Equilibrium particle shape

Lee et al. (61) measured the equilibrium shape of clean platinum by monitoring the changes in the shape of a series of micrometer-sized platinum droplets during annealing at I200°C in 10 7 Torr of oxygen. Consistent with the work of Schmidt, their results showed that the equilibrium particle shape is influenced by what gas is present. As shown in Fig. 4, at equilibrium, the clean particle shape is nearly spherical, with distinct (100) and (111) facets. The facets occupy only 16% of the surface. However, if the particle is contaminated with carbon, the particle is a cubooctahedron with large (111), (100), and (110) facets. 

Karim, A. Eosse, S. Persson, K. A., Surface Structure and Equilibrium Particle Shape of the Limn204 Spinel from First-Principles Calculations. Phys. Rev. B 2013,87,075322. 

The impact of thermal etching on the equilibrium shapes of supported particles. It is clear that particle shape and surface structure are a function of the identity of the gas. 

Fig. 7. Detailed models of surface free energies based on quasi-chemical metal-metal interactions allow detailed Wulff plots, and hence particle shapes, to be predicted as a function of temperature, (a) Interfacial phase diagram for simple cubic lattice model with nearest-neighbor and next-nearest-neighbor attraction, (b) Representative Wulff plots and equilibrium crystal shape of (a) (103).

It is known that adsorption decreases the surface energy [78]. Because the adsorption energy often depends on the type of facet, one expects a change of the equilibrium shape. Shi and Masel [106,107] have calculated the equilibrium shape of a crystal at 0 K in a presence of gases. The calculations show drastic changes of the equilibrium shape already at coverages around 0.1 ML. Then during a catalytic reaction the particle shape can evolve, which can affect the reaction kinetics, as shown recently by Monte Carlo simulations [108]. 

C. R. Amonson and I. S. Dranoff, "Nonlinear Equilibrium and Particle Shape Effects in Inlra-... 

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