Electrochimica Acta 45(2000)2559–2574
Electrocrystallization
Nucleation and growth phenomena
E.Budevski a,*,G.Staikov b ,W.J.Lorenz c
a
Central Laboratory of Electrochemical Power Sources ,Bulgarian Academy of Sciences ,Sofia 1113,Bulgaria
b
Institute of Physical Chemistry and Electrochemistry ,Uni 6ersity of Du ¨sldorf ,Uni 6ersita ¨tsstr .1,D -40225,Du ¨sldorf ,Germany
c
Institute of Nanotechnology ,Uni 6ersity of Karlsruhe ,Kairstr .12,D -76131,Du ¨sldorf ,Germany
Papers received in Newcastle,20December 1999
Abstract
A review of the prent status of the problem of metal deposition and electrochemical pha formation and growth
is made.The historical background of the problem is given with an overview of the major contributions of different electrochemical schools.Pha formation is treated in classical and atomistic terms.Some of the basic conquences of the theory concerning the equilibrium form,the influence of the substrate,the size-overpotential dependence of low-dimensional systems,and the nucleation kinetics are discusd.The basic modes of crystal growth under electrochemical conditions are described.The influence of substrate surface modification in the UPD region concerning the formation of low dimensional phas and their stability ranges are discusd.The development of recent in situ techniques for nanostructuring and nanomodification of solid surfaces and their importance for electrochemical nanotechnologies are also shortly prented.©2000Elvier Science Ltd.All rights rerved.
Keywords :Electrodeposition;Nucleation;Crystal growth;Substrate supported nanosystems;Thermodynamics and stability ranges of low-dimensional phas;Electrochemical nanostructuring
www.elvier.nl /locate /electacta
1.Historical background
考研要求条件
Electrochemical metal deposition is one of the oldest subjects within the framework of electrochemistry.Metal electrodeposition takes place at electrode /elec-trolyte interfaces under the influence of an electric field and include a number of pha formation phenomena.A typical electrochemical metal deposition process which has been attracting the attention of both scien-tists and engineers for a long time is the electrocrystallization.
First experimental studies on electrodeposition of metals date back to the beginning of the 19th century and were carried out using galvanic cells as sources of direct current.After the introduction of electric genera-tors electroplating had become soon of great technolog-ical importance and was ud for production of
different decorative and functional coatings.In spite of this early beginning,however,the electroplating tech-nology was developed and optimized on a purely em-pirical basis for a long time.
Fundamental aspects of electrocrystallization of metals are directly related to the problems of nuclea
tion and crystal growth.The basic thermodynamic concepts of nucleation and crystal growth were formulated in 1878by Gibbs in his remarkable study ‘On the Equi-librium of Heterogeneous Systems’[1].In the beginning of the 20th century the concepts were developed by Volmer [2–5],Kosl [6],Stranski [7],Stranski and Kaischew [8,9]and Becker and Do ¨ring [10]by introduc-ing statistical and molecular-kinetic approaches.Ac-cording to the early theories a nucleation step is required not only for the formation of a new crystal (three-dimensional nucleation)but also for the growth of a perfect singular crystal face by formation of new layers (two-dimensional nucleation).An important con-
*Corresponding author.
E.Bude6ski et al./Electrochimica Acta45(2000)2559–2574 2560
tribution to the theory of crystallization kinetics was made by Avrami[11],who considered the collision and overlap of the growing centers in the process of multiple nucleation and growth.In1949Frank[12] showed that at low supersaturations the growth of a singular crystal face intercted by screw-dislocations can occur without two-dimensional(2D)nucleation according to a spiral growth mechanism.The quantita-tive theory of the spiral growth was developed by Burton,Cabr
era and Frank[13]taking into account the role of surface diffusion of adatoms in the growth process.Stranski and Krastanov[14]were thefirst to show that the epitaxial growth on a foreign substrate can occur by a mechanism including formation of isolated three-dimensional(3D)islands on top of v-eral predeposited monolayers.A significant advance in the development of the theory of epitaxy was made by Frank and van der Merwe[15]who considered the influence of crystallographic substrate-deposit misfit on the orientation and growth of epitaxialfilms.
