Combined influences of A3+ and Mo6+ on monoclinic-orthorhombic phase transition of negative-thermal-expansion A2Mo3O12

More reports about monoclinic-orthorhombic (m-o) phase transition of A₂M₃O₁₂ are focusing on the influences of radius as well as electronegative of A³⁺. However, m-o phase transition temperatures (PTTs) of A₂Mo₃O₁₂ do not always increase or decrease with radius/electronegative of A³⁺ (A-Sc, Al, Cr, In, Fe). Considering the combined influences of electronegativity and radius of A³⁺ as well as radius of O²⁻, a general formula of m-o phase transition temperature (PTT) could be obtained and used to estimate PTT of A₂Mo₃O₁₂ with low relative error. Furthermore, a simple linear relationship between PTT of A₂Mo₃O₁₂ and Dr^1/4·De of A³⁺ and Mo⁶⁺ (radius difference Dr = r_A-r_Mo, electronegativity difference De = e_A-e_Mo) is obtained by considering the combined influences of A³⁺ and Mo⁶⁺. The results suggest that m-o PTT of A₂Mo₃O₁₂ should relate to the combined influences of A³⁺ and Mo⁶⁺ rather than the only influence of A³⁺.