Crystal interfacial kinetics

Another contribution to variations of intrinsic activity is the different number of defects and amount of disorder in the metallic Cu phase. This disorder can manifest itself in the form of lattice strain detectable, for example, by line profile analysis of X-ray diffraction (XRD) peaks [73], 63Cu nuclear magnetic resonance lines [74], or as an increased disorder parameter (Debye-Waller factor) derived from extended X-ray absorption fine structure spectroscopy [75], Strained copper has been shown theoretically [76] and experimentally [77] to have different adsorptive properties compared to unstrained surfaces. Strain (i.e. local variation in the lattice parameter) is known to shift the center of the d-band and alter the interactions of metal surface and absorbate [78]. The origin of strain and defects in Cu/ZnO is probably related to the crystallization of kinetically trapped nonideal Cu in close interfacial contact to the oxide during catalyst activation at mild conditions. A correlation of the concentration of planar defects in the Cu particles with the catalytic activity in methanol synthesis was observed in a series of industrial Cu/Zn0/Al203 catalysts by Kasatkin et al. [57]. Planar defects like stacking faults and twin boundaries can also be observed by HRTEM and are marked with arrows in Figure 5.3.8C [58],... 

The tip-generated interfacial undersaturation is governed by the interplay between mass transport in the tip/substrate gap and the dissolution kinetics. This concept is illustrated in Figures 15 and 16. Figure 15a and b shows the radial dependence of the steady-state concentration and flux at the crystal/solution interface for a first-order dissolution process characterized by K, = 1, 10, and 100. For rapid kinetics (K, = 100), the dissolution process is able to maintain the interfacial concentration close to the saturated value and only a small depletion in the concentration adjacent to the crystal is observed over a radial distance of about one electrode dimension. Under these conditions, diffusion in the z-direction dominates over radial diffusion. As the rate constant decreases, diffusion is able to compete with the interfacial kinetics and consequently the undersaturation at the crystal surface... 

Fig. 2. Solute distribution and transport phenomena at the interface of a growing crystal (a) Instability of the crystal-liquid interface and formation of a nonplanar pattern (schematically), (b) Faceted growth. It is assumed that the solute concentration in the liquid far from the interface (Cq) is constant due to forced and natural convection (stirring) whereas a thin solute diffusion layer (S) is quiet and possesses a solute distribution profile depending on the crystallization process type (a) interfacial control or a surface reaction (interfacial kinetics), Ce < C RJ C a difference between Cj and Cj is responsible for the driving force to buUd up the crystal surface (c) diffusion control Cj < Cj, providing a driving force for bulk diffusion in the liquid (b) mixed control.

The role of various surfactant association structures such as micelles and lyotropic liquid crystals (372), adsorption-desorption kinetics at liquid-gas interfaces (373) and interfacial rheology (373) and capillary pressure (374) on foam lamellae stability has been studied. Microvisual studies in model porous media indicate... 

Additives promote filling by diffusing to the metal surface, where they adsorb and influence the kinetics of ion-discharge and crystal-growth. The diffusion parameter can be written for an additive by replacing the current density with an interfacial flux Na-... 

Growth Rate for Inclination-Dependent Interface Velocity. For a crystalline particle growing from a supersaturated solution, the surface velocity often depends on atomic attachment kinetics. Attachment kinetics depends on local surface structure, which in turn depends on the surface inclination, n, with respect to the crystal frame. In limiting cases, surface velocity is a function only of inclination the interfacial speed in the direction of n is given by v(h). The main aspects of a method for calculating the growth shapes for such cases when v(h) is known is described briefly in this section. 

Crystal formation depends not only on the interaction energy of a particular synthon but on a wide variety of other factors, particular crystal nucleation and growth kinetics and nucleus-solution interfacial energy. Other important factors are lattice enthalpy and lattice entropy, long range interactions... 

The simplest decomposition kinetics, commonly observed for carbonates, result from a model in which nucleation and subsequent surface growth are extremely rapid. The rate of decomposition is then determined by the progression of the reaction interface into the crystal. Rate laws have been derived for various geometries, but the ones for spherical particles are most useful and have been given in several equivalent forms by various authors. In this derivation it is assumed that the reaction interface proceeds at a constant velocity into the crystal i.e for a constant interfacial area, the rate of decomposition is a constant. For a spherical particle, the reaction proceeds along a constantly diminishing interface. For such particles of initial radius R0, the fraction decomposed at time t is... 

When an ionic single crystal is immersed in solution, the surrounding solution becomes saturated with respect to the substrate ions, so, initially the system is at equilibrium and there is no net dissolution or growth. With the UME positioned close to the substrate, the tip potential is stepped from a value where no electrochemical reactions occur to one where the electrolysis of one type of the lattice ion occurs at a diffusion controlled rate. This process creates a local undersaturation at the crystal-solution interface, perturbs the interfacial equilibrium, and provides the driving force for the dissolution reaction. The perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the process. 

Refs. [i] Conway BE (1999) Electrochemical processes involving H adsorbed at metal electrode surfaces. In Wieckowski A (ed) Interfacial electrochemistry, theory, experiment, and applications. Marcel Dekker, New York, pp 131-150 [ii] Climent V, Gomez R, Orts JM, Rodes A, AldazA, Feliu JM (1999) Electrochemistry, spectroscopy, and scanning tunneling microscopy images of small single-crystal electrodes. In Wieckowski A (ed) Interfacial electrochemistry, theory, experiment, and applications. MarcelDekker, New York, pp 463-475 [Hi] Calvo E] (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

The topics covered are as follows. The structure of the interfacial region and its experimental investigation are covered in Chapter 1. The following chapter reviews the mechanisms by which heterogeneous catalysis of solution reactions can take place. The third chapter is concerned with the mechanism and kinetics of crystal growth from solution and the final contribution deals with corrosion processes at the metal-solution interface. 

---