Application of the fourth-order anharmonic theory to the prediction of equations of state at high compressions and temperatures

Abstract

The fourth-order anharmonic theory is the extension of the ordinary theory of lattice dynamics into the regime of finite strain. Exhaustive numerical applications of the theory at high pressure are made, yielding predictions for density, temperature and elastic moduli of seventeen solids under shock compression. The theory describes well most of thed density data to compressions ΔV/ V 0)max which are generally in accord with expectation (0.30), with some notable exceptions. The data at higher shock temperatures (on initially porous samples) are considerably fewer; the theoretical predictions are generally accurate. The elastic moduli data in the shock state are fewer yet; the theory gives less satisfactory predictions. The geophysical interest in these results is that that total elasticity (density, thermal expansivty and elastic velocities) of solids under upper mantle conditions can be described within a unified theoretical framework. We cannot say at present if the theory is reliable under the conditions of the lower mantle. This uncertainty is shown to include also the predictions of the Eulerian formulation of finite strain theory.