenomenon affecting not only the nucleation processes but also the growth mode and epitaxy of 3D metal phases.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

5 Growth of Crystalline Faces

5.1

Dislocation-Free Crystal Faces

A perfect crystal bound by singular faces exhibits no sites of growth. A 2D nucleation process is required for the deposition of every new layer, as first noted by Gibbs [5.1] and later by Volmer and Weber L5.21, Brandes [5.3], Erdey-Gruz and Volmer [5.41, and Kaischew [5.5]. That is because one atom deposited on the crystal face has a smaller bond energy to the crystal than a kink atom, and it stays only temporarily on the surface as an adatom (cf. Section 2.1). With U d e p , h k = Udiss,ki& at the equilibrium potential, the kink position is the only site with a 50% probability of being found occupied (cf. eq. (2.17)). A very important factor is the tendency of surface adatoms to cluster together, thereby increasing their stability on the surface. Clusters of this kind are potential nuclei of a new lattice network. Cluster formation, however, is connected initially with an increase of the Gibbs energy of the system. Therefore, even in supersaturated systems, cluster formation proceeds as an energy fluctuation process (cf. Sections 4.1 and 4.2). Only after reaching a maximum at the cluster size Ncrjt does the Gibbs energy begin to decrease, making the spontaneous growth of a cluster possible (Fig. 5.1). Hence, in full analogy to the 3D case, the critically sized 2D cluster acts as a nucleus in the formation of every new lattice network. The formation energy of 2D nuclei has been evaluated already (cf. eq. (4.25a)) as bE2

and the nucleation rate equation has been derived as an energy fluctuation process (cf. eq. (4.33)) as

and is written here in the more convenient logarithmic form, with ze/i2= qmoW

202

5 Growth of Crystalline Faces Ncit = 25 atoms

Ncit = 67 atoms

for q = - 10 mV

for q = - 6 mV I

-.

50

l

l

q = - 10 mV

.

A

l

\

--1

100

%

--ill,

150

--

Nurnbe?Qf atoms in 2D cluster, N \

-

of ion transfer vzelql \ \

\

\ \ x~

Figure 5.1 Gibbs energy of 2D cluster formation as a function of size N , according to eq. (4.16),with @(N) = 2&(b/LN)', E = 2 x lor3 J cm-', b = 4 for a square 2D cluster form, and R = 4 x cm-' 15.6-5.91. The data are taken as most probable values from nucleation rate experiments on an &*(loo)

quasi-perfect face, as described below.

TheJ-1171 relation is represented in Fig. 5.2. It is characterized by a relatively wide overvoltage range, in which J is practically zero. Only after exceeding a "critical" overvoltage does the nucleation rate show a sharp exponential rise (cf. Section 4.2). The existence of a supersaturation or overvoltage threshold is a characteristic feature of nucleation-induced processes as, e.g., electrochemical phase formation. Based on this phenomenon, several experimental techniques for electrocrystallization studies have been developed (cf. Section 4.2). Before going into further details, however, let us discuss some technical skills that can lead to the preparation of welldeveloped low dislocation density single crystal faces.

5.1 Dislocation-Free Crystal Faces

203

50

40

30

20

I0

-5

- 10

r

[mvl

F i r e 5.2 Overvoltage dependence of the 2D nucleation rateJ s-'] according to eq. (5.2). Specific edge energy, E = 2 x 1013J cm-l; b = 4 for a square form; T = 318 K; qmon= 2 x l W 4 A s cm-' for a quasi-perfect Ag*(lOO) face and A ~ D = 2 x 1013 cm2 s-' [5.6-5.93. The data are taken as most probable values from nucleation rate experiments,as described below.

Preparation of single crystal faces by electrodeposition.

In addition to flame annealing methods for the preparation of single crystal faces of metals with extended atomically smooth terraces [ 5.10-5.131, the already traditional technique of electrolytic growth of single crystals 15.6-5.91 has remained unrivaled for the preparation of perfect, screw dislocation-free faces or faces with single, isolated screw dislocations'. The technique developed by Budevski et al. 15.6-5.91 is based on one hand on the fact that under certain conditions, particularly higher concentrations and elevated temperatures, single crystals can be electrochemically grown to develop large single ' A perfect crystal face should be completely free of any surface defects. In view of its further application for crystal growth studies, however, a face not intersected by screw dislocations can be considered conditionally as perfect. All other defects have either little or no effect on the growth behavior of the face. To meet this situation, the term "quasi-ideal" or "quasi-perfect" has been introduced for the description of faces free of screw dislocations [5.14]. A quasi-perfect face is characterized by extended atomically smooth terraces separated by monatomic steps and absence of emergence points of screw dislocations. A smooth quasi-perfect face without steps can be described as an "intact quasi-perfect face".

5 Growth of Crystalline Faces

204

crystal faces [5.4, 5.151 (cf. Section 2.1, Fig. 2.4). On the other hand, it is based on a technique developed by Kaischew, Scheludko, and Bliznakov [5.16] for growing single crystal filaments in glass capillaries. For the purpose, an appropriately oriented cylindrical single crystal with a diameter of ca. 0.3 cm and a length of ca. 2 cm is enclosed in a glass tube ending as a capillary in its bottom part. The assembly is then placed in an electrolytic cell and used as a cathode against an anode of the same material as shown in Fig. 5.3.

Silver single crystal ’

0=016mm

. Growing crystal

Figure 5.3 Schematic representation of an electrolytic cell for the investigation of the growth of Ag single crystal faces. A plane parallel bottom window allows the microscopic observation of the growing front face of the crystal in the glass capillary.

5.1 Dislocation-Free Crystal Faces

205

The traditional metal is silver. At the same time, with the exception of cadmium, silver seems to be the only suitable metal for this technique. The front part of the single crystal is of a rounded shape and must be carefully annealed and cleaned to remove contamination. In the case of silver, the preferred electrolyte is 6 M AgN03. A small amount of HN03 is sometimes added to lower the pH to between 2 and 5 and to prevent Ag oxide formation. The temperature is kept about 300 to 320 K, preferably 318 K. The system Ag(hkl)/6 M &NO3 + x M HNO3 at T = 318 K will be referred to as “standard Ag(hkl)/AgNO< system in this book. Ag”(hk2) will be used to denote quasiperfect faces. The seed crystal, the cathode, is grown electrochemically at constant current conditions. After the initial formation of a flat front face, the crystal is forced to grow into the capillary ending of the tube as a single crystal filament with the orientation of the seed crystal (cf. insert in Fig. 5.3). Use of an alternating currrent (ac) superimposed on the direct current (dc) with an amplitude lower or slightly higher than the dc, depending on conditions, helps to keep the growth of the cathode as a single crystal. Some practical skills are evidently necessary here. Depending on the orientation of the seed crystal, the growing front face can be one of the close packed (singular) faces of the single crystal: octahedral (lll),cubic (100) or rhombododecahedral (110) in the case of silver. Growth conditions, particularly rate and ac/dc ratio, can be found which allow the front face to fill the whole cross section of the capillary. Further growth produces a perfection of the crystal face, leading to a decrease of the screw dislocation density*. The emergence points of the screw dislocations are observable under the microscope as pyramids of growth (c.f. Section 5.3). The slopes of the pyramids depend on overvoltage or current of growth, so that using a low current of growth the pyramids can be made flat and unobservable. By a short overvoltage pulse excitation they can be made visible again as small pyramids marking the emergence points of the screw dislocations, as shown in Fig. 5.4. In this way, the process of perfection of the crystal face can easily be followed during the growth process. Adjusting the ac/dc ratio to the perfection degree, the face can be grown completely free of screw dislocations. At the moment, when the last dislocation grows out of the face, the electrochemical behavior of the crystal face changes abruptly: * There are two mechanisms that can lead to a decrease of the screw dislocation density on a face during growth. Owing to an inclination of the Burgers vector with respect to the normal growth direction of a face, the emergence point following the dislocation line must grow out of the face borders in a later stage of growth (cf. Section 5.3). The second reason for the decrease of the screw dislocation density is a possible annihilationof screw dislocations by a transformation to edge dislocations.

206

5 Growth of Crystalline Faces

Figure 5.4 Pyramids of growth on an Ag(100) face obtained by applying a short overvoltage pulse on an initially flat crystal face in the standard system Ag(lOO)/AgNO3 15.71. The pyramids mark the emergence points of the screw dislocations. The quadratic symmetry of the pyramids corresponds to the (100) nature of the face. Face areaA(100) = 2 x cm2.

In the presence of screw dislocations, the growth overvoltage is usually low (less than 2 mv) and relatively steady. With the disappearance of the last dislocation, the overvoltage rises steeply to a value of about 6 to 10 mV and begins to perform characteristic oscillations, Fig. 5.5. This behavior is easily understood in view of the nucleation rate-overvoltage dependence of Fig. 5.2. Under galvanostatic conditions in the absence of steps of growth and consequently of kink sites, the overpotential must rise until the critical overvoltage for nucleation is reached. At that moment, one or more nuclei may be formed on the crystal face, giving birth to a new layer. This makes the deposition process easier and the overvoltage drops accordingly. The initially formed nuclei begin to propagate over the surface, thus increasing the step border line or the step edge length. This process offers an increasing number of growth sites and causes a further overvoltage decrease. Reaching the face boundaries, however, the step edge begins to decrease in length, to disappear completely with the deposition of one monatomic layer. At that moment, the overvoltage increases again to the critical overvoltage value, a new nucleus is formed, and the whole process is repeated at regular intervals as illustrated in Fig. 5.5.

5.1 Dislocation-Free Crystal Faces

207

Figure 5.5 Oscillations of the overvoltage at constant current density i = - 65 pA on a quasiperfect cubic face of silver in the standard system Ag*(lOO)/AgNO3 15.6-5.91. Time scale: 2 s div"; voltage scale: 5 mV div-'. The product of the current density and the period of oscillations gives an amount of electricity equal to qmon.

A criterion for this 2D nucleation and growth process is obviously the period of oscillations, which multiplied by the current density must give an amount of electricity equal to the deposition of one monolayer. This has been found in the experiment described above [5.6-5.91. The capillary technique for preparation of quasi-perfect faces of silver single crystals is described in detail elsewhere [5.17, 5.181. Potentiostatic double pulse technique Based on the specifics of the nucleation process and on the existence of an overvoltage threshold, a double pulse technique for the investigation of the nucleation rateovervoltage dependence has been developed, as discussed in Section 4.2 [5.19]. Quasi-perfect faces are particularly suitable for this technique. In the subcritical overvoltage range, the rate of nucleation is negligibly small and, owing to the absence of growth sites, the current is extremely low. In this overvoltage range the single

5 Growth of Crystalline Faces

208

crystal face can continue to exist practically indefinitely, behaving like an ideally polarizable electrode. The nucleation overvoltage threshold in the standard Ag*(100)/ &NO3 system has been found to be in the range - 8 mV < 17 < - 5 mV. Above this potential, - 5 mV < 77 < 0 mV, the current density is usually less than lo-’ A cm-2 [5.6-5.91. On a face, pre-polarized in the subcritical overvoltage range, - 5 mV < 77 < 0 mV, a 2D nucleus can be formed by a short overvoltage pulse excitation in the overcritical range. Under the action of the pre-polarization overvoltage, the nucleus will begin to grow, indicated by a simultaneous increase of the current, Fig. 5.6.

-2

-4

:

-6; -8

I

I

------

Y1[mVl -10

-

Cathodic current I A] no current

L

Nucleation

-In Y

c

Figure 5.6 Schematic representation of the potentiostatic double pulse technique for investigations of the nucleation rate-overvoltage dependence. qnuc and q g r o h denote the overvoltages of 2D nucleation and growth, respectively.

5.1 Dislocation-Free Ctystal Faces

209

Fig. 5.7 shows a current-time record after a cathodic pulse excitation. As seen, the cathodic current rises in the beginning (initially linearly with time as a rule), passes over a maximum, and falls to zero again after a certain period of time. The explanation of this observation is obvious: After nucleation, the new layer will begin to propagate with constant rate and the length of its edges will increase linearly with time. Following the step edge development the current will also increase linearly with time. This linear increase, however, can continue until a peripheral part of the propagating layer reaches one of the face borders where the step edge will begin to disappear. The current following the growth and decay of the step will pass a maximum and will cease at the moment when the new layer covers the whole face and the step disappears completely.

Figure 5.7 Current-time record following a voltage pulse excitation on a quasi-perfect cubic face prepolarized at a subcritical overvoltage of q g r o d = - 4 mV in the standard system Ag*(lOO)/AgNO3. Current scale: 10 nA div-', time scale 0.5 s div-'; qnuc = - 10 mV, pulse duration tnuc = 80 ps. Electrode areaA = 2.2 x lo4cm2. The current-time integral gives an electricity amount of one monolayer.

5 Growth of Crystalline Faces

210

There are several aspects of the nucleation and growth kinetics that can be investigated in detail with the potentiostatic double pulse technique as summarized in Table 5.1. Table 5.1 Potentiostatic double pulse technique applications.

Problem 1. Nucleation rate - overvoltage

relation

Technique of analysis

Measuring the current following pulse excitation qnuc, as criterion for 2D nucleation.

2. Time distribution of nucleation events

Analysis of the spontaneous nucleation sequence close to the critical overvoltage.

3. Form of growth of propagating monatomic layers

Analysis of the form of the current transients at qgrowth after nucleation pulse excitation qnuc.

4. Propagation rate of monatomic steps

Analysis of the initial linear slopes of current transients at qgrowh.

5. Space distribution of nucleation events

Analysis of the form of current transients at qgyrowh, giving information about the coordinates of the origin of the new layer.

Nucleation rateovervoltage dependence In a nucleation rateovervoltage study, the current following a nucleation pulse can be used as a criterion for nucleation. The voltage pulse, of amplitude qnuc,and duration tnuc, is of such a magnitude that in half of the trials a current is observed indicating nucleation. Then a 50%probability of formation of at least one nucleus can be ascribed to the duration tnuc = 20.5 of that pulse. The probability P of nucleation, which can be identified with the reciprocal of the average nucleation period, TnUc, in a sequence of nucleation events, is obviously sml] and the surface area of the face A [cm2]. proportional to the nucleation rate] For a random, Poissonian distribution of the nucleation events

where Pmis the probability of occurrence of exactly m nucleation events in the time of observation t. For a sufficiently large time interval, where a sufficiently large number of events can take place, the pre-exponential m-function has a maximum at m, =]At,

5.1 Dklocafion-Free Ctytal Faces

211

giving a maximum probability of finding m, events in the time interval t. In other words the average (most probable) nucleation period is TnUc E t / m , = UA)-’,and J is hence the most probable value of the nucleation rate. For the initial period, i.e., for the period immediately following the nucleation pulse excitation, the probability of observing at least one nucleation event, Pel, is equal to the complementary probability, Pm=o = (1 - Pml), that zero nucleation events are observed. Hence,

Pel

= (1 - P,=o) = 1- exp( - JAt)

which follows directly from eq. (5.3) with m = 0. For a Poissonian distribution, with Pml = 0.5 for z0.5

(5.4)

20.5 it follows that

In 2 JA

(5.5)

= -

The time lapse 20.5 can be determined at different amplitudes of the nucleation pulse, so that the J - 7 dependence is easily found. Fig. 5.8 shows a In J vs. 1/17 I plot obtained in this way. The relation is linear in this representation, as expected from eq. (5.2). The contributions of the overvoltage dependence of the Zeldovich factor r and the attachment frequency w ~ ~ are , Nobviously ~ ~ ~ small enough to produce an appreciable effect on the general 1nJ- 1/17 I relation. From the slope, the specific edge energy E = 2 x J cm-l can be calculated, where a square form (b = 4) of the nucleus is assumed. From eqs. (4.24) and (4.25a) (cf. Section 4), the size Ncrit and the formation Gibbs energy AGcrit of the critical cluster can also be estimated. The values in Table 5.2 can be assumed as typical for 2D nucleation on cubic faces in the standard system Ag*(lOO)/AgNO3. Table 5.2Typical values of Iq I, &it and AGcrit in the standard system Ag*(lOO)/AgNO3.

Overvoltage range (cathodic)

7 mV

Number of atoms in the 2D nucleus Gibbs energy of nucleus formation

80 < 10 x 1OZoJ
-', the surface part S,,(t) covered by the new layer, disregarding interference or overlapping of the individual layer islands, will be given by the integral t

Sex(t) = IJAS,(t)dr

bJv2t3 3

= -

(5.11)

0

The function JAS,(t)dz under the integral gives the differential increase of the surface occupied by new island patches nucleated in the time interval between z and z + dz. There are cases, however, particularly in the presence of a limited number of very active nucleation sites, where nuclei are formed immediately after pulse application only. This case is known as instantaneous nucleation in contrast to the previous case which is known as Drogressive nucleation (cf. Section 8.7). If 2, is the number of active sites [ ~ m -and ~ ] if all sites are occupied simultaneously after pulse application, then the number of nuclei formed during the pulse would be equal to 2,. The surface part covered by the 2, growing layer islands, disregarding overlapping, is simply Sex(t) = bZou2t2

(5.12)

since all nuclei begin to grow simultaneously at time t = 0. In both cases, with further growth, however, the propagating island patches will begin to overlap, and the actual covered surface part will become smaller than the extended one. Taking overlapping into account, the time development of the surface part, S(t), covered by the propagating islands is given by the well-known Kolmogorov-Avrami equation [5.34, 5.351, which can be written for this case in the form: S(t) = 1 - exp [- S,,(t)]

(5.13)

This equation can be understood as follows: the larger the extended surface S,,(t) the lower the probability of finding a surface part, [l-S(t)], not covered by the growing islands.

5.2 Growth Kinetics ofpelfeet Crystal Faces

The current density is given by i(t)

229

=

- q,ondS(t)/dc

hence, (5.14)

Thus, for the case of progressive nucleation, one obtains for the current density (5.15) and for the case of instantaneous nucleation

Both equations have been derived for the case of electrocrystallization by Fleischmann and Thirsk 15.36). The applicability of these equations for 2D nucleation on quasi-perfect faces can be easily proved. In analyzing current-time records from deposition on quasi-perfect faces of the native metal, however, two facts have to be remembered. First, in view of the space and time probability distribution of the process (cf. Section 5.1), the nucleation type is expected to be progressive. Second, the assumed nucleation on top of already formed new layer islands cannot be stopped. Therefore, the validity of eq. (5.15) can be expected only in the very early stages of deposition, when nucleation on a second layer level is unlikely. Fig. 5.21 shows a current transient in a i-? plot recorded on a quasi-perfect &*(loo) face [5.37]. The linear dependence seen on the Figure is in good agreement with theory and confirms the validity of its assumptions. From the slopes of a series of i-? curves recorded at different overvoltages, the value of Ju2 as a function of 1 ~ can 1 be obtained. The propagation rate u and its 1771dependence are known and expected to be linear. A In Ju2 vs. 1/1~1plot can be analyzed in terms of the 2D nucleation rate equation (5.2), neglecting the small contribution of the linear u/1~1dependence. The value of E thus obtained varies J cm-', in good agreement with that found from the between 2 x and 2.8 x time lag of single nuclei formation (cf. Section 5.1). The instantaneous nucleation case can also be easily investigated on dislocationfree faces applying the double pulse technique (5,381. In a first very short and high nucleation pulse exceeding IVcritl, a high number of nuclei is formed. These nuclei are then grown at a lower overvoltage, Iq)< 1qcritl. The current transient following the excitation pulse can be recorded and analyzed according to eq. (5.16). The oscillogram of Fig. 5.22 shows a current transient recorded in this way.

5 Growth of CrystallipseFaces

230 t[ms I 1

0

1.5

2

2.0

4

2.25

6

t 2 [ms2 ]

Figure 5.21 Current transient in an i vs. 8 plot obtained in the standard system Ag*(lOO)/AgNO3 at 71 = - 14 mV [5.37].

Figure 5.22 Current transient following a nucleation pulse on a quasi-perfect &*(loo) face in the standardsystem Ag*(lOO)/AgNO3 15.381. ~growth= - 4 mV; qnuc = - 14 mV; pulse duration tnuc = 0.12 ms; time scale: 10 ms div-'; current scale: 0.4 pA dK'; electrode surface area:A = 3.14 .x'01

5.2 Growth Kinetics ofPe$ect Crystal Faces

-5

231

L

Figure 5.23 The current transient of Fig. 5.22 in a In (lil/t) vs. 9plot [5.38].

