Total and partial ionic and electronic $c$-axis dc conductivities were measured for single-crystal ${\mathrm{Al}}_2$${\mathrm{O}}_3$:8 ppm Mg as a function of oxygen pressure and temperature. The sample is unsaturated at $T>\mathrm{}1360\mathrm{}$ °C but is saturated in equilibrium with a spinel precipitate phase at lower temperatures. The results are analyzed to give ionic mobility, thermodynamic parameters of oxidation reduction of ${\mathrm{Al}}_2$${\mathrm{O}}_3$, and the solubility of MgO as a function of temperature. Oxidized samples are grayish purple due to the presence of a broad absorption band with maximum at 480 nm. Discoloration can occur by reduction (at high temperature) or by precipitation (at $T<\mathrm{}1000\mathrm{}$ °C); both proceed from the surface, involving migration of oxygen out of or of Al into the crystal. An explanation for the rapid diffusion regulating precipitation below 1000 °C is proposed. Recoloration at low temperature proceeds without a front and possibly involves oxygen diffusing into the sample along dislocations or subgrain boundaries. Hole-release studies at low temperature indicate that the hole binding energy in the defect ${\mathrm{Mg}}_{\mathrm{Al}}^x$, $E_a\le 0.68$ eV. The combined results of the present work suggest that free holes move as large, rather than small, polarons and that $E_a=0.68\mathrm{}$ eV.

• Received 15 March 1982

DOI:https://doi.org/10.1103/PhysRevB.27.3821