The general theoretical concepts of nucleation and crystal growth described above have been successfully applied to electrocrystallization.In fact the fundamen-tal rearch on electrocrystallization of metals started with the work of Max Volmer and his school during the 1920’s and30’s[3–5,16,17].Erdey-Gruz and Volmer [17]were thefirst who recognized the formal relation-ship between the supersaturation(as a driving force of the crystallization from the vapor)and the overpoten-tial(as a driving force of electrocrystallization)and derived relations between the steady-state current den-sity and overpotential for the cas of electrocrystalliza-tion controlled by charge transfer,2D nucleation and 3D nucleation.Subquently the role of the overpoten-tial and current density in the electrochemical nucle-ation and crystal growth was investigated experimentally in various systems by Erdey-Gruz et al.
[18].
In the1930’s and1940’s Finch and his school[19,20] made extensive experimental studies on polycrystalline electrodeposits and collected important information about the factors determining the degree of orientation and the texture of metalfilms.In the same period Gorbunova et al.[21–23]investigated the influence of the substrate and electrolyte composition on the pro-cess of electrocrystallization using single crystal sub-strates and reported a formation and growth of metal whiskers induced by the adsorption of organic additives for thefirst time[23].
An important contribution to the theory was made in 1945by Kaischew[24],who applied a molecular-kinetic approach to electrocrystallization considering the fre-quencies of attachment and detachment of metal atoms at different sites of a crystal surface.This work had a great impact on the further concepts of electrochemical pha formation and growth.
The period of the1950’s is characterized with a significant advance in the development of both the theory and experiment of electrocrystallization.A sys-tematic study of the fundamental aspects of electrocrys-tallization of metals concerning the electroplating in real systems and the influence of inhibitors on nucle-ation and growth was made by Fischer and his cowork-ers[25–27],who suggested
a very uful classification of compact metal deposits according to their mi-crostructure and morphology.Piontelli and his group [28–30]performed extensive studies of the role of the crystallographic orientation of the substrate and the nature of the anion on metal deposition and dissolution kinetics and homo-and heteroepitaxy of metal de-posits.First investigations of the influence of mass transport on the current distribution in electrodeposi-tion were made by Wagner[31],Tobias et al.[32]and Ibl et al.[33].Thefirst model for the leveling in electroplating including a diffusion controlled adsorp-tion of the additive was propod by Kardos[34]. Kaischew and his school[35–38]developed new experi-mental techniques for studies of the electrochemical nucleation and confirmed quantitatively the validity of the Volmer’s relation for the3D nucleation.Lorenz [39,40]was thefirst who treated the surface diffusion growth mechanism in the ca of electrocrystallization theoretically and noted the possibility for determination of the exchange current density and the concentration of adatoms(adions)from impedance measurements. First galvanostatic transient measurements of adatom concentration were reported by Mehl and Bockris[41]. Conway and Bockris[42]discusd alternative mecha-nisms of incorporation of atoms in the kink sites by taking into account the contribution of the hydration energy.Gerischer[43]estimated the ionic character of the substrate–adatom bond on the basis of theoretical considerations and experimental results.Wranglen [44,45]performed extensive studies of crystallographic aspects of den
drite formation in electrodeposition.A systematic investigation of whisker formation in elec-trocrystallization was made by Vermilyea et al.[46,47], who propod a mechanism for electrochemical whisker growth and derived a relation between the current density and the concentration of the adsorbing additive. In the early1960’s Fleischmann and Thirsk[48] developed a general theory of multiple nucleation and growth in the ca of electrocrystallization.Later Arm-strong and Harrison[49,50]extended this theory con-sidering the process of electrochemical multinuclear multilayer growth.Extensive theoretical and experimen-tal studies of electrocrystallization of metals were per-formed in the1960’s by Bockris,Damjanovic and Despic[51–53],who made important contributions to the problems of surface diffusion,propagation and bunching of steps and dendritic growth.Epelboin,Fro-ment et al.[54,55]intensively investigated the influence
E.Bude6ski et al./Electrochimica Acta45(2000)2559–25742561
of substrate and nucleation and growth process on the texture development in compact electrodeposits us-ing X-ray analysis,TEM and SEM.
A significant progress in the experiment of electro-crystallization was the development by Budevski and Bostanov in1964[56]of the so-called capillary tech-nique for preparation of isolated‘quasi-perfect
’metal single crystal faces free of screw dislocations or with an extremely low dislocation density.Using this novel technique Budevski et al.[57,58]verified quantitatively the classical mechanism of growth by2D nucleation for thefirst time.
