Elastic properties of the lower mantle inferred from rigid ion lattice models

Abstract

Simple theoretical rigid ion lattice models, utilizing two-body central force exponential type repulsive potentials, for first and second nearest neighbor interactions, have been applied to estimate the higher order elastic constants of several alkali halides and NaCl-structure oxides. The results provided by the theoretical models for the first and second pressure derivatives of the bulk modulus ( K′ 0and K″ 0) for the alkali halides are generally consistent with available experimental data. Model calculations of K″ 0 for the oxides MgO, CaO, SrO, and BaO, are about an order of magnitude less than those for the alkali halides. Depending on the details of the lattice model, the present results suggest a value of K″ 0 for MgO in the range −1.7–−3.1 Mbar −1. In addition, the theoretical lattice models indicate values for the shear-related elastic constants C″ s, C″ 44, and μ″ 0 of the NaCl-structure oxides which are markedly lower than those of the alkali halides. The range of values for K″ 0 and the second pressure derivative of the rigidity modulus μ″ 0, which appear from the present results to characterize close-packed oxides, are consistent with estimates of these parameters for the Earth's lower mantle, assuming an adiabatic temperature gradient and compositional homogeneity. Therefore, it is not necessary to invoke a vertical compositional gradient in the deep mantle to account for the observed variation in elastic properties. However, the range of the theoretical values for K′ 0and μ″ 00 which appear to characterize lower mantle oxide materials, make it necessary to use higher order elastic properties in the equation of state in order to obtain accurate and meaningful evaluations of the composition and state of the Earth's deep interior.