Ab initio molecular dynamics study of first-order phase transitions: melting of silicon

Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a dataset of the melting points of 476 non-metallic crystalline binary compounds using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180 K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.

A Method for Predicting the Melting Temperature of Ionic Compounds

Predicting the melting temperature of materials has always been a topic of great concern. This article proposes an alternative model for determining the melting temperature of materials based on the main idea of the Lindemann melting criterion combined with the first-principles calculations of density functional theory. To verify the accuracy of the melting model, this article selected typical ionic crystals of MgO and 10 alkali metal halides as the validation objects. The calculation results indicate that the melting temperature of the MgO crystals and I-VII compounds is in good agreement with the experimental results.

Practical application of quantum neural network to materials informatics

Quantum neural network (QNN) models have received increasing attention owing to their strong expressibility and resistance to overfitting. It is particularly useful when the size of the training data is small, making it a good fit for materials informatics (MI) problems. However, there are only a few examples of the application of QNN to multivariate regression models, and little is known about how these models are constructed. This study aims to construct a QNN model to predict the melting points of metal oxides as an example of a multivariate regression task for the MI problem. Different architectures (encoding methods and entangler arrangements) are explored to create an effective QNN model. Shallow-depth ansatzs could achieve sufficient expressibility using sufficiently entangled circuits. The "linear" entangler was adequate for providing the necessary entanglement. The expressibility of the QNN model could be further improved by increasing the circuit width. The generalization performance could also be improved, outperforming the classical NN model. No overfitting was observed in the QNN models with a well-designed encoder. These findings suggest that QNN can be a useful tool for MI.

Melting temperature prediction using a graph neural network model: From ancient minerals to new materials

The melting point is a fundamental property that is time-consuming to measure or compute, thus hindering high-throughput analyses of melting relations and phase diagrams over large sets of candidate compounds. To address this, we build a machine learning model, trained on a database of ∼10,000 compounds, that can predict the melting temperature in a fraction of a second. The model, made publicly available online, features graph neural network and residual neural network architectures. We demonstrate the model's usefulness in diverse applications. For the purpose of materials design and discovery, we show that it can quickly discover novel multicomponent materials with high melting points. These predictions are confirmed by density functional theory calculations and experimentally validated. In an application to planetary science and geology, we employ the model to analyze the melting temperatures of ∼4,800 minerals to uncover correlations relevant to the study of mineral evolution.

First-principles hydration free energies of oxygenated species at water-platinum interfaces

The hydration free energy of atoms and molecules adsorbed at liquid-solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from well-defined non-interacting species to the fully interacting ones. The atomistic interactions are described by a machine-learned inter-atomic potential trained on first-principles data. The free energy calculated by the machine-learned potential is further corrected by using thermodynamic perturbation theory to provide the first-principles free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.

Accurate elemental boiling points from first principles

The normal boiling point (NBP) is a fundamental property of liquids and marks the intersection of the Gibbs energies of the liquid and the gas-phase at ambient pressure. This work provides the first comprehensive demonstration of the calculation of boiling points of atomic liquids through first-principles molecular-dynamics simulations. To this end, thermodynamic integration (TDI) and perturbation theory (TPT) are combined with a density-functional theory (DFT) Hamiltonian, which provides absolute Gibbs energies, internal energies, and entropies of atomic liquids with an accuracy of a few meV/atom. Linear extrapolation to the intersection with the Gibbs energy of a non-interacting gas-phase eventually pins-down the NBPs. While these direct results can already be quite accurate, they are susceptible to a systematic over or underbinding of the employed density functional. It is shown how this dependency can be strongly reduced and the robustness of the method increased through a simple linear correction termed λ-scaling. Eventually, by carefully tuning of the technical parameters of the approach, the walltime per element is reduced from weeks to about a day (10-20k core-hours), enabling extensive testing for B, Al, Na, K, Ca, Sr, Ba, Mn, Cu, Xe, and Hg. This comprehensive benchmark demonstrates the excellent performance and robustness of the approach with a mean absolute deviation (MAD) of less than 2% from experimental NBPs and very similar accuracy for liquid entropies (MAD 2.3 J (mol K)-1, 2% relative). In some cases, the uncertainties in the predictions are several times smaller than the variation between literature values, allowing us to clear out long-standing ambiguities in the NBPs of B and Ba.

