MMA‐EoS: A Computational Framework for Mineralogical Thermodynamics

Chust, Thomas; Steinle‐Neumann, Gerd; Dolejš, David; Schuberth, Bernhard S. A.; Bunge, Hans‐Peter

doi:10.1002/2017jb014501

Cited by 32 publications

(27 citation statements)

References 243 publications

(548 reference statements)

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“…Phase relations and physical properties of mantle minerals are evaluated self-consistently using a new implementation (Chust et al, 2017) of the thermodynamic model of Stixrude and Lithgow-Bertelloni (2011) based on a Birch-Murnaghan Mie-Grüneisen equation of state formulation. At least for density, the central property we are interested in, the model shows robust behavior beyond the P´T conditions of the lowermost mantle (Connolly and Khan, 2016).…”

Section: Mantle Modelingmentioning

confidence: 99%

A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths

Hakim

Rivoldini

Hoolst

et al. 2018

Icarus

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106

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More than a third of all exoplanets can be classified as super-Earths based on radius (1´2 R C ) and mass (< 10 M C ).Here we model mass-radius relations based on silicate mantle and iron core equations of state to infer to first order the structure and composition range of rocky super-Earths assuming insignificant gas envelopes. As their core pressures exceed those in the Earth by an order of magnitude, significant extrapolations of equations of state for iron are required. We develop a new equation of state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS) based on density functional theory results for pressures up to 137 TPa. A comparison of SEOS and extrapolated equations of state for iron from the literature reveals differences in density of up to 4% at 1 TPa and up to 20% at 10 TPa. Such density differences significantly affect mass-radius relations. On mass, the effect is as large as 10% for Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like super-Earths (core radius fraction of 0.8). We also quantify the effects of other modeling assumptions such as temperature and composition by considering extreme cases. We find that the effect of temperature on mass (< 5%) is smaller than that resulting from the extrapolation of the equations of state of iron and lower mantle temperatures are too low to allow for rock and iron miscibility for R < 1.75 R C . Our end-member cases of core and mantle compositions create a spread in mass-radius curves reaching more than 50% in terms of mass for a given planetary radius, implying that modeling uncertainties dominate over observational uncertainties for many observed super-Earths. We illustrate these uncertainties explicitly for Kepler-36b with well-constrained mass and radius. Assuming a core composition of 0.8ρ Fe (equivalent to 50 mol% S) instead of pure Fe leads to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle composition of Mg 0.5 Fe 0.5 SiO 3 instead of MgSiO 3 leads to a decrease of the core radius fraction to 0.33. Effects of thermal structure and the choice of equation of state for the core material on the core radius of Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.

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Section: Mantle Modelingmentioning

confidence: 99%

A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths

Hakim

Rivoldini

Hoolst

et al. 2018

Icarus

Self Cite

106

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“…The free-energy minimization can be carried out in two ways: by dynamic or by static implementation. Dynamic implementation means minimizing the Gibbs free-energy of the system at a particular value of pressure, temperature, and composition during the 10.1029/2018JB016032 inversion process (e.g., Afonso et al, 2013;Chust et al, 2017;Duesterhoeft & Capitani, 2013;Duesterhoeft et al, 2014;Khan et al, 2006). Alternatively in the static implementation, physical properties are calculated for a certain range of pressure-temperature conditions and stored in tables prior to the solution of the inverse problem (e.g., Zunino et al, 2011).…”

Section: Computation Of Mantle Mineral Phase Equilibriamentioning

confidence: 99%

Stochastic Inversion of P‐to‐S Converted Waves for Mantle Composition and Thermal Structure: Methodology and Application

et al. 2018

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We present a new methodology for inverting P‐to‐S receiver function (RF) waveforms directly for mantle temperature and composition. This is achieved by interfacing the geophysical inversion with self‐consistent mineral phase equilibria calculations from which rock mineralogy and its elastic properties are predicted as a function of pressure, temperature, and bulk composition. This approach anchors temperatures, composition, seismic properties, and discontinuities that are in mineral physics data, while permitting the simultaneous use of geophysical inverse methods to optimize models of seismic properties to match RF waveforms. Resultant estimates of transition zone (TZ) topography and volumetric seismic velocities are independent of tomographic models usually required for correcting for upper mantle structure. We considered two end‐member compositional models: the equilibrated equilibrium assemblage (EA) and the disequilibrated mechanical mixture (MM) models. Thermal variations were found to influence arrival times of computed RF waveforms, whereas compositional variations affected amplitudes of waves converted at the TZ discontinuities. The robustness of the inversion strategy was tested by performing a set of synthetic inversions in which crustal structure was assumed both fixed and variable. These tests indicate that unaccounted‐for crustal structure strongly affects the retrieval of mantle properties, calling for a two‐step strategy presented herein to simultaneously recover both crustal and mantle parameters. As a proof of concept, the methodology is applied to data from two stations located in the Siberian and East European continental platforms.