Schmidt et al.[59–61]were thefirst who recognized the importance of the so-called underpotential deposi-tion(UPD)of metals for the overall process of electro-crystallization and started systematic studies on this subject in the1960’s introducing a number of thin layer techniques.
In the1970’s Lorenz et al.[62–64]performedfirst UPD experiments on single crystal substrates and inter-preted the experimental results hypothetically in terms of formation of well-ordered2D metal overlayers with different‘superlattice structures’.Subquently exten-sive studies on thermodynamics and kinetics of UPD of metals in various systems were made by Yeager et al. [65,66],Bewick et al.[67],Schultze et al.[68,69], Lorenz,Schmidt and coworkers[70–73]and Kolb et al. [74,75].Staikov,Lorenz and Budevski[76–78]intro-duced in the studies‘quasi-perfect’silver single crystal faces as substrates and establishedfirst important corre-lation’s between the process of UPD and OPD(over-potential deposition)of metals.In1974Milchev, Stoyanov and Kaischew[79]developed an atomistic theory of electrochemical nucleation which has been significant for the interpretation of many experimental results.The mononuclear layer-by-layer growth,the multin
uclear multilayer growth and the spiral growth have been extensively studied on‘quasi-perfect’silver single faces by Budevski,Bostanov and Staikov[80,81]. In the last two decades,new important information on the atomic structure and morphology of substrates and metal electrodeposits was obtained by in situ appli-cation of different modern surface analytical techniques such as EXAFS(extended X-ray absorptionfine struc-ture),GIXS(grazing incident X-ray scattering),STM (scanning tunneling microscopy)and AFM(atomic force microscopy)[82,83].A better understanding of the mechanism of metal electrodeposition on an atomic level has been achieved as summarized in[84].
The aim of this paper is to discuss the atomistic aspects of electrocrystallization on the basis of experi-mental results obtained in lected model systems and to prent some new theoretical and experimental con-cepts of electrochemical metal pha formation.2.Nucleation
The theory of metal deposition is bad generally on the Butler-Volmer[17,85]equation giving the current density on a metal substrate as function of overvoltage p
i=i o exp
h zF p
RT
−
(1−h)zF p
RT
n
=i o V(p)(1)
This equation is derived under the assumption that the rate determining process is the charge transfer reaction.A cond tacitly made assumption is that the surface is homogeneous so that the current density is uniformly distributed over the entire solid surface. Recognizing that metal deposition is a crystal growth process Volmer and Weber[4]suggested that the over-potential must depend on the formation kinetics of3or 2D crystalline clusters as required by the Gibbs crystal growth theory[1,17,18,86–88].According to the pre-vailing mechanism the current can be either propor-tional to the exponent of the reciprocal of overpotential,−1/ p ,or to that of the reciprocal of the squared overpotential,−1/ p 2,for the2or3D ca,respectively.The relations expected to be valid un
der steady state conditions have not been convinc-ingly verified but2and3D nucleation has been demon-strated to play a significant role in metal deposition studying the morphology of deposits[25,26].3D nucle-ation connected with new pha formation has been clearly demonstrated particularly in the early stages of deposition[21–23,35–38,46,47].
Nucleation is a very important process in metal deposition.On one hand,the competition between growth and nucleation determines the granularity of the deposit.The higher the nucleation rate during deposi-tion,thefiner are the crystal grains of the deposit.On the other hand,the forms of the growing crystals determine the general appearance and structure of the deposit.With a higher growth rate of the crystal grains normal to the substrate surface,for instance,afibrous structure of the deposit is obtained.Or,with large developed crystal faces parallel to the substrate a brightening effect can be achieved.
The formation of a new pha,as required in the initial stages of metal deposition on a foreign substrate, is kinetically limited by the specificity of the Gibbs formation energy dependence of a cluster of the new pha on its size N,N being the number of atoms forming the cluster.
扔垃圾The Gibbs formation energy,D G(N),of a cluster of N atoms contains two terms.
D G(N)=−Nze p +b(N)(2) Thefirst term is connected with the transfer of N ions from the ambient pha(the electrolyte)to the sub-strate surface under the action of the overvoltage p .
