We benchmark exchange-correlation functionals for the calculation of fundamental band gaps of inorganic nitrides. These include conventional functionals such as the local density approximation (LDA), the generalized-gradient (Perdew-Burke-Ernzerhof) approximation (PBE), simple Slater exchange functionals (SLOC), specialized LDA/GGA-derived high local exchange (HLE16) and Armiento-Kümmel semilocal (AK13) functionals, meta-GGA functionals including TASK, the modified Becke-Johnson functional (mBJ), and Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional, as well as quasiparticle GW theory. Since inorganic nitrides remain strongly under-represented in previous extensive benchmark studies, the current subdatabase contributes towards building a future large-scale balanced materials compilation of band gaps to benchmark theory. From a literature survey, we carefully collect 25 binary and 11 ternary nitrides with a focus on semiconductors spanning the periodic table, including ionic Li3N, antibixbyite-structured X3N2 (X = Be, Mg, Ca), early transition metals and lanthanides (e.g., ScN, YN, and LaN), ultrahard Th3P4-type structured M3N4 (M = Zr, Hf) compounds, promising photocatalysts Ta3N5, different polymorphs of III-V reference covalent nitrides (BN, AlN, GaN), and many M3N4 polymorphs (M = C, Si, and Ge) such as spinel-structured phases. Consistent with previous extensive benchmark tests, conventional LDA/PBE unsystematically largely underestimate band gaps with mean absolute errors (MAE) of >1.0 eV and mean absolute percentage errors (MAPE) of about 50%. Simple Slater exchange functional, SLOC, the GGA-derived AK13LDA and HLE16 functionals show improvement over LDA/PBE with MAE of 0.5-0.6 eV (MAPE ∼ 20-25%) with mBJ and HSE06 being the most accurate, with MAE = 0.30 and 0.28 eV (MAPE 12.1% and 11.1%), respectively. Strategies for the development of machine learning and the choice of appropriate exchange-correlation functionals for high-throughput large-scale material screening are discussed in light of these results.

Water in Earth’s mantle plays a crucial role in shaping geological and geochemical processes. While previous electrical conductivity measurements on major mantle minerals have constrained water content in the Earth’s mantle down to the mantle transition zone, the water content of the lower mantle remains experimentally unconstrained. This study measures the electrical conductivity of hydrous (Fe,Al)-bearing bridgmanite, synthesized with Fe and Al compositions representative of peridotitic lithology, at pressures up to 47 GPa and temperatures up to 2210 K. The results demonstrate that proton conduction is the predominant charge transport mechanism in hydrous (Fe,Al)-bearing bridgmanite under the investigated pressure-temperature conditions. Water incorporation markedly enhances the electrical conductivity of bridgmanite, increasing it by approximately an order of magnitude relative to that of dry samples. Extrapolation of the experimental data suggests that bridgmanite in the lower mantle contains less than 40–70 wt. ppm H2O near the top and at mid-mantle depths. These findings offer insight into potential hidden water reservoirs in Earth’s lower mantle. Electrical conductivity measurements indicate that bridgmanite in the present-day lower mantle contains little water, providing constraints on water storage and transport in Earth’s deep interior.

Proton self diffusion coefficients for bridgmanite at lower mantle conditions are calculated from ab initio molecular dynamics simulations. We find that the proton self diffusion coefficient, D-self is nearly constant similar to 10(-8) m(2) s(-1) along the lower mantle geotherm but increases by nearly one order of magnitude from similar to 10(-10) m(2) s(-1) to similar to 10(-9) m(2) s(-1) along a cold slab geotherm to about 1800 km depth. These rates imply that the proton diffusion length scale is less than 10 km in lower mantle peridotite in the 150-200 million years timescale for slab material to sink through the lower mantle. Cold wet slabs probably lose less than one percent of their total water content to the ambient mantle on their journey through the lower mantle, indicating that recycled water is far from homogeneously distributed since slab delivery is highly heterogeneous. We estimate that 0.1 to 0.3 ocean masses (<100 ppm wt%) of recycled water may be currently stored in slab remnant materials within the lower mantle. This water is likely not entrained by plumes but is instead captured by background mantle flow before returning to the mid-ocean ridges. By contrast, deep-rooted mantle plumes may entrain materials containing primordial-like water from the lowermost mantle or the core, and preserve these anomalies in fairly small-scale heterogeneities. Over the age of the Earth, the proton diffusion length scale is a few tens of km, which places constraints on the size of possible primordial water reservoirs isolated from convective mixing, and indicates little flux of water across the core-mantle boundary.