Molecular Simulation of Covalent Bond Dynamics in Liquid Silicon

Many atomic liquids can form transient covalent bonds reminiscent of those in the corresponding solid states. These directional interactions dictate many important properties of the liquid state, necessitating a quantitative, atomic-scale understanding of bonding in these complex systems. A prototypical example is liquid silicon, wherein transient covalent bonds give rise to local tetrahedral order and consequent nontrivial effects on liquid-state thermodynamics and dynamics. To further understand covalent bonding in liquid silicon, and similar liquids, we present an ab initio-simulation-based approach for quantifying the structure and dynamics of covalent bonds in condensed phases. Through the examination of structural correlations among silicon nuclei and maximally localized Wannier function centers, we develop a geometric criterion for covalent bonds in liquid Si. We use this to monitor the dynamics of transient covalent bonding in the liquid state and estimate a covalent bond lifetime. We compare covalent bond dynamics to other processes in liquid Si and similar liquids and suggest experiments to measure the covalent bond lifetime.

Carbon solubility in liquid silicon: A computational analysis across empirical potentials

The nucleation and growth of SiC precipitates in liquid silicon is important in the crystallization of silicon used for the photovoltaic industry. These processes depend strongly on the carbon concentration as well as the equilibrium solubility relative to the precipitate phase. Here, using a suite of statistical thermodynamic techniques, we calculate the solubility of carbon atoms in liquid silicon relative to the β-SiC phase. We employ several available empirical potentials to assess whether these potentials may reasonably be used to computationally analyze SiC precipitation. We find that some of the Tersoff-type potentials provide an excellent picture for carbon solubility in liquid silicon but, because of their severe silicon melting point overestimation, are limited to high temperatures where the carbon solubility is several percent, a value that is irrelevant for typical solidification conditions. Based on chemical potential calculations for pure silicon, we suggest that this well-known issue is confined to the description of the liquid phase and demonstrate that some recent potential models for silicon might address this weakness while preserving the excellent description of the carbon-silicon interaction found in the existing models.

Silicon Liquid Structure and Crystal Nucleation from Ab Initio Deep Metadynamics

Studying the crystallization process of silicon is a challenging task since empirical potentials are not able to reproduce well the properties of both a semiconducting solid and metallic liquid. On the other hand, nucleation is a rare event that occurs in much longer timescales than those achievable by ab initio molecular dynamics. To address this problem, we train a deep neural network potential based on a set of data generated by metadynamics simulations using a classical potential. We show how this is an effective way to collect all the relevant data for the process of interest. In order to efficiently drive the crystallization process, we introduce a new collective variable based on the Debye structure factor. We are able to encode the long-range order information in a local variable which is better suited to describe the nucleation dynamics. The reference energies are then calculated using the strongly constrained and appropriately normed (SCAN) exchange-correlation functional, which is able to get a better description of the bonding complexity of the Si phase diagram. Finally, we recover the free energy surface with a density functional theory accuracy, and we compute the thermodynamics properties near the melting point, obtaining a good agreement with experimental data. In addition, we study the early stages of the crystallization process, unveiling features of the nucleation mechanism.

Melting Si: Beyond Density Functional Theory

The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as nonlocal many body correlation effects of the electrons. We predict a melting temperature of about 1735 and 1640 K without and with core polarization effects, respectively. Both values are within 3% of the experimental melting temperature of 1687 K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200 K too low, and hybrid functionals overestimate the melting point by 150 K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results demonstrate that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.

The melting points of MgO up to 4 TPa predicted based on ab initio thermodynamic integration molecular dynamics

The melting curve of MgO is extended up to 4 TPa, corresponding to the Jovian core pressure, based on the one-step thermodynamic integration method implemented on ab initio molecular dynamics. The calculated melting temperatures are 3100 and 16 000 K at 0 and 500 GPa, respectively, which are consistent with previous experimental results, and 20 600 K at 3900 GPa, which is inconsistent with a recent experimental extrapolation, which implies the molten Jovian core. A quite small Clapeyron slope ([Formula: see text]) of [Formula: see text] is found at 3900 GPa due to comparable densities of the liquid and B2 phases under extreme compression. The Mg-O coordination number in the liquid phase is saturated at around 7.5 above 1 TPa and remains smaller than that in the B2 phase (8) even at 4 TPa, suggesting no density crossover between liquid and crystal and thus no further denser crystalline phases. Dynamical properties (atomic diffusivity and viscosity) are also investigated along the melting curve to understand these behaviors in greater detail.

