Elasticity of mixtures and implications for piezobarometry of mixed-phase inclusions

Elastic thermobarometry (or piezobarometry) is the process of determining the P (pressure) and T (temperature) of entrapment of inclusions from their pressure, stress or strain measured when their host mineral is at room conditions. The methods and software used for piezobarometry are currently restricted to inclusions consisting of single phases. In this contribution we describe the theory of the elasticity of mixtures of different phases and combine it with the existing isotropic analysis of the elastic interactions between single-phase inclusions and their hosts to calculate the inclusion pressures of mixed-phase inclusions. The analysis shows that the reliability of calculated entrapment conditions for mixed-phase inclusions, including those containing fluid plus minerals, depends in a complex way upon the contrasts between the elastic properties of the host and the phases in the inclusion. The methods to calculate the entrapment conditions of mixed-phase inclusions have been incorporated into the EosFit7c program (version 7.6) that is available as freeware from http://www.rossangel.net.