T. P. Lebedeva

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

Abstract 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, Xf, and its steepness, ( ∂C ∂X ) f are determined analytically for N0 ⪡ C0 and numerically for all relations of N0 and C0 x f 2 =2 N 0 C 0 Dt; ( ac ax ) f =0.3C 0 3 2 ( g D ) 1 2> 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 Xf 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 Xf 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.

An explicit method for the numerical solution of the problem of the propagation of a light wave in non-linear media

A method for the numerical solution of problems of the propagation of axially-symmetric beams in media with a positive cubic non-linearity in the framework of a parabolic equation is discussed. For such problems it is established by a numerical experiment that only the use of a moving Lagrangian mesh leads to the stability of explicit methods of numerical solution. The influence of the boundary conditions on the solution of such problems is examined. The scheme proposed can be used for multidimensional problems.