Addressing the discrepancy of finding the equilibrium melting point of silicon using molecular dynamics simulations

We performed molecular dynamics simulations to study the equilibrium melting point of silicon using (i) the solid-liquid coexistence method and (ii) the Gibbs free energy technique, and compared our novel results with the previously published results obtained from the Monte Carlo (MC) void-nucleated melting method based on the Tersoff-ARK interatomic potential (Agrawal et al. Phys. Rev. B72, 125206. (doi:10.1103/PhysRevB.72.125206)). Considerable discrepancy was observed (approx. 20%) between the former two methods and the MC void-nucleated melting result, leading us to question the applicability of the empirical MC void-nucleated melting method to study a wide range of atomic and molecular systems. A wider impact of the study is that it highlights the bottleneck of the Tersoff-ARK potential in correctly estimating the melting point of silicon.

Alternative first-principles calculation of entropy for liquids

We present an alternative method for interpreting the velocity autocorrelation function (VACF) of a fluid with application to extracting the entropy in a manner similar to the methods developed by Lin et al. [J. Chem. Phys. 119, 11792 (2003)]JCPSA60021-960610.1063/1.1624057 and improved upon by Desjarlais [Phys. Rev. E 88, 062145 (2013)]PLEEE81539-375510.1103/PhysRevE.88.062145. The liquid VACF is decomposed into two components, one gas and one solid, and each contribution's entropic portion is calculated. However, we fit both the gas and solid portions of the VACF in the time domain. This approach is applied to a single-component liquid (a two-phase model of liquid Al at the melt line) and two different two-component systems: a superionic-to-superionic (bcc to fcc) phase transition in H_{2}O at high temperatures and pressures and a metastable liquid state of MgO. For all three examples, comparisons to existing results in the literature demonstrate the validity of our alternative.

First-principles calculation of entropy for liquid metals

We demonstrate the accurate calculation of entropies and free energies for a variety of liquid metals using an extension of the two-phase thermodynamic (2PT) model based on a decomposition of the velocity autocorrelation function into gas-like (hard sphere) and solid-like (harmonic) subsystems. The hard sphere model for the gas-like component is shown to give systematically high entropies for liquid metals as a direct result of the unphysical Lorentzian high-frequency tail. Using a memory function framework we derive a generally applicable velocity autocorrelation and frequency spectrum for the diffusive component which recovers the low-frequency (long-time) behavior of the hard sphere model while providing for realistic short-time coherence and high-frequency tails to the spectrum. This approach provides a significant increase in the accuracy of the calculated entropies for liquid metals and is compared to ambient pressure data for liquid sodium, aluminum, gallium, tin, and iron. The use of this method for the determination of melt boundaries is demonstrated with a calculation of the high-pressure bcc melt boundary for sodium. With the significantly improved accuracy available with the memory function treatment for softer interatomic potentials, the 2PT model for entropy calculations should find broader application in high energy density science, warm dense matter, planetary science, geophysics, and material science.

Direct first-principles chemical potential calculations of liquids

We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments.

Pressure induced structural phase transitions—A review

The contemporary status of experimental as well as theoretical advances within the special view of structural phase transitions is reviewed. A brief outline of phase transitions and its classification is presented first. High-pressure experimental techniques developed for studying the structural phase transitions and elastic properties are reviewed. The complete set of theoretical and experimental data obtained is for the group II–IV alkaline earth chalcogenides. Here the authors review the currently used calculations and high-pressure behavior of these materials and the theoretical work that has been done on them.

Melting of cubic boron nitride at extreme pressures

Due to its large pressure range of stability and inert nature, cubic boron nitride has been proposed as a potential pressure standard for high pressure experiments. It is extremely refractive upon compression, although its melting temperature is not known beyond 10 GPa. We apply first-principles molecular dynamics to evaluate the thermodynamics of zincblende structured (cubic) and liquid boron nitride at extreme temperatures and pressures, and compute the melting curve up to 1 TPa by integration of the Clapeyron equation. The resulting equations of state reveal that liquid boron nitride becomes denser than the solid phase at pressures of around 0.5 TPa. This is expressed as a turnover in the melting curve, which reaches a maximum at 510 GPa and 6550 ± 700 K. The origin of this density crossover is explained in terms of the underlying liquid structure, which diverges from that of the zincblende structured solid as the phases are compressed.

