Thermodynamic Calculations of Ti Ion Concentrations and Segregation Coefficients during Ti:Sapphire Crystal Growth

The theoretical phase diagrams of the binary Al2O3–Ti2O3 and Al2O3–TiO2, as systems calculated using FactSage software and its thermodynamic databases, are reoptimized. This has been performed on the basis of a literature survey on experimental precipitation limits of Ti2O3 and TiO2 in the Al2O3 solid solution. The appropriate oxygen partial pressure (pO2) range for controlling the valence state of Ti ions during Ti:sapphire crystal growth is obtained with respect to the calculated Ellingham type predominance diagram. Factors affecting the pO2 such as furnace gas, crucible materials, and graphite heating elements are analyzed. The influence of pO2 on Ti3+ and Ti4+ concentrations in the solid and liquid phases is derived from thermodynamic equilibrium calculations. The equilibrium segregation coefficients of Ti3+ and Ti4+ in sapphire are calculated to be 0.046 and 0.011, respectively. Taking into account the data extrapolated from experiments, a value of 0.06 ± 0.02 is proposed for the equilibrium segregation coefficient of total Ti under low pO2.