The elastic constants of MgSiO3 perovskite at pressures and temperatures of the Earth's mantle

Ab initio determination of melting and sound velocity of neon up to the deep interior of the Earth

The thermophysical properties and elemental abundances of the noble gases in terrestrial materials can provide unique insights into the Earth's evolution and mantle dynamics. Here, we perform extensive ab initio molecular dynamics simulations to determine the melting temperature and sound velocity of neon up to 370 GPa and 7500 K to constrain its physical state and storage capacity, together with to reveal its implications for the deep interior of the Earth. It is found that solid neon can exist stably under the lower mantle and inner core conditions, and the abnormal melting of neon is not observed under the entire temperature (T) and pressure (P) region inside the Earth owing to its peculiar electronic structure, which is substantially distinct from other heavier noble gases. An inspection of the reduction for sound velocity along the Earth's geotherm evidences that neon can be used as a light element to account for the low-velocity anomaly and density deficit in the deep Earth. A comparison of the pair distribution functions and mean square displacements of MgSiO3-Ne and Fe-Ne alloys further reveals that MgSiO3 has a larger neon storage capacity than the liquid iron under the deep Earth condition, indicating that the lower mantle may be a natural deep noble gas storage reservoir. Our results provide valuable information for studying the fundamental behavior and phase transition of neon in a higher T-P regime, and further enhance our understanding for the interior structure and evolution processes inside the Earth.

Ab initio insight into the physical properties of MgXH3 (X = Co, Cu, Ni) lead-free perovskite for hydrogen storage application

Renewable energy systems are vital for a sustainable future, where solid-state hydrogen storage can play a crucial role. Perovskite hydride materials have attracted the scientific community for hydrogen storage applications. The current work focuses on the theoretical study using density functional theory (DFT) to evaluate the characteristics of MgXH3 (X = Co, Cu, Ni) hydrides. The structural, vibrational, electronic, mechanical, thermodynamic, and hydrogen storage properties of these hydrides were investigated. The equilibrium lattice parameters were calculated using the Birch-Murnaghan equation of state-to-energy volume curves. The elastic constants (Cij) and relevant parameters, such as Born criteria, were calculated to confirm the mechanical stability of the hydrides. The Cauchy pressure (Cp) revealed brittle or ductile behavior. The outcomes of the Pugh ratio, Poisson ratio, and anisotropy were also calculated and discussed. The absence of negative lattice vibrational frequencies in phonon dispersion confirmed the lattice's dynamic stability. The heat capacity curves of thermodynamic properties revealed that hydrides can conduct thermal energy. The metallic character and ample interatomic distances of hydrides were confirmed by the band structure and population analysis, which confirmed that hydrides can conduct electrical energy and adsorb hydrogen. The density of state (DOS) and partial DOS unveiled the role of specific atoms in the DOS of the crystal. The calculated gravimetric hydrogen storage capacity of MgCoH3, MgCuH3, and MgNiH3 hydrides was 3.64, 3.32, and 3.49wt%, respectively. Our results provide a deeper understanding of its potential for hydrogen storage applications through a detailed analysis of MgXH3 (X = Co, Cu, Ni) perovskite hydride material.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Determination of hyper-parameters in the atomic descriptors for efficient and robust molecular dynamics simulations with machine learning forces

The atomic descriptors used in machine learning to predict forces are often high dimensional. In general, by retrieving a significant amount of structural information from these descriptors, accurate force predictions can be achieved. On the other hand, to acquire higher robustness for transferability without overfitting, sufficient reduction of descriptors should be necessary. In this study, we propose a method to automatically determine hyperparameters in the atomic descriptors, aiming to obtain accurate machine learning forces while using a small number of descriptors. Our method focuses on identifying an appropriate threshold cut-off for the variance value of the descriptor components. To demonstrate the effectiveness of our method, we apply it to crystalline, liquid, and amorphous structures in SiO₂, SiGe, and Si systems. By using both conventional two-body descriptors and our introduced split-type three-body descriptors, we demonstrate that our method can provide machine learning forces that enable efficient and robust molecular dynamics simulations.