In Fig. 5.23 the i-t dependence is represented in In (lillt) vs. t z plot according to eq. (5.16). T h e slope and the ordinate intercept of that curve contain the product bZov2. The number of initially formed nuclei 2, is simply given by 2, =J tnuc, where tnucis the tnuc) vs. 1/1VI plot of data obtained at duration of the excitation pulse. A In (bZov2/ different overvoltages of the excitation pulse again gives a possibility for an accurate estimation of E, since all other parameters involved, v, b, and tnuc,with I 7 7 g r O ~=l const. are either constant or known. The analysis yields values of E in the range 2 x 1 0 - lJ~cm-’ 5 E 5 2.8 x 10-l~ J cm-l.

Deposition kinetics on quasi-perfect crystal faces The mononuclear layer-by-layer growth of idealized perfect faces suggested by Erdey-Gruz and Volmer [5.4] takes place on quasi-perfect faces only at overvoltages, in the vicinity or slightly above the critical overvoltage. At higher cathodic overvoltages as soon as the nucleation becomes more frequent, and at later stages when the surface occupied by the islands on the first and/or subsequent nucleation levels becomes appreciable, nucleation on top of the preceding layers becomes likely. In this case the process is known as multinuclear multilayer growth. This mechanism was extensively

5 Growth of Crystalline Faces

232

theoretically investigated by Borovinskii and Zindergosen [5.39], Armstrong and Harrison [5.40], and Rangarajan [5.41]. All of these treatments are based on the Kolmogorov-Avrami theory [5.34, 5.351, Bertocci 15.421, Gilmer [5.43], and Obretenov [5.44] carried out Monte Carlo simulations of the multinuclear multilayer deposition process. Theoretical calculations have shown that the current transient after an initial rise passes through several oscillations, and after deposition of a limited number of layers levels out to a final steady state value. Oscillations very closely resembling this description have been observed on dislocation-free &*(loo) faces, Fig. 5.24. In Fig. 5.25 theoretical and experimental current transients are compared. All transients are normalized to the parameters of the current transient maximum of the first layer formation according to eq. (5.15):

and i1,mm =

- qmon(4bJ~~)’’~ exp ( -2/3)

(5.

in

The transient corresponding to the deposition of the first monatomic layer calculated from eq. (5.15) is also shown on the Figure.

Figure 5.24 Oscillogram of a current transient at multinuclear multilayer growth in the standard system Ag* (lOO)/AgNO3 [ 5.451. Overvoltage: 17 = - 14 mV current scale: 2 p.4 dN1; time scale: 5 ms dW’ .

5.2 Growth Kinetics ofPe$ect C w a l Faces

0

0

233

.

I

I.

1

2

I 3

4

f J fl,rnax

Figure 5.25 Experimental and theoretical current transients for polynuclear multilayer growth [5.45]. Theoretical: solid line 15.401; dashed line 15.391: circles, Monte Carlo simulation 15.431; dotted line: first monolayer according to eq. (5.15) with$ from the initial part of the transients. The shadowed area represents the range of variation of the experimental i-t curves obtained at diflerent overpotentials on quasi-perfect &*(loo) faces in the standard system Ag*(lOO)/AgNO3 [5.45, 5.461. All transients are normalized to the il,ma and of the first layer formation.

As seen from Fig. 5.25, in the initial monolayer region, calculated and simulated transients follow the quadratic law given by the pre-exponential term of eq. (5.15). In the further course of the transients, the theoretical curves go slightly astray. This is obviously connected with the different approximations used in the calculation of the contribution of the (n + 1)th layer on top of the nth layer. The most reliable results seem to be obtained by nucleation and disk growth Monte Carlo simulations (circles in Fig. 5.25) [5.43, 5.441. As already discussed, it has been found that the initial parts of the current transients follow the i-t2 relation of the pre-exponential term of eq. (5.15). Values of Ju2 obtained from the slopes of the i vs. t 2plots can be used for the calculation of t1,mm and z j m a needed for a comparison of the theoretical and experimental curves in normalized coordinates. Potentiostatic transients recorded at different overvoltages and normalized in the way described give a package of curves lying in the hatched region of Fig. 5.25 [5.45, 5.461.

234

5 Growth of CIystalline Faces

The steady state current density, iss,which is directly related to the normal growth rate of a quasi-perfect face, has in all theoretical calculations or simulations the following form:

where P is a constant which varies from theory to theory and has a value of the order of unity. An analysis of In is, as a function of In (bJu2) obtained from the initial i-? region of the transients for different overvoltages showed a linear dependence with a slope of 1/3 in agreement with eq. (5.18). The value of p has been found to be about 0.72. A In i vs. 1/1q I plot gives the possibility for an evaluation of the exponential term in J and an estimation of E. The variation of the propagation rate constant, being linear, makes only a small contribution to the logarithmic representation of the steady state current, and can be neglected, Experimentally, a value of E u 2.5 x 1013J cm-' was found, which is in good agreement with the values referred to above 15.30, 5.451, Despite the reported good agreement with theory, the steady state parts of the transients lie in the range well below any of the theoretical predictions, as seen from Fig. 5.25. The most important fact, however, is that the first maximum of the experimental transients lies in a range around or below the maximum of the current-time curve for the deposition of the first layer. This is obviously impossible within the model of nucleation on a homogeneous surface. One possible explanation is to assume that nucleation proceeds on active nucleation centers [5.47]. There is much evidence that active sites play an important role in what is believed to be this very simple case of metal deposition. The logarithmic scale analysis used in the experiments referred to is sensitive to the energetics of the nucleation process. The good agreement between the values obtained for E in so many different and completely independent ways (cf. Section 5.3) shows that the energetics is only slightly affected by possible changes of the state of to 2.8 x J cm-' with the surface. Still, a marked increase of E from 1.9 x activation at higher deposition rates cannot be disregarded. Larger deviations were , a strong influence of the state of the observed in the kinetic factor A ~ Dshowing surface, primarily due to active centers. This conclusion seems to be supported by the rather small influence of "fresh" (activated) or "aged" surfaces on the propagation rate tr of monatomic steps, which varies by not more than a factor of 2.

5.3 Real Crystal Faces

5.3

235

Real Crystal Faces

Real crystals exhibit various structural imperfections such as atomic disorder, dislocations, stacking faults, etc. (Section 2.1). These crystal imperfections lead to different surface inhomogeneities, which can significantly influence the growth and dissolution of crystals. Dislocations are the most important defects playing the major role in the process of crystal growth. Therefore, before starting the discussion of growth of real crystal faces, it will be helpful to review briefly the main dislocation types and their properties.

Dislocations

A dislocation is a 1D or line imperfection representing a crystal region where atoms are not properly surrounded by their neighbors. Fig. 5.26 shows schematically two typical examples of dislocations.The dislocation in Fig. 5.26a is denoted by the symbol (A). The corresponding dislocation line coincides is with the edge of an incomplete crystal plane. Therefore, this dislocation is called an edge dislocation. A screw dislocation is shown in Fig. 5.26b. As can be seen, the crystal containing a screw dislocation can be considered as consisting of a single atomic plane in the form of a helicoid. A dislocation is characterized by a displacement vector or Burgers vector, 6,which can easily be defined using the so-called Burgers circuit [5.48, 5.491. As illustrated in Fig. 5.26 a Burgers circuit is made up of atom-to-atom steps. It encircles the dislocation emergence point and lies entirely in a "good" (perfect) material. The same sequence of atom-to-atom steps in an ideal reference crystal lattice form a closed loop. The closure failure of a Burgers circuit encircling a dislocation gives the Burgers vector of this dislocation. As seen in Fig. 5.26 the Burgers vector, b, of an edge dislocation is perpendicular to the dislocation line, while the Burgers vector of a screw dislocation is parallel to the dislocation line. Dislocations shown in Fig. 5.26 are known as perfect dislocations, and have Burgers vectors which are lattice vectors. Another class of dislocations called partial dislocations is characterized,by Burgers vectors corresponding to a translation of an atom from a lattice position to a twinlattice position. Such dislocations are related to stacking faults in close-packed crystal structures and appear at the boundaries of stacking faults ending inside a crystal 15.491. Although the theory of dislocations was initially developed to explain mechanical properties and plastic deformation of crystals, various studies clearly showed that

236

5 Growth of Crystalline Faces

dislocations and in particular screw dislocations also play an important role in crystal growth.

F i r e 5.26 Edge dislocation (a) and screw dislocation (b) in crystals with a simple cubic lattice. The symbol (1 denotes ) the edge dislocation. The lattice atoms involved in a Burgers circuit construction are denoted as (0).

5.3 Real C m a l Faces

23 7

Spiral growth mechanism Frank 15.501 was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). The growth spiral is polygonized if the propagation rate of the step is anisotropic, i.e., depends on its crystallographic orientation. It should be noted, however, that formation of absolutely polygonized spirals with sharp corners can only be expected at very low temperature. At room temperature the corners of a polygonized spiral are usually curved on a nanometer scale as demonstrated in Fig. 5.28 for a triangular growth spiral on an Ag(ll1) surface imaged by STM [5.51].

Figure 5.27 Successive stages of formation of a growth spiral around the emergence point of a screw dislocationon a singular crystal face.

5 Growth of Crystalline Faces

238

370 nm

Figure 5.28 In sib STM iniage showing a growth spiral on a flame annealed Ag(ll1) crystal face in thesy~ternAg(lll)/lO-~M CuSO4+5x 1W2MH2S04at T=298Kand~E=SOmV(5.511.

In the case of an isotropic advancement rate of the step, a growth spiral with "circular symmetry" is formed. Due to the character of its origin the spiral step can never disappear and the crystal face grows perpetually even at relatively IOU supersaturations without the need of a two-dimensional nucleation, Screw dislocations are also active in crystal dissolution. As in the case of crystr: growth, a step arising from an emergence point of a screw dislocation winds up into spiral during the dissolution process. For a given dislocation, however, the sense a the dissolution spiral is opposite to that of the corresponding growth spiral. P example of a dissolution spiral on an Au(ll1) surface observed by STM is shown Fig. 5.29 [5.52]. It should be noted, however, that in contrast to the growth process other crys imperfections such as point defects, edge dislocations, and stacking faults as well the edges of the crystal also play an important role in crystal dissolution L5.9, 5.53-5.60 The most important parameters characterizing spiral growth are the Burg vector, b, of the screw dislocation and the rotation period, T,,of the spiral. component of the Burgers vector normal to the surface determines the height, h the spiral step. In metal crystals the modulus of the Burgers vector, b, usually does exceed atomic dimensions, so that single screw dislocations produce steps monatomic height, h,,, (cf. Figs. 5.28 and 5.29). The number of turns of the s passing a faed point in unit time is given by Tr-'. Consequently, the product h,, gives the normal rate of growth of the crystal face and is denoted as the activity screw dislocation. '

5.3 Real Crystal Faces

239

Figure 5.29 In situ STM image showing a dissolution spiral on an electropolished Au(ll1) crystal face in the system Au(lll)/fi x M AgClO4 + 5 x 10' M HClO4 at T = 298 K and AE = 200 mV 15.521.

Theory of spiral growth The theory of spiral growth has been quantitatively developed by Burton, Cabrera, and Frank f5.61-5.641. They considered a circular growth spiral with a monatomic step arising from a single screw dislocation which intersects an otherwise perfect singular crystal face. The theoretical treatment is based on an analysis of the rate of advancement of the spiral step in polar co-ordinates (r,O),leading to the evaluation of the stationary shape r(I3) and the rotation speed of the growth spiral. In the isotropic case, the normal propagation rate, o, of a part of a spiral step with radius of curvature, p, is given by [5.61-5.641: (5.19) whereu, (q) is the rate of propagation of a straight step with p = co , and pc*t(q) represents the radius of the critical 2D nucleus at an overpotential q (cf. eq. (4.29b)). Equation (5.19) shows that for cathodic overpotentials (q < 0) a step cannot grow before reaching a radius of curvature corresponding topCit(q). As discussed by Cabrera and Levine [5.64] in the general case, the influence of the lattice strain energy

5 Growth of Crystalline Faces

240

associated with the screw dislocation has also to be considered in eq. (5.19). However, this strain energy effect is only important for relatively large values of b and can be neglected in the case of metal crystals, where b usually does not exceed atomic dimensions. Different approximations have been used to find the stationary form and the period of rotation of the spiral satisfying eq. (5.19). The best approximation is given by Cabrera and Levine [5.64],who found the following relation for the rotation period of a spiral in the isotropic case:

Tr

=

Pcrit 19 -

(5.20)

vcn

The anisotropic case of a polygonized spiral has been discussed by many authors 15.15, 5.65-5.671. The rotation period of a k-cornered polygonized spiral arising from a single screw dislocation is given by

T,=

(5.21)

kt

where z is the time needed for a new step at the spiral center to reach the side length, L,it($, of the critical 2D nucleus. The value of z is related to the propagation rates of all adjacent steps in the spiral, which depend on step length, L, according to 15.671 v ( L , q ) = v,(v)

[1

-

y]

(5.22)

where v, (7)denotes the advancement rate of an infinitely long step. The analytical evaluation of 4 and Tr is complicated since the rotation of the spiral is described by a system of differential equations L5.671. Thus, in most theoretical treatments[5.15, 5.65, 5.661, the propagation rate of steps forming the spiral is considered to be independent of their length, L,except for steps with L < Lcrjt(q). A better approach to this problem has been proposed by Budevski et al. 15.671, who applied a numerical calculation procedure to find the steady state values of z and Tr for polygonized spirals with different k. Considering pcrit(q)as a radius of the inscribed circle in the regular kcornered polygon of the 2D nucleus, the stationary period of rotation of a k-cornered polygonized spiral was found to be independent of k and given by eq. (5.20). Fig. 5.30 shows the stationary shapes of a circular spiral and a quadrangular (12 = 4) spiral estimated in [5.64] and 15.671, respectively.

5.3 Real Crystal Faces

241 210" 150"

180"

i50" 210" 120" 240"

90' 270'

60"

300" 330" 30"

0"

30" 330"

Figure 5.30 Stationary shapes of a circular and a quadrangular spiral calculated according to refs. L5.64) and 15.671, respectively.

In both cases the distance, dstep,' between spiral turns sufficiently far off the center is given by

The sides of the quadrangular spiral in Fig. 5.30 appear as tangents to the turns of the circular spiral in directions normal to the sides of the nucleus polygon. This result shows that the shape of a polygonized spiral can be approximately estimated by a modified Wulff construction (cf. Section 4.1). The theory of spiral growth discussed above assumes that the growing crystal face is only intersected by one single screw dislocation. This situation is in fact very rarely found in the growth of real crystal faces. Usually more than one screw dislocation intersect a crystal face [5.61-5.631. If these dislocations have equal activities and are separated by a distance much larger than the size of the 2D nucleus, they operate independently of each other and the growing spirals can be described by the theory for a single screw dislocation given above. In this case the rate of growth of the crystal face in steady state does not depend on the number of screw dislocations. ~~

*

dstep in eq. 5.23 corresponds to 2 & , in, Figs. 2.11 and 3.40.

242

5 Growth of Crystalline Faces

A more complex situation is obtained if the emergence points of two or more screw dislocations on a crystal face are located at distances comparable to the size of the 2D nucleus. This case has been discussed by different authors [5.61-5.63, 5.68-5.721. When a crystal face is intersected by two screw dislocations of opposite sign, they produce only one step at equilibrium which connects both emergence points of the dislocations (Fig. 5.31).

t

t

t

Figure 5.31 Successive stages of step loop formation by pairs of screw dislocations with opposite sign 15.71, 5.721. (a): Dislocation emergence points situated along a l i e parallel to the step edges; = Grit;(b): dislocation emergence points situated along a line at an angle of 45" with respect to the step edges; ddis] = &,it.

Ji

5.3 Real Crystal Faces

243

If the distance, ddisl, between these dislocations is smaller than Lcrit(q) the step cannot grow at the given overpotential 77. For ddisl > Lcrit(q) the screw dislocation pair produces loops of steps. In the case of an anisotropic rate of step propagation, the period of loop production and the corresponding step spacing, dstep, do not only depend on the ddisl /Lcrit(v) ratio but also on the orientation of the line connecting the emergence points of both dislocations with respect to the edges of the polygonized growth steps. This case has been considered in detail by Nanev [5.69,5.701 using different approximations. An exact numerical evaluation of dstep(q)/Lcrit(q) as a function of /Lcrit(v) has been made by Budevski et al. [5.71, 5.721 for a pair of screw dislocations of opposite sign producing polygonized step loops with a quadrangular symmetry &,it = 2 R r i J and situated in two different orientations with respect to the step edges (cf. Fig 5.31). The corresponding results are presented in Fig. 5.32. 30

h

F

20 -

v

e

B

4 \

h

F

v

a

d

m" 10 -

Fmre 5.32 Relative step spacing dstep(q)/Lrit(q) as a function of the relative dislocation distance ddisl /&rit( q) for a pair of screw dislocations of opposite sign, producing polygonized step loops with quadrangular symmetry (&-it = 2 ~ r i t )15.71, 5.721. (0):Dislocation emergence points situated along a line parallel to the step edges (cf. Fig. 5.31a); (0):dislocation emergence points situated along a l i e at an angle of 45" with respect to the step edges (cf. Fig. 5.31b).

244

5 Growth of Crystalline Faces

For relatively low values of I?)!, where Lcrit(v) approaches ddisl, the step spacing, dstep(v),becomes infinitely large while with increasing I q~I, i.e., decreasing &it($, the ratio dStep($/&it(q) decreases rapidly below the value 9.5 corresponding to a single screw dislocation(cf. eq. (5.23) with &,it= 2pcriJ. Afurther increase of 1171 leads to an increase of the dstep(v)/lcrit(q) value to 9.5 since two non-interacting spirals are formed. The case of two or more screw dislocations of same sign located at distances comparable to the size of the 2D nucleus has been analyzed by Burton, Cabrera, Frank [5.611 and Nanev [5.71]. Iftwo screw dislocations of the same sign are closer together than the size of the 2D nucleus, they produce two non-intersecting growth spirals (Fig. 5.33a).

F’igure 5.33 Growth spirals produced by groups of screw dislocations with same sign [5.61].(a): Pair of screw dislocations at a distance ddisl c 2npcrit; (b): group of six screw dislocations with emergence points arranged in a line. Dislocation distance ddisl< 2 n ~ r i t .

5.3 Real Cystal Faces

245

Such a screw dislocation pair generates steps at twice the rate for a single screw dislocation, i.e., it has an activity twice that of a single screw dislocation. Similar behavior is shown by a group of n screw dislocations of same sign which are closer than the size of the 2D nucleus (Fig. 5.33b). The resultant activity of such a group is approximately n times that of the activity of a single dislocation. The above considerations show that real crystal faces exhibit different growth patterns depending on degree of perfection and growth conditions. Growth morphology Circular or polygonized growth spirals or loops of steps generated by screw dislocations macroscopically appear as low cones or pyramids. Generally the slope of a growth pyramid (cone) is given by tana

=

(5.24)

___ hmon dstep

(d

where a represents the angle between the side face and the base of the pyramid. Thus, using eqs. (4.29b),(5.23), and (5.24) one obtains for the slope of a growth pyramid arising from a single screw dislocation tan a =

hmon

19 Pcrit ( 7 )

-

hmon qmon

19&

17

I

(5.25)

where Pcrit(7) denotes the radius of the circle inscribed in the geometrical shape of the 2D nucleus and E is the specific edge energy of monatomic steps. As discussed above, however, pairs or groups of screw dislocations located at distances comparable to the sue of a 2D nucleus produce pyramids with slopes which can deviate significantly from the slope given by eq. (5.25). Growth pyramids or cones are often observed in electrochemical growth of metal single crystal faces [5.9, 5.55, 5.56, 5.73, 5.741. However, well-defined and relatively simple conditions for an experimental investigation of spiral growth have only been obtained on silver single crystal faces with a high degree of perfection prepared by the so-called capillary technique [5.6, 5.17, 5-74] described in Section 5.1. Using this technique, both the morphology and kinetics of electrochemical growth of Ag(100) and Ag(ll1) faces have been studied in the standard system Ag(htzl)/AgNO3 (cf. Section 5.1) [5.9, 5.29, 5.55, 5.56, 5.71, 5.72, 5.751 and Ag(hkl)/AgNO3 (melt) at T = 573 K I5.741. In an advanced stage of growth, the silver single crystal faces prepared by the capillary method are usually intersected by only few dislocations and show growth pyramids or cones with an uniform slope (Figs. 5.34 and 5.35).

246

5 Growth of Crystalline Faces

Figure 5.34 Pyramids and cones of growth on Ag(100) crystal faces in aqueous and in molten electrolytes. (a): Standard system Ag(100)/AgN03(aq) at T = 318 K. [5.72, 5.751; (b): system Ag(lOO)/~gN03(melt) at T=573 K 15.741. Face areaA(100) = 2 x cm2.

5.3 Real Cvstal Faces

24 7

Figure 5.35 Striped pyramids of growth on an Ag(ll1) crystal face obtained by application of a pulsating current in the standard systemAg(lll)/AgN03 15.9, 5.551. Face areaA(111) = 2 x cm2.

