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

Abstract

We applied a lattice vibrational technique, based on representing the vibrational density of states with multiple-Einstein frequencies, to determine consistency of data on thermophysical properties and phase diagrams in the system MgO-FeO-SiO 2. We present analyses of these data in the temperature range between 0 and 2000 K and pressure range between 0 and 20 GPa. The result is a database containing phases relevant to the Earth upper mantle and transition zone. We show that consistency of different datasets associated with the dissociation of the ringwoodite form of Fe 2 SiO 4 depends on the crucible material that has been used to perform partitioning experiments between ringwoodite and ferropericlase, and that this results in different phase diagrams for FeSiO 3 and the post-spinel part of Mg 2 SiO 4-Fe 2 SiO 4. We show that the existence of a phase field coesite + ringwoodite in the phase diagram of FeSiO 3 is possible and that it might be used to fine-tune pressure scales. We demonstrate that the phase boundary between coesite and quartz is very sensitive to the low-temperature heat capacity of coesite and that heat capacity data of β-quartz are too large to be reconciled with the phase boundary between β-quartz and coesite. We compare our results with seismic data associated with the 410 km seismic discontinuity.

Thermodynamic properties of geikielite (MgTiO3) and ilmenite (FeTiO3) derived from vibrational methods combined with Raman and infrared spectroscopic data

“…( 1) takes into account crystal-field electronic effects in ilmenite. These effects were modelled in the same way as by Jacobs et al (2019):…”

“…The analysis is based on a lattice vibrational method, from which we derive thermodynamic models for the end members and the solid solution phase formed from them. Jacobs et al (2019Jacobs et al ( , 2017Jacobs et al ( , 2007 demonstrated that models derived from lattice vibrational methods, such as the multiple-Einstein or Kieffer (1979) methods, result in accurate phase diagrams and thermodynamic properties free from unphysical behavior in the pressure-temperature regime of the Earth's (and the Moon's) interior. Besides, that, the formalism allows incorporating microscopic properties as model parameters, such as vibrational frequencies, Grüneisen, and anharmonicity parameters, which are derived from spectroscopic measurements or ab initio techniques.…”

“…Besides, that, the formalism allows incorporating microscopic properties as model parameters, such as vibrational frequencies, Grüneisen, and anharmonicity parameters, which are derived from spectroscopic measurements or ab initio techniques. This characteristic, absent in conventional methods based on independent parameterizations of 1-bar properties (e.g., Saxena 1996;Holland and Powell 2011), puts extra constraints on a thermodynamic analysis, and that appears to be especially useful for discriminating between the quality of different experimental data sets, such as shown for, for instance, the heat capacity of the wadsleyite and ringwoodite forms of Mg 2 SiO 4 , the akimotoite and perovskite forms of MgSiO 3 , and the coesite and stishovite forms of SiO 2 (Jacobs et al 2019(Jacobs et al , 2017 This characteristic is also advantageous when experimental data are missing, such as is the case for bulk modulus for both geikielite and ilmenite. Because thermodynamic properties are interdependent due to their relation to microscopic and static energy properties, missing experimental data on the bulk modulus can be compensated by available microscopic data, such as frequencies of vibrational modes in P-T space, in addition to thermodynamic data.…”

“…For the sake of transparency, the resulting thermodynamic descriptions are converted to multiple-Einstein models. Just as in previous works of Jacobs et al (2017Jacobs et al ( , 2019, we have stored our results in a small database, which is together with open source computational software, freely available on website http:// www. geo.…”

Evolution of diamond-forming systems of the mantle transition zone: ringwoodite peritectic reaction (Mg,Fe)2SiO4 (experiment AT 20 GPa)

“…Железосодержащий компонент FeSiO 3 вовлечен как стабильный в твердый раствор (Mg,Fe)SiO 3 . При этом соединение FeSiO 3 является нестабильным в качестве промежуточной фазы двойной системы FeO-SiO 2 при 20 ГПа (обзор в Jacobs et al, 2019). Экспериментально определено, что железосодержащий компонент может входить в состав (Mg,Fe)SiO 3 до 20−40 мол%, тем самым определяя предел растворимости данного компонента (Tomioka et al, 2002 Магнезиовюстит MWus присутствует в экспериментальных образцах двух стартовых составов и представляет собой твердые растворы периклаза и вюстита.…”