Diffusion of point defects participating in solid-phase chemical reactions (trap diffusion): Demonstration for the Ti3+ → Ti4+ transition in corundum

A problem of trap diffusion, that is diffusion of point defects in crystals participating in a solid-phase chemical reaction with motionless impurity ions, is solved. Time dependences of the reaction-front displacement, X_f, and its steepness, $\text{(}\text{?C}\text{?X}\text{)}{}_{\mathrm{f}}$ are determined analytically for N₀ ? C₀ and numerically for all relations of N₀ and C₀$\text{x}{}_{\mathrm{f}}{}^2\text{=2}\text{N}{}_0\text{C}{}_0\text{Dt; (}\text{ac}\text{ax}\text{)}{}_{\mathrm{f}}\text{=0.3C}{}_0{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(}\text{g}\text{D}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2></mtext>}}$where C₀ and N₀ are the initial concentration of impurity and the eqilibrium defect concentration, respectively, D is a diffusion coefficient, and g is a chemical reaction constant. Dependence of X_f vs C₀ and t is confirmed for oxygen annealing of corundum crystals doped with titanium which, reacting with the point defects, changes its valency. The data are obtained for dependence of displacement X_f upon partial oxygen pressure and thermotreatment temperature as well as upon the sign of the constant electric field applied to the sample. From these data we conclude that the reaction of titanium impurity, changing from the three-valent to the tetravalent state at the activation energy of 80 ± 8.5 kcal/mole is due to anisotropic diffusion of charged aluminum vacancy and holes in the valence band. The diffusion coefficient for that process at 1500°C is estimated to be larger than 10^?5 cm²/sec. Using the trap-diffusion features, the concentration of optical centers of the 0.315-μm absorption band in ruby is also estimated.