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%