Probing the role of MgSiO3 polymorphs in deep mantle processes

This Ph.D. Thesis presents a completely theoretical study, based on state-of-the-art hybrid DFT calculations, on the thermodynamics and phase stability of candidate minerals that have been selected due to their relevant role in determining the mineralogical composition and physico-chemical properties of the Earth’s mantle. Such minerals are the polymorphs of MgSiO3, in particular the MgSiO3 pyroxenes. The choice of these minerals derives from their large stability field that spans the shallower portions of the Earth’s mantle, down to the mantle transition zone. In fact, pyroxenes make up as much as 30% vol of the Earth’s upper mantle and are involved in several processes that take place in the interior of our planet that are of great interest from a geochemical, petrological and geophysical point of view, such as partial melting and the occurrence of global seismic discontinuities. Moreover, stable and metastable pyroxenes are strongly involved in the dynamics of subducting slabs. In fact, the presence of metastable pyroxenes in subducting slabs directly affects the density of the down-going plate, modifying its buoyancy and favouring slab stagnation at the mantle transition zone. Despite their importance, information on physico-chemical and thermodynamic properties of these minerals is lacking and affected by large uncertainties in current databases, hindering the possibility not only to obtain a clearer picture of their phase stability, but also to better comprehend their rheological behaviour at mantle conditions, preventing the interpretation of the global-scale processes in the Earth. This study focused on the theoretical simulation of thermodynamic and thermoelastic properties of MgSiO3 pyroxenes [namely, low-pressure clinoenstatite (LP-CEn), orthoenstatite (OEn), protoenstatite (PEn), high-temperature clinoenstatite (HT-CEn), high-pressure clinoenstatite (HP-CEn)], performed by ab initio DFT calculations up to conditions compatible with their stability in the deep mantle. The ab initio thermodynamic data computed in this work represent the first attempt to build up a complete dataset of both physically- and internally-consistent properties for MgSiO3 pyroxenes in a broad range a P-T conditions. This first-principles dataset includes all the main thermodynamic properties necessary for the calculation of the Gibbs free energy (i.e.: enthalpy, entropy, heat capacity, volume thermal expansion, bulk modulus and its pressure and temperature derivatives elastic moduli and seismic properties), hence to investigate phase stability relations of pyroxenes from subsolidus to liquidus conditions. The calculation of the Gibbs free energy at high-pressure and high-temperature conditions and its minimisation provides information on the relative stability of MgSiO3 pyroxenes, hence allows the calculation of phase diagrams. Moreover, thermoelastic properties computed at high pressure and temperature, such as the thermal equation of state and volume thermal expansion, are fundamental to predict volume and density changes at mantle conditions, which in turn allows to constrain the rheological role of pyroxenes in mantle processes. Computed data also include the elastic and seismic properties (i.e. the full elastic constant tensor and longitudinal and transverse wave velocities), that can be used to infer seismic velocity jumps and impedance contrasts, allowing for a direct comparison with seismological observations on mid-mantle global seismic discontinuities and providing thermodynamic constraints on their origin. In particular, the origin of the so-called X-discontinuity in the mantle, between 270 and 330 km depths, has been temptatively interpreted in the literature as closely related to mineralogical phase transitions that include the OEn to HP-CEn phase transformation as a viable candidate. The main results, implications and open issues that came out from this work can be summarized as follows:  An initio hybrid DFT-QHA calculations at the B3LYP level of theory improve the accuracy on the thermodynamic properties of high-pressure magnesium silicates with respect to less sophisticated LDA and GGA density functionals. In order to test the performance of B3LYP, a first stage in the development of this PhD project has been dedicated to the theoretical simulation of thermodynamic and thermoelastic properties of γ-Mg2SiO4 ringwoodite, using this mineral as a sort of beta test for calculations on more complex crystal structures. The obtained results not only show that ab initio B3LYP calculations are able to accurately predict thermodynamic and thermoelastic properties of this fundamental mineral phase up to lowermost mantle transition zone conditions, but clearly demonstrate that empirical extrapolation of thermoelastic data to deep mantle conditions should be taken with care to avoid inaccurate or spurious predictions in phase equilibrium modelling (cf. Belmonte et al., 2022).  