An original physico-chemical model is proposed that accounts for the conversion mechanism between Ti3+ and Ti4+ during Ti:sapphire crystal growth process. This model involves release of O2 from the crystal surface, which consumes aluminum vacancies. Consequently, these vacancies diffuse from the bulk crystal toward the surface, leading to the conversion of Ti4+ into Ti3+. A set of mass balance differential equations is established for these chemical species, taking into account diffusion and chemical reaction. The boundary condition for concentration of aluminum vacancies on crystal surface is given as the function of PO2 and temperature. A preliminary numerical simulation is performed to study the proposed model, using COMSOL Multiphysics® software. The obtained radial concentration distribution profiles of Ti3+ and Ti4+ are in qualitative agreement with the experimental results, showing that the proposed model has potential for further studying point defect reactions during crystal growth of ionic crystals.
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