Thermal expansivity, heat capacity and bulk modulus of the mantle

SUMMARY We derive exact expressions for the thermal expansivity, heat capacity and bulk modulus assemblages with arbitrarily large numbers of components phases, including influence phase transformations chemical exchange. illustrate results in simple two-component, two-phase systems, Mg–Fe olivine-wadsleyite Ca–Mg clinopyroxene-orthopyroxene a multicompontent model mantle composition form pyrolite. For latter we show expansivity over entire pressure–temperature regime to 40 GPa, or depth 1000 km. From new expression buoyancy parameter that is valid phases which defined at every point space. Results reveal regions where magnitude larger than those transitions are most commonly included convection simulations. These include wadsleyite garnet ferropericlase transition, encountered along hot isentropes (e.g. 2000 K potential temperature) transition zone, stishovite bridgmanite cold shallow lower mantle. also typical isentrope relate it Bullen inhomogeneity parameter. All computed our code HeFESTo, updates improvements discuss, implementation modulus, generalization allow pressure dependence non-ideal solution parameters an improved numerical scheme minimizing Gibbs free energy. Finally, present global inversion updated incorporate more recent from experiment first principles theory, as well (nal phase), species: Na-majorite NaAlO2 end-member ferropericlase.