Bulk modulus—volume relationship for cation‐anion polyhedra

Abstract

A bulk modulus—volume relationship is demonstrated for cation coordination polyhedra in a variety of structure types including oxides, silicates, halides, sulfides, phosphides, and carbides: K p 〈d〉3/S2z c z a = 7.5 (Mbar Å 3), where K P is the polyhedral bulk modulus (in megabars), 〈d〉 is the mean cation‐anion separation (in angstroms), z c and z a are the cation and anion formal charge, and S2 is an empirical ionicity term, defined as 0.50 for oxides and silicates and calculated to be 0.75 for halides; 0.40 for sulfides, selenides, and tellurides; 0.25 for phosphides, arsenides, and antimonides; and 0.20 for carbides. The bulk modulus of a substance depends on the bulk moduli of component polyhedra and the manner in which these polyhedra are linked. In corner‐linked structures, such as quartz and framework silicates, mineral bulk moduli are significantly less than those of constituent corner‐linked polyhedra, because of accommodations resulting from changes of the metal‐oxygen‐metal angles. In layer structures such as micas, with extensive edge sharing within the layers but weak bonds between the layers, compression is highly anisotropic. Structures such as periclase, spinel, and garnet, with extensive edge sharing between polyhedra in three dimensions, have large bulk moduli similar to those of constituent polyhedra. Bulk moduli of mantle mineral phases approximate the moduli of component polyhedra because most mantle mineral structure types have edge sharing in three dimensions. Compression for a given polyhedron does not appear to depend upon the linkage topology of the structure.