Compositional and thermal state of the lower mantle from joint 3D inversion with seismic tomography and mineral elasticity

The compositional and thermal state of Earth's mantle provides critical constraints on the origin, evolution, and dynamics of Earth. However, the chemical composition and thermal structure of the lower mantle are still poorly understood. Particularly, the nature and origin of the two large low-shear-velocity provinces (LLSVPs) in the lowermost mantle observed from seismological studies are still debated. In this study, we inverted for the 3D chemical composition and thermal state of the lower mantle based on seismic tomography and mineral elasticity data by employing a Markov chain Monte Carlo framework. The results show a silica-enriched lower mantle with a Mg/Si ratio less than ~1.16, lower than that of the pyrolitic upper mantle (Mg/Si = 1.3). The lateral temperature distributions can be described by a Gaussian distribution with a standard deviation (SD) of 120 to 140 K at 800 to 1,600 km and the SD increases to 250 K at 2,200 km depth. However, the lateral distribution in the lowermost mantle does not follow the Gaussian distribution. We found that the velocity heterogeneities in the upper lower mantle mainly result from thermal anomalies, while those in the lowermost mantle mainly result from compositional or phase variations. The LLSVPs have higher density at the base and lower density above the depth of ~2,700 km than the ambient mantle, respectively. The LLSVPs are found to have ~500 K higher temperature, higher Bridgmanite and iron content than the ambient mantle, supporting the hypothesis that the LLSVPs may originate from an ancient basal magma ocean formed in Earth's early history.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.

Density functional theory calculations and thermodynamic analysis of bridgmanite surface structure

Bridgmanite, a high temperature and pressure form of MgSiO₃, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of the chemical potential of oxygen and magnesium. The vibrational contribution to the Gibbs free energy is found to be essential for obtaining a stability region of bridgmanite in the phase diagram. The most stable surface termination of bridgmanite varies between three different atomic structures depending on the chemical potential of oxygen and magnesium. The results presented provide a basis for further theoretical studies of the chemical processes on bridgmanite surfaces in the Earth's mantle and slip plane analysis.

Modeling the melting of multicomponent systems: the case of MgSiO3 perovskite under lower mantle conditions

Knowledge of the melting properties of materials, especially at extreme pressure conditions, represents a long-standing scientific challenge. For instance, there is currently considerable uncertainty over the melting temperatures of the high-pressure mantle mineral, bridgmanite (MgSiO3-perovskite), with current estimates of the melting T at the base of the mantle ranging from 4800 K to 8000 K. The difficulty with experimentally measuring high pressure melting temperatures has motivated the use of ab initio methods, however, melting is a complex multi-scale phenomenon and the timescale for melting can be prohibitively long. Here we show that a combination of empirical and ab-initio molecular dynamics calculations can be used to successfully predict the melting point of multicomponent systems, such as MgSiO3 perovskite. We predict the correct low-pressure melting T, and at high-pressure we show that the melting temperature is only 5000 K at 120 GPa, a value lower than nearly all previous estimates. In addition, we believe that this strategy is of general applicability and therefore suitable for any system under physical conditions where simpler models fail.

Temperature-dependent elastic stiffness constants of α- and θ-Al2O3 from first-principles calculations

Temperature-dependent elastic stiffness constants (c(ij)s), including both the isothermal and isoentropic ones, have been predicted for rhombohedral α-Al(2)O(3) and monoclinic θ-Al(2)O(3) in terms of a quasistatic approach, i.e., a combination of volume-dependent c(ij)s determined by a first-principles strain versus stress method and direction-dependent thermal expansions obtained by first-principles phonon calculations. A good agreement is observed between the predictions and the available experiments for α-Al(2)O(3), especially for the off-diagonal elastic constants. In addition, the temperature-dependent c(ij)s predicted herein, in particular the ones for metastable θ-Al(2)O(3), enable the stress analysis at elevated temperatures in thermally grown oxides containing α- and θ-Al(2)O(3), which are crucial to understand the failure of thermal barrier coatings in gas-turbine engines.

