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 behavior of a number of commonly used pressure media, including nitrogen, argon, 2‐propanol, a 4:1 methanol–ethanol mixture, glycerol and various grades of silicone oil, has been examined by measuring the X‐ray diffraction maxima from quartz single crystals loaded in a diamond‐anvil cell with each of these pressure media in turn. In all cases, the onset of non‐hydrostatic stresses within the medium is detectable as the broadening of the rocking curves of X‐ray diffraction peaks from the single crystals. The onset of broadening of the rocking curves of quartz is detected at ∼9.8 GPa in a 4:1 mixture of methanol and ethanol and at ∼4.2 GPa in 2‐propanol, essentially at the same pressures as the previously reported hydrostatic limits determined by other techniques. Gigahertz ultrasonic interferometry was also used to detect the onset of the glass transition in 4:1 methanol–ethanol and 16:3:1 methanol–ethanol–water, which were observed to support shear waves above ∼9.2 and ∼10.5 GPa, respectively, at 0.8–1.2 GHz. By contrast, peak broadening is first detected at ∼3 GPa in nitrogen, ∼1.9 GPa in argon, ∼1.4 GPa in glycerol and ∼0.9 GPa in various grades of silicone oil. These pressures, which are significantly lower than hydrostatic limits quoted in the literature, should be considered as the practical maximum limits to the hydrostatic behavior of these pressure media at room temperature.

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EosFit7-GUI is a full graphical user interface designed to simplify the analysis of thermal expansion and equations of state (EoSs). The software allows users to easily perform least-squares fitting of EoS parameters to diffraction data collected as a function of varying pressure, temperature or both. It has been especially designed to allow rapid graphical evaluation of both parametric data and the EoS fitted to the data, making it useful both for data analysis and for teaching.