Na‐ion batteries (NIBs) need new anode materials to improve energy density. Metal chalcogenides, such as Sb 2 Se 3 , represent a promising alternative to commonly used hard carbon materials, demonstrating high‐rate performance up to 5 A g −1 with minimal capacity losses. However, Sb 2 Se 3 is believed to operate under the conversion/alloying mechanism, typically linked with large structural transformations and volumetric changes—quite contrary to its performance. Herein, by combining multiple operando techniques and atomistic simulations, a new fully sodiated phase, Na 5− x SbSe, is unambiguously revealed as the origin of the high‐rate performance of Sb 2 Se 3 . Na 5− x SbSe is stable within 0.01–0.80 V versus Na/Na + and crystallizes in I 4/ mmm . The remarkable structural flexibility of Na 5 SbSe to changes in Na‐content allows the anode to be (de)sodiated with minimal volumetric changes (≈3.4%). This unique “breathing effect” is intimately linked to high inherent vacancy concentration, disordered, and structurally flexible anion sublattice, providing a stable framework for fast Na diffusion, contributing to the fast‐charging properties of Sb 2 Se 3 . The study showcases the power of operando methods for discovering new phases that are hidden in the mechanistic paths of well‐studied reactions and underlines the intertwined nature of various characterization methods assisted by atomistic insights for a comprehensive understanding of complex (de)sodiation mechanisms.

The diffusion of noble gases in SiO2 phases is studied using ab initio molecular dynamics based on the density functional theory, covering pressure and temperature conditions from the crust to the core. Our results show that the diffusion of noble gases in SiO2 minerals is not only controlled by external conditions such as temperature and pressure but is also highly sensitive to the structure of the host mineral as well as the size of the noble gas. We show that the diffusion coefficient of He in quartz at 1700 K is two orders of magnitude larger than that of He in seifertite at 5000 K. In quartz, the larger the noble gas, the slower the diffusion. Nudged elastic band (NEB) computations in quartz also give Ea(Ar) < Ea(Kr) < Ea(Xe). Interestingly, we predict that Ne diffuses faster than He in dense SiO2 phases at a given temperature, in apparent contradiction with the common assumption that heavier atoms diffuse slower. We explain this phenomenon in seifertite by greater repulsive interactions between Ne and its local environment than for He in the minimum energy configuration, triggering the rapid jumps of Ne toward the lower-coordinated transition site. In agreement with other studies, we predict He and to a lesser extent Ne are quickly released from the continental crust with limited storage in the deepest part of the mantle. However, Ar can be transported deeper than lighter noble gases, potentially trapped in stishovite, CaCl2-type and seifertite in the deep lower mantle. Given the abundance of these minerals in mantle basaltic compositions and the continental crust, their contribution to the volatile cycle of noble gases is far from negligible.

The melting curve of pure silica (SiO2) was determined using ab initio density functional theory together with the solid -liquid coexisting approach, thermodynamic integration, and the Z method. The melting curves are consistent with a smooth, slow increase in a large region from 50 GPa (dT/dP ti 15 K/GPa) to about 500 GPa (dT/dP ti 5 K/GPa) without any abrupt changes at around 120 and 300 GPa as seen in some recent experimental and computational studies. The topography of the melting curve above 50 GPa is consistent with a gradual change in the distribution of the Si coordination numbers in the liquid state and the absence of large changes in the density following solid -solid phase transitions. The pair distribution functions show that the structural correlation in the liquid is mainly short range and that the Si -O bond is stiff. The densification of the melt structure with pressure above 50 GPa is therefore due to an increase in seven- and eightfold coordinated silicon.