E .Bude 6ski et al ./Electrochimica Acta 45(2000)2559–2574
2562This term is always negative.The cond term,b (N ),reprents an excess free energy taking into account energy contributions derived from the deviation of the new pha from the bulk pha.Along with the cre-ation of new boundaries additional internal strains,deviation from the bulk atom arrangement,etc.can also affect this term.The relation Z G (N )−N is a function with a maximum determining an energy bar-rier Z G crit (N )at a cluster size N crit ,known as the nucleus.
The existence of an energy barrier makes the nucle-ation a probability process,with a rate J (nuclei /cm −2s −1)given by the probability for their formation:J =A J exp
−
D G crit
kT
(3)
where A J is a constant of proportionality.The energy (fluctuation)barrier D G crit can be found as the maxi-mum of the D G (N )function,Eq.(2).
2.1.The classical or continuity approach
In the simplest ca b (N )is given by the free energy
of creation of the new boundaries with extension X (for a 3D cluster X reprents the surface area,A 3D ,of the cluster,while for a 2D cluster X is equal to the perime-ter,P ,of that cluster)times the corresponding specific boundary energy (|and m ,respectively).Hence,b (N )= X (N )contains an intensive term =d b /d X ,giving the free energy per unit boundary extension and an extensive factor,X ,giving the boundary extension as function of the cluster size N .
b (N )or X (N )are unambiguous functions of N only if the form of the cluster is independent on cluster size,so that the relations are valid for any arbitrary con -r 6ati 6e form of a cluster.X (N )=a w D N 1
−1/6淘宝营销策略
(4)
where w is the dimensionality of the cluster including an one dimensional pha:w =1,2or 3.The constant of
proportionality h 6D is h 3D =B 6m 2/3and h 2D =b d m 1/2
in the 3or 2D ca,respectively.In the 1D ca X (N )is a constant independent on N .B and b are constants of proportionality depending on the cluster form geome-try.6m and d m are the volume and the surface occupied by one atom in the crystal.
N crit and D G crit are readily obtained from (2)and (4):N crit =(1−1w )
w w h w D
w (ze p )w (5)D G crit =
(w -1)w -1 w h w D
w (ze p )(6)
The following relations derived from the equations above are uful
D G crit =
ze p N crit w −1=1w
X (N crit )=1
w b (N crit )
(7a,b,c)
Of interest is the one dimensional ca,where N crit and D G crit =0.This shows that the process of 1D nucleation is quasi-barrierless and the deposition of the first atom gives ri to the 1D pha.The only barrier is the transfer of the first atom across the double layer.The 0D ca can not be treated within the framework of classical thermodynamics becau a 0D system con-sists of only few particles and has the specifics of a clod nanopha.The prence of the nanopha,how-ever,can enhance the nucleation acting as an active site.The formation of low-dimensional metal systems (LMDS)will be discusd in the last ction of this paper.
2.2.Nucleus size and nucleation rate入职培训心得
The relations (5)to (7)are valid for any arbitrary geometrical form of the cluster,accounted for only by the values of the geometrical factors B and b ,for the 3D and 2D ca,respectively.For the different cluster shapes the equilibrium form [86,89]having the lowest Gibbs free energy of formation D G crit will give the highest rate of cluster formation.
In the anisotropic ca the excess free energy b 6D is given by the energy contributions of all boundaries (faces or sides for the 3D or 2D ca,respectively)with their specific boundary energies i and individual exten-sions x i .
The crystallographic form of a crystalline 3or 2D cluster is given by the radius vector normal to the face planes or to the side lines of the polyhedron or the polygon,respectively,or by (hkl )in the Miller notation.The distance from the origin is given by the radius vector modulus h i .According to the Gibbs–Wulff [86,90]rule extended by Kaischew [91,92]for heteroge-neous nucleation the modulus h i divided by i is a constant:
锚链u =h i
美国二战电影i =
h j * j −i w D =(w −1)w %h i x i
N crit ze p
(8)
where i is the adhesion energy of the cluster (3or 2D)
to the respective substrate boundary interface (surface or step),as introduced by Kaischew [91,92]but e also [93].As en,the adhesion energy i modifies the spe-cific boundary energy of the contact crystal–substrate interface to j *= j −i j D .