Finite-temperature magnetism in bcc Fe under compression

We investigate the contributions of finite-temperature magnetic fluctuations to the thermodynamic properties of bcc Fe as functions of pressure. First, we apply a tight-binding total-energy model parameterized to first-principles linearized augmented plane-wave computations to examine various ferromagnetic, anti-ferromagnetic, and noncollinear spin spiral states at zero temperature. The tight-binding data are fit to a generalized Heisenberg Hamiltonian to describe the magnetic energy functional based on local moments. We then use Monte Carlo simulations to compute the magnetic susceptibility, the Curie temperature, heat capacity, and magnetic free energy. Including the finite-temperature magnetism improves the agreement with experiment for the calculated thermal expansion coefficients.

How does tetrahedral structure grow in liquid silicon upon supercooling?

We present an extensive set of isothermal-isobaric first-principles molecular-dynamics simulations of liquid silicon over a temperature range of 950-1700 K. We find that the tetrahedral order gradually grows upon cooling to approximately 1200 K, but that the growth accelerates significantly below approximately 1200 K. This growth process gives rise to anomalous changes in density and liquid structure upon supercooling. In particular, we find that the atomic coordination number remains constant to approximately 1200 K and then begins to decrease below approximately 1200 K, which resolves the existing controversy regarding liquid structure in the supercooled regime [T. H. Kim, Phys. Rev. Lett. 95, 085501 (2005)10.1103/PhysRevLett.95.085501].

Deformation textures produced in diamond anvil experiments, analysed in radial diffraction geometry

Diamond anvil cells may not only impose pressure upon a sample but also a compressive stress that produces elastic and plastic deformation of polycrystalline samples. The plastic deformation may result in texture development if the material deforms by slip or mechanical twinning, or if grains have a non-equiaxed shape. In radial diffraction geometry, texture is revealed by variation of intensity along Debye rings relative to the compression direction. Diffraction images (obtained by CCD or image plate) can be used to extract quantitative texture information. Currently the most elegant and powerful method is a modified Rietveld technique as implemented in the software package MAUD. From texture data one can evaluate the homogeneity of strain in a diamond anvil cell, the strain magnitude and deformation mechanisms, the latter by comparing observed texture patterns with results from polycrystal plasticity simulations. Some examples such as olivine, magnesiowuestite, MgSiO(3) perovskite and ε-iron are discussed.

Ab initio thermodynamics of MgSiO3 perovskite at high pressures and temperatures

Using quantum-mechanical simulations based on density-functional perturbation theory, we address the problem of stability of MgSiO3 perovskite to decomposition into MgO and SiO2 at pressures and temperatures of the Earth's lower mantle. We show that MgSiO3 perovskite (and its post-perovskite phase) is more stable than the mixture of oxides throughout the pressure-temperature regime of the Earth's mantle. Structural stability and lattice dynamics of phases in the system MgO-SiO2 are discussed.

MgSiO3 postperovskite at D'' conditions

The postperovskite transition in MgSiO(3) at conditions similar to those expected at the D'' discontinuity of Earth's lower mantle offers a paradigm for interpreting the properties of this region. Despite consistent experimental and theoretical predictions of this phase transformation, the complexity of the D'' region raises questions about its geophysical significance. Here we report the thermoelastic properties of Cmcm postperovskite at appropriate conditions and evidences of its presence in the lowermost mantle. These are (i) the jumps in shear and longitudinal velocities similar to those observed in certain places of the D'' discontinuity and (ii) the anticorrelation between shear and bulk velocity anomalies as detected within the D'' region. In addition, the increase in shear modulus across the phase transition provides a possible explanation for the reported discrepancy between the calculated shear modulus of postperovskite free aggregates and the seismological counterpart in the lowermost mantle.