The melting curve of pure silica (SiO_2) was determined using ab initio density functional theory together with the solid-liquid coexisting approach, thermodynamic integration and the Z method. The melting curves are consistent with a smooth slow increase in a large region from 50 GPa (dT/dP ≈ 15 K/GPa) to about 500 GPa (dT/dP ≈ 5 K/GPa) without any abrupt changes at around 120 GPa and 300 GPa as seen in some recent experimental and computational studies. The topography of the melting curve above 50 GPa is consistent with a gradual change in the distribution of the Si coordination numbers in the liquid state and the absence of large changes in the density following solid-solid phase transitions. The pair distribution functions show that the structural correlation in the liquid is mainly short-ranged and that the Si-O bond is stiff. The densification of the melt structure with pressure above 50 GPa is therefore due to an increase in 7- and 8-fold coordinated silicon.

The Z method is a popular atomistic simulation method for determining the melting temperature where a sequence of molecular dynamics runs are carried out to target the lowest system energy where the solid always melts. Homogeneous melting at the limit of critical superheating, Th, is accompanied by a drop in temperature as kinetic energy is converted to potential energy and the equilibrium melting temperature, Tm, can be calculated directly from the liquid state. Implementation of the Z method interfaced with modern ab initio electronic structure packages use Hellmann-Feynman forces to propagate the ions in the microcanonical(NVE) ensemble where the Mermin free energy plus the ionic kinetic energy is conserved. The electronic temperature, Tel, is kept fixed along the trajectory which may introduce some spurious ion-electron interactions in MD runs with large temperature changes such as often seen in homogeneous melting and freezing processes in the NVE ensemble. We estimate systematic errors in the calculated melting temperature to choice of Tel for two main mantle components, SiO2 and CaSiO3 at high pressure. Comparison of the calculated melting temperature from runs where the Tel=Th and Tel=Tm representing reasonable upper and lower boundaries respectively to choice of Tel shows that the difference in melting temperature is 200-300 K for our two test systems. The melting temperature decreases with increasing Tel due to the increasing entropic stabilisation of the liquid and the systems melts typically about 3 times faster in MD runs with Tel = Th compared to runs where Tel = Tm. A careful choice of electron temperature in BOMD simulations where the ions are propagated using Hellmann-Feynamn forces with the Mermin free energy + the ionic kinetic energy being conserved is therefore essential for the critical evaluation of the Z method and in particular at very high temperatures.

This chapter highlights the power and usefulness of atomistic computer simulations in the field of mineralogy, with particular emphasis on their applications to extreme conditions in planetary interiors. The ability of density functional theory simulations to accurately predict the physical and chemical properties of minerals and melts, together with the increasing availability of large datasets from ab initio simulations, has enabled researchers to make advances in understanding the evolution of the Earth, other terrestrial planets and protoplanetary disks. Additionally, machine learning algorithms have been used to develop accurate interatomic potentials and to accelerate the discovery of new materials. Overall, this chapter provides an overview of the recent advances in the field of computational mineralogy and their applications to the study of planetary interiors.

Melting curves of Ca‐perovskite (pure CaSiO3) were determined by ab initio density functional theory, using two solid‐liquid coexistence methods and two free energy approaches, in the form of thermodynamic integration and two‐phase thermodynamics. The melting curves based on the solid‐liquid coexistence methods and thermodynamic integration rise steeply from 2000 K at 14 GPa to 7000 K at 136 GPa. The melting temperature at 136 GPa is 1400 K higher than previous ab initio predictions. The high thermal stability of Ca‐perovskite is linked to its high‐symmetry isometric structure and consistent with experiments, demonstrating that Ca‐perovskite is the most refractory phase in basaltic compositions in the lower mantle pressure range. The steep dT/dp slope of the melting curve also shows that the Ca‐perovskite liquidus field expands relative to those of bridgmanite and silica with increasing pressure, in agreement with experimental evidence from simple and complex systems.

We present inelastic neutron scattering measurements of Y3Al5O12. The measured neutron-weighted phonon density-of-states and optical phonon frequencies are compared with the results from atomistic calculations within the Quasi-Harmonic Approximation (QHA) over a wide temperature range, using both first principles density functional theory calculations and also an extended empirical interatomic-potential shell model scheme. The phonon-related thermodynamic and elastic properties calculated within the QHA are in excellent agreement with the available experimental data.

