Thermodynamic mixing properties of olivine derived from lattice vibrations

Abstract

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe 2 SiO 4 . This semi-empirical technique is based on an extension of Kieffer's model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict thermodynamic mixing properties of olivine (Mg,Fe) 2 SiO 4 solid solutions by using results of our previous work on the system MgO-SiO 2 . Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium-iron solid solutions of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity for temperatures below 100 K.

Thermophysical properties and phase diagrams in the system MgO–SiO2–FeO at upper mantle and transition zone conditions derived from a multiple-Einstein method

“…Figure 1 shows that this has a significant effect on the heat capacity. Aronson et al (2007) and Jacobs and de Jong (2009) used a crystal-field expression via the partition function, Z, to express the Helmholtz energy contribution as:…”

“…Equation (2) contains the factor 1/g 1 to constrain the entropy contribution to zero at zero temperature and zero pressure, commensurate with the third law of thermodynamics. Expressions for thermodynamic properties derived from the Helmholtz expression are detailed in Jacobs and de Jong (2009). Because the effect of volume on the energies, ε i , is unknown experimentally for all iron endmembers, we assume that they have constant values.…”

“…(3) alone. Jacobs and de Jong (2009) described it with an empirical expression for the Gibbs energy given by Hillert and Jarl (2)…”

“…Some remarks about selecting data in our analysis are necessary. For the description of excess volume of olivine we used, just as in Jacobs and de Jong (2009), experimental data obtained by Schwab and Küstner (1977) for synthetic (Mg 1−x Fe x ) 2 SiO 4 olivine mixtures, which cover the complete composition range. These investigators showed that natural olivines have larger volumes than synthetic ones, resulting in larger excess volumes for the solid solutions.…”

Complex phase distribution and seismic velocity structure of the transition zone: Convection model predictions for a magnesium-endmember olivine–pyroxene mantle

“…This requires the extension of our thermodynamic data base with iron, which 570 is currently in progress (Jacobs and de Jong, 2009 and magnesium-pyroxene system.…”