Mechanisms of surface evolution

If the criterion for a stable equilibrium configuration is that entropy assumes a maximum value, it follows immediately from (9.5) that an equivalent statement for the class of systems described is that a stable equilibrium configuration is one in which free energy assumes a minimum value. Furthermore, it follows from the second law (9.3) that, if a nonequilibrium system of this class alters its configuration spontaneously, it must do so with 

In light of these observations on equivalence of various statements of stability and equilibrium, evolution of configurations of material systems is discussed in terms of free energy variations in the sections to follow. 

The particular evolution phenomena in material systems considered in this chapter include the transition from a nominally flat surface to a wavy surface in a stressed solid, the spontaneous growth of epitaxial islands due to deposition of a material on a substrate with lattice mismatch, stress relaxation by grain boundary diffusion, the role of stress in altering compositional variations in solid solutions, and stress-assisted diffusion in the presence of an electric field or electromigration. 

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One of the questions in the mechanism of hydrogen evolution, and ancillary topics connected with the surface hydrogen involved in corrosion, is the dependence of the surface hydrogen upon overpotential. This topic has importance not only because of the... 

The intermediate remains on the electrode until it is transformed into another particle during the consecutive steps that make up the overall reaction. The simplest example is (Section 7.6.2) the mechanism of hydrogen evolution, in which one possible step involves chemical recombination between adsorbed H s, put onto the electrode surface by means of the discharge of H20+ from acid or H20 from alkaline solutions. The adsorbed H is the intermediate radical. 

In previous material—when discussing the mechanisms of hydrogen evolution— the value 0H has been an important factor in the argument. For example, if Gjj is laige (approaching unity), it is likely that the mechanism of desorption of H from the surface to form H2 will be via the electrochemical desorption step rather than that of recombination. 

The rate and characteristics of surface evolution depend on the particular transport mechanisms that accomplish the necessary surface motion. These can include surface diffusion, diffusion through the bulk, or vapor transport. Kinetic models of capillarity-induced interface evolution were developed primarily by W.W. Mullins [1-4]. The models involving surface diffusion, which relate interface velocity to fourth-order spatial derivatives of the interface, and vapor transport, which relate velocity to second-order spatial derivatives, derive from Mullins s pioneering theoretical work. 

Fig. 16.8 Schematic representation of mechanisms of H evolution over Pt / HPt2Nb3Oi0 Pt exists in the interlayer region in (a) and only or. the external surface in (b).98)...

The mechanism may change from acids to alkalis in some cases [365], This may be related to the higher sensivity of the Fe surface to oxidation in alkaline solutions [365, 367], Actually, the corrosion of Fe proceeds also under moderate cathodic load [368]. Impedance measurements have suggested that the classical mechanisms of hydrogen evolution is probably inadequate to describe the situation on Fe [377], A surface diffusion step with spillover of hydrogen to sites with lower M-H energy has been suggested. Adsorption of CN- interferes with such a diffusion. 

These observations are consistent with an indirect mechanism of oxygen evolution, involving the photogeneration and the subsequent photo-oxidation of the surface peroxo-titanates. Apparently, the photo-oxidation of the peroxo species constitutes the slow step of the overall reaction and proceeds at a significant rate only in the presence of an anodic... 

It is, of course, tempting to draw a parallel between the photo-oxidation of water at titanium dioxide and the well-known irreversibility of O2 generation at the anodes with metallic conductivity. There are, however, some indications that the pathway involving surface-bonded peroxo-titanate intermediates is not the only possible one. Recent experiments, performed with beryllium-doped Ti02 photoanodes, have shown no evidence for the formation of any perceptible amount of the peroxo spedes l This coincided with a substantial cathodic shift of the onset potential and a strong increase of the anodic photocurrent for these electrodes , suggesting a different mechanism of oxygen evolution. 

H. Houda, Y. Naoki, and H. Obanawa, Characteristics of Plasma-Sprayed NiO Cathode and Mechanism of Hydrogen Evolution Reaction at its surface. In Proc. Vol 98-10, The Electrochemical Society Inc. (1998), p. 329. 

Cyclic voltametric measurements shown in Figure 14 indicate that only one surface layer is reduced. It is interesting to note that the reduction and reoxidation depends on the crystal faces.Capacity measurements proved that a new Helmholtz layer is formed after cathodic polarization " (see also Chapter 2). It could be further shown that the electronic level of the surface radical Ge is a surface state which is located between the conduction and valence bands, and which appears only as an intermediate state during the surface reduction process. Since the same surface state was detected again in the potential range in which H2 is finally formed, it has been postulated that the radical occurs as an intermediate state also in the mechanism of H2 evolution as given by ... 

In addition to the mechanisms of oxygen evolution at nickel anodes [44], the surface properties of C03O4 electrodes have also been investigated [45]. Another possibility is the use of mixed oxides of a spinel or perovskite type for anode oxygen evolution examples are Lao.sSro.sCoOs, NiCo204-PTFE, and C03O4 [46]. Representative results of electrochemical measurements in an alkahne electrolyzer are given in Table 8.5. 

The nature of the adsorbed intermediate (Hajs) and its impact on the mechanism of hydrogen evolution has been a major concern in HER electrocatalysis. Platinum has long been known to form adsorbed hydrogen [4], and the adsorption of hydrogen holds a particular significance in the overall development of modern electrochemical surface science. 

In this section, situations are considered for which the surface of a stressed solid is initially flat, or nearly so, and for which the slope of the evolving surface is everywhere small in magnitude throughout the evolution process. Chemical potential for a one-dimensional sinusoidal surface shape was developed in Section 8.4.1, for a two-dimensional sinusoidal shape in Section 8.5.3, and for a general small amplitude surface profile in Section 8.5.2. These results are used to examine surface evolution by either the mechanism of surface diffusion or condensation, as described in Section 9.1. In all cases considered in this section, surface energy is assumed to have the constant value 70, independent of surface orientation and surface strain. Implications of surface energy anisotropy and strain dependence are examined subsequently. 

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