An investigation into thermodynamic consistency of data for the olivine, wadsleyite and ringwoodite form of (Mg,Fe)2SiO4

Thermodynamic mixing properties of olivine derived from lattice vibrations

“…Static lattice and vibrational contribution to the Helmholtz energy for a mixture In Jacobs and de Jong (2005b) we used the Gibbs energy to derive element partitioning and phase diagrams for the olivine, wadsleyite and ringwoodite forms of (Mg,Fe) 2 SiO 4 solid solutions. The Gibbs energy of olivine was expressed on a one-site mixing basis, (Mg,Fe)Si 1/2 O 2 , as:…”

“…The second term represents the Gibbs energy contribution due to random (ideal) mixing of the Mg and Fe atoms. The last term is the excess Gibbs energy representing the deviation from ideal mixing of these atoms, which is expressed as a polynomial function in composition in Jacobs and de Jong (2005b). In the present work, we attempt to partition this contribution due to changes in the static lattice and lattice vibrations when mixing occurs.…”

“…According to models G and I the excess volume at Earth's mantle transition zone is not significantly different from the 1-bar experimental data of Schwab and Küstner (1977). The calculation of thermodynamic properties using our vibrational formalism is more complicated than that used by Jacobs and de Jong (2005b), in which we used polynomial functions to represent excess properties. For transparency we have calculated excess properties, including excess volume, in pressure-temperaturecomposition space with our vibrational formalism and subsequently fitted the results using polynomial functions.…”

“…For the static lattice contribution to the mixing properties we took the Helmholtz energy to be a linear combination of the Helmholtz energies for the endmembers at the volume of the mixture. Here, we shall explore the behavior of excess properties in P-T space and investigate if the results are significantly different from those derived by Jacobs and de Jong (2005b) where excess properties were parameterized using polynomial functions.…”

“…An empirical model incorporating the change of magnetic ordering has been included as well. Because our vibrational model incorporates more physical properties relative to polynomial models used by, e.g., Fabrichnaya (1998), Holland and Powell (1998), Saxena (1996) and used in our previous work Jacobs and de Jong (2005b), the thermodynamic description of substances is more unambiguously constrained. For instance, in Jacobs et al (2006) we have shown for c-Mg 2 SiO 4 that this results in a better discrimination of the quality of different experimental data sets.…”