In the standard system Ag(100)/AgN03 the growth pyramids are quadrangular (Fig. 5.34a), whereas in the standard system Ag(lll)/AgN03 they are triangular (Fig. 5.35), reflecting the crystallographic symmetry of the growing crystal face. In contrast, growth cones are observed on both Ag(ll1) and Ag(100) faces in the system Ag(hkZ)/AgN03(melt) (cf. Fig. 5.34b). The isotropic step propagation rate leading to the formation of cones in this case can be related to the elevated temperature (T= 573 K). The slope of the growing pyramids or cones changes if the current density or overpotential are changed during the growth process. This is illustrated in Fig. 5.35. The propagation of the stripes appearing on the sides of the pyramids can, be used for a determination of the propagation rate of spiral steps. The pyramid slopes as a function of the overpotential can easily be investigated on crystal faces intersected by only a few screw dislocations using the following polarization routine [5.9, 5.721. A short cathodic current pulse with a relatively high amplitude is applied to a crystal face, which is initially flattened by growth at extremely low current density. As a result, well-separated regular growth pyramids appear at the

5 Growth of Crystalline Faces

248

emergence points of screw dislocations (cf, Fig. 5.4)*.A galvanostatic pulse has been used in this case in order to obtain a more exact value for the charge amount during the pulse excitation. The overpotential, which is almost constant during the pulse duration, can be obtained from the corresponding galvanostatic voltage transient. Assuming that the charge amount injected during the pulse is uniformly distributed among these pyramids, their slopes can be easily calculated. Fig. 5.36 represents experimental results obtained by this polarization routine in the standard Ag(lOO)/AgN03 system [5.9, 5.721. A linear relation between the slope of the pyramids and the overpotential is found in accordance to eq. (5.25). Considering the growth pyramids as arising from single screw dislocations, a value of E = 1x J cm-l is estimated from the data in Fig. 5.36 in good agreement with results obtained in this system by other methods (cf. Section 5.1). 0.15

0.10 tj f

m

c

0.05

Figure 5.36 Slope of pyramids of growth (tan a) as a function of overpotential lql obtained in the standard system Ag(lOO)/AgNO3 15.9.5.721. ' This technique has also been

used for a determination of the displacement of the emergence points of screw dislocations during the growth process and an estimation of the direction of corresponding Burgers vectors [5.9, 5.561. In good agreement with theoretical predictions, Burgers vectors with a 4lOr direction have been found in most cases in the system Ag(100)/6M AgNO3(aq).

5.3 Real Crystal Faces

249

In some cases, growth pyramids with different slopes appear simultaneously on a crystal face growing at a constant overpotential i5.721. This is particularly observed in the early stages of the electrochemical growth of crystal faces with a lower degree of perfection, and indicates a participation of pairs or groups of screw dislocations in the growth process. The slopes of pyramids, however, do not give any information about the number of screw dislocations participating in the formation of each growth pyramid. Such information can only be obtained using in situ local probe techniques (STM, AFM) which allow direct observation of monatomic steps at the spiral center (cf. Figs. 5.27 and 5.28). Another aspect of the growth morphology in electrodeposition of metals is the formation of macrospirals characterized by spiral steps with a height of more than 10 nm and a step separation of more than 1 pm.Such macrospirals have been observed in various studies [5.15, 5.731. Fig. 5.37 shows an example of macrospiral growth observed during electrodeposition of copper [5.73].

Figure 5.37 Macrospiral growth observed during electrodeposition of copper in the system: Cu(lOO)/lM CuSO4 + 1M H2SO4, T =298 K 15.731.

250

5 Growth of Crystalline Faces

The exact mechanism of macrospiral formation is not yet clarified. Their appearance is usually related to the presence of large groups of screw dislocations and/or to specific growth conditions leading to a bunching of monatomic steps. Growing silver single crystal faces with a high degree of perfection shows peculiar morphological features if an alternating current (ac) with a frequency f = 50 Hz is superimposed on a direct current (dc). Various etch figures have been observed under electrochemical growth conditions involving low direct current densities and ac amplitudes exceeding about ten times the corresponding dc value l5.57, 5.59, 5.761. The appearance of these etch figures is related to the anodic ac period which causes a selective local dissolution of crystal imperfections at the surface [5.57, 5.591. This effect seems to be more pronounced in the system Ag(hkl)/AgNOs(melt), where the selective dissolution is additionally enhanced by the temperature [5.76]. Fig. 5.38 shows a typical growth morphology of an Ag(ll1) crystal face growing in molten &NO3 under ac modulated growth conditions [5.76], The growth morphology is characterized by small round pits and narrow grooves forming regular equilateral triangles. Some of these etch figures appear and/or disappear during the growth process. The formation of etch pits is caused by crystal imperfections such as atomic disorder (OD), dislocations (1D) or larger impurity inclusions (2D or 3D), while the appearance of etch grooves forming equilateral triangles can be related to 2D crystal imperfections intersecting the growing crystal face. During the growth process, the triangles increase in size (Fig. 5.38). A quantitative analysis of this increase shows that the 2D crystal imperfections responsible for the formation of etch grooves lie in the oblique (117) planes intersecting the growing Ag(ll1) face [5.76]. This result indicates that the 2D imperfections are most probably stacking faults (cf. Section 2.1) propagating along (117) planes and forming inverted stacking fault tetrahedra which intersect the growing Ag(ll1) face as equilateral triangles (Fig. 5.38). This suggestion is supported by the morphological behavior of the face observed after switching off the alternating current (Fig. 5.39) L5.761. The corresponding growth morphology is characterized by an appearance of shallow triangular pits due to the blocking effect of stacking fault intersection lines on the growing steps. Stacking fault tetrahedra have been observed in various studies of vapor deposition of Si on native Si(ll1) substrate and different mechanisms have been proposed to explain the formation of these defects [5.76-5.821. The formation of such stacking fault defects during the electrochemical growth of an Ag(ll1) face in molten &No3 (cf. Figs. 5.38 and 5.39) is obviously related to the elevated temperature and the specific ac-modulated growth regime. It is assumed that under these conditions an enhanced

5.3 Real Cwtal Faces

251

nucleation in twin-lattice positions takes place on the Ag(ll1) face during the cathodic ac period which is characterized by a relatively high amplitude i5.761.

Figure 5.38 Morphological features of an Ag(111) crystal face growing under ac modulated growth conditions in the system Ag(lll)/AgNO3 (melt) at dc current density idc = 18 mA cm-2, ac amplitude iac= 150 r n A ~ r nand . ~ T = 573 K 15.761. t/s = 0 (a); 600 (b); 1200 (c); 1800 (d). Front face areaA(111) = 1.57 10-4 cm2.

252

5 Growth of Crystalline Faces

Figure 5.39 Growth morphology of an Ag(111) crystal face grown under ac-modulated growth conditions as in Fig. 5.38 after switching off the alternating current I5.761. Front face areaA(111) = 1.7 cm2.

Steady state and transient current densities Generally, the current density, i($, on a growing singular crystal face is proportional to the step propagation rate, u, (v), and step density, Ls(v), as given by eq. (2.50). The step density Ls(q) is defined by

Ls(v> =

1

(5.26)

~

dstep ( 7 )

and from eq. (2.50) for the corresponding steady state current density, iss, follows (5.27) For a crystal face intersected by well separated single screw dislocations the step distance dstep(v) is related to pcrit(v) by eq. (5.23). Then, using eqs. (2.50), (4.29b), (5.23), and (5.27), one obtains for low cathodic overpotentials forv < 0

(5.28)

5.3 Real Crystal Faces

253

where E is the specific edge energy and +sV = u, (q)/lql represents the propagation rate constant of monatomic steps (cf. Section 5.2). Simple experimental conditions for an investigation of the relation (5.28) can be obtained in the case of electrodeposition of silver on silver single crystal faces prepared by the capillary technique 15.29, 5.74, 5.751. As already shown, such crystal faces are usually intersected by only a few single screw dislocations which produce growth pyramids or cones with an uniform slope (cf. Fig. 5.31). The parabolic iss-v2 dependence (5.28) has been experimentally found in the systems standard Ag(hkl)/ &No3 [5.29, 5.751 and Ag(hkZ)/&NO3(melt) L5.741 as shown in Figs. 5.40 and 5.41. From the slopes of the linear iss-v2plots in Figs. 5.40 and 5.41, the values of the specific edge energy, E, have been estimated. The propagation rate of spiral steps and the corresponding +sV values have been determined by direct measurement of the propagation of the single stripe appearing on the sides of the growing pyramids (cones) after a short overvoltage pulse excitation (cf. Fig. 5.35). The experimental values of E and +sV obtained in the systems standard Ag(hkZ)/AgN03 and Ag(hkZ)/ &NO3 (melt) are summarized in Table 5.4.

Figure 5.40 Steady state current density is, as a function of q 2 obtained by a spiral growth in the standard system Ag(hkl)/AgNO3 15.751. (hkl) = (111) ( 0 ) ;(100) (0).

5 Growth of Crystalline Faces

254

0

0.25

0.75

0.50

q2

I.oo

1.25

w21

2

Figure 5.41 Steady state current density iss as a function of obtained by a spiral growth in the systemAg(hM)/AgNOg(melt) at T =573 K L5.741. (hM) = (111) (0);(100) (0).

The results show that the specific edge energy of spiral steps is of the same order of magnitude in both systems, indicating that the surface energetics is not significantly affected by the solvent. The K~ values determined in the system Ag(hkl)/AgN03(melt) are about one order of magnitude higher than those in the system standard Ag(hkl)/AgNO3. This is obviously due to the elevated temperature in the first system and shows that the spiral growth kinetics is determined mainly by the step propagation rate constant K~ which is directly related to the exchange current density (cf. Chapter 2). Different K~ values obtained on Ag(100) and Ag(ll1) faces have been attributed to the specific adsorption of some electrolyte component on the Ag(100) face [5.74]. Table 5.4 Experimental values of the specific edge energy, E, and the propagation rate constant, xV,of spiral growth steps obtained by electrocrystalliiationof silver in Werent systemsI5.67,5.74,5.75].

Ag(100)/6 M &NO3 (as), T = 318 K

2.5 10-l~

0.9

Ag(lll)/6 M &NO3 (as), T

2.8

1.5

Ag(lOO)/AgNO3 (melt), T = 573 K

1.0 10-l~

7.4

Ag(lll)/AgNO3 (melt), T

0.9 1013

20

= 318 K

= 573 K

5.3 Real Crystal Faces

255

As already discussed above, the application of a cathodic overpotential step to a crystal face growing at steady state conditions leads to the formation of new growth pyramids at the emergence points of screw dislocations. The slope of these new pyramids is determined by the new final overpotential, qy, and is steeper than that of the pyramids growing at the initial overpotential, qi, before application of the potential step. If the new pyramids grow at qf independently, i.e., without interaction or overlapping effects, they cover a part, Sex(t),of the crystal face surface given by [5.83] (5.29) where Ndisl is the number of screw dislocations or growing pyramids, b is a geometrical factor depending on the shape of the pyramid bases, r ( t ) = v,t represents the radius of the circle inscribed in the geometrical shape of pyramid bases at time t, and A is the area of the growing crystal face. The corresponding current density transient can be expressed by [5.83]

i(t) = i(0) [ 1 - S ( t ) ] + is, S ( t )

(5.30)

where S(t) is the actual part of A covered by the growing new pyramids and i(0) = - qmonv, L,(q = q i ) represents the current density at t = 0, which is related to the surface part [ 1 - S(t) ] characterized by a step density Ls(q = qJ produced at qi. The steady state current density is, is given by eq. (5.28). In the case of a sufficiently large crystal face intersected by a large number Ndisl of randomly distributed single screw dislocations, the overlapping of the growing new pyramids can be taken into account using the Avrami equation (5.13). Then, from eqs. (5.13), (5.29), and (5.30) one obtains

(5.31) This equation shows that in contrast to the steady state current density is, (c.f. eq. (5.28)) the current density transient depends on the screw dislocation density, Ndisl/A. At short times, i.e., before overlapping of growing new pyramids occurs, eq. (5.31) is reduced to:

i(t)

=

i(O) + [iss

-

(5.32)

5 Growth of Crystalline Faces

256

The transient behavior of Ag(ll1) and Ag(100) crystal faces intersected by only one screw dislocation (&is1 = 1) has been investigated in the system standard Ag(hkZ)/AgNO3 [5.83].A typical current density transient obtained on an Ag(ll1) face is shown in Fig. 5.42. A linear i vs. t 2 dependence is obtained for the initial part of the transient (Fig. 5.42b) in agreement with eq. (5.32).

(a) 1

1.75

0

I

I

I

4

I

8 t2 [s2]

Figure 5.42 Current density transient obtained on an Ag(ll1) crystal face intersected by one screw = - 1.15 mV dislocation in the standard system Ag(lll)/AgNO3 at qi = - 0.25 mV and 15.831.(a): Overall transient; (b): i vs. t2 plot of the initial part of the transient in (a).

5.3 Real Crystal Faces

257

From current density transients the values of i(0) and iss can directly be obtained. The propagation rate, vm, and the propagation rate constant, K", of the spiral steps can be derived from the slope of experimental i vs. t 2 dependencies. The K~ values are used for an estimation of the specific edge energy E from is, and eq. (5.28). The values for K~ and E obtained in this way from the analysis of experimental current density transients in the system standard Ag(hkZ)/AgNO3 15.831 have been found to be in good agreement with those determined by other methods (cf. Table 5.4). Impedance behavior.

The impedance behavior of real crystal faces has been investigated by different authors [5.29, 5.84-5.931. The results show that the impedance is characterized by various low frequency features (inductive loop and hysteresis) which are related to the non-steady state conditions of the electrochemical crystal growth process. Quite different impedance features are observed at relatively low cathodic dc overpotential bias on silver single crystal faces without and with screw dislocations as illustrated in Fig. 5.43 15.931.

I

?

0.20

0.15-

0.10-

0.05-

0

I

0

0.05

0.10

0.15

0.20

,

0.25

Re {Z)[acmL]

Figure 5.43 Impedance behavior of the standard system Ag(lOO)/AgNO3 at vddc= - 2.5 mV 15.931. ( 0 ) :Quasi-perfect Ag*(lOO) face; (A): Ag(100) face intersected by two screw dislocations. Re{a and I m ( 2 represent the real and imaginary part of the complex impedance2,respectively.

5 Growth of Crystalline Faces

258 0.25

0.20 N -

c5:

0.15

-

0.10

-

Y

Ez E I

1 kHz

0.05

0 0

0.05

0.10

0.15

0.20

0.25

Re {z) [SZ cm2]

Figure 5.44 Influence of the frequency sweep direction on impedance behavior of an Ag(100) crystal face intersected by one screw dislocation in the standard system Ag(lOO)/AgNO3 at qdc = - 2.5 mV [5.93]. (0): forward frequency sweep; (0):backward frequency sweep.

These different types of impedance behavior are due to the fact that at low cathodic overpotentials (I q I < 5 mV) a quasi-perfect crystal face is atomically flat and does not grow (cf. Section 5,1), while a crystal face intersected by screw dislocations grows via a spiral growth mechanism. In the latter case, as already discussed, the monatomic step density strongly depends on the overpotential. Thus, even a smallsignal ac perturbation induces significant changes of pyramid slopes and the corresponding surface morphology (cf. Fig. 5.35). These morphological changes are also frequency-dependent and lead to an appearance of a hysteresis of the impedance in the low frequency range by changing the direction of the frequency sweep (Fig. 5.44) [5.93]. In other words, the "time-stability precondition" for impedance measurements is not fulfilled for the system under test and a quantitative transfer function analysis becomes rather difficult t5.52, 5.941. This hysteresis disappears by applying a measurement delay of 10 s for each frequency, but the impedance data at different frequencies correspond to different surface topographies. These results show that low frequency measurements on growing real crystal faces require a simultaneous in situ microscopic control of the number of screw dislocations and the surface topography in order to obtain reproducible impedance

5.3 Real Crystal Faces

259

data and to be able to analyze these data quantitatively. Impedance measurements at relatively high frequencies allow an estimation of the charge transfer resistance and the corresponding exchange current density io,Me/MeZ+ [5.29, 5.901 (cf. Chapter 5.2). The theory of spiral growth was quantitatively verified in the case of silver electrocrystallization (cf. Figs. 5.40 and 5.41). This allows the preparation of stepped silver crystal faces with a defined step density using the following technique. A silver single crystal face intersected by few screw dislocations is electrochemically grown at a constant overpotential q, After reaching a steady state, characterized by a steady state current density is, and a regular surface profile, the growth is stopped and the corresponding step density Ls(q) is calculated using eqs. (5.26)-(5.28). This technique of preparation of stepped crystal faces with an exactly known regular step spacing is of great importance for the investigation of electrochemical phenomena at solid/liquid interfaces. Such defined silver crystal faces have been successfully used in dBerent studies on electrocrystallization L5.291, double layer properties L5.95, 5.961, and UPD of metals (cf. Chapter 3). L, [cm-’1 0

2

4

I

1

6

8 I

10.10~ I

/

0.6,-

el-

6

0.4 -

9

Figure 5.45 Overall exchange current density io, as a function of the step density Ls(r])of a Ag(100) crystal face intersected by few screw dislocations in the standard system Ag(lW)/AgNO3 [5.291. Different step densitiesLs(r])are obtained by electrochemical growth at different overpotentials 1171.

5 Growth of Crystalline Faces

260

Impedance measurements at high frequencies performed at E = EMe,MeZ+ on Ag(100) faces with a defined step density Ls showed that the exchange current density, i0,&/&+ depends linearly on & (Fig. 5.45) in good agreement with eq. (2.53) [5.291. The extrapolated value of i9,&/&+ (Ls = 0) is equal to the value of exchange current density &,,ads = 0.06 A cm- obtained from high frequency impedance measurements on an atomically flat screw dislocation free Ag(100) crystal face [5.28, 5.29, 5.971. From the slope of the linear dependence in Fig. 5.45, a value of = 180 Acm-2 has been estimated using eq. (2.53) and do,& = 0.29 nm. This value correlates very well with the value i$$, = 200 AcmV2obtained from the step propagation rate measurements (cf. Section 5.2), 1

it:&

5.4

Conclusions

A major breakthrough in the understanding of basic concepts of crystal growth has been achieved in model systems with single crystal substrate faces, either free of screw dislocations (quasi-perfect) or with a low screw dislocation density. 2D nucleation and growth including single nuclei formation as well as multinuclear and multilayer growth have been extensively studied on quasi-perfect faces. The observed growth rate of monatomic steps, as well as its independence on the step density, suggest a preferred direct transfer mechanism to step edges. From the specific step edge energy, E, a first neighbor bond energy in the order of J per bond and a specific surface energy of about 300 J cm-2can be estimated, which can be considered as reasonable. Although the 2D nucleation process shows a randomness in the space and time domains, a significant effect of active centers has to be taken into account. This conclusion follows firstly from the observed wide scattering of the preexponential factor, A ~ D in , the nucleation rate equation, and secondly from the deviation of experimental transients from theoretical ones in multinuclear multilayer growth. At higher deposition rates, an activation of the surface is observed, resulting in an increase of the propagation rate of steps by a factor of two. This activation process has a considerable effect on the pre-exponential factor, A ~ DHowever, . 'it does not significantly affect the energetics of nucleation, i.e., the Gibbs energy of nucleus formation, Accrathe number of atoms of the nucleus, NCrit, and E. The nature of subsequent surface "aging" is a slow process which is still not clearly understood. The investigation of the spiral growth mechanism of faces with a low screw dislocation density represents the first quantitative confirmation of Frank's theory. First, the parabolic dependence of the normal growth rate on the supersaturation was

5.4 Conclusions

261

verified. Second, the propagation rate and the specific edge energy of monatomic steps were found to be the same for both the spiral growth and 2D nucleation and growth kinetics. In general, the propagation rate of steps proved to be anisotropic at lower (room) temperatures, producing polygonized growth steps. At lower pH values and higher temperatures, the growth rate becomes isotropic. Based on Frank’s parabolic growth rate law, surfaces with uniform and defined step density can be prepared by electrochemical growth of faces with low screw dislocation density. Such faces can be used for different studies of the metal/electrolyte interface in connection with double layer properties, exchange current densities, UPD, and surface reconstruction phenomena. The exchange current density is composed of two parts, one attributed to adatoms and the other to kink and step edge atoms. The adatom exchange current density was found to be several orders of magnitude lower than that of kinks, indicating a direct charge transfer mechanism at monatomic steps. The direct transfer of metal ions to kink sites and/or to step edges, unambiguously found first in the deposition of silver, seems to be a general phenomenon in electrochemical metal deposition and dissolution. From a theoretical point of view, Gerischer [5.98] was the first to recognize the role of direct transfer in metal deposition processes.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

