Theoretical study on local lattice structure distortion for octahedral Fe3+ center in several germanate garnets

Local structure distortion of octahedral Fe3+ centre in garnets Ca3M2Ge3O12 (M = Al, Ga, Sc, In, Lu). R0, θ0 are the structure parameters of host crystals. R, θ are the structure parameters when Fe3+ replaces M3+ (M = Al, Ga, Sc, In, Lu). ΔR, Δθ denote the structure distortion. Although the local lattice structures around the M3+ (M = Al, Ga, Sc, In, Lu) ions are obviously different, the local lattice structures around the dopants are rather similar. Moreover, it is noted that the empirical impurity-ligand distance is not suitable for Fe3+ in garnets Ca3M2Ge3O12 (M = Al, Ga, Sc, In, Lu).