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We investigated the effect of lattice relaxation in the trivalent transition metal ions doped α-Al 2 O 3  crystal (α-Al 2 O 3 : TM 3+ ). The transition metal ions are Sc 3+ , Ti 3+ , V 3+ , Cr 3+ , Mn 3+ , Fe 3+ , and Co 3+ . The lattice relaxation effect was considered by comparing two different methods such as Shannon’s crystal radii methods and Cambridge Serial Total Energy Package (CASTEP) methods. In the Shannon’s crystal radii methods, the lattice relaxation effect was estimated as the ratio of the crystal radii of the substituted ion and the replaced ion. On the other hand, in the CASTEP method, the lattice relaxation effect was estimated by geometry optimization. The detail results show that in the case of Shannon’s crystal radii method, the lattice relaxation ratio was ca. 111.0 - 100.5%. Whereas in the case of CASTEP method, the lattice relaxation ratio was ca. 107.8 - 102.1%. However, the lattice relaxation ratio of α-Al 2 O 3 : Sc 3+ , Ti 3+ , V 3+ , Cr 3+ , Mn 3+ , Fe 3+ , and Co 3+  is unique depends on the ion type.

A non-empirical lattice-relaxation estimation of TM3+ doped α-Al2O3

A non-empirical lattice-relaxation estimation of TM³⁺ doped α-Al₂O₃