Classical and Quantum Simulation of the Surface Properties of $\alpha $-Al$_{2}$O$_{3}$ [and Discussion]

Classical simulations are described of the fully relaxed surface lattice structures of the five lowest-index planes of $\alpha $-Al$\_{2}$O$\_{3}$ and the resulting crystal morphology. The surface coverage by yttrium and magnesium as a function of temperature is evaluated on the basis of a non-Arrhenius isotherm and calculated heats of surface segregation. The calculated morphology, surface coverages and heats of segregation are compared with experiment. A quantum simulation of a relaxed {0001} surface is presented and the surface structure and energy compared with the classical results. Estimates are made of the adsorption energy of HF at the {0001} surface.