Chemical composition, crystal structure, and their relationships with the intrinsic properties of spinel-type crystals based on bond valences

Spinel-type crystals may possess complex and versatile chemical composition and crystal structure, which leads to difficulty in constructing relationships among the chemical composition, crystal structure, and intrinsic properties. In this work, we develop new empirical methods based on bond valences to estimate the intrinsic properties, namely, compressibility and thermal expansion of complex spinel-type crystals. The composition-weighted average of bond force constants in tetrahedral and octahedral coordination polyhedra is derived as a function of the composition-weighted average of bond valences, which can be calculated according to the experimental chemical composition and crystal structural parameters. We discuss the coupled effects of tetrahedral and octahedral frameworks on the aforementioned intrinsic properties. The bulk modulus could be quantitatively calculated from the composition-weighted average of bond force constants in tetrahedral and octahedral coordination polyhedra. In contrast, a quantitative estimation of the thermal expansion coefficient could be obtained from the composition-weighted average of bond force constants in octahedral coordination polyhedra. These empirical methods have been validated by the results obtained for a new complex quaternary spinel-type oxynitride Mg0.268Al2.577O3.733N0.267 as well as MgAl2O4 and Al2.85O3.45N0.55 from the literature. Further, these empirical methods have the potential to be extensively applied in other types of complex crystals.