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PROPERTIES 82 dissociation of molecularly adsorbed NO occurs more slowly on supported Rh than on Rh(111) (Oh et al., 1986). Studies of the crystal faces exposed on supported metal catalysts have made use of comparisons with adsorption information determined on single-crystal surfaces. For example, the infrared frequencies for CO adsorbed on supported Pd have been used to determine which low index plane CO is adsorbed onto and how the adsorbate structure is changed with pretreatment (Palazov et al., 1982). In another study in which the infrared spectra for very small amounts of CO adsorbed onto Pd/Al2O3 were compared with CO IR spectra for Pd(111), it was shown that CO was adsorbed initially onto (111) facets on alumina-supported palladium crystallites (average diameter 8.4 nm) and that this adsorption could be blocked by preadsorption of CH3C (Beebe and Yates, 1986). The crystallite morphology of supported palladium particles has been shown to influence the catalytic activity of Pd/La2O3 for methanol synthesis: Pd(100) was nearly 3 times more active than Pd(111) (Hicks and Bell, 1984). Masel (1986) has successfully applied orbital symmetry models to predict the preferred crystal face orientation for NO decomposition on Pt. Strong metal support interaction (SMSI) refers to an interaction between the metal particles and the catalyst support causing suppressed H2 and CO chemisorption (Tauster et al., 1978). The recent literature on SMSI has heightened awareness of the role of the support in determining catalyst activity and selectivity. Studies of the causes of SMSI have been complicated by the difficulty of looking at powders by modern surface techniques. As a result, some researchers have turned to model catalysts to discover the causes of these observations. For example, Belton and coworkers (1984), making use of Rh films on oxidized Ti, showed that both encapsulation of the metal overlayers and electronic effects contribute simultaneously to SMSI. This encapsulation was shown by both AES and temperature-programmed static secondary ion mass spectroscopy. STABILITY The evolution of a microstructure with a characteristic dimension on the order of 1 to 100 nm is different from that of coarser microstructures in two important ways: (1) Since the interface-to-volume ratio in these materials is exceptionally high, the driving force for coarsening and grain growth is much greater than in conventional microstructures; (2) in multiphase or multicomponent systems, the thermodynamics of homogeneous systems must be adapted to take into account contributions from gradients in density or composition. The driving force for grain growth is the increased chemical potential µ = KgW/r, where is the interfacial tension, is the atomic volume, r is the average grain size, and K is a constant on the order of unity. For the smallest grains (1 nm), this could be as high as 50 meV per atom. The grain
PROPERTIES 83 growth rate in the early stages can therefore be many orders of magnitude greater than is observed for conventional microstructures. Only limited information on the grain growth in nanophase materials is presently available, and this indicates a relatively deep metastability of the initial grain-size distribution. Grain-growth measurements by TEM in Fe with an initial average grain size of about 7 nm (Hort, 1986) and TiO2 (rutile) with an initial average grain size of about 12 nm (Siegel et al., 1988) have demonstrated a rather wide temperature range over which grain growth is quite small. An example of these data is shown in Figure 22. Figure 22 Average grain size (diameter) of nanophase TiO2 (rutile) determined by TEM as a function of sintering temperature. The sintering anneals were 0.5 hour in duration at each successive temperature (Siegel et al., 1988). Some of the kinetic factors that determine the boundary mobility could also be affected for very small grain sizes. For example, if impurity segregation were to affect the grain boundary mobility, a large interface-to-volume ratio may lead to a decrease in the interfacial concentration of impurity, and hence to faster grain growth. The decrease in the chemical potential resulting from the interfacial tension is also the driving force for coarsening of two-phase systems. This is well known from the study of eutectics. Figure 23 illustrates an important
PROPERTIES 84 mechanism identified in the coarsening of eutectic lamellae. The highest driving force is found at the tip of a receding fault line. Diffusion from this tip to the adjacent lamellae leads to thickening. Figure 23 Schematic diagram of the coarsening mechanism in a lamellar structure (Spaepen, 1985). In this mechanism, the coarsening rate, dr/dt, is independent of the scale, r, of the microstructure. A fine microstructure, however, is still relatively more affected by coarsening--for example, as measured by the time required to double r--than a coarse one. Since the coarsening rate is also proportional to the density of fault lines, the stability of artificial multilayers is greatly enhanced by the greater perfection of the individual layers. A coarsening mechanism for perfect layers, illustrated in Figure 23, is much less efficient than that of Figure 24. Figure 24 Schematic diagram of the coarsening of perfect layers by diffusion-induced doubling (Spaepen, 1985). The thermodynamics and stability of systems that are inhomogeneous, either in density or composition, on a very fine scale was first fully formulated by Cahn and Hilliard (1958). They pointed out that the free
PROPERTIES 85 energy, F, of such a system must include terms due to the gradients in concentration or density: In this expression, c is the composition (or density), f(c) is the free energy per unit volume of a homogeneous system of composition (density) c, and k is the gradient energy coefficient. This results in a modified interdiffusivity, where = 2 / is the wavelength of one Fourier component of the concentration profile. To predict the evolution of a very-fine-scale compositional inhomogeneity, it is therefore necessary to know both the bulk thermodynamics (f'') and the gradient energy coefficient of the system. Figure 25 illustrates some of the possibilities for a continuum approximation. The amplitude of the fine-scale composition modulation either vanishes by homogenization (Dl > 0) or grows to its two-phase equilibrium value (Dl < 0), after which coarsening sets in. Figure 25 Dependence of the interdiffusivity and amplification factor R = D 2 on the wavelength of a composition modulation: (a) phase separating system inside the spinodal; (b) phase separating system outside the spinodal; (c) ordering system (Spaepen, 1985).