The energy landscape of the fast-ion conductor Bi 4 V 2 O 11 is studied using density functional theory. There are a large number of energy minima, dominated by low-lying thermally accessible configurations in which there are equal numbers of oxygen vacancies in each vanadium–oxygen layer, a range of vanadium coordinations and a large variation in Bi–O and V–O distances. By dividing local minima in the energy landscape into sets of configurations, we then examine diffusion in each different layer using ab initio molecular dynamics. These simulations show that the diffusion mechanism mainly takes place in the 〈110〉 directions in the vanadium layers, involving the cooperative motion of the oxide ions between the O(2) and O(3) sites in these layers, but not O(1) in the Bi–O layers, in agreement with experiment. O(1) vacancies in the Bi–O layers are readily filled by the migration of oxygens from the V–O layers. The calculated ionic conductivity is in reasonable agreement with the experiment. We compare ion conduction in δ-Bi 4 V 2 O 11 with that in δ-Bi 2 O 3 . This article is part of the Theo Murphy meeting issue ‘Understanding fast-ion conduction in solid electrolytes’.

The energy landscape concept is increasingly valuable in understanding and unifying the structural, thermodynamic and dynamic properties of inorganic solids. We present a range of examples which include (i) structure prediction of new bulk phases including carbon nitrides, phosphorus carbides, LiMgF3 and low-density, ultra-flexible polymorphs of B2O3, (ii) prediction of graphene and related forms of ZnO, ZnS and other compounds which crystallise in the bulk with the wurtzite structure, (iii) solid solutions, (iv) understanding grossly non-stoichiometric oxides including the superionic phases of δ-Bi2O3 and BIMEVOX and the consequences for the mechanisms of ion transport in these fast ion conductors. In general, examination of the energy landscapes of disordered materials highlights the importance of local structural environments, rather than sole consideration of the average structure.

Links between dynamical Frenkel defects and collective diffusion of fluorides in β -PbF 2 are explored using Born–Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10 −5 cm 2 s −1 and 2.4 Ω −1 cm −1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective ‘multi-ion’ diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear ‘kick-out’ chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction. This article is part of the Theo Murphy meeting issue ‘Understanding fast-ion conduction in solid electrolytes’.

In this paper, we highlight the connection between the local structure and collective dynamics of the defective fluorites La2Ce2O7 and Nd2Ce2O7. The local and average structure is explored by investigating a large number of different structural models and snapshots from Born-Oppenheimer Molecular dynamics calculations. Both compounds show a strong preference for local oxygen vacancy order similar to that found in the C-type structure. This suggests that previous studies, where Nd2Ce2O7 and La2Ce2O7 are viewed as disordered defective fluorites, or as a pyrochlore for the latter, did not capture the nature of local order in the disordered phase. We observe more collective chains of migrating oxygen in Nd2Ce2O7- a manifestation of a stronger preference for a dynamic local oxygen vacancy order - than in La2Ce2O7. The stronger preference for 〈210〉 vacancy-vacancy alignments can explain why long range ordering is identified by distinct C-type like superlattice peaks in neutron diffraction patterns for Nd2Ce2O7 whereas they appear to be almost invisible in La2Ce2O7.

The delta phase of Bi2O3 has the highest known value of oxide ion conductivity within the solid state and, therefore, remains a benchmark for the development of future generations of electrolyte materials to fuelcell technologies. Conventionally, the high value of conductivity in delta-Bi2O3 has been explained by a large concentration of inherent vacancies together with a strongly polarizable Bi-O bond. We show from ab initio molecular dynamics simulations that short "chains" of collective migrating oxygens also contribute strongly to the high value of conductivity with the single-particle Nernst-Einstein (N.E.) conductivity to collective (dc) conductivity sigma(N.E.)/sigma(dc) similar to 0.57 +/- 0.05 at 1033 K. The nature of collective events is investigated from a hopping model, the distinct part of the van Hove function and from the extent of dynamical heterogeneities in the superionc regime. Results from this analysis indicate that the main contribution to collective ionic diffusion in delta-Bi2O3 involves short collinear chains of two or three oxygens. These chains are either initiated by an oxygen that jumps into an already occupied oxygen cavity (where they coexist for a very short time before the residential oxygen is kicked out of its cavity) or from a jump into a vacant cavity which triggers a next-nearest-neighboring oxygen to migrate. Since delta-Bi2O3 is easily stabilized in a range of environments, the nature of these collective chains can give important insight into the design of delta-Bi2O3-based fuel cells for the future.