The kinetics of homogeneous melting beyond the limit of superheating

Molecular dynamics simulation is used to study the time-scales involved in the homogeneous melting of a superheated crystal. The interaction model used is an embedded-atom model for Fe developed in previous work, and the melting process is simulated in the microcanonical (N, V, E) ensemble. We study periodically repeated systems containing from 96 to 7776 atoms, and the initial system is always the perfect crystal without free surfaces or other defects. For each chosen total energy E and number of atoms N, we perform several hundred statistically independent simulations, with each simulation lasting for between 500 ps and 10 ns, in order to gather statistics for the waiting time τ(w) before melting occurs. We find that the probability distribution of τ(w) is roughly exponential, and that the mean value <τ(w)> depends strongly on the excess of the initial steady temperature of the crystal above the superheating limit identified by other researchers. The mean <τ(w)> also depends strongly on system size in a way that we have quantified. For very small systems of ~100 atoms, we observe a persistent alternation between the solid and liquid states, and we explain why this happens. Our results allow us to draw conclusions about the reliability of the recently proposed Z method for determining the melting properties of simulated materials and to suggest ways of correcting for the errors of the method.

Real-world predictions from ab initio molecular dynamics simulations

In this review we present the techniques of ab initio molecular dynamics simulation improved to its current stage where the analysis of existing processes and the prediction of further chemical features and real-world processes are feasible. For this reason we describe the relevant developments in ab initio molecular dynamics leading to this stage. Among them, parallel implementations, different basis set functions, density functionals, and van der Waals corrections are reported. The chemical features accessible through AIMD are discussed. These are IR, NMR, as well as EXAFS spectra, sampling methods like metadynamics and others, Wannier functions, dipole moments of molecules in condensed phase, and many other properties. Electrochemical reactions investigated by ab initio molecular dynamics methods in solution, on surfaces as well as complex interfaces, are also presented.

First-principles simulations of lithium melting: stability of the bcc phase close to melting

We report large-scale first-principles simulations of melting of four different phases of Li at pressures ranging from 0 to 50 GPa. We find excellent agreement with existing experimental data at low pressures, and confirm that above 10 GPa the melting line develops a negative slope, in parallel to what occurs for Na at 30 GPa. Surprisingly, our results indicate that the melting temperature of the bcc phase is always higher than that of fcc Li, suggesting the intriguing possibility of the existence of a narrow field of bcc stability separating the fcc and liquid phases, as predicted by Alexander and McTague [Phys. Rev. Lett. 41, 702 (1978)].

Ab initio method for locating characteristic potential-energy minima of liquids

It is possible in principle to probe the many-atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids by Wallace [Phys. Rev. E 56, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential-energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid molecular dynamics configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations.

Improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of +/-2% among elemental liquids and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of +/-0.1% to the available experimental high-temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/theta_{0}) , where T is temperature and theta_{0} is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/theta_{tr}) , where theta_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived in a single formula applying to normal and anomalous melting alike. An ab initio calculation of theta_{0} , based on density-functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.

Interaction potential for indium phosphide: a molecular dynamics and first-principles study of the elastic constants, generalized stacking fault and surface energies

Indium phosphide is investigated using molecular dynamics (MD) simulations and density-functional theory calculations. MD simulations use a proposed effective interaction potential for InP fitted to a selected experimental dataset of properties. The potential consists of two- and three-body terms that represent atomic-size effects, charge-charge, charge-dipole and dipole-dipole interactions as well as covalent bond bending and stretching. Predictions are made for the elastic constants as a function of density and temperature, the generalized stacking fault energy and the low-index surface energies.

Ab initio statistical mechanics of surface adsorption and desorption. I. H2O on MgO (001) at low coverage

We present a general computational scheme based on molecular dynamics (MD) simulation for calculating the chemical potential of adsorbed molecules in thermal equilibrium on the surface of a material. The scheme is based on the calculation of the mean force in MD simulations in which the height of a chosen molecule above the surface is constrained and subsequent integration of the mean force to obtain the potential of mean force and hence the chemical potential. The scheme is valid at any coverage and temperature, so that in principle it allows the calculation of the chemical potential as a function of coverage and temperature. It avoids all statistical mechanical approximations, except for the use of classical statistical mechanics for the nuclei, and assumes nothing in advance about the adsorption sites. From the chemical potential, the absolute desorption rate of the molecules can be computed, provided that the equilibration rate on the surface is faster than the desorption rate. We apply the theory by ab initio MD simulation to the case of H2O on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof (PBE) form of exchange correlation. The calculations yield an ab initio value of the Polanyi-Wigner frequency prefactor, which is more than two orders of magnitude greater than the value of 10(13) s(-1) often assumed in the past. Provisional comparison with experiment suggests that the PBE adsorption energy may be too low, but the extension of the calculations to higher coverages is needed before firm conclusions can be drawn. The possibility of including quantum nuclear effects by using path-integral simulations is noted.