6 Metal Deposits and Surface Structuring and Modification

6.1

Formation of Compact 3D Me Deposits

The electrochemical formation of compact metal deposits, S/Me, had already become of significant technical importance by the nineteenth and first half of the twentieth century in the fields of electrowinning and electrorefining of metals, as well as in the field of electroplating for the production of galvanic replicas and different decorative, protective, and functional coatings. The technology of these processes was developed for a long time on a purely empirical basis. Electrochemical systems and environmental conditions such as temperature, electrolyte composition, pH, additives, current density, current distribution, electrode potential, etc., have been optimized from practical experience as summarized, for example, in the "Handbook of Galvanotechnique" r6.11. Fundamental studies on metal deposition and electrocrystallization processes started in the first half of the twentieth century with thework of Volmer i6.31, ErdeyGruz and Volmer i6.41, Brandes [6.5], Gorbunova and Dankov [6.61, and Kaischew [6.7]. A first attempt at a systematic study of the phenomenological aspects of electrodeposited metal coatings was made by Fischer i6.81. Phenomenological classification of 3D Me deposits

Fischer recognized that the process of electrochemical crystal growth cannot be realized under "ideal" conditions. This is caused firstly by the presence of inhibitors in electrolyte solutions and secondly by the crystallographic properties of the substrate and the metal deposit itself [6.8-6.181. Models of the mechanism of crystal growth under "real" electrochemical conditions were developed by Fischer, distinguishing:

A discontinuous mechanism of crystal growth induced by nucleation phenomena forming macrosteps [6.19-6.261, ii) A continuous mechanism of crystal growth initiated by screw dislocations forming spirals with macrosteps L6.27-6.291. i)

6 Metal Deposits and S u ~ a c eStructuring and Modijication

264

The influence of inhibitors on both mechanisms was studied extensively. 2D and 3D nucleation processes, the thickness of macrosteps, and the step height of spirals were found to depend on the nature and concentration of inhibitors i6.8-6.181. The inhibition mechanisms were first classified as interface and interphase inhibition [6.30, 6.311. Later, this concept was extended with respect to the different dimensionality of surface defects in real systems [6.32, 6.331. In the ffiies, Fischer suggested a classification of compact 3D metal deposits according to their microcrystalline morphology [6.8, 6.19-6.24, 6.34-6.361, The following general texture types can be distinguished: i)

Field-oriented isolation type @I),

ii) Base-oriented reproduction type (BR), iii) Field-oriented texture type

0,

iv) Randomly-oriented dispersion type 0). The sequence i)-iv) corresponds to increasing inhibition of the electrocrystallization process accompanied by increasing cathodic overvoltage i6.27, 6.28, 6.371. Examples are shown in Fig. 6.1 [6.8]. A special texture type is produced by the so-called rhythmic-lamellar crystal growth, representing an oscillation reaction (Fig. 6.2) [6.381. Inhibitors were found to be incorporated in 3D metal deposits preferentially at grain and subgrain boundaries [6.39-6.431. The influence of internal strain on the macroscopic metal deposit properties such as hardness, brittleness, corrosion, etc., was considered in different systems r6.8, 6.41, 6.42, 6.44-6.531.

Texture, epitaxy, and morphology of 3D Me deposits Texture and morphology of compact 3D Me deposits determine their physical, mechanical, and chemical properties. 3D Me phase formation includes the formation of isolated 3D crystallites, their further growth and overlapping, and the final formation of the compact 3D metal deposit. Growth forms of isolated 3D Me crystallites and the transition to compact 3D Me deposits were extensively studied in the middle of the twentieth century by Kaischew, Budevski and Malinovski [6.54], Vermilyea and Price [6.55],and Russian authors [6.6, 6.56-6.581, A review of the Russian activities in this field was recently published by Polukarov [6.59].

6.1 Fornation of Compact 30 Me Deposits

265

Figure 6.1 Different types of compact 3D metal deposits according to Fischer [6.8]. (a): Fieldoriented isolation type Q of an Ag deposit; @): field-oriented texture type @T). Cross section of Cu deposit from acid CuSOq solution with addition of pnaphthaquinoline; (c): base-oriented reproduction type (BR). Cross section of Cu deposit; (d): randomly-oriented dispersion type 0). Cross section of Cu deposit from acid CuSO4 solution with addition of pnaphthaquinoline.

266

6 Metal Deposits and Surface Structuring and Modfication

Figure 6.2 Cross sections of Cu deposits from acid CuSO4 solution [6.38]. (a): Texture type produced by rhythmic-lamellar crystal growth in presence of o-phenanthroline; (b): texture type produced by deposition from electrolyte solution without additives.

Interactions between the substrate and isolated crystallites as well as compact 3D Me phases with respect to epitaxy and texture have been intensively investigated by Froment et al. since 1960 [6.60-6.711 using X-ray analysis, transmission electron microscopy (TEW, and scanning electron microscopy (SEW. They mainly studied one of the most important structural features of many electrodeposits, namely their fiber texture, i.e., the preferred orientation of their crystallites with a particular crystal axis aligned along the growth direction. Previous theoretical explanations were not able to fully account for the textures which were experimentally observed. However, significant progress has been achieved by Froment et al. I6.60-6.711, studying nickel electrodeposition from a Watts solution under various plating conditions. It was shown that for a given electrolyte composition, the texture mainly depends on the cathodic potential (or current density) and the pH of the solution [6.601. Fig. 6.3 shows five domains obtained under different plating conditions. The crystal structure and the morphology of each texture were carefully studied using electrochemical methods, Xray diffraction, and electron microscopy. It was proved that the fiber textures are determined by a specific orientation of the first nuclei, but result from growth rate

6.1 Formation of Compact 30 Me Deposits

267

competition between crystallites of various orientations. The selection mechanism is effectively driven by interfacial inhibition of growing faces of the crystallites [6.61]. The [loo] texture is regarded as a free growth mode, whereas the other preferred orientations are associated with reaction products resulting from the hydrogen codeposition depending on the electrode potential and pH. For example, Hads stabilizes [llO] orientation, H2 favors 12101 orientation, and Ni(OH)a inhibits the growth of every orientation except that of [2111. Pulse electrolysis, which is often used to improve the quality of electrodeposits (see below), was found to have a strong effect on the structure of nickel deposits by modifying the interfacial sorption properties 16.621. Molecular species such as H2 or Ni(OH)2 are easily desorbed during the relaxation time, improving the electrocrystallization process. Conversely, specifically adsorbed species such as Hads or anions inhibit the electrodeposition process of nickel. TEM studies showed that [110], [211], and [210] textures exhibit specific internal organization characterized by particular arrangements of twin planes leading to crystallites with either a two-fold (Fig. 6.4a) or a five-fold (fig. 6.4b) symmetry [6.63, 6.641, The emergence of constitutive twin planes provides preferential sites for nucleation and promotes crystal growth in a given direction [6.65]. Furthermore, this internal organization of 2D effects is reflected in the formation of 3D atomic clusters exhibiting perfect icosahedral and decahedral structures (Fig, 6.5) [6.66].

1

2

5

10

20

30

100

200

- iNi[mA ern-'] F i r e 6.3 Stability of various fiber textures of nickel electrodeposits vs. pH of a Watts bath and partial current density of nickel deposition [6.61].

268

6 Metal Deposits and Sulrface Structuring and Mod$cation

Figure 6.4 TEM images of textured nickel electrodeposits L6.641. (a): 12111 texture (notice the parallel twin planes crossing the grains); (b): [I101 texture ( notice the five convergent twin planes).

6.1 Formation of Compact 3 0 Me Deposits

269

Figure 6.5 Icosahedral particles formed during the initial stages of nickel electrodeposition [6.66].

The conversion of these clusters into multi-twinned particles with pseudo fivefold or two-fold symmetries must be related to a strong inhibition. It gives rise to a strong selection process whereby the growth of these defective crystallites overcomes that of the regular ones and leads to preferred orientations such as [211], a texture which cannot be predicted by conventional growth models. It is worth noting that similar multi-twinned structures are currently found in other fcc metals such as silver, gold, or copper. In the case of cobalt or lead, twist boundaries play the same role as parallel twin planes for nickel, and can also trigger dendritic growth [6.66]. The epitaxy of nickel electrodeposits has been studied by electron microscopy using a new method for the preparation of sections 16.67, 6.681. It was demonstrated that the electrodeposit structure results from competition between a simple epitaxial growth process maintaining substrate orientation and the formation of new randomly oriented nuclei which are rapidly submitted to the selection process, giving a fiber texture. This competition depends on both the substrate orientation and the nucleation and growth processes leading to the final texture. Organic inhibitors in the nickel bath also influence the texture of nickel deposits. The inhibition effects are related to their molecular structure 16,691. In the presence of brightners with unsaturated ethylenic or acetylenic compounds, the 11101 texture is preferentially formed. With aryl-sulfonic compounds used as leveling agents, the [1001 or [211] textures are favored. The modification of the crystal growth has been interpreted by an adsorption-hydrogenation-desorption model. The nature and the strength of a bond between a metallic surface and an adsorbed species depend on the

270

6 Metal Deposits and &$ace Structuring and Modification

crystallographic orientation of the surface and the type of unsaturated compound [6.70]. TEM studies of nickel electrodeposits reveal that the organic molecules are preferentially adsorbed and incorporated along growth steps [6.71],

Impedance studies of 3D Me deposition The kinetics and mechanisms of 3D Me deposition have been intensively studied by electrochemical impedance spectroscopy (EIS) as well as classical electrochemical techniques during the last two decades. Different simplified models of 2D nucleation and growth were theoretically treated in terms of their impedance behavior by Armstrong and Metcalfe t6.721 and Eppelboin et al. [6.731. Later, a more realistic model of a partially blocked electrode surface was developed and analyzed by Schmidt, Lorenz et al. i6.75-6.781. Nickel deposition from a Watts bath in the absence and presence of inhibitors was thoroughly studied by Wiart et al. [6.79-6.811. The appearance of an inductive loop at low frequencies has been ascribed to an adsorbed intermediate (NiOH),d,. The same authors also investigated zinc electrodeposition from acidic and alkaline electrolytes without and with inhibitors t6.82-6.861. It was suggested that the deposition mechanism involves an autocatalytic step

Silver electrodeposition was studied by different authors [6.75-6.78, 6.87-6.891. An exact interpretation of EIS data was found to be only possible on the basis of partially blocked electrode surfaces. The high overall exchange current density of the Ag/Ag+ electrode requires a special high-frequency (HF)EIS technique L6.77, 6.781. EIS measurements were also applied to investigate the kinetics and mechanisms of electrodeposition of copper [6.9O-6.93], cobalt t6.79, 6.911, palladium [6.94], gold [6.95], cadmium [6.96], and tin [6.97]. It should be mentioned, however, that surface inhomogeneities of different dimensionality (cf. Section 2.1) significantly influence the kinetics of metal electrodeposition and the time-dependent surface morphology. Therefore, an exact analysis of corresponding EIS spectra is rather difficult. The necessary presumptions of stationarity and linearity for EIS measurements and quantitative interpretation of EIS data are often violated. The lack of direct local information on surface dynamics strongly hinders a quantitative analysis of the impedance behavior of time-dependent systems. Such considerations have been mainly disregarded in previous EIS data interpretations. In future, a combination of EIS measurements with in situ local probe

6.1 Formation of Compact 30 Me Deposits

271

techniques (STM, AFM, etc.) will help towards a better understanding of the role of surface heterogeneities in the kinetics and mechanisms of 3D Me nucleation and growth processes.

Metal deposition by pulse techniques Bulk phase formation by current or voltage pulses results in different nucleation and crystal growth conditions compared to dc deposition and depends on the electrolyte and the pulse regime (unipolar, bipolar, pulse reverse, etc.) itself [6.98]. Several effects, which are of significance for the pulse plating process, can be distinguished. i)

Capacitance effect. Nucleation and crystal growth by metal pulse deposition is influenced by capacitance effects if the pulse duration is less or comparable to the charge or discharge time of the electrochemical double layer. In this case, the flowing Faradaic current is not influenced by applied pulses. From a practical point of view, the double layer charging time tc and discharging time td can be estimated from the double layer capacity and the exchange current density as well as the charge transfer data of the Faradaic process. For example, typical values for copper deposition from acidic copper sulfate solutions are: c d l = 50 PF cm", io,cu,cu~+ = 5 mA and CL = 0.5. With these values tc = 17 x 10-6/ipand td = 120 x lU6/ip are obtained in seconds for the pulse current density, ip, given in A cm-2 [6.99]. These characteristic time constants have to be considered in dimensioning the pulse "on" and "off durations.

ii) Average current density.

In pulse plating, the average current density, i , is given by a7 = a.P -

ton

ton + toff

where ton and toff are the corresponding "on" and "off' times of pulses, respectively. iii) Mass transport effect. Mass transport plays an important role in pulsed metal deposition. On the one hand it limits the maximum rate of deposition and influences the structure and properties of deposits. On the other hand it effects the macrothrowing and microthrowing power. Under dc conditions, the maximum deposition rate is given by the limiting current density, id, where the metal ion concentration

6 Metal Deposits and Sulface Structuring and Modification

272

at the electrode surface is equal to zero. As a result, deposits formed under these conditions usually show a dendritic or powdery structure [6.100]. Under pulse deposition conditions, two distinct diffusion layers can be defined instead of one as under dc conditions L6.1011: In the immediate vicinity of the cathode, the metal ion concentration pulsates with the frequency of the pulsating current. The metal ions, discharged during the pulses, diffuse from the bulk of the solution towards the pulsating diffusion layer. Therefore, a second concentration gradient builds up into the bulk of the electrolyte. The thickness of this stationary diffusion layer corresponds essentially to that of the Nernst diffusion layer which would be established under dc at the same hydrodynamic conditions. The formation of the two diffusion layers is schematically illustrated in Fig. 6.6. The thickness of the pulsating diffusion layer, however, becomes extremely small (less than 0.lpm) if the pulse current density is high. Therefore, smooth metal deposits may be obtained even at limiting average current densities as long as the limiting pulse current density, ipd, is not reached. This is illustrated for the case of copper deposition from an acidic copper sulfate bath in Fig. 6.7. The ordinate shows the ratio ip/ipd and the abscissa the ratio i /id. It follows that, if i /id exceeds a value of about 0.5, powdery or noncompact (nodular) deposits are formed [6.1021. ci

6s

C;

ci (x = "p)

Figure 6.6 Schematic concentration profile at the cathode for pulse plating conditions I6.1011 $: pulsating diffusion layer thickness; 4: stationary diffusion layer thickness; 6 ~Nernst : diffusion layer thickness.

6.1 Formation of Compact 30 Me Deposits

273

10

I

GRANULAR -1

NODULAR

ms 100

ms

.I

0.01

I

0.1

I

b

I

c

I

3.0 3.0

0.3 0.1-30

I

100 0.3-100

0.3

I

I

1

10

i I id Figure 6.7 Influence of pulse parameters on deposit morphology for copper deposition from a copper sulfate/sulfuric acid electrolyte [6.1021. ip: pulse current density; ipd: limiting pulse current density; ’t : average current density; id: limiting current density under ak conditions.

iv) Kinetic effects. Pulse deposition can be influenced by kinetic effects if, e.g., more than one reaction is involved. This is important for alloy deposition and codeposition of hydrogen. Furthermore, sorption processes occurring during the “off’ time may influence nucleation and growth processes in the subsequent “on“ time period. Simultaneously incorporation of adsorbates can occur. v) Crystallization effects.

As the nucleation rate increases exponentially with increasing overpotential, the formation of new nuclei is favored under pulse polarization conditions. Therefore, a decrease in the grain size of deposits can generally be observed [6.103]. As a result, the deposits are less porous and of bright appearance, helping to reduce the amount of brightening additives and consequently showing better corrosion resistance and mechanical properties [6.104, 6.1051. During the “off time, recrystallization phenomena are possible. For copper and gold, for example, grain size increases with increasing “off time as bigger grains are thermodynamically more stable. Other systems such as cadmium tend to passivate during the “off time, reducing the formation of

274

6 Metal Deposits and %$ace Structuring and Mod$ication

new nuclei because of blocking active surface sites. Additionally, the desorption of hydrogen or the decomposition of unstable hydride intermediates can play an important role during the deposition process, as found for zinc and chromium plating, respectively [6.106]. Fig. 6.8 shows the hydrogen content in Pd deposits as a function of the “off time [6.107]. Further on, the incorporation of polymeric material in gold deposits from gold cyanide complex solutions decreases significantly with increasing “off’ time [6.105], Pulse metal deposition offers the possibility of producing alloy layers as well as multilayered systems. If, e.g., the metal ion discharge of the components of an alloy follows different Tafel characteristics, a defined alloy composition can be achieved by an appropriate potentiostatic pulse routine as shown for the deposition of brass, bronze, and other binary and ternary alloys within a wide compositional range. Furthermore, alloys with changing composition gradients, which are of high technical interest, can be produced. Electroplating of cyclic multilayered alloy coatings leads to new laminated composite materials with mechanical, electronic, optical, and magnetic properties differing from those of thick layer systems [6.108]. Improvement of mechanical properties such as hardness and tensile strength can be expected if the individual layer thicknesses are small (normally in the nanometer range) and if the elastic constants of the two materials are different. A large number of material combinations have been investigated, particularly the Cu-Ni system [6.109-6.1111,

!O

Figure 6.8 Hydrogen content in Pd pulse plated deposits as a function of “off time 16.1071. mA/cmS2;ip/A cm-2 = 1 (0);0.5 (0); pH = 9.

= 150

6.1 Formation of Compact 30 Me Deposits

275

Figure 6.9 SEM image of a modulated Cu-Ni alloy with a single layer thickness down to about 30 nm [6.111].

Fig. 6.9 shows an SEM image of a modulated Cu-Ni alloy with a thickness down to about 30 nrn for each single layer. Laminated chromium layers being crack-free and with reduced internal stress are of great technical interest t6.1121. Different authors have shown that compositionally modulated 3D metallic alloys can be electrochemically deposited using cyclic polarization conditions and multicomponent electrolytes [6.108, 6.109, 6.113, 6.1141. Alloy formation takes place alternately by diffusion and charge transfer control of the deposition reactions of different metal components. Similar conditions have been used for the deposition of ultrathin metal films and heterostructures (cf. Section 6.4). Iaser-induced metal deposition Localized reactions at solid/liquid interfaces driven by focused laser light can be phenomenologically divided into deposition and dissolution processes as well as substrate modification. They can be used either for analytical or preparative purposes. An example is a direct writing procedure for the preparation of microstructures on macroscopic substrates without any masking technique.

276

6 Metal Deposits and Suflace Structuring and Modijication

The local resolution of laser-induced reactions depends on primary effects, i.e., the laser light, and secondary effects induced by the system. Laser-induced metal nucleation and crystal growth and the relevant mechanisms depend mainly on the electronic properties of the substrate, but also on interfacial and electrolyte properties. Depending on the system parameters, focused laser light can influence overvoltagedependent terms particularly by local heat formation or by local activation of the solid state/electrolyte interface. As the electric properties of the substrate material is of strong influence, the effects will briefly be discussed for metal, semiconductor and polymer substrates. Metallic substrates

Laser light, being absorbed by the metal substrate, generates photoexcited electrons which recombine, dissipating energy in the form of heat. Laser heating of the metal/solution interface, therefore, reaches its optimum at the wavelength at which the optical absorption coefficient of the substrates has its maximum. It results in a thermal gradient at the metal/solution interface i6.1151 and gives rise to (i) a shift of the rest potential of the redox system used for deposition and (ii) strong localized microstirring of the solution. The first effect can be used for local 3D phase formation using electroless plating systems [6.116]. The heat gradient at the metal/solution interface may even lead to cavitation and, due to the strong stirring effect, to a significant reduction in the diffusion layer thickness. Consequently, all deposition reactions under mass transport control will be enhanced by orders of magnitude since concentration gradients are strongly reduced [6.117]. Extremely high rate selective metal deposition processes are possible if, e.g., a laser is used in combination with a pressurized jet: this is known as laser enhanced jet plating (LEJP) [6.118]. In this case, the jet has a double function. First, it ensures a high material supply rate, and second, it acts as an optical waveguide as shown in Fig. 6.10. For example, gold plating experiments yielded deposition rates up to a few pm min-' with modular layer morphology. Photoexcited hot electrons may further be emitted from metals into electrolyte solutions [6.119]. Once electrons have been emitted into the solvent, they can diffuse back to the emitter and be recaptured by the electrode, or they are scavenged by redox acceptor species within the picosecond time range. Protons appeared to be a very effective scavenger [6.1201. Particularly, subpicosecond laser-induced nonequilibrium hot electrons lead to high emission electron rates which can react with acceptors to form intermediates. This is followed by localized metal nucleation [6.121].