The subsolidus phase diagram of silica in the 80-220 GPa pressure range was determined by density functional theory (DFT). The transition pressures calculated using the generalized gradient approximation (GGA) in the static limit (at 0 K, without zero point vibrational energy) for the beta-stishovite (CaCl2-structure) to seifertite and the seifertite to pyrite-type transitions are 95 and 213 GPa, respectively. These are in good agreement with those calculated using hybrid functionals, giving transition pressures of 96 and 215 GPa. This indicates that previous local density approximation (LDA) results underestimate the transition pressure by 10-15 GPa. Density functional perturbation theory calculations, carried out using GGA within the quasi-harmonic approximations, give Clapeyron slopes of 5.4 and -2.8 MPa/K for the beta-stishovite to seifertite and seifertite to pyrite-type transitions, respectively. This suggests that the seifertite-forming transition occurs at 109 GPa (470 km above the core-mantle boundary, CMB) at an ambient mantle geotherm, whereas the pyrite-type transition occurs at 200 GPa (620 km below the CMB) at 4700 K, which is close to the core adiabat. We also calculate the equation of state and show that the stability of seifertite in the lowermost mantle contributes negative buoyancy to recycled oceanic crust, although not as much as in some previous studies. Nevertheless, the increased density of seifertite over beta-stishovite may lead to layers with elevated proportions of basaltic material within the large low S-wave velocity provinces. The seifertite to pyrite-type silica transition in the outer core will affect the silica liquidus surface in the system Fe-Si-O and forms a basis for further investigations of silica crystallization in the protocore.