Electronic and structural transitions in dense liquid sodium

At ambient conditions, the light alkali metals are free-electron-like crystals with a highly symmetric structure. However, they were found recently to exhibit unexpected complexity under pressure. It was predicted from theory--and later confirmed by experiment--that lithium and sodium undergo a sequence of symmetry-breaking transitions, driven by a Peierls mechanism, at high pressures. Measurements of the sodium melting curve have subsequently revealed an unprecedented (and still unexplained) pressure-induced drop in melting temperature from 1,000 K at 30 GPa down to room temperature at 120 GPa. Here we report results from ab initio calculations that explain the unusual melting behaviour in dense sodium. We show that molten sodium undergoes a series of pressure-induced structural and electronic transitions, analogous to those observed in solid sodium but commencing at much lower pressure in the presence of liquid disorder. As pressure is increased, liquid sodium initially evolves by assuming a more compact local structure. However, a transition to a lower-coordinated liquid takes place at a pressure of around 65 GPa, accompanied by a threefold drop in electrical conductivity. This transition is driven by the opening of a pseudogap, at the Fermi level, in the electronic density of states--an effect that has not hitherto been observed in a liquid metal. The lower-coordinated liquid emerges at high temperatures and above the stability region of a close-packed free-electron-like metal. We predict that similar exotic behaviour is possible in other materials as well.

Extended multicanonical method combined with thermodynamically optimized potential: Application to the liquid-crystal transition of silicon

A novel method is proposed to study first-order phase transition in real materials. It is applied to the liquid-crystal transition of silicon successfully. It consists of two parts: a direct simulation of the transition by an extended multicanonical ensemble with an order parameter defined with structure factors that characterize the transition, and optimization of a model interatomic potential in terms of the ensemble from an accurate one. These provide a principle to project a first-principles approach on a model-based approach conserving thermodynamic properties of multiple phases.

Absolute rate of thermal desorption from first-principles simulation

We present a technique for computing by first-principles simulation the absolute desorption rate γ of adsorbate molecules from a surface for any coverage and temperature. The technique is valid when the thermal equilibration rate on the surface is faster than γ, and is based on an exact expression for γ in terms of the difference of non-configurational chemical potentials of gas-phase and adsorbed molecules. This difference is expressed in terms of a potential of mean force, which is computed by constrained first-principles molecular dynamics. The technique is applied to D(2)O on the MgO(001) surface at low coverage, using the generalized gradient approximation (GGA) for exchange-correlation energy. Comparisons with experimental temperature programmed desorption data allow an assessment of the accuracy of the GGA for the adsorption of D(2)O on MgO(001).

Carbon under extreme conditions: phase boundaries and electronic properties from first-principles theory

At high pressure and temperature, the phase diagram of elemental carbon is poorly known. We present predictions of diamond and BC8 melting lines and their phase boundary in the solid phase, as obtained from first-principles calculations. Maxima are found in both melting lines, with a triple point located at approximately 850 GPa and approximately 7,400 K. Our results show that hot, compressed diamond is a semiconductor that undergoes metalization upon melting. In contrast, in the stability range of BC8, an insulator to metal transition is likely to occur in the solid phase. Close to the diamond/liquid and BC8/liquid boundaries, molten carbon is a low-coordinated metal retaining some covalent character in its bonding up to extreme pressures. Our results provide constraints on the carbon equation of state, which is of critical importance for devising models of Neptune, Uranus, and white dwarf stars, as well as of extrasolar carbon-rich planets.

Carbon phase diagram from ab initio molecular dynamics

We compute the free energy of solid and liquid diamond from first-principles electronic structure theory using efficient thermodynamic integration techniques. Our calculated melting curve is in excellent agreement with the experimental estimate of the graphite-diamond-liquid triple point and is consistent with shock wave experiments. We predict the phase diagram of diamond at pressures and temperatures that are difficult to access experimentally. We confirm early speculations on the presence of a reentrant point in the diamond melting line but find no evidence for a first order liquid-liquid phase transition near the reentrant point.

