Thermodynamic Predictions of Thermal Expansivity and Elastic Compliances at High Temperatures and Pressures Applied to Perovskite Crystals

Abstract

The possibility of near zero thermal expansion coefficients at very high pressures is explored for application to the Earth’s core materials and mantle dynamics. The pressures in the Earth are large enough to effectively reduce thermal expansion coefficients to values which will decouple heat from mechanical work. It is shown that at pressures below the bulk modulus the thermal expansion coefficient will approach zero in all simple linear-elastic crystalline models. Advanced models of crystalline elastic solids based on interatomic potentials and density functional theory are shown to violate Gibb’s potential for a solid, crystalline material described by three elastic matrix compliance entries; it is established that the temperature dependence of S 11 and S 12 are thermodynamically identical; it is also established that the pressure dependence of S 11 and S 12 are thermodynamically identical. The basis for thermal energy in materials is the phonon energy in solids. However, it is noted that heat capacity measurements which are obtained from constant pressure heat capacity conditions converted to constant volume values on isobars are not in the correct state when compared to theoretical models; at atmospheric pressure there may be very little difference between these states but at very high pressures the effect may be major. Very large pressures always reduce thermal expansion coefficients; the importance of very small thermal expansion coefficients is discussed in relation to physical processes deep in the core and mantle of the Earth.