The physical and chemical composition of the lower mantle

This article reviews some of the recent advances made within the field of mineral physics. In order to link the observed seismic and density structures of the lower mantle with a particular mineral composition, knowledge of the thermodynamic properties of the candidate materials is required. Determining which compositional model best matches the observed data is difficult because of the wide variety of possible mineral structures and compositions. State-of-the-art experimental and analytical techniques have pushed forward our knowledge of mineral physics, yet certain properties, such as the elastic properties of lower mantle minerals at high pressures and temperatures, are difficult to determine experimentally and remain elusive. Fortunately, computational techniques are now sufficiently advanced to enable the prediction of these properties in a self-consistent manner, but more results are required.A fundamental question is whether or not the upper and lower mantles are mixing. Traditional models that involve chemically separate upper and lower mantles cannot yet be ruled out despite recent conflicting seismological evidence showing that subducting slabs penetrate deep into the lower mantle and that chemically distinct layers are, therefore, unlikely.Recent seismic tomography studies giving three-dimensional models of the seismic wave velocities in the Earth also base their interpretations on the thermodynamic properties of minerals. These studies reveal heterogeneous velocity and density anomalies in the lower mantle, which are difficult to reconcile with mineral physics data.

Structure and freezing of MgSiO3 liquid in Earth's lower mantle

First-principles molecular-dynamics simulations show that over the pressure regime of Earth's mantle the mean silicon-oxygen coordination number of magnesium metasilicate liquid changes nearly linearly from 4 to 6. The density contrast between liquid and crystal decreases by a factor of nearly 5 over the mantle pressure regime and is 4% at the core-mantle boundary. The ab initio melting curve, obtained by integration of the Clausius-Clapeyron equation, yields a melting temperature at the core-mantle boundary of 5400 +/- 600 kelvins.

High-pressure melting of MgSiO3

The melting curve of MgSiO(3) perovskite has been determined by means of ab initio molecular dynamics complemented by effective pair potentials, and a new phenomenological model of melting. Using first principles ground state calculations, we find that the MgSiO(3) perovskite phase transforms into post perovskite at pressures above 100 GPa, in agreement with recent theoretical and experimental studies. We find that the melting curve of MgSiO(3), being very steep at pressures below 60 GPa, rapidly flattens on increasing pressure. The experimental controversy on the melting of the MgSiO(3) perovskite at high pressures is resolved, confirming the data by Zerr and Boehler.

The elasticity of the MgSiO3 post-perovskite phase in the Earth's lowermost mantle

MgSiO3 perovskite has been assumed to be the dominant component of the Earth's lower mantle, although this phase alone cannot explain the discontinuity in seismic velocities observed 200-300 km above the core-mantle boundary (the D" discontinuity) or the polarization anisotropy observed in the lowermost mantle. Experimental and theoretical studies that have attempted to attribute these phenomena to a phase transition in the perovskite phase have tended to simply confirm the stability of the perovskite phase. However, recent in situ X-ray diffraction measurements have revealed a transition to a 'post-perovskite' phase above 125 GPa and 2,500 K--conditions close to those at the D" discontinuity. Here we show the results of first-principles calculations of the structure, stability and elasticity of both phases at zero temperature. We find that the post-perovskite phase becomes the stable phase above 98 GPa, and may be responsible for the observed seismic discontinuity and anisotropy in the lowermost mantle. Although our ground-state calculations of the unit cell do not include the effects of temperature and minor elements, they do provide a consistent explanation for a number of properties of the D" layer.

Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth's D" layer

The Earth's lower mantle is believed to be composed mainly of (Mg,Fe)SiO3 perovskite, with lesser amounts of (Mg,Fe)O and CaSiO3 (ref. 1). But it has not been possible to explain many unusual properties of the lowermost approximately 150 km of the mantle (the D" layer) with this mineralogy. Here, using ab initio simulations and high-pressure experiments, we show that at pressures and temperatures of the D" layer, MgSiO3 transforms from perovskite into a layered CaIrO3-type post-perovskite phase. The elastic properties of the post-perovskite phase and its stability field explain several observed puzzling properties of the D" layer: its seismic anisotropy, the strongly undulating shear-wave discontinuity at its top and possibly the anticorrelation between shear and bulk sound velocities.

High density amorphous form and polyamorphic transformations of silicon

Polyamorphic transformations of silicon have been investigated by constant-pressure first-principles molecular-dynamics simulations. By pressurizing a normal amorphous Si with tetrahedral coordination, a new high density amorphous (HDA) form that has a strong resemblance to HDA water is obtained. We find that the HDA form can be also obtained through vitrification of liquid Si under pressure. Both HDA and liquid Si contain deformed tetrahedral configurations with interstitial atoms. These findings indicate that HDA Si is directly connected with liquid Si, which is of particular importance in understanding phase relations of polyamorphs of Si.