Melting curve of MgO from first-principles simulations

First-principles calculations based on density functional theory, both with the local density approximation (LDA) and with generalized gradient corrections (GGA), have been used to simulate solid and liquid MgO in direct coexistence in the range of pressure 0 < or = p < or = 135 GPa. The calculated LDA zero pressure melting temperature is T(LDA)m = 3110 +/- 50 K, in good agreement with the experimental data. The GGA zero pressure melting temperature T(GGA)m = 2575 +/- 100 K is significantly lower than the LDA one, but the difference between the GGA and the LDA is greatly reduced at high pressure. The LDA zero pressure melting slope is dT/dp approximately 100 K/GPa, which is more than 3 times higher than the currently available experimental one from Zerr and Boehler [Nature (London) 371, 506 (1994)]. At the core mantle boundary pressure of 135 GPa MgO melts at Tm = 8140 +/- 150 K.

Phase diagram of silicon from atomistic simulations

In this Letter we present a calculation of the temperature-pressure phase diagram of Si in a range of pressures covering from -5 to 20 GPa and temperatures up to the melting point. The phase boundaries and triple points between the diamond, liquid, beta-Sn, and Si34 clathrate phases are reported. We have employed efficient simulation techniques to calculate free energies and to numerically integrate the Clausius-Clapeyron equation, combined with a tight-binding model capable of an accuracy comparable to that of first-principles methods. The resulting phase diagram agrees well with the available experimental data.

Transitions between disordered phases in supercooled liquid silicon

We have investigated the transitions between disordered phases in supercooled liquid silicon using computer simulations. The thermodynamic properties were directly obtained from the free energy, which was computed using the recently proposed reversible scaling method. The calculated free energies of the crystalline and liquid phases of silicon at zero pressure, obtained using the environment dependent interatomic potential, are in excellent agreement with the available experimental data. The results show that, at zero pressure, a weak first-order liquid-liquid transition occurs at 1135 K and a continuous liquid-amorphous transition takes place at 843 K. These results are consistent with the existence of a second critical point for the liquid-liquid transition at a negative pressure.

Ab initiomelting curve of copper by the phase coexistence approach

Ab initio calculations of the melting properties of copper in the pressure range 0-100 GPa are reported. The ab initio total energies and ionic forces of systems representing solid and liquid copper are calculated using the projector augmented wave implementation of density functional theory with the generalized gradient approximation for exchange-correlation energy. An initial approximation to the melting curve is obtained using an empirical reference system based on the embedded-atom model, points on the curve being determined by simulations in which solid and liquid coexist. The approximate melting curve so obtained is corrected using calculated free energy differences between the reference and ab initio system. It is shown that for system-size errors to be rendered negligible in this scheme, careful tuning of the reference system to reproduce ab initio energies is essential. The final melting curve is in satisfactory agreement with extrapolated experimental data available up to 20 GPa, and supports the validity of previous calculations of the melting curve up to 100 GPa.

Melting of lithium hydride under pressure

We have computed the melting line of lithium hydride up to 200 GPa using the two-phase simulation technique coupled with first-principles molecular dynamics. Our predicted melting temperature at high pressures varies slowly with compression, ranging from 2000 to 2450 K at 50-200 GPa pressures. The compressed fluid close to the melting line retains the ionic character of the low pressure molten state, while at higher temperatures dynamical hydrogen clustering processes are observed, which are accompanied by changes in the electronic structure.

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

The temperature anomalies in the Earth's mantle associated with thermal convection can be inferred from seismic tomography, provided that the elastic properties of mantle minerals are known as a function of temperature at mantle pressures. At present, however, such information is difficult to obtain directly through laboratory experiments. We have therefore taken advantage of recent advances in computer technology, and have performed finite-temperature ab initio molecular dynamics simulations of the elastic properties of MgSiO3 perovskite, the major mineral of the lower mantle, at relevant thermodynamic conditions. When combined with the results from tomographic images of the mantle, our results indicate that the lower mantle is either significantly anelastic or compositionally heterogeneous on large scales. We found the temperature contrast between the coldest and hottest regions of the mantle, at a given depth, to be about 800 K at 1,000 km, 1,500 K at 2,000 km, and possibly over 2,000 K at the core-mantle boundary.