Thermodynamics of mantle minerals - II. Phase equilibria

Abstract

S U M M A R YWe complete the development and description of a thermodynamic method for the computation of phase equilibria and physical properties of multiphase mantle assemblages. Our previous paper focused on the computation of physical properties. In this paper, our focus shifts to the phase equilibria. We further develop our theory to specify the ideal and excess contributions to solution properties and derive properties of multiphase assemblages. We discuss our global inversion strategy for determining the values of the free parameters in our theory and compare inverted parameter values with expectations based on scaling arguments. Comparisons between our method and experimental phase equilibria data encompass the pressure-temperature regime of Earth's mantle. Finally, we present applications of our method that illustrate how it may be used to explore the origins of mantle structure and mantle dynamics. Continuing rapid advances in experimental and theoretical petrology and mineral physics have motivated an expansion of the scope of our model via the addition of several new phases, and of the soda component: an appendix lists all parameters in our model and references to the experimental and theoretical studies that constrain them. Our algorithm for global minimization of the Gibbs free energy is embodied in a code called HeFESTo, and is detailed in a second appendix.

Spin crossover in ferropericlase and velocity heterogeneities in the lower mantle

“…1-4). The bulk and shear moduli of CaPv are those listed in Stixrude and Lithgow-Bertelloni's tables (60). The elastic moduli of MgPv are those reported earlier in ref.…”

Melting in super-earths

“…For the silicate melting point, we assume the Lindemann melting law [58] 8) wherem andv are the mean atomic mass and volume, respectively, k B is the Boltzmann constant, h is the Planck constant divided by 2π , θ is the Debye temperature and f is the critical ratio of vibration amplitude to atomic spacing at melting. For applications to the core-mantle boundary of super-earths, we assume that the solid phase is MgSiO 3 post-perovskite [59,60], and compute the volume and Debye temperature as a function of pressure along the 1600 K adiabat from the thermodynamic model of [38]. We chose the value of f = 0.…”

“…Melt fraction is assumed to vary linearly with temperature between solidus and liquidus, and the dependence of viscosity on melt fraction is taken from experiment [36,37]. The isentropic temperature (2400 K) is computed with HeFESTo assuming a potential temperature of 1600 K [38]; the solidus (3950 K) and liquidus (4950 K) temperatures are from an experimental study [39]. The cooling time is computed from equation (1.7) up to the temperature of the viscosity collapse, and from the scaling appropriate for hard turbulence and an overlying thick atmosphere at higher temperature [35].…”

“…The mantle adiabat is computed from the code HeFESTo [38], whereas the core adiabat is computed from the results of ab initio lattice dynamics calculations [57]. We determine the variation of pressure and density with radius by solving the equations of hydrostatic equilibrium and mass conservation [15], using the HeFESTo equation of state for the mantle, assumed to be of pyrolite composition [38], and for the core, an equation of state fit to the seismologically determined properties of the Earth's core [15].…”

The elastic solid solution model for minerals at high pressures and temperatures

“…This is true both of disordered models appropriate at high temperatures (Stixrude and Lithgow-Bertelloni 2011;Holland et al 2013) and of models including order-disorder (e.g., Carpenter 1988;Ghiorso 1990;Putnis 1992;Salje 1993;Holland and Powell 1996;Ghiorso and Evans 2002;Holland and Powell 2006). In these models, parameter values describing interaction energies are typically either constant, or linear functions of pressure and temperature.…”