Unstrained bond lengths and corresponding cation radii in crystals with perovskite structure

Abstract

A method for determining average lengths of unstrained bands A-X (l _0AX ) and B-X (l _0BX ) and the ratio of the rigidity constants of these bonds for ABX ₃ compounds with perovskite structure is proposed. The values of l _0AX and l _0BX correspond to the minimum energies of cation-anion interaction of the crystal sublattices. Values of l _0AX and l _0BX are obtained for several groups of halide and oxide compounds: A ⁺ B ²⁺F₃, Cs ⁺ B ²⁺Cl₃, A ⁺ B ⁵⁺O₃, A ²⁺ B ⁴⁺O₃, and A ³⁺ B ³⁺O₃. It is ascertained that, for most compounds studied, the values of l _0AX and l _0BX are equal or close to the interatomic distances in crystals of binary compounds. The values of l _0AX and l _0BX are compared with the sums of the radii of the corresponding cations (R _A , R _B ) and anions ($^{VI} R_{O^{2 - } } ,^{VI} R_{F^ - } ,^{VI} R_{Cl^ - }$). It is found that the differences $l_{0AO^ - } ^{VI} R_{O^{2 - } } (L_{0AF^ - } ^{VI} R_{F^ - } )$ and $l_{0BO^ - } ^{VI} R_{O^{2 - } } (l_{0BF^ - } ^{VI} R_{F^ - } )$, regarded as the radii of the A and B cations in unstrained bonds, are close to the Shannon radii for a coordination number of six. It is shown that the rigidity constant for A-X bonds is several times smaller than that for B-X bonds.