Bulk Modulus-Density Systematics

Abstract

The elastic constants of crystals show a general tendency to increase as the mean molar volume 〈V〉 = 〈M〉/ρ decreases. The role of other factors, such as cation radius, crystal field effects, and anion-cation coordination, can now be discussed with available elastic constant data. For a given coordination the parameter ψ_0 = (ρ_0/〈M〉) Φ^(−⅓)_(0) (where ρ_0 is the zero-pressure density, 〈M〉 is the mean atomic weight, and Φ_0 is the ratio of the zero-pressure bulk modulus to the density) decreases with increasing cation radius and with cell volume per oxygen atom unless a nonspherical transition element ion, such as Fe++, substitutes for a nontransition ion, such as Mg++. The calcium effect discovered by G. Simmons is a special case of the cation radius effect. The elastic ratio Φ0 for complex oxides is approximately a molar average of the Φ0 of the component simple oxides. For silicates it appears that an empirical table of Φ_0(SiO_2) can be constructed for various mineral groups. Tentatively, Φ0(SiO_2) is roughly that of α quartz for the feldspars, β quartz for olivines and pyroxenes, coesite for garnets, and stishovite for spinels.