About the relations between finite strain in non-cubic crystals and the related phenomenological P-V Equation of State

The notion of scalar strain in minerals is crucial for the formulation of P-V Equations of State (EoS). A scalar strain, , holding for any crystal symmetry has been derived by a rigorous and general approach, and then used to develop the related phenomenological P-V EoS. , which depends on V and the trace of the G*G0 matrix, can be split into two components, M and , where the former takes values close to those of the scalar strain according to Birch. M, providing the main contribution (often larger than 80%) to , is appropriate for the formulation of an EoS as M/V behaves regularly in the limit of an unstrained configuration. The phenomenological EoS based on M shows the same dependence on the elastic parameters (bulk modulus and derivatives versus pressure) of the usual Birch-Murnaghan EoS, and yields comparable results. Slight deviations occur for low symmetry minerals. This work is meant to contribute (i) to shed light on the relationships between scalar strain and related P-V EoS’s, and (ii) to provide a most general EoS which includes, as a particular case, the Birch-Murnaghan model and explains why this latter is reliable for crystal symmetry other than the cubic one, for which it was originally derived.