Elastic properties,chemical composition,and crystal structure of minerals

The observed systematic relations between velocities, density, and crystal structure in minerals are viewed as part of the general problem of the interactions of ions and electrons in solids. A complete explanation of these systematics would result from an adequate physical model of interactions between atoms in a crystal. For ionic models, understanding such interactions mainly requires knowledge of inter-ionic repulsive forces, which can be calculated from solutions for the electronic energy levels. The main forms of systematics developed in the last few years can be classed either as bulk modulus-molar volume (K-V _M ) or, equivalently, velocity-density (v-p) relations. Isostructural and isochemical (having constant mean atomic weight ) trends exist, and for both classes of systematics it is possible to produce semi-empirical universal expressions with the ability to predict elastic properties to a few percent. The best estimates of composition of the Earth's interior come from comparisons of mineral elastic properties with seismic data. On the basis of current velocity profiles of the Earth, the mantle appears to be chemically homogeneous.