Thermoelastic properties of MgSiO(3)-perovskite: insights on the nature of the Earth's lower mantle

We have determined by means of first principles quasiharmonic calculations the elastic constants and acoustic velocities of MgSiO3 perovskite, the most abundant mineral of the Earth's lower mantle (LM), at pertinent pressures and temperatures. Using these results, along with the effects of low concentration iron alloying and the thermoelasticity of the most important secondary LM phase, MgO, we predict the isotropic elastic moduli of likely LM aggregates. Comparison with seismic values extracted from the preliminary reference Earth model indicates that the top of the LM behaves as a typical aggregate of pyrolitic composition, likewise the upper mantle. But systematic deviations that cannot be accounted for by alterations in the geotherm alone develop toward the deep LM. This result could be viewed as evidence in support of radially inhomogeneous LM models.

Geodynamic and seismic constraints on the thermochemical structure and dynamics of convection in the deep mantle

We revisit a recent study by Forte & Mitrovica in which global geophysical observables associated with mantle convection were inverted and the existence of a strong increase in viscosity near a depth of 2000 km was inferred. Employing mineral-physics data and theory we also showed that, although there are chemical anomalies in the lowermost mantle, they are unable to inhibit the dominant thermal buoyancy of the deep-mantle mega-plumes below Africa and the Pacific Ocean. New Monte Carlo simulations are employed to explore the impact of uncertainties in current mineral-physics constraints on inferences of deep-mantle thermochemical structure. To explore the impact of the high-viscosity peak at a depth of 2000 km on the evolution of lower-mantle structure, we carried out time-dependent convection simulations. The latter show that the stability and longevity of the dominant long-wavelength heterogeneity in the lowermost mantle are controlled by this viscosity peak.

Computational mineral physics and the physical properties of perovskite

The inherent uncertainties in modern first-principles calculations are reviewed using geophysically relevant examples. The elastic constants of perovskite at lower-mantle temperatures and pressures are calculated using ab initio molecular dynamics. These are used in conjunction with seismic tomographic models to estimate that the lateral temperature contrasts in the Earth's lower mantle are 800 K at a depth of 1000 km, and 1500 K at a depth of 2000 km. The effect of Al(3+) on the compressibility of MgSiO(3) perovskite is calculated using three different pseudopotentials. The results confirm earlier work and show that the compressibility of perovskites with Al(3+) substituted for both Si(4+) and Mg(2+) is very similar to the compressibility of Al(3+)-free perovskite. Even when 100% of the Si(4+) and Mg(2+) ions are replaced with Al(3+), the bulk modulus is only 7% less than that for Al(3+)-free perovskite. In contrast, perovskites where Al(3+) substitutes for Si(4+) only and that are charge balanced by oxygen vacancies do show higher compressibilities. When corrected to similar concentrations of Al(3+), the calculated compressibilities of the oxygen-vacancy-rich perovskites are in agreement with experimental results.

Mid-mantle deformation inferred from seismic anisotropy

With time, convective processes in the Earth's mantle will tend to align crystals, grains and inclusions. This mantle fabric is detectable seismologically, as it produces an anisotropy in material properties--in particular, a directional dependence in seismic-wave velocity. This alignment is enhanced at the boundaries of the mantle where there are rapid changes in the direction and magnitude of mantle flow, and therefore most observations of anisotropy are confined to the uppermost mantle or lithosphere and the lowermost-mantle analogue of the lithosphere, the D" region. Here we present evidence from shear-wave splitting measurements for mid-mantle anisotropy in the vicinity of the 660-km discontinuity, the boundary between the upper and lower mantle. Deep-focus earthquakes in the Tonga-Kermadec and New Hebrides subduction zones recorded at Australian seismograph stations record some of the largest values of shear-wave splitting hitherto reported. The results suggest that, at least locally, there may exist a mid-mantle boundary layer, which could indicate the impediment of flow between the upper and lower mantle in this region.