HR: 10:50h
AN: V21E-03    [PDF]
TI: A statistical approach to atomistic simulation of geophysical solid solutions
AU: Bukowinski, M S
EM: markb@socrates.berkeley.edu
AF: Earth & Planetary Science, UC Berkeley, Berkeley, CA 94720 United States
AU: * Akber-Knutson, S
EM: sofia@eps.berkeley.edu
AF: Earth & Planetary Science, UC Berkeley, Berkeley, CA 94720 United States
AB: Many materials of geophysical importance are solid solutions rather than pure minerals. Mascropic modeling of the thermodynamic properties of these minerals often necessitates ideal mixing assumptions. While atomistic models make it possible to model solid solutions without the ideal mixing approximation, such calculations were not computationally feasible until recently. Nevertheless, no convenient methodology for studying the configurational aspects of geophysical solid solutions currently exists, especially for the high temperatures of the earth. We introduce a technique for studying solid solutions at high temperature and apply it to the MgSiO$_3$-Al$_2$O$_3$-MgO system at lower mantle conditions. We use a statistical mechanics based approach that samples calculated Gibbs free energies of the solid solutions corresponding to different, and often very numerous, mixing configurations ({\em i.e.} ways to arrange atoms in mixing sites). Vibrational contributions to the Gibbs free energies are calculated from phonon spectra calculated under the quasiharmonic approximation. We then use the sampled configurational free energies to estimate configurational thermodynamic properties of the solid solutions. We first discuss the choice of an appropriate unit cell size that properly samples a space of mixing configurations and avoids imposing artificial ordering. We then compare Boltzmann-derived entropies of mixing with those resulting from ideal mixing. We also discuss the role of configurational heat capacity on the energetics of solid solutions at high temperatures. Finally, we introduce a technique for approximating configurational high temperature thermodynamic properties of solid solutions from 0 Kelvin energy distributions (over mixing configurations). Combining these results with only a few high temperature configurations greatly reduces the number of computations necessary to determine the full high temperature thermodynamic properties of complex mineral assemblages.
DE: 3210 Modeling
SC: Volcanology, Geochemistry, Petrology [V]
MN: 2003 Fall Meeting