Mechanical and phase equilibria in inclusion–host systems

Mechanical and phase equilibria in inclusion–host systems are investigated in this paper. An inclusion–host system that is initially under lithostatic pressure and in mechanical and phase equilibria may undergo pressure–temperature change. The new elastic and plastic equilibrium, possible viscous relaxation, and phase equilibrium are considered. The new inclusion pressure typically differs from both the initial pressure and the pressure on the outside surface of the host. The inclusion is under isotropic stress (a single pressure) but the host is anisotropically stressed. The relative volume change of the inclusion differs from that of the inclusion-free host by 0.75(Pin−Pout)/Gh where Pin and Pout are the pressures on the inside and outside surfaces of the host, and Gh is the shear modulus of the host. Different inclusions in a single host may be under different pressures. A simple case of elastic anisotropy is also considered and the result shows that incorporation of elastic anisotropy is necessary for accurate calculations of volume and strain effect. For inclusions with roughly constant bulk modulus, the time scale of viscous relaxation is found to be 4ηh/(3Ki) where ηh is the viscosity of the host phase and Ki is the bulk modulus of the inclusion phase. If the host mineral does not relax viscously and does not fracture into pieces, the host mineral partially protects the inclusion and phase transition in the inclusion–host system is partial and spans a large T–P range even for one-component systems, in contrast to sharp phase transitions under isobaric and isothermal conditions. For example, a graphite inclusion in a diamond host does not completely convert to diamond when pressure on the diamond host increases. Using the chemical potential formulation of Kamb, about 1% of graphite would convert to diamond for every 1 GPa increase in host pressure. Because the inclusion pressure may be different from the lithostatic pressure on the host, pressure obtained from thermobarometers using inclusion–host pairs may not have depth significance. Correct `readingʹ of information stored by inclusion–host pairs requires an understanding of mechanical and phase equilibria involving the inclusion and host.