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“…However, only a limited number of slabs sink into 170 the lower mantle, given that most of the subducted slabs 171 flatten and seem to stagnate at either $660 km or 172 $1000 km depth (Fukao and Obayashi, 2013 (Irifune et al, 1996;McDonough, 197 2016;Nestola et al, 2018 Palme and O'Neill, 2014). Although the Na 2 O occurrence 206 has a modest impact on the large-scale geophysical and geo-207 chemical modelling (Bina and Helffrich, 2014;Palme and 208 O'Neill, 2014;Chust et al, 2017), it is still important in 209 terms of the resulting minor mineral phases that affect the 210 Al distribution in the lower mantle. Experiments and obser-211 vations on natural samples reveal that potential Al bearing 212 lower mantle phases may also include K, Fe 3+ and OH as 213 major elements (i.e.…”

mentioning

confidence: 99%

“…618 618 619 (Chust et al, 2017). Its solution, expressed by 638 n closed system , yields the composition of Al bearing perovskite 639 that minimises the Gibbs energy of Eq.…”

mentioning

confidence: 99%

Aluminium distribution in an Earth’s non–primitive lower mantle

Merli

Bonadiman

Pavese

2020

Geochimica et Cosmochimica Acta

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10The aluminium incorporation mechanism of perovskite was explored by means of quantum mechanics in combination with 11 equilibrium/off-equilibrium thermodynamics under the pressure-temperature conditions of the Earth's lower mantle (from 24 12 to 80 GPa). Earth's lower mantle was modelled as a geochemically non-primitive object because of an enrichment by 3 wt% of 13 recycled crustal material (MORB component). The compositional modelling takes into account both chondrite and pyrolite 14 reference models. 15 The capacity of perovskite to host Al was modelled through an Al 2 O 3 exchange process in an unconstrained 16 Mg-perovskite + Mg-Al-perovskite + free-Al 2 O 3 (corundum) system. Aluminium is globally incorporated principally via an 17 increase in the amount of Al bearing perovskite [Mg-Al-pv(80 GPa)/Mg-Al-pv(24 GPa) % 1.17], rather than by an increase 18 in the Al 2 O 3 content of the average chemical composition which changes little (0.11-0.13, mole fraction of Al 2 O 3 ) and tends 19 to decrease in Al. The Al 2 O 3 distribution in the lower mantle was described through the probability of the occurrence of given 20 compositions of Al bearing perovskite. The probability of finding Mg-Al-perovskite is comparable to Mg-perovskites. Per-21 ovskite with Al 2 O 3 mole fraction up to 0.15 has an occurrence probability of $28% at 24 GPa, increasing up to $43% at 22 80 GPa; on the contrary, perovskite compositions in the range 0.19-0.30 Al 2 O 3 mole fraction drop their occurrence proba-23 bility from 9.8 to 2.0%, over the same P-range. In light of this, the distribution of Al in the lower mantle shows that, among 24 the possible Al bearing perovskite phases, the (Mg 0.89 Al 0.11 )(Si 0.89 Al 0.11 )O 3 composition is the likeliest, providing from 5 to 25 8% of the bulk perovskite in the pressure range from 24 to 80 GPa. The occurrence of the most Al rich composition, i.e. 26 (Mg 0.71 Al 0.29 )(Si 0.71 Al 0.29 )O 3 , is a rare event (probability of occurrence < 1.7%). This study predicts that perovskite may glob-27 ally host Al 2 O 3 in terms of 4.3 and 4.8 wt% (with respect to the non-primitive lower mantle mass), thus accounting for $90% 28 and 100% of the bulk Al 2 O 3 estimated in the framework of pyrolite and chondrite reference models, respectively. A calcium-29 ferrite type phase (on the MgAl 2 O 4 -NaAlSiO 4 join) seems to be the only candidate that can compensate for the 10% gap of the 30 perovskite Al incorporation capacity, in the case of a pyrolite non-primitive lower mantle model.31

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MMA‐EoS: A Computational Framework for Mineralogical Thermodynamics

Cited by 32 publications

References 243 publications

A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths

A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths

Stochastic Inversion of P‐to‐S Converted Waves for Mantle Composition and Thermal Structure: Methodology and Application

Aluminium distribution in an Earth’s non–primitive lower mantle

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