6.1 Formation of Compact 30 Me Deposits

AIR BLEEDR

7

r

277

ELECTROLYTE J

SPECIMEN HOLDER

INLET

TO RESERVOIR

QUARTZ WINDOW

Figure 6.10 Schematic representation of the jet cell and the waveguide effect [6.118].

Furthermore, laser light may activate chromophoric metal-containing molecules of the electrolyte in the vicinity of the substrate surface. This activation process is followed by almost instantaneous metal deposition.

Semiconductor su$aces Photc-assisted deposition of catalytically active transition metais on semiconductors has attracted considerable attention in recent years. The basic mechanism of photoelectrochemical metal deposition is the reduction of metal ions from solution by photogenerated electrons in the conduction band or holes in the valence band. The generation of these charge carriers is induced by illumination of the semiconductor surface from below. The rectifying nature of the electrolyte/semi-conductor junction acts to separate the photogenerated electron-hole pairs at the surface [6.122]. Electroless as well as potential-influenced plating processes are possible depending on the relative positions of the Fermi levels of the semiconductor and the redox system in the electrolyte. An example is electroless silver plating on Ti02 i6.1231. Laser irridiation results in a negative shift of the open circuit electrode potential, depending on the laser power density, and finally in discharging Ag ions from the electrolyte. To obtain higher deposition rates, a hole scavenger, e.g., methanol, can be added to the electrolyte. During the last decade, photoelectrodeposition of metals on ptype semiconductors has been studied extensively, e.g., for GaP 16.1241, GaAs 16.1256.1281, InP [6.126], and InSe [6.129]. There seems to be a substantial difference in the

6 Metal Deposits and Sutface Stmcturing and Modification

278

behavior of Si and other semiconductors as far as metal deposition is concerned. This difference appears to be caused by the native oxide. Best results for selective laserassisted metal deposition on p t y p e Si were found by damage etching of Si followed by a controlled oxide layer formation in the nanometer range [6.130]. Metal ion discharge takes place via tunneling of the photogenerated minority carriers from the conductance band through the oxide to the redox system in the electrolyte. Nucleation and growth were studied by potentiodynamic current measurements in combination with scanning electron microscopy. An example of typical laser pulse-induced Zn deposition is shown in Fig. 6.11. The initial current peak reflects the instantaneous nucleation of Zn. Further investigations on the nuclei formation of Ni on n-Si (111) were carried out using in situ second harmonic generation (SHG) measurements [6.131]. Successive growth of the nuclei is expressed by an approximately linear portion of the current transients characteristic for a 1D or needle growth mode. At longer times (t 2 300 ms), the growth mode changes. This is indicated by a slope of nearly 0.5 in a In i vs. In t plot which is characteristic for diffusion controlled growth of 3D nuclei. This is confirmed

10

30

t

50

200

tsl

Figure 6.11 Photocurrent, liphl as a function of time t for the laser-induced deposition of Zn in the system ptype Si (lOO)/O.l M ZnSOq, at E = - 1.15V vs. SCE, /z = 647 nm, power dcnsity: 110 r n W ~ r n - ~ 16.1221.

6.1 Formation of Compact 30 Me Deposits

279

Figure 6.12 Hemispherical Ni nuclei on polycrystallinep-type Si substrate I6.1221.

by scanning electron microscopy showing that needle bundles coalesce to approximately hemispherical metal clusters. The hemispherical cluster formation for Ni deposits on polycrystalline p t y p e Si substrate is illustrated in Fig. 6.12. Again, photoelectron emission of semiconducting substrates can take place in metal nucleation. In addition, a complementary photoeffect, the photoemission of excited holes and oxidative decomposition of water, has to be considered in analogy to n-type semiconductors. Polymer substrates For insulating polymers, a local activation can be achieved by appropriate laser light. Cleavage of chemical bonds is followed by local electronic conductivity and the possibility of metal ion discharge. Another type of activation is the light-induced polyimide transformation from imide to amide producing free electrons [6.132]. The different interactions between a substrate and 3D compact metallic deposit determine the physical, mechanical and chemical properties of compound materials which are of great importance in modern electronic devices [6.133]. The aim of these investigations is to produce deposits with predesignable, variable, and controllable composition for the realization of custom-tailored materials.

280

6 Metal Deposits and S u ~ a c eStmcturdng and Mod8cation

Electrodeposition of 3D Me alloys Electrodeposited Me alloys are of great practical importance because of their unconventional electric, magnetic, mechanical and protective properties. The problem of electroplating of alloys is related to the processes of codeposition of metals from multicomponent electrolyte systems. Thermodynamic and kinetic aspects of electrochemical codeposition of metals and the processes of alIoy phase formation have been discussed in details by Brenner [6.134], Gorbunova and Polukarov [6.135] and Despic [6.136]. Electrodeposition of alloys is a rather complex process, which requires not only a careful control of the deposition conditions, but also an understanding of the involved phase formation and phase transition phenomena. The relationship between electrodeposition conditions and the structure, morphology, chemical and phase composition and properties of compact alloy deposits has been investigated in a number of electrochemical systems using different methods [6.134-6.140], Recently, nucleation and growth processes taking place in the initial stages of electrodeposition of alloys were studied theoretically and experimentally by Milchev and Lacmann [6.141-6.1431.

6.2

Theoretical Considerations

Generally, the formation of compact 3D Me deposits on foreign substrates S occurs via nucleation and growth, as described in Chapters 4 and 5. The crystal growth process of 3D Me phases (native substrate) can occur either by 2D nucleation and lateral monolayer or multilayer growth mode in the absence of screw dislocations or by spiral growth mode in the presence of screw dislocations as described in Chapter 5. In case of spiral growth mode, 2D nucleation proceeds at relatively high supersaturation. A macroscopic theory of nucleation and lD, 2D, and 3D growth of Me deposits was first developed by Fleischmann and Thirsk [6.144]. Under potentiostatic conditions, the current density ikee accompanying the nucleation and growth of islands without taking into account overlapping and nucleation on top of already formed islands is given by (cf. L6.1441 and eq. (3.66))

to an isolated island, (dZ,,,/dt) is the where f l ( t ) denotes the flux of Me:," nucleation rate, and * represents the convolution product. No overlapping conditions ,, and short times. For higher ,Z ,, and/or extended times, can be realized for low,Z

6.2 Theoretical Considerations

281

overlapping of growth islands takes place. In this case, the overall current density is given by:

where S(t) is the part of the surface covered by the growing new phase which can be expressed by the Avrami equation (cf. eqs. (3.65) and (5.13)):

where Sex(t) represents the part of the surface related to extended growth without overlapping of the new phase according to eq. (6.3). The measurable cathodic current density depends on the rate-determining step of metal deposition (charge transfer, linear diffusion, hemispherical diffusion to a single island, ohmic control) and on the nucleation type (instantaneous or progressive nucleation, cf. Appendix 8.7). It can be calculated using eqs. (6.3)-(6.5) and corresponding kinetic equations. In Table 6.1, the results are summarized for lD, 2D, and 3D growth modes involving different rate-determining steps without overlapping [6.144-6.1471. Relations between i and t for progressive and instantantaneous 2D nucleation and growth with overlapping under charge transfer control have already been discussed (cf. Section 5.2). The derivation of corresponding expressions under different bulk diffusion conditions is complicated. The problem has been extensively studied by Rangarajan [6.1481, Fletcher L6.1491, and Hills 16.146, 6.150, 6.1511. The shape of growing 3D Me crystallites determines the general structure and morphology of the metal deposit. The shape of crystallites in the deposit is determined, in the simplest case, by the nucleation rate and the normal and lateral growth rates. Different limiting cases can be considered: i)

In case of instantaneous nucleation, a fiber structure is obtained which strongly depends on the nucleation site density.

ii) In case of progressive nucleation, a columnar structure is formed depending on the ratio of the normal growth rate to the lateral growth'rate. The higher the lateral growth rate, the flatter the crystal grains will be and a layer-bylayer-like growth mode occurs for a negligible normal growth rate Furthermore, the nucleation rate plays an important role. The ratio of the nucleation rate to the growth rate defines the grain size. Finally, the surface roughness is determined by the lateral and vertical growth rates.

282

6 Metal Deposits and Sulfate Structuring and Modt3cation

Table 6.1 Current density, i f p e ,as a function of time, t, for different nucleation types, growth modes, and rate-determining steps 16.1444.1471. The symbols used are explained at the bottom of the table.

Growth Mode

1D

Shapeof

Rate-

Nucleation type

growing

determining

CryStalliteS

step

needles

charge

transfer

instantaneous progressive instantaneous

ifree =

ZF rn2 vm

-A-

f l 2 ifree= - n-rn Jv,t

Vm

ikee

=

ZF - 2n - h Z o vf t

Vm

charge transfer

2D

progressive

ZF h / u 12 t 2 ikee = - n Vm

discs cylindrical diffusion

cones

charge transfer

zF h 0; D Z , Vm

instantaneous

ihee = - n

-

progressive

ikee = - n

-

instantaneous

ifree =

-

-

progressive

ikee =

--

zF h 8; D j t V-

zF Vm

3D

control

t2

-J U u 2 t 3 " I ZF

instantaneous

ifree = - 2~

progressive

ikee = - - n

ikee = - A

instantaneous

ikee = - n (

Vm

ikee = --?A

J u3 t 3

-

Vm

zF

-

vrn

2

v3 t 2

- Z,

2 z F

3

instantaneous

progressive

v" u2 I

3 VIM

hemispheres hemispherical

ohmic

0

A z F

charge transfer

Zoun

032

SV, q 3 K 3 zF

(

~ Z , 1t ' / 2 2

~

8vmq3,3

zF

)

1/2

)

z,t 1 / 2

1/2

Jt3/2

r, is the radius of the growing needles; V n = un( q) and u1 = q( q) denote the normal and lateral growth rate of crystallites; h is the height of growing discs; u = u(q) is the growth rate by hemispherical growth (u = u, = ui); 0 1 = @(q) and 0 2 = @($ are terms defined in Ref. [6.145]; D is the mutual diffusion coefficient of Mezt; K is the electrolyteconductivity.

6.3 Ultrathin Metal Films and Heterostmctures

283

The rates of nucleation and of normal and lateral growth are also influenced by the following parameters: crystal orientation, surface imperfection density, adsorption and incorporation of inhibitors, electric field, and diffusion. Under real conditions, leveling and bunching effects, twinning, etc. complicate the process of 3D Me phase formation and growth and lead to special structural and morphological properties. The phenomenological classification of compact 3D Me deposits by Fischer (cf. Section 6.1) can be related to the nucleation and growth parameters discussed above. For example, the field-oriented isolation @I) and texture (FT) types are caused by electric field-enhanced normal growth, the base-oriented reproduction (BR) type corresponds to a relatively low nucleation rate and comparable normal and lateral growth rates, and the randomly-oriented dispersion (RD) type to an enhanced nucleation rate.

6.3

Ultrathin Metal Films and Heterostructures

The formation of ultrathin Me films on foreign substrates S (metals, superconductors, and semiconductors), S/Me, plays an important role in modern fields of technology such as micro- and nano-electronics, sensorics, electrocatalysis, etc. The process is often carried out by physical or chemical vapor deposition (PVD or CVD) of metals [6.152]. However, the difficult adjustment and control of the supersaturation via the gas flw is a great disadvantage of vapor deposition techniques. T h e situation becomes even more complicated, if more than one metal is deposited to form metallic sandwich layers and/or surface alloys. Therefore, electrochemical processes for the formation of ultrathin metal films and heterostructures became of great interest in modern thin layer technology. The electrochemical formation of ultrathin metal films, sandwich-structured layers and surface alloys with a defined thickness ranging from one to several monatomic layers on S can be obtained by metal deposition in the UPD and OPD ranges using special polarization routines. In the case of strong Meads-S interaction, expanded commensurate Meads overlayers as well as one or two close-packed commensurate or incommensurate Meads monolayers can be formed in the UPD range depending on BE (Fig. 6.13). Then, metal deposition in the OPD range follows either the Frank-van der Merwe (Fig, 6.13a) or the Stranski-Krastanov (Fig. 6.13b) growth mechanisms in the absence or presence of significant crystallographic Me-S misfit, respectively. In the first case, a

284

6Metal Deposits and Sutjhce Structuring and Mod@ation

layer-by-layer growth mode is observed which makes it possible to deposit at low overpotentials epitaxial ultrathin metal j h s , S/Me, with a well-defined thickness on top of a foreign substrate S (cf. Chapter 1 and Section 4.3). In case of the StranskiKrastanov growth mode, the structure and morphology of thin metal films deposited in the OPD range on top of Me UPD modified S are strongly determined by the structure of the 2D UPD monolayer as well as by the nucleation and growth kinetics involving the internal strain due to the crystallographic Me-S misfit (cf. Chapters 3 and 4). In this case, the 2D Me UPD monolayer acts as a precursor for the 3D Me phase formation (cf. Section 4.3). After deposition of a finite number of Me monolayers (2 < n < 20), the strain associated with the crystallographic Me-S misfit is usually compensated €or by the formation of misfit dislocations pig, 6.13b).

Figure 6.13 Schematic representationof the growth modes in Me film formation on S in systems with strong M e 4 interaction depending on the crystallographic Me-S misfit, f = (&,M~- do,d/do,s. (a): Frank-van der Menve growth mode ( f w 0); (b): Stranski-Krastanov growth mode (f# 0).

6.3 Ultrathin Metal Films and Heterostmctures

285

In the case of weak Mead& interaction, thin metal films are deposited at higher overvoltage in the OPD range on top of unmodified S according to the Volmer-Weber growth mode. Again, the structure and morphology of deposited ultrathin metal films are determined by the nucleation and growth kinetics of the 3D Me phase. The "degree of perfection" of ultrathin metal films strongly depends on the nucleation and growth kinetics. Coalescence of growing 2D or 3D islands can lead to the formation of crystal imperfections [6.1531. First, the so-called rotational misfit due to different azimuthal orientation of coalescing 2D or 3D islands generates edge dislocations (Fig. 6.14a). A typical example is the so-called low-angle boundary (Fig. 6.14b). Second, coalescence of 3D fcc or hcp islands with (111) or (0001) orientation, which have a different stacking sequence, produces double positioning boundaries and stacking faults in the metal film (Fig. 6.14~).

I

position 1

t

; 1 #

position 2

a b C

6

Figure 6.14 Formation of crystal imperfections during coalescence of growing islands 16.153). (a) and (b): accommodation of a rotational misfit; (c): double positioning boundary in a fcc metal deposit.

286

6 Metal Deposits and Su$ace Structuring and Modification

In electrochemical "multicomponent systems", i.e., using electrolytes containing different Me?, mixed UPD and OPD deposition of different metals can be used for a sequential deposition of different Mei monolayers forming sandwich-structured ultrathin metal films, S/Mel/Mea/ ...Me,. The formation of 2D Me-S and MepMej surface alloys and 3D Me-S bulk alloys can be utilized to form ultrathin sufluce alloy films such as S/Me-S, S/Mei-Mej, and S/Mei-S/Mez-Mej. Ultrathin sandwichstructured films and surface alloys will be denoted as heterostructures. The experimental conditions for the deposition of ultrathin metal films and heterostructures depend on system-specific properties. In general, the following technological parameters have to be coordinated to reach the goal 16.154-6.1661:

9 The multicomponent system S/ Me? ,...Me? should generate 2D Meads overlayers, 2D Me-S surface alloys and/or 3D Me-S bulk alloys in the UPD range. ii) The UPD and OPD ranges of different Me? have to have an optimum overlap, which can be adjusted by the Me? activities within the electrolyte. iii) The kinetics (transfer and/or diffusion control) of the deposition processes of each Me? component have to be selected in order to get potentiostatically different Me? deposition rates.

iv) Special polarization routines using steady state and non-steady state polarization techniques with polarization times at different potentials in the UPD and OPD range must be applied. iv) Other parameters such as substrate pretreatment, temperature, electrolyte composition, etc. must be optimized. The electrochemical formation of ultrathin metal films and heterostructures represents a modern aspect of science and technology. However, most reliable results in the nanometer range have recently been obtained by combining electrochemical and in situ local probe studies in well-defined electrochemical systems with single crystal substrates [6.156-6.1671.

Ultrathin metal films on foreign metal substrates The system Au(hkl)/Ag+is a typical example of strong Me-S interaction but negligible Me-S misfit (doA,,= 0.2884 nm, do&= 0.2890 nm). Therefore, the Frank-van der Merwe or layer growth mechanism is expected to operate in this system (Figs. 1.1and 6.13a). UPD investigations of silver on gold single crystal surfaces showed a strong influence of the crystallographic orientation on the Ag overlayer structure depending on hE (cf. Section 3.4). Cyclic voltammetric studies, isotherm measurements, and in

6.3 ultrathin Metal Films and Heterostmctures

287

situ STM investigations indicated a stepwise formation of commensurate 2D UPD adlayers depending on the substrate matrix and AE [6.159-6.1611. At relatively low AE, condensed 2D Au(hkZ)-(l x 1) Ag phases are formed, as found by in situ STM measurements (Fig. 3 . 2 1 and ~ 3.22~)16.159-6.1611, 2D Ag-Au surface alloy formation can be thermodynamically expected and could be observed at relatively low AE at elevated temperatures and/or extended polarization time [6.161]. Long term polarization experiments, carried out especially at higher Ag' concentrations, gave evidence for Ag-Au surface alloy formation in the underpotential range 0 mV < AE < 100 mV starting at step edges and surface defects (cf. Section 3.6). Therefore, surface alloying effectscan play an important role in this system. UPD-OPD transition investigations in the system Au(hkl)/Ag+ carried out under diffusion control using a low Ag' concentration in the electrolyte and a special polarization routine with defined waiting time at AE and 7 have already been discussed (cf. Section 4.3). Under these conditions, ultrathin Ag films with a defined number of Ag monolayers (1 < n < 40) could be deposited. The silver deposition was found to follow initially (n < 10) a layer-by-layer or Frank-van der Menve growth mechanism (Figs. 1.1 and 6.13a). The further growth in the OPD range follows a multilayer growth mode generated by screw dislocations. This is illustrated in Fig. 6.15, showing the overpotential dependence of the steady state current density in this system.

06

v-

5

a

E

0.4

I

.

Lo

0.2

0 0

20

40

60

80

100

q2 [ m 9 1

Figure 6.15 Steady state current density, iss,as a function of $ for Ag OPD in the system Au(100)/0.1 M AgClO4 + 0.5 M HCl04 at T = 298 K 16.1611.The overvoltage q is corrected by ohmic drop and diffusion overvoltage assuming D k + = 2 x cm2s-1 and a diffusion layer thickness S= 0.01 cm for natural convection.

6 Metal Deposits and &?$ace Structuring and Modification

288

The result agrees well with the spiral growth model (cf. eq.(5.28)) and indicates that the screw dislocations of the substrate were inherited by the 3D Ag film. The ultrathin Ag film was found to be epitaxially oriented, as already shown in Fig. 4.4. Heterostructures on foreign metal substrates

UPD-OPD transition phenomena can be used for the deposition of heterostructured ultrathin metal films from multicomponent Me? systems using, for example, the polarization routine for i = 2 shown in Fig. 6.16. Different heterostructures were prepared in the following multicomponent systems [6.156-6.1671: S(hkZ)/MeT+ with S = Au, Ag and Me? = Ag', Pb2'; Me? = Pb2', T l ' , Cd2'; M e c = 1 ' The possible heterostructures which can be formed by this technique are schematically illustrated in Fig. 6.17.

t

I

t Figure 6.16 Schematic representation of the polarization routine used for the deposition of heterostructured ultrathin metal films 16.1591.

6.3 Ultrathin Metal Films and Heterostmctures

289

Figure 6.17 Possible sandwich-layered metal films and heterostructures, which can be formed by UPD and OPD in mdti-component systems Ag(h@/Pb2", T I ' , Au(kM)/Ag+, Pb2+, m,i and Au(hkE)/Agi, Cd2+, using different polarization routines [6.159].

