Abstract
A method for the self-consistent description of the large variations of unit-cell parameters of crystals with pressure and temperature is presented. It employs linearized versions of equations of state (EoSs) together with constraints to ensure internal consistency. The use of polynomial functions to describe the variation of the unit-cell angles in monoclinic and triclinic crystals is compared with the method of deriving them from linearized EoSs for d spacings. The methods have been implemented in the CrysFML Fortran subroutine library. The unit-cell parameters and the compressibility and thermal expansion tensors of crystals can be calculated from the linearized EoSs in an internally consistent manner in a new utility in the EosFit7c program, which is available as freeware at http://www.rossangel.net.
Highlights
The measurement of the response of the unit-cell parameters and the volume of crystals to hydrostatic pressure (P) and temperature (T) provides fundamental information about the nature and anisotropy of the bonding within the structures of crystals
Except for cubic crystals, as pressure is increased the different axial moduli increase at different rates, and the symmetry constraints relating the bulk modulus and its derivatives to the linear moduli and their derivatives are violated if conventional volume and axial equations of state (EoSs) are used to describe the variation of the moduli with pressure
Whether or not the effects of anisotropy on the calculation of cell parameters and volumes is significant depends on the elastic properties of the crystal and on the precision of the experimental data, the pressure and compression range being considered, and the precision and internal consistency required in calculations
Summary
The measurement of the response of the unit-cell parameters and the volume of crystals to hydrostatic pressure (P) and temperature (T) provides fundamental information about the nature and anisotropy of the bonding within the structures of crystals. These methods can be extended to any direction within the unit cell In most cases they provide an accurate description of the variation of the individual unitcell parameters with P and/or T, and yield linear compressibilities and moduli that agree with those determined by direct measurements of the elastic tensors. We use the method of Paufler & Weber (1999) to calculate the compressibility and thermal expansivity tensors directly from these linearized EoSs at any P and T This allows the elastic behaviour of any direction in the crystal structure to be described in a consistent manner and the principal axes of the tensors, which include the directions of greatest and least strain, to be unambiguously defined. The architecture of the EosFit7c program allows it to be called from other software such as MATLAB (The MathWorks Inc., Natick, MA, USA) to perform EoS calculations without the need to cross-compile software directly with the CrysFML library
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