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Published July 15, 1969 | Published
Journal Article Open

Bulk Modulus-Density Systematics


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.

Additional Information

© 1969 American Geophysical Union. Manuscript Received: 1 April 1969. The author would like to thank Taro Takahashi, Gene Simmons, Stan Marsh, and Edward Schreiber for making available unpublished data from their laboratories. He is grateful to Ed Gaffney and Tom Ahrens for many stimulating discussions. This research was supported by National Science Foundation grant GA 1003.

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