As typical examples, formation of ultrathin sandwich-structured films can be demonstrated in the multicornponent systems Ag(hkt)/Pb2', Tl" and Au(hkl)/Ag+, Pb2', T I ' . The first system offers the possibility to form ultrathin sandwich films consisting of two monolayers with different composition of Pb and T l depending on the polarization routine, as shown in Fig. 6.18. The first monolayer may contain either only Pb adatoms (Fig. 6.18a) or both Pb and TI adatoms (PbzTlywith 0.5 s x s 1,x + y = 1,

6 Metal Deposits and Surface Structuring and Modijication

290

Fig. 6.18b), depending on the polarization time at a potential El which is located in the UPD ranges of both Pb and T1: = El - Epb/pb2+ and AEy = El - Ey/y+.The second monolayer containing only T I adatoms (Fig. 6.18) is formed on top of the first by changing the potential from El to E2, which is located in the OPD range of Pb (?pb = E;i - Epb/pb2+ < O), but still remains within the UPD range of T1 (AET~ = E2 - E,rlrii+ 2 0). In this experiment, the sweep rate was chosen in such a way that 3D Pb bulk deposition, which occurs very slowly under diffusion control, can be neglected. Combining these results with those obtained in the system Au(hkl)/Ag’ described above and in Section 4.3, a defined number of Ag monolayers, one Pb,Tl, monolayer and a pure T1 monolayer can be deposited successively in the multicomponent system 80 I

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Figure 6.18 Anodic stripping of heterosttucturedfilms formed by UPD of Pb and TI on Ag(ll1) using the polarization routines shown in the insets [6.159]. System: Ag(111)/2.5 x l W 5 M Pb(ClO4)2 + lo3 M TIC104 + 0.5 M NaClO4 + M HClO4 at T = 298 K and I dE/dtI = 10 mV/s. (a): Without polarization time, tp; (b): with $1 = 150 s at El = - 213 mV corresponding to AEpb = 60 mV and AEn = 317 mV.

6.3 UlfrafhinMetal Films and Heterosfnrcfures

291

Au(hkl)/Ag+, Pb2', Tl' using an appropriate polarization routine [6.159, 6.160, 6.1626.1671. The composition of the heterostructure is illustrated in the desorption spectrum of the multicomponent system in Fig. 6.19. 2D Me-S surface alloy formation and 3D Me-S bulk alloy formation processes can affect the composition of ultrathin metal films forming heterostructurs as schematically illustrated in Fig. 6.17. Well-known for 3D alloy formation, even occurring in the UPD range at low AE and extended polarization, are the systems Au(hkl)/Ag', Ag(hkl)/Cd2', and Au(hkl)/Cd2' (cf. Section 3.6). By analyzing the UPD adsorptiondesorption spectra of Pb UPD as a fingerprint in the system Au(hkl)/Ag', characteristic features of both systems Au(hkl)/Pb2' and Ag(hkl)/Pb2+ were found after deposition of one Ag monolayer as illustrated in Fig, 6.20. This observation can be attributed to either the formation of a 2D Ag-Au surface alloy or the coexistence of Ag and Au domains. DTS measurements at AE = 100 mV yielded different effective barrier heights on top of and beside islands [6.168]. This result supports the second

125 -

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.*

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-

Figure 6.19Anodic stripping of a heterostructured film formed on Au(ll1) by OPD of Ag and UPD of Pb and TI using the polarization routine shown in the insert (6.1591. System: Au(lll)/lU5 M AgClO4 + M TIC104 + 0.5 M NaC104 + M HClO4 at T = 298 K and I dE/dt I = 2.5 x lo5M Pb(C104)2 + 10 mV/s. tP,l = 3600 s at El = 350 mV corresponding to T,, = - 150 mV, AEpb = 623 mV and AEm = 880 mV; tp,2 = 150 s at E2 = - 213 mV corresponding to T,& = - 713 mV, AEpb = 60 mV and = 317 mV.

6 Metal Deposits and Surface Structuring and Modification

292

argument, but a site exchange between Au atoms from the substrate and Ag atoms

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I = 10 mV s-l and T = 298 K 16.1561. (a): Anodic stripping curve in the system Au(111)/5 x M Pb(C104)2 + 0.5 M NaC104 + 10-3 M ~ ~ 1 0 (b): 4 : cyclic voltammograms in the system ~~(111)/10-5 M A ~ C I O+ ~5 x 10-~ M Pb(C104)~+ 0.5 M NaC104 + M HClO4 with three different degrees of Ag coverage, O A ~in, + mV and E2 = 350 mV; monolayer units: @& = 1 (1); 1.5 (2); 2.5 (3), formed at El = E A ~ / A =~ 500 (c): anodic stripping curve in the system Ag(111)/5 x lo9 M Pb(C104)2 + 0.5 M HCIO4. Figure 6.20 Voltammograms in different systems at

6.3 Utrathin Metal Films and Heterostmctures

293

from the UPD monolayer cannot be excluded. If the amount of Ag deposited on Au(hkl) exceeds two monolayers, characteristic features only of the system Ag(hkl)/Pb2' are observed. In other words, only two Ag monolayers deposited on Au(hkl) are necessary to transform the Au(hkl) substrate into an Ag(hkl) substrate, In the two-component system Au(hkl)/Ag', Cd2' the formation of mixed monolayers consisting of Au(hkl)/Cd,AgFAux with x + y + z = 1 becomes possible depending on the polarization routine as illustrated in Fig. 6.17 [6.157, 6.159, 6.1691. In Fig. 6.21, the solid state diffusion-controlled kinetics of the alloy formation process in the multicomponent system Au(hkZ)/Ag+, Cd2' is compared with those in the one-component systems Au(hkl) /Cd2' and Ag(hkl)/Cd2+. In all experiments, a constant silver layer thickness of three monolayers was initially deposited. In the multicomponent system, Cd diffuses towards S under "thin layer conditions" established by a 2D Cd&, surface alloy. In the one-component systems, Cd diffuses towards S under semi-infinite conditions. A phase transition (curve 1) is observed in the system Au(hkl)/Cd2' after a relatively short polarization time. The observation of the formation of a second CdAu, surface alloy is obviously connected with a relatively high solid-state diffusion constant and a relatively low value of z. In contrast to this, in the system Ag(hkl)/Cd2+ the formation of only one Cd&, surface alloy phase is observed in the time window studied (curve 2). The

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Figure 6.21 Kinetics of underpotential alloy formation in different systems at hECd = 10 mV and T = 298 K [6.159].(1): Au(lll)/Cd+'; (2): Ag(lll)/Cd"; (3): Au(lll)/Ag(3 monolayers)/Cd+'. Drawn lines correspond to simulation data.

294

6 Metal Deposits and Suvface Stmcturivlg and Mod8cation

kinetics of the surface alloy formation process in the two-component system Au(hkl)/Ag', Cd2+is determined by the thickness of the ultrathin film of silver initially deposited on the Au(hkl) substrate. After transformation of this Ag film into CdzAgy, the process of 3D CdJu, alloy formation starts in the bulk of the Au(hkl) substrate. Obviously, the kinetics of this alloy formation process is inhibited by the presence of 2D Cd&, and 2D Cd&,Au, surface alloys which obviously act as a diffusion barrier. The experimental data were found to be in good agreement with a simulation of an appropriate diffusion model [6.169]. The penetration depth of the diffusing Mei species, surface alloy phase transitions, and the local composition of the surface alloy could be determined from these investigations. A similar UPD technique called "electrochemical atomic layer epitaxy" (ECALE) was introduced by Stickney et al. [6.170-6.1721 to form mixed 2D MexMey UPD overlayers using simultaneously electrochemical reduction and oxidation of different electrolyte components. The results show that the formation mechanism and kinetics of ultrathin metal films and heterostructures on well-defined foreign single crystal substrates can be well understood on an atomic level combining electrochemical and in situ local probe techniques. The results obtained are important for the nanotechnology dealing with structuring and modification of electron-conducting surfaces (metals, semiconductors, superconductors) in not only the vertical but also the lateral direction in the nanometer range. A laterally-limited structuring of electron-conducting solid state surfaces by electrochemical phase formation processes will become possible if the nucleation and growth mechanisms of 2D and 3D Me phase formation are well known and can be combined with local metal deposition using in situ local probe techniques.

Ultrathin metal films on semiconductor substrates Electrochemical processes on semiconductor electrodes are much more complicated than on metals and superconductors since charge carriers from the conduction and/or valence band as well as from surface states located within the band gap can participate in the charge transfer step 16.1731. The difference between metal deposition on a metal substrate and that on an n-type semiconductor is illustrated in Fig. 6.22. Neglecting the influence of surface states, metal deposition occurs at relatively low I q I on metals but at relatively high lyl on semiconductors due to the band gap and bandbending. The necessary shift of the Fermi level is reduced in the presence of surface states, Therefore, the application of in situ STM is complicated by high tunneling voltages. Additionally, currentless metal deposition processes can occur if

6.3 ultrathin Metal Films and Heterostmctures

295

the Fermi level of the Me/MeZ+system overlaps with either the conducting or valence band of the semiconductor, leading to an exchange of electrons or holes, respectively [6.174]. The formation of condensed 2D Me phases on semiconductor surfaces is less probable due to the weak Mead& interaction and the special properties of the semiconductor substrate t6.174, 6.1751, Therefore, the formation of 3D Me phases follows the Volmer-Weber or island growth mechanism (cf. Fig. 1.1). Electrodeposition of metals on semiconductor surfaces has been used by Allongue et al. to form nearly ideal Schottky barriers on G A S [6.1761 and InP [6.177], and to stabilize photoelectrodes with ultrathin and transparent metal films [6.174, 6.178, 6,1791. Selective metal deposition has also been performed to reveal p n junctions and transistors on silicon chips [6.180].

Metal

Electrolyte

Se

Electrolyte

Figure 6.22 Schematic energy diagram of a metal/electrolyte interface (a) and n-semiconductor/ electrolyte interface (b) for equilibrium (i) and deposition (ii) conditions. E;" E p , and EF' denote the Fermi levels of the metal, semiconductor, and the redox system of the electrolyte, respectivley. Ec represents the energy at the bottom of the conduction band of the semiconductor, Ev is the energy at the top of the valence band, and A h is the flatband potential. While for metal electrodes a small negative shift of the Fermi level is mostly sufficient to start metal deposition, semiconductors in general require a much greater negative shift to compensate for the potential drop inside the material.

6 Metal Deposits and Surface Structuring and Mod$fcation

296

More fundamental work was carried out on 111-V compounds as substrates to analyze the parameters influencing nucleation and growth kinetics [6.173, 6.177, 6.181-6.1831. In initial stages of metal deposition on semiconductor surfaces, the electrochemical charge transfer may occur at the conduction band edge or at surface states as shown in Fig. 6.23a i6.177, 6.1811. In darkness, minimum overpotentials are larger at n-type semiconductors than at metals because the band bending must be reduced to supply a sufficient density of surface electrons [6.173]. For ptype substrates, illumination is necessary under reverse bias. The two photocapacitance spectra in Fig. 6.24 show that a new peak appears after Ru deposition on GaAs, indicating that metal adatoms induce surface states located within the band gap [6.1821.This result seems to be general and has important consequences regarding the subsequent metal cluster growth because metal-induced states degenerate above a critical density of clusters of about 1OI2 cm-2 16.1741. If the deposition reaction is faster on the metal than on the semiconductor, the electrode very soon behaves like a Schottky electrode despite a coverage smaller than unity (see Fig. 6.23b) [6.173, 6.174, 6.1801. 3D Me growth occurs via deposition on initially deposited single Me clusters as in the case of Cu and Ag deposition on GaAs [6.181].

Semiconductor -

Electrolyte

Semiconductor

-1-

surface state metal-induced stale

I+ 1.q p1

4 E:

metal cluster

Figure 6.23 Band diagram of the interface during deposition of metal on a semiconductor substrate. (a): Initial stage; (b): after reaching the critical density of nuclei.

6.3 ultrathin Metal Films and Heterostmctures

297

However, if the reaction is slower on metal clusters, Me charge transfer occurs on the uncovered semiconductor surface and a 2D growth mode is observed i6.1731. The epitaxial growth of Ni on GaAs [6.181, 6.1831 (Fig. 6.25a) is the best example of this type. It is caused by an inhibition of the growth of Ni on Ni due to hydrogen codeposition. With metals of the platinum group (pt, Ru, Pd), the growth is only pseudo 2D (at low pH) with small 3-5 nm elementary platelets nucleating progressively over the surface prior to 3D Me growth 16.173, 6.181l.The distribution of particles may, however, be controlled by surface pretreatment as shown in Figs. 6.25b and 6 . 2 5 ~for Pt and Ru deposits on G A S (100). Clusters are nanocrystallites with no preferential orientation. While their distribution looks similar after chemical etching, the differences seen in Fig. 6.25 are attributed to a preferential nucleation of Pt and Ru adatoms, respectively, on As- and Ga-related surface sites whose spatial distribution is controlled by the surface preparation [6.181,6.1821.

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"igure 6.24 Photocapacitance spectra of n-GaAs before (a) and after (b) Ru deposition I6.1821.

298

6 Metal Deposits and SulrfaceStructuring and Mod$cation

Figure 6.25 Structures of different Me deposits on GaAs (hkl) I6.1811. (a): RIIEED pattern of Ni deposit on GaAs (111); (b): TEM image (replica technique) of a Pt deposit on photo-etched ( i d s (100); (c):TEM image of Ru deposit on photo-etched GaAs (100).

6.4 &$ace Structuring and Modijication

6.4

Surface Structuring and

299

Modification

At present, defined local structuring and modification of electron-conducting solid state surfaces (metals, superconductors, semiconductors) is performed indirectly using physical or chemical vapor deposition techniques (PVD or CVD) or electrochemical phase formation processes of metals in combination with lithographic techniques. Usual photolithographic techniques operate in the micrometer range of lateral resolution. A well known example is the lithographic galvanic deposition technique (LIGA) to form structures and objects on the micrometer scale [6.184]. A higher lateral resolution in the range 100 nm < x < 1 pm can be obtained using expensive electron beam lithography. The lateral resolution is limited by the wavelength of the intermittent irradiation. Therefore, nanotechnology in the range of a few nanometers or even Angstrums cannot be realized using these conventional techniques. A "direct writing" with electron beam excitation is only possible when metal deposition processes are started indirectly in a MeZt medium covering the substrate surface. A great disadvantage using PVD, CVD, and electron beam techniques is the less controllable and only very slowly changeable supersaturation. Additionally, metal nucleation and growth follow different thermodynamics and kinetics in the gas phase compared to the condensed electrolyte phase. Pronounced local fluctuation phenomena in the gas phase lead to a local distribution of the supersaturation and, therefore, to a distribution function of critical nuclei size which is termed "magic numbers" I6.185, 6.1861, In contrast, supersaturation is more or less homogeneously distributed in electrochemical systems leading to a unique value of the critical nucleus size at constant overpotential. Thus, controlled epitaxial growth is difficult to obtain by metal deposition from the gas phase. Usually, polycrystalline deposits of different microstructures are formed (cf. Section 6.1). This problem is, for example, well known for laser-deposited epitaxial thin films of high Tc superconductors. Furthermore, PVD, CVD, and electron beam processes increase the temperature of the substrate surface. Dry-etching processes on illuminated lithographic domains often lead to damage of the substrate surface which is dEicult to control. Finally, the indirect structuring and modification processes require multiple environmental changes under ultrapure external conditions. The multiple changes of the environment represent a key factor for contamination and resulting degradation mechanisms, thus affecting the quality of micro- or nano-devices in electronics. In contrast, structuring and modification of solid state surfaces by electrochemical means provide a number of great advantages, In electrochemical systems, supersaturation and undersaturation can be precisely controlled and rapidly changed

300

6 Metal Deposits and Su$ace Structuring and Mod$cation

via the electrode potential (cf. eq. (1.4)). In such a way, cathodic metal deposition and anodic metal dissolution (electrochemical etching) within the same system can be applied depending on the electrode potential only, thus avoiding multiple environmental changes. Thermodynamics and kinetics of nucleation and growth processes are well-defined (cf. Chapter 4 and 5). Epitaxial metal deposition as well as selective etching are rather easily obtained. The absence of beam-based lithographic procedures in electrochemical processes avoids a localized increase of temperature via dissipative energy transfer. An important aim of modern science and nanotechnology is the structuring and modification of solid state surfaces in the nanometer or subnanometer range. An implementation can only be realized if metal deposition or dissolution processes can be locally focused. This can be achieved either from the gas phase or from the electrolyte phase using in situ local probe techniques as a powerful tool. In this case, the tip and cantilever of STM and AFM instruments operate as miniaturized electrodes. Again, the execution of localized metal deposition or dissolution reactions in the vapor phase environment features the same disadvantages discussed above. In particular, localized metal deposition occurs only using high energy differences between the tip or the (metallized) cantilever and the substrate. In the contrast, localized metal deposition or dissolution processes that are electrochemically induced involve energy differences orders of magnitude lower. Furthermore, the electrochemical potentials (Fermi levels) of both the tip or metallized cantilever and the substrate can be separately adjusted and controlled. This means, tip or cantilever induced localized metal deposition or dissolution processes can be realized using appropriate polarization routines. Investigations on local structuring and modification of electron-conducting solid state surfaces under electrochemical conditions and using in situ SPM techniques are just beginning. Recently, interesting experiments were carried out on surfaces of metal single crystals, highly oriented pyrolytic graphite (HOPG), epitaxial thin films of high Tc superconductors (HTSC), and semiconductor single crystal surfaces. Metal single crystal surfaces

A so-called "tip-induced local metal deposition" was recently achieved in systems Au(hkl)/Cu2' and Ag(hkl)/Cu2+ with (hkl) = ( l o ) , (111) using the in situ STM technique by Kolb et al. [6.187, 6.1881. First, a certain amount of metallic copper is cathodically deposited on the tip. Copper is then transferred from the tip to the substrate by bringing the tip closer to the substrate surface. Originally, this was achieved by pulse polarization changing the sign of the tunneling voltage, UT.The

6.4 Sut$ace Structuring and Modilication

301

momentary null of UT causes the tip to approach the surface, physical contact being prevented by appropriate selected parameters of the feedback circuit of the STM. Another possibility for approaching the tip to the substrate surface is direct external control of the z-piezo. In this case, a computer pulse program produces highly regular metal cluster patterns. The procedure is schematically shown in Fig. 6.26. As a result, single copper clusters of defined diameter and height as well as cluster arrays could be formed by this technique, as shown in Fig. 6.27. Predeposited Cu clusters could be erased by an electrical field induced on a cluster by a highly positive polarized tip. A different concept for surface structuring in the nanometer range was developed independently by Gewirth [6.1891 and Froese [6.190] which is called "defect-induced local metal deposition". The idea is to produce surface defects mechanically, using in situ local probe techniques. In particular, the contact mode of the in situ AFM technique obviously leads to surface imperfections. Such defects can act as nucleation centers for subsequent metal deposition and etching processes. First studies were carried out in the systems Au(hkZ)/Cu2+ and Cu(hkl)/Cu2+. As a result, defined Cu clusters with a minimum diameter of about 20 nm and a minimum height of about 1 nm could be deposited at selected local surface positions and afterwards erased using in situ AFM technique in contact mode. Examples are shown in Fig. 6.28.

STM tip

\

Au surface

Figure 6.26 Model for tipinduced Cu deposition I6.1881.

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6 Metal Deposits and Suflace Structuring and Modzlication

I so 11111

I so 11111 Figure 6.27 Demonstration of a local deposition and selective removal of Cu clusters on Au(ll1) in the system Au(111)/0.05 M H2SO4 + 0.1 mM CuSO4 at T = 298 K [6.188]. (a) local deposition of copper clusters and (b) selective removal of a cluster by applying a very positive tip potential ET = 500 mV vs. Cu/Cu2+.

The results obtained in the system Au(hkZ)/Cu2', where 2D Me UPD phenomena occur followed by a Stranski-Krastanov growth mechanism in the OPD range, show that electrochemical 3D Me phase formation processes can be used for structuring and modification of metal single crystal surfaces in the nanometer range. Local electrochemical processes are initiated by in situ local probe methods using appropriate polarization routines. The results obtained in the system Cu(hkZ)/CU2+ clearly correspond to 3D Me phase formation on the native substrate involving spiral growth and/or 2D nucleation and multilayer growth. It is evident that experiments in such systems are solely carried out to demonstrate local metal deposition, but not for surface heterostructuring and modification. However, 2D Me UPD phenomena represent a general problem in nanostructuring of metal surfaces in systems with strong Mead& interaction (cf.

6.4 Suflace Structuring and Modz3cation

303

Chapter 3). The formation of 3D Me clusters on top of a stable 2D Me UPD monolayer may restrict some practical applications.

SdQ

0

nn

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0

250

-0 500 nn

(b)

Figure 6.28 Local metal deposition of copper on Au(100) in the system: Au(100)/5 x lW3 M CugSOq M H2SO4 at T = 298 K I6.1901. (a): Bare substrate at AE = 10 mV; (b): alter cantilever-induced local metal deposition at 17 = - 10 mV.

