Surface-energy-anisotropy-induced orientation effects on Rayleigh instabilities in sapphire

Arrays of controlled-geometry, semi-infinite pore channels of systematically varied crystallographic orientation were introduced into undoped m-plane (101¯0) sapphire substrates using microfabrication techniques and ion-beam etching and subsequently internalized by solid-state diffusion bonding. A series of anneals at 1700 °C caused the breakup of these channels into discrete pores via Rayleigh instabilities. In all cases, channels broke up with a characteristic wavelength larger than that expected for a material with isotropic surface energy, reflecting stabilization effects due to surface-energy anisotropy. The breakup wavelength and the time required for complete breakup varied significantly with channel orientation. For most orientations, the instability wavelength for channels of radius R was in the range of 13.2R-25R, and complete breakup occurred within 2-10 h. To first order, the anneal times for complete breakup scale with the square of the breakup wavelength. Channels oriented along a 〈112¯0〉 direction had a wavelength of ≈139R, and required 468 h for complete breakup. Cross-sectional analysis of channels oriented along a 〈112¯0〉 direction showed the channel to be completely bounded by stable c(0 0 0 1), r{1¯012}, and s{101¯1} facets.