The nucleus size can be given by the inscribed radius z crit (i.e.the lowest value of the moduli h i )and can be found as function of p :z crit =
26m |min ze p
and
z crit =
d m m min z
e p
(9a,b)
E.Bude6ski et al./Electrochimica Acta45(2000)2559–25742563 for the3and the2D ca,respectively.This relations
are a generalized form of the Gibbs–Thomson(Lord
Kelvin)equation applied to the electrochemical ca.
A very uful relation can be derived from the equa-
tions connecting N crit,D G crit and p [94,95]
d D G crit
d p
=−zeN crit(10)
Z G crit is accessible from nucleation–overvoltage ex-
难忘的岁月periments using the derivative of ln J with respect p of
relation(3),hence,with(10)
d ln J d p =−
ze
kT
N crit(11)
It has been shown by Kashchiev[94]that this equa-tion is general and applicable with a sufficient accuracy in all cas of nucleation where b(N crit)is a weak function of p ,including2D nucleation and are not restricted by any assumptions about size and form of the nucleus.
Returning back to the nucleation rate equation(3) with(6)we obtain for J in a logarithmic form
ln J=ln A J−(w-1)w-1 w h w D w
kT(ze p )
(12)
As en ln J is inverly proportional to the squared overpotential,−1/ p 2,or inverly proportional to the overpotential,−1/ p ,for the3D or2D ca,respec-tively,as suggested by Volmer and Weber.
2.3.The atomistic approach
Experiment has shown that in most of the cas of metal deposition the size of the nuclei are of atomic N crit is only few atoms high.Macro-scopic quantities,such as volume,surface,surface ener-gies,etc.lo their physical meaning and the u of atomic forces of interaction becomes more reasonable. The atomistic approach for the calculation of the de-pendence of the nucleation rate on supersaturation was first suggested by Walton[96–98]and later developed to a general nucleation theory,bad on the Becker and Doering model,by Stoyanov[99,100].In this approach the value of the formation energy,D G(N),can be calculated using the binding energies i where i is the binding energy of an atom in position i to the cluster, including the interaction between the atom and the substrate.
The excess energy is given by the difference of the binding energy of the cluster including its interaction with the substrate i and that of N atoms in the bulk of the crystal N kink,where N kink is th
e binding energy of a kink atom(equal to the average binding of an atom in the bulk of the crystal).The excess energy N kink− i is obviously connected with the unsatu-rated 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 connected with a possible different atomic arrangement from that of a regular crystal lattice.Internal strain in the cluster can be included in the calculation of the i values for every atom individually,or can be extracted from the sum as a property of the enmble of N atoms in the form m N,where m is the average strain energy per cluster atom(cf.[101–104]).Then
J=A J exp
:
−
(N crit kink−% i)
kT
;
exp (N crit+i*)ze p
kT
exp
−
N crit m
饼干的简笔画kT
(14)
In the small cluster model an additional atom to the nucleus is needed to convert the nucleus in a growing cluster.i*denotes the charge transfer coefficient.In the ca of direct transfer,i*=0.5,or it is equal to unity if surface diffusion prevails,e Section3.Here N crit being an integer can take only discreet values so that the ln J− p curve will be reprented by a cusped line,each ctor corresponding to a given number of atoms.For any of the ctors N crit is constant and can be obtained from the slope of the ln J− p curve of that ctor.The value of the internal strain m can be c
hanged by changing the starting potential D E,particu-larly in the UPD region.Changing thefinal overpoten-tial in the interval of constant N crit the ln J− p relation allows the estimation of the m−D E dependence [101–104].
2.4.The experiment
For the evaluation of the J− p dependence in dif-ferent electrochemical systems veral techniques have been developed.Most of them are bad on the fact that at low overpotentials the nucleation rate is negligi-bly small and ris steeply only after a critical overpo-tential is exceeded.
Using this specifics of the J− p relation,the most straightforward technique,is the application of a voltage double pul.The amplitude of thefirst pul is chon in the range of nucleation.According to the duration of the pul one or veral nuclei may be formed which are grown at a succeeding lower overpo-tential to a visible size[105–107].The number of the formed nuclei are then related to time at constant p , d N/d t giving the nucleation rate,and then the rate is analyzed as function of overpotential.
A cond uful technique is to apply a short nucle-ation pul and to record the following current tran-sient in the region of growth.From the resulting i−t1/2 relation the number of nuclei can be evalu
ated.This i−t relation corresponds to instantaneous nucleation