+

304

6 Metal Deposits and Sugace Structuring and Modification

HOPG surfaces In electrochemical systems with HOPG as a substrate, the Mead& interaction is relatively low, thus avoiding 2D Me UPD phenomena. 3D Me phase formation follows the Volmer-Weber growth mechanism, i.e., formation of 3D Me clusters on an unmodified HOPG surface. It is evident that 3 b Me phase formation processes on defined single crystal faces of HOPG represent an ideal model system for surface structuring and modification in the nanometer range. HOPG (0001) faces are commonly used as a foreign substrate since they can easily be prepared, and exhibit large atomically flat terraces separated by monatomic steps. Moreover, HOPG is electrochemically inert within an extended potential range. The fundamentals of 3D Me phase formation processes were studied in the system HOPG(OOOl)/Ag+ (cf. Section 4.3). In situ STM observations show that at low Iql the deposition process on the atomically flat terraces of HOPG(0001) is extremely inhibited, and Ag is deposited preferentially at step edges (Fig. 6.29) and other surface defects [6.191]. Applying an ac modulation superimposed to the dc bias of the substrate potential (AE= Iql = 0), the corresponding 3D Me deposition/dissolution cycles at a step edge are well reflected by in situ STM x-t line scans (Fig. 6.30) [6.192]. In contrast, the silver deposition process also occurs on flat terraces at relatively high Iql.

Figure 6.29 In situ STM images of a stepped HOPG surface in the system HOPG(OOOl)/10-2 M kc104 + 1 M HClO4 at T = 298 K 16.1911. IT = 5 I-& Pt-Ir tip. (a): At AE = 100 n i t (b): after Ag deposition at q = - 125 mV.

6.4 &$ace Strmcturing and Modipcation

0

100

305

zoo

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Figure 6.30 In situ STM x-t l i e scan image of a stepped HOPG surface in the system HOPG(OOOl)/10~2M AgClO4 + 1 M HClO4 at T = 298 K 16.1921. ZT = 5 & Pt-Ir tip. Substrate potential hE = 0 mV is modulated by an ac amplitude of 80 mV.

First studies on a local structuring of HOPG(0001) surfaces were carried out by Penner using "electric field-induced local metal deposition" [6.193-6.1951. In the AgF, local metal deposition was performed by in situ system HOPG (0001)/5 x STM applying a potentiostatic two-probe pulse technique with high tunneling voltage amplitudes (UT= ET - Es I 6 9 . A preferred 3D Ag cluster formation under the tip was achieved as shown in Fig. 6.31. The 3D Ag clusters had a diameter of 20 nm < d I 40 nm and a height of about 5 nm. The mechanism of this local metal deposition process is interpreted by the electric field-induced initial formation of surface defects (shallow pits) at the HOPG surface as schematically shown in Fig. 6.32. Different metals such as Ag and Cu could be successively deposited by changing the aqueous electrolyte solutions containing Me:& , forming nanometer scale Ag-Cu galvanic cells as shown in Fig. 6.33.

35A

160OA

1200A

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0.4

Figure 6.31 In situ STM image of an Ag nano-disk structure on HOPG in the system HOPG(0001)/ 5 x I F 4 M AgF at T = 298 K (6.1931. ZT = 5 nA and ET - Es = 20 mV. Reprinted by permission of Kluwer Academic Publishers.

6 Metal Deposits and S u ~ a c eStructuring and Modification

306

B

W

-4 100-2oz

1

D

Figure 6.32 Schematic diagram depicting the mechanism of electrochemical metal deposition on graphite surfaces in the scanning tunneling microscope [6.193].Reprinted by permission of Kluwer Academic Publishers.

Similar experiments were carried out in the system HOPG(0001)/10-2 M AgC104 + lo-' M HC104 with varying pulse amplitudes and pulse durations [6.191, 6.1921. It was found that the 3D Ag cluster size strongly depends on the charge amount transferred during the pulse. Minimum cluster sizes with a diameter less than 10 nm and a height less than 2 nm could be formed as shown in Fig. 6.34.

6.4 Sul;face Structuring and Modification

307

Figure 6.33 In situ STM image of Cu and Ag n a n d i s k structures on HOPG in the systems deposited from a 0.5 mM CuSO4 and a 0.5 mM AgF solution, respectively at T = 298 K 16.1931. Reprinted by permission of Kluwer Academic Publishers.

The results in these model systems confirm the introductory expectations that a defined local surface structuring and modification in the nanometer range can be realized by electrochemical means in combination with the inhomogeneous field distribution below the STM tip. However, the two-probe technique substrate-tip requires relatively high tunneling voltages. Attempts are being made to replace the two-probe technique by the conventional three-probe technique to drastically reduce UT.

Figure 6.34 In situ STM images of Ag clusters subsequently deposited on a flat HOPG terrace using two-probe technique and applying tunneling voltage pulses with a high amplitude, UT = ET - Es = 6 V in the system HOPG(OOOl)/lO~zM AgClO4 + 1M HClO4 at T =298 K 16.1921. f~ = 5 nA; Pt-Ir tip.

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6 Metal Deposits and Suflace Structuring and Modilication

HTSC film surfaces First electrochemical studies on structuring and modification of different high Tc superconductor surfaces have recently been started [6.190]. One of the main problems is the instability of oxide ceramic material in neutral and acidic aqueous electrolyte solutions at room temperature [6.196-6.198]. HTSC surfaces corrode, and superconductivity was found to decrease within the topmost layers of HT!X samples after water contact. This aging effect decreases in alkaline media [6.197]. However, sufticient long term stability of HTSC samples was only found in aprotic solvents such as acetonitrile. Therefore, experiments were carried out in acetonitrile-containing tetrabutyl ammonium perchlorate as supporting electrolyte and 3 x M CuOI) acetylacetonate as electroactive species [6.190]. Thin films of YBazCu307-8with 6 I0.5 and BizSrzCaCu208 epitaxially grown on (100) oriented SrTiO3 single crystal faces were used as substrates. The thickness of the HTSC films was about 100 nm. The critical temperatures, T,,were found to be 89 f 2 K for YI3azCu307.6 and 112 2 K for Bi2Sr2CaCu208. Different YBazCu307-8 films either c- or a-b-axis oriented, were studied. Different growth modes of these films depending on the preparation conditions could be observed by in situ AFM as illustrated in Fig. 6.35. The c-axis oriented YBagCu307-~filrnswere grown according to a spiral growth mode pig. 6.35a), whereas the a-b-axis oriented film exhibits an orthogonal polygonized growth mode of 3D crystallites (Fig. 6.35b). The c-axis oriented films showed relatively large atomically flat terraces separated by monatomic steps whereas the a-b-oriented films are less smooth in the nanometer range. 3D Cu crystallites were formed on top of the HTSC surfaces preferentially at crystal imperfections, for example at monatomic steps, by cathodic pulse polarization using relatively high amplitudes in the overpotential range - 400 mV I; 77 I - 100 mV, as illustrated in Fig. 6.36. An analysis of potentiostatic current density transients indicates progressive nucleation and a cluster growth controlled by hemispherical diffusion (cf. Section 6.2), as shown in Fig. 6.37. From the initial part of the transients, the nucleation rate, J, as a function of q was determined. The number of atoms forming the critical nuclei, NCrit = 2, was determined from the slope of the log J vs. 177 I plot in the overpotential range - 210 mV I 77 I - 100 mV. These results show that localized metal deposition under electrochemical conditions using in situ local probe techniques and appropriate polarization routines seems to be realistic.

6.4 &$ace Structuring and Modification

309

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.

-3 00

.

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un

(b)

In situ AFM images of a YBa2Cu307.6 thin film surface c-axis oriented (a) and a-b-axis oriented @)I at AE = 50 mV in the system:YBqCu307.dCH3CN + 0.1 M C16H36C1N04 + 3.3 x l W 3 M [CH3COCH=C(O-)CH3]2Cuat T = 298 K (6.1901.

Figure 6.35

6 Metal Deposits and Suflace Structuring and Modification

310

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0.75 I)n

(b)

Figure 6.36 In situ AFM images of a YBagCu307.6 thin film surface (c-axis oriented) under electrochemical conditions in the system Y B ~ ~ C U ~ O ~ . ~ / C+ H 0.1~ M C NC16H36ClN04 + 3.3 x l o 3 M [CH~COCH=C(O-)CH~]~CU at T =298 K I6.1901. (a): Before; (b): after copper deposition.

6.4 Sul;faceStructuring and Modification -24

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0

40

0

16

24

32

40

40

t Is1

Figure 6.37Current density transients for Cu OPD on YBa2Cu307-6 thin film (c-axis oriented) in the system YBa2Cu307.dCH3CN + 0.1 M C16H36ClN04 + 3.3 x lW3 M [CH3COCH=C(O)CH3]2Cu at T =298 K L6.1901. (a): Current density transients; (b): ifree 213 vs. tplots of the transients shown in (a).

Semiconductor single crystal surfaces Early experiments aimed at localized metal deposition on semiconductor surfaces were carried out by Hartnagel et al. in the system n-GaAs/commercial KAu(CN)2 solution using a simple two-probe technique without potentiostatic control [6.199]. At very

6 Metal Deposits and Suflace Structuring and Modt2cation

312

c

Figure 6.38 Au dots deposited on ~ G A byS localized STM tipinduced photoelectrodeposition from an acidic gold cyanide solution [6.200].

high voltages between the substrate and a moving needle electrode, localized metal deposition in form of lines in the micrometer range was achieved. These experiments demonstrate the possibility of "direct writing" by electrochemical means. On semiconductor substrates, light illumination is an additional parameter which influences the metal deposition process. Lindsay et al. [6.200] used light-assisted gold deposition on n- and p G a A s surfaces to form nanodots. The tip was retracted from the substrate by a few tens of nm and its potential was pulsed anodically by ET + 4 V. On p G a A s , Au dots with a diameter in the range 100 nm < d < 1 pm and unknown height were obtained as shown in Fig. 6.38. The mechanism of metal deposition involves a screening of the positive charge on the tip by formation of a local depletion layer in the p G a A s substrate (decreasing of the band-bending). In contrast, on nGaAs the procedure leads to local corrosion of the semiconductor surface under the tip.

Further experiments are necessary to study tipinduced local electrochemical reactions on semiconductor surfaces in order to form defined metallic surface structures for nanoelectronic applications.

6.5

Conclusions

Previously, compact 3D Me deposits could be classified only phenomenologically on the basis of structural and morphological properties. Later, macroscopic theories were developed to understand 3D Me phase formation and growth. However, the initial stages of 3D Me phase formation were found strongly to depend on atomistic

6.5 Conclusions

313

properties of the substrate and the deposit as discussed in the foregoing chapters. Therefore, the initial stages of 3D Me deposition and their phenomenological classification can only be connected on the basis of an atomistic interpretation level. This knowledge can be applied for the preparation of ultrathin metal films and heterostructures as well as for the local structuring and modification of electron conducting solid state surfaces in the nanometer range.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

7 Outlook

This book shows that the initial stages of 2D and 3D metal phase formation under electrochemical conditions are, in general, well developed and understood on an atomic level. The knowledge of the substrate surface properties is necessary for a well-defined preparation of 2D and 3D metal phases, surface alloys, ultrathin films, and heterostructures. The structural and epitaxial behavior of metal deposits determines their physical and chemical properties. Although experimental observations on an atomic level are state-of-the-art using in situ local probe techniques, theoretical considerations, particularly involving atomic forces of interaction, can only be considered as semi-quantitative at present. A further development of theories and corresponding experiments on an atomic level is needed, particularly for a full understanding of the processes required for the formation of ultrathin films, surface alloys, heterostructures, and custom tailored metal deposits. In future, in situ and direct surface structuring and modification of metals, superconductors, and semiconductors in the nanometer range can be invisaged.

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

8 Appendices

8.1

Compilation of Experimentally Studied Me-S(hkl) Systems

Substrate S

Metal S Me orientation

(M)

Cd

t. ..I

.***

(111)

Propylene carbonate Tetra-n-butylammonium perchlorate Tetrahydrofuran Dimethoxyethane ~

Electrolyte

References

UPD

8 Appendices

318

Substrate Metal S Me

S orientation

Electrolyte

References

(hw Ag

Pb

(100)

H', CH3COO-

I651 [I21 110-13, 15, 19, 22, 27, 31, 60, 611 [I21

H', C10, H', ClO;, IH', SO-: H', SO:-, C10[ H', C1H', CH3COOC6H50:H', C10, H', ClO,, IH', SO,-: C1Oc H', C1H', C10, H', ClO;, IH', SO:-, C1Oc H', C1H', CE, H', SO-: H', NO; H', CH3COOH', ClO,

12, 22, 23, 31, 45, 66-70] [691 [6, 71-74] [lo, 14, 16-18, 22, 68, 75, 761 [66,771 [el 161 122, 31, 66-691 [691 [lo, 16, 17, 22, 61, 751 [66, 77, 781 166,691 [691 [lo, 61, 751 [66,771 [2, 46-50,79471 [80-82,8&92] [80-82] [81,821 146-50, 83,931

(100) (110)

H', ClO, H', SO-: H', NO< H', C10, H', C10;

[2, 27,31, 81,94-1001 [991 [991 [27, 31,94,971 127, 31,94,971

(111)

H', ClO,

[2, 7,40, 47, 831

[101, 1021 [91

(100) (110)

H', 50:PC',TBAP**, LiClO, H', SO:H', SO$

(110)

Tl

(111)

(100)

(110)

Au

Ag

(111)

(100) Bi

Cd

H', C1H', CH3COOH', ClO,

(111)

[101,1021 [101,1021

8.1 Compilation of Experimentally Studied Me-S(hk1) UPD Systems

Substrate S

Metal S Me orientation

Electrolyte

319

References

(hkl) Au

cu

(111)

(100) (110)

Hg

AU

(111)

H', C10, H', ClOi-, C1H', SO-:

[2, 11, 80, 94, 103-111, 2441 11121

H', H', H', H', H', H', H', H',

SO,"-, SO,"-, SO,"-, NO; C10, SO,"ClO, SO:-,

245,2461 [128, 129, 1411 [I291 [I291 1801 [ l l , 94, 1031 [120,122,2471 i l l , 941 [2481

H', H', H', H',

C10,

C1BrI-

C10;

SO,"-

NO; CH3COO-

[80,105,106,109,113-140,

[82,143-1461 [823 [82, 1471 [a21

Ni

(100)

H', SO,"-

11421

Pb

(111)

H', C10,

(100)

PC*,TBAP", LlCll)P, THF , LiC104 DME*"', b c i o 4 H', C1Oc

[2, 9, 22, 27, 31, 40, 83, 88, 94, 97,98,14&1583 [91

(110)

H', ClO,

[22, 27, 31, 83, 94, 97, 148153, 159, 1601 [22, 27, 31,94,97, 148-1531

Sb

(111) (100) (110)

H', ClO, H', C10; H', C10;

[941 1941 1941

Te

(111) (100) (110)

H', SO,"H', SO:H', SO-:

[101, 102, 1611 [lOl, 102,1611 [101, 102, 1611

T1

(111)

H', ClO, H', SO$

[31,94,162-1641 1881

[91

pi

320

8 Appendices

Substrate Metal S S Me orientation

Au

Tl

Zn

Bi

cu

cs Cd

(111) (100) (110) (111) (100) (110) (111) (110) (211) (111)

(100) (110)

Pb

(111)

(100)

(110)

Pd

Tl cu

(111) (111) (100)

Pt

Ag

(111)

(100)

Electrolyte

OHH', C1Oc H', SO,"H', ClO, H', ClOL, C1H', ClO:, ClH', ClO,, ClEthanol Ethanol Ethanol H', C10, H', SO,"H', SO,"H', SO,"-

References

[1661 [1671

[1671 [1671 [1681

H', ClO, H', CIO;, CHSCOOH', NO; H', ClOL, CH&OO-, ClH', SO:H', ClO;, CH3CO0H', ClO,, CH3COO-

[ 171-173,2501

H', H', H', H', H',

SO,"-

[ 176-1781

C1Oc C10,

D791

SO,"-

[1801

C10, H', SO-: H', ClO,, SO,"H', C10,

[173, 1741 [172, 1751 [1731

[1761 [1741

D741

[181,182,2511

H', SO,"H', ClO,, SO-:

Bi

(110)

H', SO,"-

(111)

H', ClO,

[ 193-1961

8.1 Compilation of hkperintentally Studied MeS(hk1) UPD Systems

Substrate S

Metal

Pt

Bi

Pt

cu

(100) (110) (111)

pt

cu

(100)

Me

(110)

Pb

(111)

(100) (110)

Tl

Rh

Electrolyte

S orientation

H', C10; H', C10; H', C10; H', SO:H', F H', SO,"-, ClH', SO?-, BrH+, SO^-, IH', CIOL H', SO,"

References

H', F

[193-1961 [ 193-1951 [197-203, 2521 [197,202, 204218,253, 2541 [202, 203, 2191 [129, 213, 220, 2211 [I291 [I291 (197, 202, 203,222,2231 [197, 202, 204, 206, 207, 214, 215,224,2251 [202, 203, 2191 [220,221] [226, 2271 [204,205, 207,214, 215, 226, 2551 [2191

H', H', H', H', H', H', H',

ClO,

[194,228-2331 [2291 [2341 [2351 [194, 228-231, 2361 12291 1194,226, 228,2311

C10, C10, C10, C1Oc SO,"-, ClO,

[194, 238, 2561 [I941 [I941 [2391 [239]

H', H', H', H',

F SO,"-, C1ClO, SO:-

C10,

F C1Br-, C10;

F

(111) (100) (110) (111)

H', H', H', H', H',

cu

(111) (100) (110)

H', ClO, H', ClO, H', ClO,

[2401 [2401 P401

Pb

(111) (100)

H', C10, H', C10,

12401 12401

Ag

321

322

8 Appendices

Substrate Metal S S Me orientation

Rh

Electrolyte

References

Pb

(110)

H', ClO;

12401

Pt

(100)

H', SO-:

12411

References to Appendix 8.1 1

2 3

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

J.W. Schultze, K.R. Brenske,]. Electroanul. Chem. 1 9 8 2 , 137,331. F.M. Romero. R1. Tucceri, D. Posadas, Sutf Sci. 1988,203,186. M.F.Toney, J.G. Gordon, M.G. Samant, G.L. Borges, U.R. Melroy, D. Yce, L.B. Sorensen, Langmuir 1 9 9 1 , 7, 796. H. Bort, K. Jiittner, W.J. Lorenz, G. Staikov, Electrochim. Actu 1983,28,993. J. Miragliotta, T.E. Furtak, Phys. Rev. B 1988,37,1028. V.D. Jovic, B.M. Jovic, A.R. Despic,]. Electroanul. Chem. 1990,288,229. X. Xing,D.A. Scherson, C. Mak.]. Electrochem. Soc. 1990,137,2166. X. Xing, P. Abel, R. McIntyre, D.A. Scherson,]. Electrounul. Chem. 1987,216,261. X. Xing, I. Tae Bae. D.A. Scherson, Electrochim.Acfu 1995,40,29. A. Bewick, B. Thomas,J Electroanul. Chem. 1 9 7 6 , 70,239. D. Dickertmann, F.D. Koppitz, J.W. Schultze, Electrochim. Actu 1976,21,967. A. Bewick, B. Thomas,]. Elecfrounal. Chem. 1977,84,127. A. Bewick, B. Thomas,]. Electroanul. Chem. 1977,85,329. K. Jiittner, G. Staikov, W.J. Lorenz, E. Schmidt,]. Electrounul. Chem. 1977.80,67. W.J. Lorenz, E. Schmidt, G. Staikov, H. Bort, Furuduy Symp. 1977,12,14. G . Staikov, K. Jiittner, W.J. Lorenz, E. Budevski, Electrochim. Actu 1978,23,319. K. Jiittner, W.J. Lorenz, G. Staikov, E. Budevski, Elecfrochim.Actu 1978,23,741. G. Staikov, K. Jiittner, W.J. Lorenz, E. Schmidt, Electrochim. Actu 1978,23,305. H. Bort, K. Jiittner, W.J. Lorenz, E. Schmidt,]. Electrourul. Chem. 1979,90,413. H. Siegenthaler, K. Jiittner, Electrochim. Actu 1979,24,109. K. Takayanagi, D.M. Kolb, K. Kambe, G. Lehmpfuhl, S u d Sci. 1980,100.407. K. Jiittner, W.J. Lorenz, Z. Phys. Chem. NF 1980,122,163 E. Schmidt, H. Siegenthaler,]. E6ectroanul. Chem. 1 9 8 3 , 150, 59. H. Bort, K. Jiittner, W.J. Lorenz, G. Staikov, E. Budevski, Electrochim. Actu 1983,28,985. RL. Deutscher, S. Fletcher,]. Electrounul. Chem. 1983,153,67. J.N. Jovicevic, V.D. Jovic, A.R. Despic, Electrochim. Actu 1984,29, 1625. K. JIittner, Electrochim. Acfu 1984,29,1597. V.D.Jovic, J.N. Jovicevic, A.R. Despic, Electrochim. Actu 1985,30, 1455. J.C. Farmer, R.H. Muller,]. Electrochem. Soc. 1985,132,39. T. Vitanov, A. Popov, G. Staikov, E. Budevski, W.J. Lorenz, E. Schmidt, Electrochim. Actu 1986,31,981. K. Jiittner, Electrochim. Actu 1986,31,917. A. Popov, N. Dimitrov, 0. Velev, T. Viatnov, E. Budevski, E. Schmidt, H. Siegenthaler, Electrochim. Actu 1989,34,265. G. Staikov, E. Budevski, W. Obretenov, K. Jiittner, W. J. Lorenz, Surf Sci. 1991,248,234. N. Dimitrov, A. Popov, D. Kashchiev, T. Vitanov, E. Budevski, Electrochim. Actu 1991,36,1259. N . Dimitrov, A. Popov, T. Vitanov, E. Budevski, Electrochim.Actu 1991,36,2077. M. Hopfner, W. Obretenov, K, Jiittner, W.J. Lorenz, G. Staikov. V. Bostanov, E. Budevski, Sud Sci. 1 9 9 1 , 248,225. W.J. Inrenz, L M . Gassa, U. Schmidt, W. Obretenov, G. Staikov. V. Bostanov, E. Budevski. Electrochim. Actu 1992,37,2173. W. Obretenov, U. Schmidt, W.J. Lorem, G. Staikov, E. Budevski, D. Carnal, U.Miiller, H. Siegenthaler, E. Schmidt, FuruduyDisc. 1992,94,107.

