Meads phase

Fig. 7.146. 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 AE > AP for FMend- 3d. (Reprinted from E. Budevski, G. Staikov, and W. J. Lorenz, Electrochemical Phase Formation and Growth, p. 116, copyright 1996 John Wiley Sons. Reproduced by permission of John Wiley Sons, Ltd.)...

First theoretical interpretations of Me UPD by Rogers [3.7, 3.12], Nicholson [3.209, 3.210], and Schmidt [3.45] were based on an idealized adsorption model already developed by Herzfeld [3.211]. Later, Schmidt [3.54] used Guggenheim s interphase concept" [3.212, 3.213] 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, 3.215] and Schultze et al. [3.116-3.120, 3.216] used classical concepts to explain the kinetics of Me UPD and UPD-OPD transition processes including charge transfer, Meloiy 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, 3.217-3.225]. 

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 [3.54, 3.212, 3.213]. 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. Furthermore, it is assumed that the chemical potential //Meads is a definite function of the Meads surface concentration, F, and the electrode potential, E, at constant temperature and pressure Meads (7", ). Such a model system can only be... 

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

D Mcads phases formed in the UPD range are not necessarily Meads overlayers with a monatomic thickness. The Meads overlayer thickness is a function of the Meads-S binding energy, V Meads-s- the lateral Meads-Mcads interaction energy, V Meads-Meads > the underpotential, hE. At the equilibrium potential (A = 0), a 2D Meads phase with a finite number of Meads overlayers can coexist with the 3D Me bulk phase (cf. Fig. 1.1). 

Structural properties of the 2D Meads phase and S as well as the lateral interaction energy between Me adatoms, V Meads-Meads other 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 Leiva [3.234-3.239]. In addition, local density full potential linearized augmented plane wave calculations were carried out by Neckel [3.240, 3.241). Both approaches are important for a better understanding of Me UPD phenomena on single crystal surfaces taking into account structural aspects. 

The function f(r) can be considered as the activity of the 2D Meads phase in the UPD range compared to the Me activity (aue = 1) of a 3D Me bulk phase (cf. eq. (1.2)). The explicit form of f(r) depends on the Meads-S and Meads-Meads interactions and the crystallographic structure of S, and can be derived using appropriate adsorption isotherm models. 

In the case of a first order phase transition, the equilibrium underpotential of a 2D Meads phase, AE, 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 Meads phase. 

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. TTie term superlattice stmcture" is frequently used for commensurate overlayers which can be characterized by either the Wood or the matrix notation [3.271-3.274]. 

Explicit expressions for i(f) and i s/Me" r Quire the knowledge of the adsorption isotherm (cf. Section 3.3). For example, 2D Meads phase formation according to the Frumkin-Fowler adsorption isotherm gives by combining eqs. (3.18) and (3.20) ... 

Cyclic voltammetric and potentiodynamic measurements in the system Ag(hkl)/Bi, H, CIO4 (+ Cl ) show that the kinetics of 2D Meads phase formation and dissolution depend on the structure of the substrate surface [3.119]. It was suggested that Meads surface diffusion may play an important role in the desorption kinetics. 

A 2D first order phase transition is unequivocally characterized by a discontinuity in the T E) isotherm at / = constant. At this special point in the r E) isotherm an expanded" 2D Meads phase is transformed into a more condensed" 2D Meads phase. Expanded and condensed Meads phases have to coexist. Therefore, 2D nucleation and growth occur in the presence of a preformed expanded but supersaturated Meads adsorbate. The surface concentration of the expanded Meads adsorbate, F, is continuously changing according to the actual polarization state of the UPD system. As long as corresponding -amounts (cf. eq. 3.4) contribute significantly to the overall measured -values, an identification of 2D nucleation and growth is not possible. 

In the following, a general model [3.94] including formation of an expanded 2D Meads phase on a homogeneous substrate as well as a first order phase transition leading to a condensed 2D Meads phase is discussed for potentiostatic pulse polarization experiments. In this treatment, surface diffusion of Meads is neglected. 

An expanded (ep) 2D Meads phase is polarized by a potentiostatic cathodic pulse (large signal system perturbation) leading to the formation of a condensed (cd) phase ... 

Analogously to 3D nucleation processes, a supersaturated state of an expanded structure is formed first which is characterized by actual Fep () and 9ep(0 values kinetically controlled by Me oiy 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 cdfAEf). 

The part of the substrate surface covered by the condensed 2D Meads phase will be denoted by S(f). The charge balance of Me oiy is given by... 

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 [3.249], 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 Meads phase formation is briefly discussed. 

According to the classical nucleation theory, the Gibbs energy for the formation of a critical 2D nucleus of a 2D Meads phase on an atomically flat terrace (T), AGcrit,T, is given by [3.249] (cf. eq. (4.25a)) ... 

Figure 3.42 Formation of 2D and ID Meads phases on stepped foreign substrates, (a) 2D nucleation on atomically flat terraces (b) 2D nucleation at monatomic steps (c) ID Meads phase formation along...

Figure 3.44 Schematic representation of i(f) transients of condensed 2D Meads phase formation at monatomic steps, (a) substrate surface with regular step spacing (b) substrate surface with irregular step spacing (arbitrary step distribution).

Bewick and Thomas [3.110-3.114, 3.270] measured electrochemically and by optical means different Me UPD systems Ag(A 0/Pb, H, ClOd", acetate and citrate, CnQikt)/ h H C104, acetate, and AgQikt)m SOd with Qikt) = (111), (100), and (110). Potentiostatic pulse measurements showed non-monotonous current transients for Ag(lll) substrates which are attributed to a first order phase transition. As an example, a current transient in the system Pig hkt)/Vf, H, SOd is shown in Fig. 3.46. In the case of Ag(lOO) and Ag(llO) substrates, higher order phase transitions were supposed. Clear evidence of a participation of 2D nucleation and growth steps in the 2D Meads phase formation process was found in the system Cu(lll)/Pb H", ClOd", acetate [3.270]. Non-monotonous current transients and a discontinuity in the q(lsE,fi) isotherm were observed (Fig. 3.13). 

Schultze and Dickertmann [3.117-3.120] measured current and potential transients under potentiostatic and galvanostatic conditions, respectively, for the adsorption and desorption processes of Bi UPD on Au(lll). All transients were non-monotonous. A typical example is given in Fig. 3.47. The results are interpreted in terms of nucleative 2D Meads phase formation and dissolution processes. 

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