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Published June 10, 1970 | Erratum + Published
Journal Article Open

The Bulk Modulus-Volume Relationship for Oxides


The relationship KV_0 = constant is shown to hold for oxides as well as for alkali halides. The product of bulk modulus and volume depends on the crystal structure, valance product, and a repulsive parameter. The exponential repulsive parameter ρ is calculated for oxides in the halite, wurtzite, corundum, spinel, perovskite, and rutile structures for which elastic constant data are available. This parameter satisfies the relationship ρ = 0.05 (1 + R + 3ΔR where R is the cube root of the molecular volume and ΔR is the difference between R and the radius of the small cation. The reduced Madelung constant α = A/mz_1z_2 (where A is the conventional Madelung constant, z_1z_2 is the valence product, and m is the number of ions in the chemical formula) satisfies the relation α = 0.20 + 0.45ΔR. The calculated values for the bulk modulus and the repulsive parameter can be used to estimate densities at pressures of a megabar with an accuracy of about 1%.

Additional Information

© 1970 American Geophysical Union. Received January: 2, 1970; revised March 13, 1970. Contribution 1654, Division of Geological Sciences, California Institute of Technology, Pasadena. Lamont-Doherty Geological Observatory Contribution No. 1512. The authors profited greatly from discussions with Edward Gaffney and Charles Sammis. We are greatly indebted to Robert Liebermann for measurements on iron-nickel oxides that provided the data to make the conclusions on the KV_o = constant law to apply to oxides with high iron content. This research was supported by NSF Grants GA-12703 and GA-1208, and DASA 01-70-C-0021.

Attached Files

Published - DLAjgr70b.pdf

Erratum - Anderson_et_al-1970-Journal_of_Geophysical_Research.pdf


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August 21, 2023
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