Equilibrium shape of internal cavities in sapphire

The equilibrium shape of internal canities in sapphire was determined through the study of submicrometer internal cavities in single crystals, Cavities formed from indentation cracks during annealing at 1600 degrees C, Equilibrium could be reached only for cavities that were smaller than approximate to 100 nm, Excessive times mere required to achieve equilibrium for cavities larger than approximate to 1 mu m. Five equilibrium facet planes were observed to bound the cavities: the basal (C) {0001}, rhombohedral (R) {<(1)over bar 012>}, prismatic (A) {<1(2)over bar 10>}, pyramidal (P) {<11(2)over bar 3>}, and structural rhombohedral (S) {<10(1)over bar 1>}. The surface energies for these planes relative to the surface energy of the basal plane mere gamma(R) = 1.05, gamma(A) = 1.12, gamma(P) = 1.06, gamma(S) = 1.07, These energies mere compared with the most recent theoretical calculations of the surface energy of sapphire, The comparison was not within experimental scatter for any of the surfaces, with the measured relative surface energies being lower than the calculated energies, Although the prismatic (M) {<10(1)over bar 0>} planes are predicted to be a low-energy surface, facets of this orientation mere not observed.