The terrestrial planets accreted from a diverse suite of solar system materials ranging from strongly O-deficient materials similar to enstatite chondrites via ordinary chondrite materials to fully oxidised carbonaceous chondrite and cometary materials. Heliocentric zoning with increasingly oxidised planetesimals outwards through the protoplanetary disc is broadly reflected in core fraction and FeOmantle concentration, ranging from 68 wt% core and 0.5 wt% FeOmantle for Mercury to 18 wt% core and 24 wt% FeOmantle for Vesta. Mercury, Venus and Earth grew mostly from materials which were isotopically similar to enstatite chondrites, although Earth and Venus also received more oxidised material. The elevated (Mg + Fe)/Si ratio, compared to chondrites, in the bulk silicate fraction of the terrestrial planets, except for Mercury, may be related to a combination of nebular fractionation associated with forsterite condensation, concentration of olivine-rich chondrules near the midplane of the accretion disc and multi-cycle impact erosion of protocrusts. For the extremely reduced Mercury the silicate magma ocean (MO) and a core with 15 wt% Si might have equilibrated with a melt layer of FeS at the core-mantle boundary (CMB). Recent data from the MESSENGER mission combined with experimentally derived phase relations, support estimates of about 0.5 wt% FeO and 10 wt% S in the MO and the current mantle. Core segregation at very high temperatures for the largest planets, Venus and Earth, led to cores with high Si content, even at relatively high oxygen fugacities and FeOmantle contents, because increasing temperature shifts the equilibrium: SiO2MO + 2Fe(core) = 2FeO(MO) + Si-core towards the products (right side). The hot protocores of Venus and Earth might have started with about 5-7 wt% Si and 2-3 wt% O. Mars and Vesta segregated S-rich cores at high oxygen fugacity and low pressure. Strong partitioning of Fe and Mg to melt and solids, respectively, caused neutrally buoyant bridgmanite (bm) to crystallise from the MO at 1700-1860 km depth (72-80 GPa), resulting in a separate basal magma ocean (BMO) within Earth, and probably also in Venus. Slow cooling of a thermally insulated BMO and core, accompanied by protracted crystallisation of bm and ferropericlase (fp), would facilitate core-BMO chemical exchange by reversing the equilibrium SiO2MO + 2Fe(core)( )= 2FeO(MO )+ Si-core towards the reactants. Transfer of silica crystals and a liquid SiO2 component from the core to the BMO, and liquid FeO and Fe2O3 components from the BMO to the core, would increase the Si/Mg, Mg/Fe and bm/fp ratio of the resulting cumulates. Because the solidus temperature of peridotite is < 200-300 K above the present temperature of the outermost core, and the melting interval of late-stage BMO melt enriched in Al, Fe, Ca and Na would be lower than that of peridotite, the BMO might have persisted through the Hadean and possibly also the Archean. Low solid state diffusion rates, especially in bm, would have restricted the core-mantle interaction upon BMO solidification, but limited coremantle interaction could possibly occur via partially molten ultra-low velocity zones. An outermost stagnant low-density and low-velocity core layer (E'-layer), with reduced Si and elevated O contents relative to the convecting core, appears to trace the core-BMO exchange. The E'-layer is compositionally gradational towards the convecting core at 445 km below the CMB. High thermal conductivity and minimal convective entrainment in the low-viscosity core fluid might have developed and stabilised such a gradational layer since the Hadean or early Archean. The primordial bm-dominated cumulates with high Mg/Fe ratios and viscosities may have become convectively aggregated into large refractory domains, remaining neutrally buoyant in the middle to upper parts of the lower mantle and resistant to convective destruction. Late-stage dense BMO cumulates with elevated Fe/Mg ratios relative to the bulk mantle composition might represent a suitable material for 100-200 km thick thermochemical piles at the bottom of the large low S-wave velocity provinces (LLSVPs) under Africa and the Pacific. A degree-2 convection pattern, possibly initiated and stabilised during Earth's early rapid rotation, involving antipodally ascending columns in equatorial positions and an intermediary descending longitudinal belt, might have swept the late-stage, dense bridgmanitic cumulates with high Fe/Mg-ratios, viscosity and bulk modulus towards the root zones of the upwelling columns.

We show how a genetic algorithm (GA) generates efficiently the energy landscape of the equimolar calcite–magnesite (CaCO 3 —MgCO 3 ) solid solution. Starting from a random configuration of cations and a supercell containing 480 atoms, the lowest energy form of ordered dolomite was found in all runs, in 94% of which it was located with less than 20,000 fitness evaluations. Practical implementation and operation of the GA are discussed in detail. The method can also generate both low-lying and high-lying excited states. Detailed analysis of the energy-minimised structures of the different configurations reveals that low energies are associated with reduction of strain associated with rotation of the carbonate groups, a mechanism possible only when a carbonate layer lies between a layer of just Ca and a layer of just Mg. Such strain relief is not possible in the equimolar MgO–CaO solid solution despite the similarity of the crystal structures of these binary oxides to calcite–magnesite, and therefore, the enthalpy of mixing is very high. Implications for thermodynamic configurational averaging over the minima in the energy landscape are briefly considered. Overall, the genetic algorithm is shown to be a powerful tool in probing non-ideality in solid solutions and revealing the ordering patterns that give rise to such behaviour.

Genetic algorithms (GAs) together with classical pair potentials and density functional theory (DFT) are used to investigate cation order in MgAl2O4 (Spinel). To efficiently locate the global minimum/minima on the system potential energy surface, corresponding to the ordered and fully equilibrated low-temperature phase, local structural optimizations are essential. Such energy minimizations are expensive at the DFT level, but a comparison of the distribution of the energy minima from DFT and popular classical pair potentials allows one to rapidly tune the GA parameters. We show that GAs are able to find, not only the global minimum on the potential energy, but also other low-energy cation configurations representing possible frozen-in disordered or metastable phases after quenching. The nature of these low-energy configurations can help to interpret the extent of kinetic trapping which hampers the comparison between different experimental studies.