Efficient parametrization of high-pressure elasticity

Since high-pressure physics quite generally involves large deformations, it usually calls for a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) accurately into account. In a recent paper [A. Troster, W. Schranz, and R. Miletich, Phys. Rev. Lett. 88, 55503 (2002)], as a by-product of formulating a Landau theory of high-pressure phase transitions, we have constructed a parametrization of the elastic behavior of crystals of cubic, tetragonal, or orthorhombic symmetry which is customized to purely hydrostatic stresses. Under plausible assumptions this parametrization allows one to simultaneously describe the pressure dependence of the crystal lattice parameters and elastic constants in terms of comparatively simple expansions in powers of the pressure which involve a much smaller number of parameters than needed in, e.g., an approach using nonlinear elastic constants of higher order. In addition, the resulting formulas give rise to certain consistency checks for a set of unit cell parameters and elastic constants, which any such set-obtained from experiments or computer simulations-has to pass without approximation. However, the validity of our assumptions remained to be checked against experimental data. In this work we present detailed derivations of the approach sketched in the paper cited above and show that it can be successfully applied to describe data of recent high-pressure experiments on olivine, fluorite, garnet, magnesium oxide, and stishovite. (c) 2006 American Institute of Physics.