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.

High-pressure x-ray diffraction studies on vaterite-type borates were reported on the above paper and their room-temperature P-V equation of state (EOS) determined. YBO₃/Eu³⁺ and GdBO₃ were found to have bulk moduli around 320 GPa, 90% larger than the bulk modulus obtained for EuBO₃. Consequently, it was stated that vaterite-type borates are as incompressible as cubic BN. Such a different compressional behavior of isomorphic borates contradicts the known systematic of related borates. Here, we show that the conclusions reported on the above article could be hindered by experimental errors and artifacts. Ab initio calculations support our criticism giving similar bulk moduli (130–141 GPa) in the three compounds. Based upon these arguments, we conclude that the high-pressure behavior of vaterite-type borates should be revised using accurate experimental techniques. Finally, a methodological critic on EOS fits and to structural refinements is also presented.