Precise measurements of enthalpy of postspinel transition in Mg₂SiO₄ and application to the phase boundary calculation

Abstract

Drop solution enthalpies (ΔH°d‐s) of Mg2SiO4 ringwoodite, Mg2SiO4 forsterite, perovskite‐type MgSiO3 (bridgmanite), and MgSiO3 enstatite were measured using a single batch of 2PbO · B2O3 solvent at 978 K. From the obtained ΔH°d‐s values of Mg2SiO4 ringwoodite, MgSiO3 bridgmanite, and MgO, an enthalpy of the postspinel phase transition, Mg2SiO4 ringwoodite = MgSiO3 bridgmanite + MgO, was determined to be 78.54 ± 2.28 kJ/mol. Thermodynamic calculations using the obtained phase transition enthalpy and available thermochemical and thermoelastic data provided the phase transition pressure of 23.1 ± 1.4 GPa at 298 K. This value is comparable to those at about 2000 K determined by previous experimental and theoretical studies, implying a considerably gentle Clapeyron slope. Thermodynamic calculations of the postspinel boundary at high temperatures in the anhydrous condition by changing thermochemical and thermoelastic parameters within the uncertainties suggested that the postspinel transition pressure of Mg2SiO4 at high temperature is lower than the pressure corresponding to the global average depth of the “660 km” seismic discontinuity in the Earth's mantle (~23.5 GPa) estimated from one‐dimensional reference Earth models and that a most likely Clapeyron slope is about −1 MPa/K. The postspinel transition in the hydrous condition with about 2 wt % H2O, which shows higher transition pressure and steeper Clapeyron slope than those in the anhydrous condition, gives a plausible explanation for seismic observations on the 660 km discontinuity, and therefore, hydrous mantle transition zone would be required.

First Principles Thermodynamics of Minerals at HP–HT Conditions: MgO as a Prototypical Material

“…The ab initio phase boundary is localized at slightly higher pressures (≈1-2 GPa) than those determined by other HP-HT experiments [124,127,129,130,133] (see Figure 11a). The calculated Clapeyron slope (i.e., dP/dT = −2.53 MPa/K) agrees well with those obtained by the most part of experimental investigations (ranging from −4.0 to −2.0 MPa/K) [121,[124][125][126][127]131,132,135], while other works [129,130,133,134] suggest a more gentle slope of the phase boundary (i.e., between −2.0 and −1.0 MPa/K or even less) (see Table 5). B3LYP results are in qualitative agreement with previous GGA calculations [137][138][139], whereas LDA [137] severely underestimates transformation pressures of the post-spinel reaction (see Figure 11b).…”

“…Ab initio B3LYP results show an excellent agreement with the in situ LH-DAC X-ray diffraction study of Shim et al [128] and the multi-anvil experiments of Ishii et al [132], as well as with calculations based on accurate calorimetric measurements by Akaogi and Ito [126] and Akaogi et al [131] (Figure 11a; see also Figure Table 5), although a recent study found a lower enthalpy of reaction [134]. The ab initio phase boundary is localized at slightly higher pressures (≈1-2 GPa) than those determined by other HP-HT experiments [124,127,129,130,133] (see Figure 11a).…”

“…The effect of lattice vibrations seems to be crucial to correctly predicting the high-pressure phase transformation; ab initio static enthalpy calculations [137][138][139]141] give transition pressures that are overestimated (by ≈1−2 up to 10 GPa) compared with those obtained by including vibrational contributions to thermodynamic properties (i.e., by minimizing Gibbs free energies instead of static enthalpies). [121,[124][125][126][127][128][129][130][131][132][133][134][135] and other ab initio calculations [137][138][139]. Figure 11.…”

“…Owing to its geophysical implications, the Mg2SiO4 post-spinel phase transformations have been investigated by several experimental studies in the last decades [124][125][126][127][128][129][130][131][132][133][134][135]. Although experimental results are not consistent with each other concerning the P-T localization of the phase equilibrium boundary, there is general agreement about its most important thermodynamic feature; that is, the negative Clapeyron slope (i.e., dP/dT < 0) or endothermic character (i.e., ∆Hrxt > 0).…”

Researching the Earth—and a Few of Its Neighbors

“…However, in applications where ab initio calculations are not possible, practical, or necessary, the simpler models are still being used. For example, Kojitani et al (2015) used the model in Kieffer (1979c) to estimate heat capacities for MgSiO 3 (bridgmanite) in calculations of the postspinel phase boundary in Mg 2 SiO 4 . Gavrikov et al (2015) and Gavrichev et al (2015) used the methodology to smooth measured data for new structural complexes in the lanthanide acetylacetonates and for samarium-monazite (SmPO 4 ) in the context of properties of pegmatites and granites.…”