The relationship between linear elasticity theory of solids and their equations of state (EoS) is reviewed, along with the commonly-used types of isothermal EoS, thermal expansion models, and P-V-T EoS. A new console program, EosFit7c, is presented. It performs EoS calculations and fitting for both volume and linear isothermal data, isobaric data and P-T data. Linear data is handled by cubing the quantities and treating them as volumes in all EoS formulations. Least-squares fitting of EoS to data incorporates the option to weight the fit with the measurement uncertainties in P, V and T simultaneously. The EosFit7c program is built with a new library of subroutines for EoS calculations and manipulation, written in Fortran. The library has been incorporated as a module, cfml_eos, in the publicly-available CrysFML library. The module handles Murnaghan, Tait, Birch-Murnaghan, Vinet, and Natural Strain EoS. For P-V-T calculations any of these isothermal EoS can be combined with a variety of published thermal expansion models, including a model of thermal pressure. The entire library has been revalidated against other software and against an ab-initio re-derivation of the EoS, which identified a number of small errors in published formulae for some EoS.

The concept of the phonon-mode Grüneisen tensor is reviewed as method to determine the elastic strains across crystals from the changes in the wavenumbers of Raman-active phonon modes relative to an unstrained crystal. The symmetry constraints on the phonon-mode Grüneisen tensor are discussed and the consequences for which combinations of strains can be determined by this method are stated. A computer program for Windows, stRAinMAN, has been written to calculate strains from changes in Raman (or other phonon) mode wavenumbers, and vice-versa. It can be downloaded for free from www.rossangel.net.

Minerals trapped as inclusions within other host minerals can develop residual stresses on exhumation as a result of the differences between the thermo-elastic properties of the host and inclusion phases. The determination of possible entrapment pressures and temperatures from this residual stress requires the mutual elastic relaxation of the host and inclusion to be determined. Previous estimates of this relaxation have relied on the assumption of linear elasticity theory. We present a new formulation of the problem that avoids this assumption. We show that for soft inclusions such as quartz in relatively stiff host materials such as garnet, the previous analysis yields entrapment pressures in error by the order of 0.1 GPa. The error is larger for hosts that have smaller shear moduli than garnet.

Elastic geothermobarometry is a method of determining metamorphic conditions from the excess pressures exhibited by mineral inclusions trapped inside host minerals. An exact solution to the problem of combining non-linear Equations of State (EoS) with the elastic relaxation problem for elastically isotropic spherical host-inclusion systems without any approximations of linear elasticity is presented. The solution is encoded into a Windows GUI program EosFit-Pinc. The program performs host-inclusion calculations for spherical inclusions in elastically isotropic systems with full P-V-T EoS for both phases, with a wide variety of EoS types. The EoS values of any minerals can be loaded into the program for calculations. EosFit-Pinc calculates the isomeke of possible entrapment conditions from the pressure of an inclusion measured when the host is at any external pressure and temperature (including room conditions), and it can calculate final inclusion pressures from known entrapment conditions. It also calculates isomekes and isochors of the two phases.