Ab initio B3LYP thermodynamic properties of all the pyroxene polymorphs of MgSiO3 (i.e. PEn, OEn, LP-CEn, HP-CEn and HT-CEn) allow to obtain the full phase diagram of MgSiO3, hence to provide original insights on the thermodynamic behaviour of such phases at P-T conditions compatible with their stability in the Earth’s mantle. Despite the lack of experimental results, B3LYP calculations compare favourably with the few experiments available in the literature. Thermodynamic properties of most of the investigated phases have been determined for the very first time. For instance, the first comprehensive ab initio thermodynamic dataset for high-temperature clinoenstatite (HT-CEn) has been defined in this work, considering that no experimental data exist on this phase and the only information currently available come from thermodynamic assessments. Thermoelastic properties of protoenstatite (PEn), like volume thermal expansivity and thermal equation of state parameters, were previously almost unknown due to experimental difficulties in the synthesis and characterization of this phase. Ab initio calculations performed in this work on high-pressure clinoenstatite (HP-CEn) help to fill the gap in terms of thermodynamic information about this unquechable phase.  All the pyroxene phase transitions occurring in the MgSiO3 system have been investigated and calculated by employing the thermodynamic dataset obtained via first principles in this work. The following univariant equilibria have been determined: MgSiO3 (low-pressure clinoenstatite) = MgSiO3 (orthoenstatite), MgSiO3 (orthoenstatite) = MgSiO3 (protoenstatite), MgSiO3 (protoenstatite) = MgSiO3 (high-temperature clinoenstatite), MgSiO3 (orthoenstatite) = MgSiO3 (high-pressure clinoenstatite), MgSiO3 (low-pressure clinoenstatite) = MgSiO3 (high-pressure clinoenstatite). The investigation of these phase equilibria allowed to obtain novel information on the stability of pyroxenes at mantle conditions. Moreover, ab initio Clapeyron slopes and density contrasts calculated at high temperature and pressure conditions provide physical constraints to numerical modelling of subduction processes. The computational study shows how some of the phase equilibria involving pyroxenes are extremely sensible to small variations in the Gibbs free energy, thus difficult to reproduce even employing modern DFT-QHA calculations. In particular, some uncertainties still remain in some portions of the MgSiO3 phase diagram, such as the location of the LP-CEn - OEn phase transition boundary at ambient pressure and that of the triple point between PEn, OEn and liquid. These uncertainties seem to be related to a limitation of the DFT-QHA theory in accurately predicting the thermodynamic properties of orthoenstatite (OEn), which can be explained by the presence of relevant anharmonic effects in this phase (Zucker & Shim, 2009).  High-temperature clinoenstatite (HT-CEn) turns out to be unstable in the whole T(-P) range according to our investigation. This result strongly questions the role of this mineral as stable phase on the liquidus of MgSiO3 system at low pressures, as claimed by some Authors in the literature on the basis of unphysical thermodynamic data (e.g. Shi et al., 1994 and 1996; Gasparik, 2014).  The predicted melting curve of the MgSiO3 system, as determined by assessing thermodynamic properties for the liquid phase that are thermodynamically-consistent with those determined ab initio for the solid phases (cf. Belmonte et al., 2017), is in excellent agreement with experimental results in the pressure range 0 -10 GPa (Boyd et al., 1964; Presnall & Gasparik, 1990; Dalton and Presnall, 1997). Subsolidus and melting phase relations of pyroxenes in the theoretical phase diagram of MgSiO3 are thus fully consistent with each other.  Predicted P-T stability fields of orthoenstatite and high-pressure clinoenstatite in the MgSiO3 phase diagram are compatible with the observed depth range of the seismic X-discontinuity in the mantle (i.e. 250-350 km depths). Nevertheless, the theoretical seismic velocity jumps and impedance contrasts calculated for OEn and HP-CEn at mantle conditions turn out to be much higher than those inferred by global seismological studies, thus disregarding the OEn to HP-CEn phase transition as the only responsible for the origin of the X-discontinuity.