4 - Equations of state of terrestrial materials

Summary

Introduction

The dynamical properties of a planet depend on the way in which the density varies with radius, and seismological properties depend also on the way in which the elastic moduli and elastic dissipation vary with radius. The data we have for the Earth are sufficiently complete that the variations of density and elastic moduli with radius can be derived from them and we are then presented with the problem of inferring the mineralogical and chemical composition consistent with them. When, as for the other planets, seismic data are lacking, we must proceed in a different way and derive the variation of density from a postulated composition, asking if it leads to the observed mass and moment of inertia. In either case, we must know how the density depends on pressure, temperature and composition, for all these vary with radius, and when we discuss the Earth and the Moon, for which we have seismic data, we must also examine the dependence of the elastic moduli upon the three variables. Some idea of the problems that arise, of the theoretical principles, of possible experimental methods, and of the systematics of equations of state of minerals has already been given in Chapter 1, and it is the aim of this chapter to give a more extensive and systematic account.