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 ( 1 0 1 ¯ 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 〈 1 1 2 ¯ 0 〉 direction had a wavelength of ≈139R, and required 468 h for complete breakup. Cross-sectional analysis of channels oriented along a 〈 1 1 2 ¯ 0 〉 direction showed the channel to be completely bounded by stable c(0 0 0 1), r { 1 ¯ 0 1 2 } , and s { 1 0 1 ¯ 1 } facets.