How large are departures from lithostatic pressure? Constraints from host-inclusion elasticity

Minerals trapped as inclusions within other host minerals will develop non-lithostatic pressures during both prograde and retrograde metamorphism because of the differences between the thermoelastic properties of the host and inclusion phases. There is only a single possible path in P-T space, the entrapment isomeke, along which no residual pressure would be developed in a host-inclusion system; non-lithostatic pressures are developed in inclusions as a result of the external pressure and temperature deviating from the isomeke that passes through the entrapment conditions. With modern equation of state and elasticity data for minerals now available, it is possible to perform precise calculations of the isomekes for mineral pairs. These show that isomeke lines are not straight lines in P-T space at metamorphic conditions. We show that silicate inclusions in silicate hosts tend to have flat isomekes, with small values of (partial derivative P/partial derivative T)(isomeke), because of the small range of thermal expansion coefficients of silicate minerals. As a consequence, the general behaviour under decompression is for soft silicate inclusions in stiffer hosts to develop excess pressures, whereas a stiff silicate inclusion in a softer matrix will experience lower pressures than lithostatic pressure. The opposite effects occur for compression after entrapment on the prograde path. The excess pressures in inclusions, including allowance for mutual elastic relaxation of the host and inclusion, are most easily calculated by using the isomeke as a basis. Analysis of the simplest possible model of a host-inclusion system indicates that deviations from lithostatic pressure in excess of 1GPa can be readily produced in quartz inclusions within garnet in metamorphic rocks. For softer host minerals such as feldspar, the pressure deviations are smaller, because of greater elastic relaxation of the host. The maximum pressure deviation from lithostatic pressure in the host phase around the inclusion is one-third of the pressure deviation in the inclusion. Routines for performing these calculations have been added to the EosFit7c software package.