Elasticity of Solids at High Pressures and Temperatures : Theory, Measurement, and Geophysical Application

Citation

Davies, Geoffrey Frederick (1973) Elasticity of Solids at High Pressures and Temperatures : Theory, Measurement, and Geophysical Application. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SK7X-EE20. https://resolver.caltech.edu/CaltechTHESIS:02072018-154915291

Abstract

A theory for describing the elasticity of solids at simultaneous high pressures and high temperatures is developed by incorporating the fourth-order ahnarmonic theory of lattice dynamics into finite strain theory. The theory is applied to the analysis of a variety of data for MgO, SiO₂ and NaCl, and the results for MgO and SiO₂ used as the basis of a discussion of the constitution of the lower mantle. New results are reported of measurements of elastic properties of MgO shock-compressed to over 500 Kb.

The condition that finite strain equations be frame- indifferent is shown to require that only strain tensors belonging to a class of frame-indifferent strain tensors be used in finite strain expansion. It is shown that the generality of finite strain theory is not impaired by the inclusion of an explicit theory of thermal effects. Explicit equations for isotherms, isentropes and Hugoniots and for the effective elastic moduli of materials of cubic symmetry under hydrostatic stress are derived. The primary parameters of these equations are related to the elastic moduli and their pressure and temperature derivatives in an arbitrary reference state using thermodynamic identities, some of which are derived here.

Hugoniot data corresponding to different initial sample densities of MgO, SiO₂ and NaCl and original ultrasonic data of NaCl are used to test both the compressional and thermal parts of the theory, and to refine the equations of state of these materials. The frame-indifferent analogue, E, of the usual "Eulerian" strain tensor, ε, is found to usually give faster convergence of finite strain expansions than the "Lagrangian" strain tensor, η. The effect of usinq differ­ent strain measures on the values of parameters derived from data is demonstrated, and the adverse effects of using inappropriately derived parameters in extrapolation equations is demonstrated. Thermal effects in Hugoniot data are reasonably well described, but higher-order anharmonic effects appear to be required in the theory in order to describe the high temperature ultrasonic and thermal expansion data.

Measured velocities of rarefaction waves propagating into shocked MgO are in accord with a two-stage longitudinal (elastic)-hydrodynamic (plastic) decompression model, and constrain the high-pressure elastic moduli of MgO.

The effects on the determination of the lower mantle constitution of temperature, varying composition, the presence of phases denser than oxides mixtures, and the presence of iron in the "low-spin" electronic state are estimated, and a trade-off between many of these factors demonstrated. Iron content could range between 6% and 15% by weight of FeO. Silica content could range from 33% to 50% or more by weight. Phases a few percent denser than oxides mixtures seem to be likely. The temperature is very indeterminable.

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