8.1 Compilation of Experimentally Studied MeS(hk1) UPD Systems 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

323

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8 Appendices 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131

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8.1 Compilation of Experimentally Studied Me-S(hk1) UPD Systems 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187

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326 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239

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8.2 Thermodynamics of an Ideally Polarizable Electrode 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256

8.2

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Thermodynamics of an Ideally Polarizable Electrode

According to Schmidt [8.1],let us consider an electrochemical system with an ideally polarizable substrate, S, and a reversible X/X* reference electrode (Fig. 8.1). The system consists of the inert substrate phase (S), an electrolyte phase (El), the interphase (IP) and a reference electrode (RE). The components (z] of this system in the different phases 0') are substrate cations (S?, electrons (e- ), solvent 0 ,dissolved cations @?) and (Me"), as well as anions (X- ). This system is a composite system consisting of different subsystems (phases j ) .

Substrate (S)

lnterphase UP)

s+. .s+

Electrolyte (El)

I

Me':

t

I

K+

+ K'

: I I

e-.

e-

II

X'

Reference Electrode (RE)

Me'+ X-IX'

Me2

-

X'

; w + *w I

Figure 8.1 Phase scheme of an electrochemical system containing an ideally polarizable substrate (S), contacted by the metal Mel, electrolyte (El) containing Me:&, , K', R ions, and solvent W, the interphase (IP) between (S) and (El), and a X-/X*-reversible reference electrode (RE), which is in contact with the metal Me2, to derive the electrochemical equilibrium conditions for IP.Me1 and Me2 are chemically identical Me.

8 Appendices

328

Each subsystem is thermodynamically described by a fundamental equation in the energy representation

where the inner energy, U,is a function of the following extensive parameters: entropy, S, volume, V , area of interface, A (A = 0 for ( j ) f (IP)), and mole numbers of charged and uncharged components, Nj. The total differential of d3)is given by

where the intensive parameters T, P, D, and Ei denote temperature, pressure, specific surface energy, and electrochemical potential, respectively. The electrochemical potential within a phase j is defined by:

with the Galvani or inner potential @(j). For T, V = constant, the system is better described by the free energy, F, which represents the following partial Legendre transform U[flof U [8.2]:

The total differential of F ( j ) is given by

MCi) = - s(i)dT(i) - p(i)dV(i) +

,(IP)u(IP)

+

cj-$i)w!i, I

(8.5)

r

For T, P = constant, the Gibbs energy or Gibbs function, G, representing another partial Legendre transform of U,is properly used:

The total differential of G ( j ) is given by

Introducing the enthalpy as another partial Legendre transform of U

8.2 Thermodynamicsof an Ideally Polarizable Electrode

329

(8.8) one obtains by combining eqs. (8.6) and (8.8)

The total Gibbs energy of a composite system is given by the sum of the Gibbs energies of the subsystems (phases):

G = cG(j) i

(8.10)

At constant T and P,the total differentials of the Gibbs energy, dG@,for both bulk phases j = S, El and that of the Gibbs energy, dGoP),for the interphase j = IP, are given bY

i

(8.11)

Using the Euler equations for G")

i

(8.12) i

and combining their total differentials with the corresponding eqs. of (8.11), one gets the Gibbs-Duhem equations for the different phases i:

(i = S+,e-) (8.13)

330

8 Appendices

An electrochemical equilibrium within a phase j , e.g., reaction in eq. (3.2) with /2=1

is according to eq. (8.11) withA = const. given by

(8.14) The electrochemical equilibrium between two ambient phases can be derived from eq. (8.11). ForA = constant, one obtains:

(i = s+, e-) (i = W, K',X, Me" )

(8.15)

The electroneutrality within each phase j = S, El , IP requires:

(8.16)

Combining eqs. (8.13)-(8.16) through elimination of N("), N(E'),and d,dEDyields:

x-

x-

W

8.2 Thermodynamicsof an Ideally Polarizable Electrode

331

The following expressions will be introduced:

dj$ED

MeZ+

ii)

+zd~(El= ) dP M (El)d ,

MeXz dissolved in (El)

X-

(8.17a)

d&(El) - dp6) = dEmeZ) - di;yel) = F e

x-

e-

(8.17b)

e

e-

The electrode potential E = A E E i i # = #OMel) - #OMez) denotes the Galvani potential difference vs. a reversible X/X* reference electrode with the following redox reaction:

X(E1)

+

X*(EI) + e-(Mez)

with p(E1) x* -- constant. The electrochemical equilibrium analogous to eq. (8.15) gives d z y = d j i ~ e 2 ) . A change of the electrode potential measured vs. the constant Galvani potential of the reference electrode is:

a = d#OMel)for d#(Me2)

= 0.

(8.17~)

fi(w represents the relative surface excess concentration of particles i = K', X, Me" with respect to the reference component i = W (solvent).

q represents the relative specific ionic surface charge.

Combining eqs. (8.12) and (8.17), Gibbs adsorption isotherm is derived:

which

represents the total p(ED , &$) with

CT = 0 (E,

Ma,

T K + ( W ) dpKx (ED -

qdE

differential of

the

(8.18)

specific

surface

energy

332

8 Appendices

(8.19)

These relative surface excess parameters can be determined experimentally using different methods: can be determined by radiotracer studies, o-measurements, electroanalytical techniques (twin-electrode thin-layer, flow-through thin layer, rotating ring-disk experiments) etc., whereas q can be determined by charging curves, capacitance measurements etc. Isotherm conversion q-co is obtained by the corresponding Maxwell relations: (8.20)

Conclusions: i)

A thermodynamically defined relative surface excess may be assigned to independent system components i only.

ii) The relative surface excess concentration rather than the absolute surface concentration of a given species i arises as the thermodynamically relevant parameter of interphase composition, iii) The relative surface excess concentration of a given species i is

- invariant to the position of the interphase/electrolyte boundary as long as it is not shifted into the region of non-vanishing potential gradients,

-

the natural balance parameter of adsorption/desorption experiments.

iv) The relative surface excess concentration of a given species i is

- easily split into diffuse and compact double layer contributions: Tim (diffuse) + l-j(w, (compact),

=

8.3 Mean Field Theory and Adsorption I s o t h e m

333

- close to the absolute surface concentration of the species i in the compact E f i (compact), for trace layer (Lea,specifically adsorbed) contribution, components of i in solutions with an excess of supporting electrolyte.

8.3

Mean Field Theory and Adsorption Isotherms

Under electrochemical conditions and T,P = constant, adsorption isotherms can be derived using standard statistical considerations to calculate the Gibbs energy of the adsorbate in the interphase and the equilibrium condition for the electrochemical potentials of the adsorbed species i in the electrolyte and in the adsorbed state (eq. (8.15) in Section 8.2). A model for the statistical considerations consists of a 2D lattice of arbitrary geometry with Ns adsorption sites per unit area. In the case of a 1/1 adsorption, each adsorbed particle can occupy only one adsorption site so that the maximal number of adsorbed particles per unit area in the compact monolayer is determined by Nma = Ns. Then, this model corresponds to the simple king model. The number of adsorbed particles, Nads, and the number of unoccupied adsorption sites, No, per unit area are given by

(8.21)

where 8 and (1 - 0) represent the probabilities for an adsorption site to be occupied and unoccupied, respectively. Normally, B is denoted as the degree of coverage in adsorption processes. The contribution of Me& to the Gibbs energy of the adsorbate in the interphase is given by (cf. Section 8.2): (8.22)

To find the exact dependence of Hads on B, different contributions have to be taken into account. According to the so-called mean field approximation [8.3, 8.41, this dependence is given by (8.23)

8 Appendices

334

where Ho,ads and Ha& are the enthalpies of unoccupied and occupied adsorption sites, c represents the number of first nearest neighbors in the compact monolayer given by the symmetry of the 2D adsorption site lattice, Y M ~ corresponds ~ ~ ~to the- lateral ~ ~ interaction energy per bond Meads-Meads (positive for attraction and negative for repulsion), and h~ is the thermal term of H$!ads , The configurational entropy term, S,, is determined in the microcanonical formalism according to Boltzmann:

(8.24) The thermal entropy term, ST,is given by

where A is the substrate area and ST denotes the thermal entropy of Meads. Using the Stirling approximation, In (x!) x In x - x, and eqs. (8.21), (8.24), and (8.25), one gets for the total entropy of the adsorbate, ; I :

Sgids

Sg\ds= S,+ ST =-k N,A[ Qln Q + (1-9 In (1-91 + N , A e q Combining eqs. (8.22), (8.23), and (8.26), one obtains G$:d8 differentiated with respect to Nads giving pop) (8.8) in Section 8.2),

,ug)ads is given by:

Meads

(8.26) which can be

. On the other hand (cf. eqs. (8.7) and

(8.27)

(cf. Section 8.2) and a Introducing the electrode potential E instead of reference state E = E* for Q = 0.5, one obtains the following adsorption isotherm: (8.28) with w =

VMeads-Meads

kT

~

~

8.4 Monte Carlo Simulation of l / n AdsorPtion

335

Monte Carlo Simulation of l/nAdsorption

8.4

As an example, 1/2 adsorption on a square lattice is discussed. The corresponding simulation model is shown schematically in Fig. 8.2 [8.3, 8.51. In this case each adatom occupies only one adsorption site but blocks neighboring sites, thereby not allowing their occupation by other adatoms. A 2D lattice with 40 x 40 adsorption sites is used as substrate, and periodic boundary conditions are imposed to eliminate edge effects. The elementary frequencies of single atom adsorption (kt ) and desorption (kj- ) are defined by the expressions: exp @,

if the site is free if the site is occupied or blocked

(8.29)

and

(8.30) with

p=

ZF RT

- - (a-AE*)

(8.31)

and

k,

=

'o,S/MeZ+

(AE= AE*)O N , ZF

(8.32)

where j is the actual number of nearest neighbors of the adatom, c is the number of nearest neighbors of an adatom in the compact Me overlayer, O is the area of an adsorption site, and io,S,MeZ+ is the exchange current density at the reference underpotential AE* which corresponds to a degree of monolayer coverage 0 = 0.5 (cf. eqs. 3.18-3.20). The lateral interaction parameter, u, is related to the interaction energy, WMead,-Mead, by = ~MMeads-Meads / kT * A typical adlayer structure obtained by the Monte Carlo simulation of 1/2 adsorption on a square lattice is shown in Fig. 8.3. As can be seen, two domains with completely ordered structure are separated by a mismatch boundary. The sublattices corresponding to these domains may be illustrated by the nets of white and black fields on a chess-board.

8 Appendices

336

h

A

h

Figure 8.2 Empty (@),blocked (8)and occupied (0)adsorption sites in case of 1/2 adsorption on a square lattice.

The simulation adsorption isotherms for 1/2 adsorption on a square lattice at different values of the interaction parameter o are shown in Fig. 8.4. The interaction energy, Y ~ ~ ~, can~ be,evaluated - ~ using ~ ~ a fit ~ of ,experimental isotherm data of a Me UPD system with 1/2 adsorption on a square lattice.

F i r e 8.3 Structure of an adsorbed monolayer at 0 = N,ds/Nmax = T/Tm, = 0.8 (cf. eq. (8.21)) ~ ~ obtained by Monte Carlo simulation for 1/2 adsorption on a square lattice at o = ~ M ~ , /(M) = 1.0 and p = 0.7 [8.3]. Two ordered domains with a S(100)42 x 2) overlayer structure, which are separated by a mismatch boundary, are clearly seen.

M

~

~

8.5 Transfer Function ofMe UPD on Inhomogeneous Substrate Sulfaces

33 7

10

0

0.5

0 -2

-1

0

1

2

P orption isotherms for 1/2 adsorption on a square lattice obtained by -.-mte Carlo Figure 8.. simulation [8.3]. w = 2.0 (0);1.6 ( X ) ; 1.4 ( A ) ; 1 . 2 0 ; 1.0 (0); 0.8 (0); 0.6 (+); O (+).

A similar Monte Carlo simulation can be used for l / n adsorption with n 2 1on any regular lattice of adsorption sites [8.3,8.6].

8.5

Transfer Function of Me UPD on Inhomogeneous Substrate Surfaces

The derivation of the transfer function of a kinetic model including surface inhomogeneities, gradients of Meads, and surface diffusion is described [8.7-8.91. The substrate surface is assumed to consist of domains with atomically flat terraces with a mean width of x = 2&, separated by line discontinuities, i.e., monatomic steps (Fig. 3.40). For simplicity, a periodic arrangement of these surface domains with identical thermodynamic and kinetic properties and a linear transport geometry are suggested. Me": bulk diffusion is neglected. at line Three different fluxes are assumed: charge transfer of Me": discontinuities, J(x = 0), charge transfer of at terraces (0 < x < &step), j ( x ) , and superimposed surface diffusion of Meads,jsd. At x = &tep, the model system is free of r gradients and, therefore, closed with respect to all fluxes.

8 Appendices

338

The local and time deviation of the relative surface excess, Anx, t), from the initial value fi is described by the following: (8.33)

with the following boundary conditions Anx,t) = 0 J ( X = 0)

+ Dsd

am,

ti = 0 b

fort = 0

(initial equilibrium)

(8.34)

for x = 0

(continuitiy at x = 0)

(8.35)

for x =

(close condition at x = &ep) (8.36)

&tep

where the fluxesj(x) and J(x = 0) in the absence of Me:& bulk diffusion are given by

and (8.38)

Dsd is the surface diffusion coefficient of Meads and Rdt denotes the charge transfer resistance at line discontinuities at x = 0. This system of differential equations differs in boundary condition (8.33) from the well-known adatom diffusion model of Me deposition on native substrate [8.10-8.12]. Principally, it allows A r t 0 be described as a function of x and t. The relation between A 4 4, and the “local“ cathodic current density in the range 0 < x I Sstep, i(x), is given bY (8.39) (8.40) The mean current density of the entire domain, i, is given by (8.41)

8.6 Thermodynamics of a 30 Me-S Bulk Alloy Electrode

339

Solution of the differential equation system (eqs. (8.31)-(8.39)) using Laplace transformation yields:

(8.42) with

1

A =

(8.43)

Rct Cads

(8.44) and

(8.45) The capacity parameters, cdl = -

(g)

c d l and Cads,

are defined by

(double layer capacity)

(8.46)

(adsorption capacity)

(8.47)

f

and Cads =

-yF(g) P

The transfer resistances, Rct and Rdt, for charge transfer on terraces and at line discontinuities, respectively, are related to the corresponding Met&, flux densities, i(x) and& = 0), by eqs. (8.37) and (8.38) (cf. [8.9, 8.131 and eq. (3.41)).

8.6

Thermodynamics of a 3D M e 4 Bulk Alloy Electrode

According to Schmidt and Wuthrich [8.1, 8.141, let us consider an electrochemical system with a 3D Me-S bulk alloy electrode and a reversible X/X* reference electrode (Fig. 8.5). The system consists of the inert substrate phase (S), the 3D Me-S bulk alloy phase, an electrolyte phase (El), the interphase (IP), and the reference electrode (RE). The components (2)’ of this system in the different phases are substrate dissolved cations (K‘) and (Me”), as well as cations (S?, electrons ( e - ) ,solvent 0,

8 Appendices

340

-Me,

S

Me-S

El (Me")

Figure 8.5 Phase scheme of an electrochemical system containing substrate (S) being in contact with metal Mel, 3D metal-substrate bulk alloy (Me-S), electrolyte (El) with Met&, and metal Me2 to derive the electrochemical equilibriumconditions for 3D M e S bulk alloy phase and 3D Me bulk phase. Me1 and Me2 are chemically identical metals Me.

anions (X). Dissolved Me:& cations are assumed to be in equilibrium with MeZ' in the interphase and in the 3D Me-S bulk alloy phase. Therefore, MeZ+in the 3D Me-S bulk alloy phase is not an independent variable. Such a composite system is thermodynamically described by a formalism similar to that given in Section 8.2. The necessary changes will be mentioned in the following using the notation of corresponding equations in Section 8.2. The Gibbs-Duhem equation for a 3D Me-S phase (cf. eq. (8.11)) must be replaced by:

(8.48) The electrochemical equilibria between Me-S and the interphase and S and Me-S (cf. eq. (8.15)) are given by:

(i = e-)

(8.49)

Electroneutrality within a 3D Me-S phase (cf. eq. (8.16)) requires (8.50) Eq. (8.17) has to be replaced by

8.6 Thermodynamicsof a 30 Me-S Bulk Alloy Electrode

341

and q and in eqs. (8.17~)and (8.17d), The relative surface excess quantities, TMeZ+(W) respectively, are given by:

represents the relative surface excess concentration of Me" rMez+ ( W) with respect to the reference component W (solvent).

(8.51d) q represents the relative specific ionic surface charge.

The Gibbs adsorption isotherm corresponds to eq. (8.18) in Section 8.2

and q in eq. (8.51~)and eq. taking into account the different definitions of TMeZ+(W) (8.51d) compared to those in eqs. (8.17~)and (8.17d), respectively.

8Appendices

342

8.7

Instantaneous and Progressive Nucleation

Generally, the process of nucleation in electrodeposition of metals can be considered as occuring on ideal or real substrates. Ideal substrates are considered free of crystal imperfections and are characterized by an atomically smooth, homogeneous surface which does not exhibit preferred nucleation sites. On such substrates the number of nucleation sites, Z,, is equal to the number of adsorption sites Ns (cf. Section 8.3). Nucleation on real crystal substrates usually occurs at preferred sites (z, < Ns). The number of these active sites depends on the degree of perfection of the substrate. The nucleation process on a substrate with a fKed number, Z,, of randomly distributed, equally active sites is described by a first order law [8.111: (8.53) where Znu,(t) denotes the number of nuclei or the number of nucleation sites converted to nuclei at time t and Tnuc is the mean nucleation time. For the initial time range, eq. (8.53) gives two limiting cases: (i) If T n , is very small, all nucleation sites 2, are converted to nuclei virtually instantaneously: (8.54) This case is known as instantaneous nucleation. The corresponding nucleation rate can be expressed by (8.55) with 6(t) being the Dirac delta function. (ii)

For relatively high values of 7 , eq. (8.53) can be linearized to

t & l u c ( t ) = 2, r

(8.56)

7nuc

and the active sites are converted to nuclei progressively with time. Therefore, this process is called progressive nucleation, with a nucleation rate given by

Electrochemical Phase Formation and Growth E. Budevski, G. Staikov & W J. Lorenz 0 VCH Verlagsgesellschaft mbH, 1996

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10 Abbreviations and Symbols 10.1

Abbreviations

OD 1D

onedimensional

2D

two-dimensional

3D

three-dimensional

ac

alternating current

AES

Auger electron spectroscopy

AFM

atomic force microscopy

CVD

chemical vapor deposition

dc

direct current

DTS

distance tunneling spectroscopy

EIS

electrochemical impedance spectroscopy

El

electrolyte

EXAFS

extended X-ray absorption fine structure

fcc

face centered cubic

FlTL GIXS

flow-through thin layer technique

GSSP

galvanostatic small signal pulse polarization

hCP

hexagonal close-packed

(hk0

Miller indices of crystallographic surface orientation

[hkll