The Wulff Shape of Alumina: IV. Ti4+‐Doped Alumina

Abstract

Controlled‐geometry cavities, initially ≈20 μm × 20 μm × 0.5 μm, were introduced into ‐plane titanium‐doped (≈210 ppma;≈500 wt. ppm) sapphire substrates using photolithographic methods, and subsequently internalized by diffusion bonding. The samples were annealed in air for prolonged periods at 1600° and 1800°C to convert the titanium to the 4+ state and to allow the pore shapes to adjust. Pores with an equivalent spherical radius of ≈3.6 μm reached a quasi‐equilibrium shape within 160 h at 1600°C and within 48 h at 1800°C. The Wulff shape was determined using optical microscopy, scanning electron microscopy, and atomic force microscopy. The Wulff shape of Ti4+‐doped alumina includes well‐defined c(0001), , and facets and smoothly curved sections. The and a facets, which are components of the Wulff shape of undoped sapphire, are not discernable. In contrast to undoped alumina, for which the r‐plane has the lowest energy, the c‐plane is the lowest energy plane in Ti4+‐doped alumina. The surface energy sequence of the stable c, r, and p surfaces differs from that in undoped alumina. The Wulff shape varies with temperature. Samples equilibrated at 1800°C were re‐annealed at 1600°C. Pore shape changes were reversible, indicating that the observed pore shapes were close to the equilibrium (Wulff) shape.