0000000000378753
AUTHOR
Alessandro Pavese
Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling
Intrinsic and extrinsic stability of the (Mg, Fe) O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth's mantle is investigated by the combination of quantum mechanical calculations (Hartree-26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg, Fe) O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23-42 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg, Fe) O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanit…
Melting temperature prediction by thermoelastic instability: An ab initio modelling, for periclase (MgO)
Abstract Melting temperature (TM) is a crucial physical property of solids and plays an important role for the characterization of materials, allowing us to understand their behavior at non-ambient conditions. The present investigation aims i) to provide a physically sound basis to the estimation of TM through a “critical temperature” (TC), which signals the onset of thermodynamic instability due to a change of the isothermal bulk modulus from positive to negative at a given PC-VC-TC point, such that (∂P/∂V)VC,TC = -(∂2F/∂V2) VC,TC = 0; ii) to discuss the case of periclase (MgO), for which accurate melting temperature observations as a function of pressure are available. Using first princip…
Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature
Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)c…
Aluminium distribution in an Earth's non–primitive lower mantle
The aluminium incorporation mechanism of perovskite was explored by means of quantum mechanics in combination with equilibrium/off-equilibrium thermodynamics under the pressure-temperature conditions of the Earth's lower mantle (from 24 to 80 GPa). Earth's lower mantle was modelled as a geochemically non-primitive object because of an enrichment by 3 wt% of recycled crustal material (MORB component). The compositional modelling takes into account both chondrite and pyrolite reference models. The capacity of perovskite to host Al was modelled through an Al2O3 exchange process in an unconstrained Mg-perovskite + Mg-Al-perovskite + free-Al2O3(corundum) system. Aluminium is globally incorporate…
Low-pressure ferroelastic phase transition in rutile-type AX2 minerals: cassiterite (SnO2), pyrolusite (MnO2) and sellaite (MgF2)
The structural behaviour of cassiterite (SnO2), pyrolusite (MnO2) and sellaite (MgF2), i.e. AX2-minerals, has been investigated at room temperature by in situ high-pressure single-crystal diffraction, up to 14 GPa, using a diamond anvil cell. Such minerals undergo a ferroelastic phase transition, from rutile-like structure (SG: P42/mnm) to CaCl2-like structure (SG: Pnnm), at ≈ 10.25, 4.05 and 4.80 GPa, respectively. The structural evolution under pressure has been described by the trends of some structure parameters that are other than zero in the region of the low-symmetry phase’s stability. In particular, three tilting-angles (ω, ω′, ABS) and the metric distortion of the cation-centred oc…
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…
The formation of silica high temperature polymorphs from quartz: Influence of grain size and mineralising agents
Abstract The formation of high-temperature silica polymorphs in presence of Na and K has been studied at various temperatures and soaking times, starting from quartzes of different grain size, ex situ as well as in situ. The results show that cristobalite and tridymite formation is strongly influenced by the nature and the amount of mineraliser added. In particular, K seems to discriminate more between the two structures, as it produces the largest observed amount of cristobalite. The disappearance of quartz can be controlled by the proper combination of mineraliser/temperature/time, which in turn control the amount and the type of polymorph formed, together with the amount of amorphous mat…
Lower mantle hydrogen partitioning between periclase and perovskite : a quantum chemical modelling
Abstract Partitioning of hydrogen (often referred to as H2O) between periclase (pe) and perovskite (pvk) at lower mantle conditions (24–80 GPa) was investigated using quantum mechanics, equilibrium reaction thermodynamics and by monitoring two H-incorporation models. One of these (MSWV) was based on replacements provided by Mg2+ ↔ 2H+ and Si4+ ↔ 4H+; while the other (MSWA) relied upon substitutions in 2Mg2+ ↔ Al3+ + H+ and Si4+ ↔ Al3+ + H+. H2O partitioning in these phases was considered in the light of homogeneous (Bulk Silicate Earth; pvk: 75%–pe:16% model contents) and heterogeneous (Layered Mantle; pvk:78%–pe:14% modal contents) mantle geochemical models, which were configured for lower…
About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO
Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…
Maximum entropy method : an unconventional approach to explore observables related to the electron density in phengites
The maximum entropy method (MEM) is used here to get an insight into the electron density [rho(r)] of phengites 2M (1) and 3T, paying special attention to the M1-formally empty site and charge distribution. Room temperature single crystal X-ray diffraction data have been used as experimental input for MEM. The results obtained by MEM have been compared with those from conventional structure refinement which, in turn, has provided the prior-electron density to start the entropy maximization process. MEM reveals a comparatively non-committal approach, able to produce information related to the M1-site fractional occupancy, and yields results consistent with those from the difference Fourier s…
Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members
Abstract A method has been developed, herein presented, to model binary solid solutions' volume, enthalpy and Gibbs energy using the energy state functions, E ( V , S ) , of the end-members only. The E ( V , S ) s are expanded around an unknown mixing volume, V Mix , and the fundamental equilibrium equation − ( ∂ E / ∂ V ) S = P is used to determine V Mix . V Mix allows us to model enthalpy, straightforwardly. The same argument holds using Helmholtz energy, F ( V , T ) , in place of E ( V , S ) , and the equilibrium equation becomes − ( ∂ F / ∂ V ) T = P . One can readily determine the Gibbs free energy, too. The method presented remarkably simplifies computing of solid mixings' thermodynam…