Theoretical bounds for thermal expansion, specific heat, and strain energy due to internal stress

Theoretical bounds on the strain energy due to internal stress in polycrystalline materials are found using energy principles. These bounds are used to derive bounds on bulk thermal expansion; the expressions depend only upon the single-crystal stiffness and compliance tensors, the thermal expansion tensors, and the partial volumes of the mineral components. A description of the geometric configuration of the phases is not required in the analysis. Calculations based on published data for corundum, rutile, calcite, and quartz show that bounds on thermal expansion for polycrystalline calcite, which is the most anisotropic of the four minerals, differ by only 6%. The specific heat of the polycrystalline forms of these minerals is found to be very nearly equal to the single-crystal values. Theory is used to find hot-pressing pressure and temperature required for minimizing internal stresses at room conditions and to estimate internal stresses in surface rock that is free of internal stress at depth.