Calculations of physical properties of pure and doped crystals: Ab initio and semi-empirical methods in application to YAlO₃:Ce³ and TiO₂

In this paper we demonstrate that two independent methods of calculations (DFT based ab initio and semi-empirical crystal field theory) can be used to form a complementary picture of the optical and electronic properties of the doped host and impurity ion. The crystals considered in the present paper are: (i) YAlO₃:Ce³ and (ii) two dominant phases of TiO ₂rutile and anatase. As an example, detailed calculations of the band structure and crystal field energy level scheme of YAlO₃:Ce ³ are reported. From the analysis of the band structure and density of states, the character of the YAlO₃ energetic bands and positions of the Ce impurity energy levels were established. It was also shown how the ab initio methods can be used for calculations of the structural properties of solids under elevated pressure. Taking the two dominant phases of TiO ₂ as an example, it was demonstrated how the elastic properties can be extracted from the calculated unit cells volume at different pressures. Particular attention was paid to the microscopic effects of crystal field, which were evidenced by the pressure-induced changes of the structure and shape of distribution of the Ti 3d electrons density of states. It was demonstrated how the difference in crystal structure of the anatase and rutile phases leads to remarkable difference in microscopic crystal field effects, which was explained by different TiO distances in both phases. In addition, the pressure dependence of the band gaps for anatase and rutile was investigated. It was shown that the hydrostatic pressure leads to the band gap narrowing in anatase and band gap widening in rutile, with pressure coefficients 0.00681 eV/GPa for rutile and -0.0088 eV/GPa for anatase.