Phase diagram of carbon at high pressures and temperatures

A database of high-pressure crystal structures from hydrogen to lanthanum

This paper introduces the HEX (High-pressure Elemental Xstals) database, a complete database of the ground-state crystal structures of the first 57 elements of the periodic table, from H to La, at 0, 100, 200 and 300 GPa. HEX aims to provide a unified reference for high-pressure research, by compiling all available experimental information on elements at high pressure, and complementing it with the results of accurate evolutionary crystal structure prediction runs based on Density Functional Theory. Besides offering a much-needed reference, our work also serves as a benchmark of the accuracy of current ab-initio methods for crystal structure prediction. We find that, in 98% of the cases in which experimental information is available, ab-initio crystal structure prediction yields structures which either coincide or are degenerate in enthalpy to within 300 K with experimental ones. The main manuscript contains synthetic tables and figures, while the Crystallographic Information File (cif) for all structures can be downloaded from the related figshare online repository.

Ab initio structural dynamics of pure and nitrogen-containing amorphous carbon

Amorphous carbon (a-C) has attracted considerable interest due to its desirable properties, which are strongly dependent on its structure, density and impurities. Using ab initio molecular dynamics simulations we show that the sp2/sp3 content and underlying structural order of a-C produced via liquid quenching evolve at high temperatures and pressures on sub-nanosecond timescales. Graphite-like densities ([Formula: see text] 2.7 g/cc) favor the formation of layered arrangements characterized by sp2 disordered bonding resembling recently synthesized monolayer amorphous carbon (MAC), while at diamond-like densities ([Formula: see text] 3.3 g/cc) the resulting structures are dominated by disordered tetrahedral sp3 hybridization typical of diamond-like amorphous carbon (DLC). At intermediate densities the system is a highly compressible mixture of coexisting sp2 and sp3 regions that continue to segregate over 10's of picoseconds. The addition of nitrogen (20.3%) (a-CN) generates major system features similar with those of a-C, but has the unexpected effect of reinforcing the thermodynamically disfavored carbon structural motifs at low and high densities, while inhibiting phase separation in the intermediate region. At the same time, no nitrogen elimination from the carbon framework is observed above [Formula: see text] 2.8 g/cc, suggesting that nitrogen impurities are likely to remain embedded in the carbon structures during fast temperature quenches at high pressures.

Atomic and Electronic Structure of Solid-Density Liquid Carbon

A liquid carbon (l-C) sample is generated through constant volume heating exposing an amorphous carbon foil to an intense ultrashort laser pulse. Time-resolved x-ray absorption spectroscopy at the C K edge is used to monitor the dynamics of the melting process revealing a subpicosecond rearrangement of the electronic structure associated with a sudden change of the C bonding hybridization. The obtained l-C sample, resulting from a nonthermal melting mechanism, reaches a transient equilibrium condition with a temperature of about 14 200 K and pressure in the order of 0.5 Mbar in about 0.3 ps, prior to hydrodynamic expansion. A detailed analysis of the atomic and electronic structure in solid-density l-C based on time-resolved x-ray absorption spectroscopy and theoretical simulations is presented. The method can be fruitfully used for extending the experimental investigation of the C phase diagram in a vast unexplored region covering the 10^{3}-10^{4}  K temperature range with pressures up to 1 Mbar.

Characterization of three phases of liquid carbon by tight-binding molecular dynamics simulations

We have performed tight-binding molecular dynamics simulations to study the structures and properties of liquid carbon with the density ranging from 1.4 to 3.5 g cm⁻³, and identified three liquid carbon phases at different density regime.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

Free energy model for solid high-pressure phases of carbon

Analytic free energy models for three solid high-pressure phases--diamond, body centered cubic phase with eight atoms in the unit cell (BC8), and simple cubic (SC)--are developed using density functional theory. We explicitly include anharmonic effects by performing molecular dynamics simulations and investigate their density and temperature dependence in detail. Anharmonicity in the nuclear motion shifts the phase transitions significantly compared to the harmonic approximation. Furthermore, we apply a thermodynamically constrained correction that brings the equation of state in accordance with diamond anvil cell experiments. The performance of our thermodynamic functions is validated against Hugoniot experiments.

Probing the complex ion structure in liquid carbon at 100 GPa

We present the first direct experimental test of the complex ion structure in liquid carbon at pressures around 100 GPa, using spectrally resolved x-ray scattering from shock-compressed graphite samples. Our results confirm the structure predicted by ab initio quantum simulations and demonstrate the importance of chemical bonds at extreme conditions similar to those found in the interiors of giant planets. The evidence presented here thus provides a firmer ground for modeling the evolution and current structure of carbon-bearing icy giants like Neptune, Uranus, and a number of extrasolar planets.

The liquid<−>amorphous transition and the high pressure phase diagram of carbon

The phase diagram of carbon is mapped to high pressure using a computationally-tractable potential model. The use of a relatively simple (Tersoff-II) potential model allows a large range of phase space to be explored. The coexistence (melting) curve for the diamond crystal/liquid dyad is mapped directly by modelling the solid/liquid interfaces. The melting curve is found to be re-entrant and belongs to a conformal class of diamond/liquid coexistence curves. On supercooling the liquid a phase transition to a tetrahedral amorphous form (ta-C) is observed. The liquid <−> amorphous coexistence curve is mapped onto the pT plane and is found to also be re-entrant. The entropy changes for both melting and the amorphous −> liquid transitions are obtained from the respective coexistence curves and the associated changes in molar volume. The structural change on amorphization is analysed at different points on the coexistence curve including for transitions that are both isochoric and isocoordinate (no change in nearest-neighbour coordination number). The conformal nature of the melting curve is highlighted with respect to the known behaviour of Si. The relationship of the observed liquid/amorphous coexistence curve to the Si low- and high-density amorphous (LDA/HDA) transition is discussed.

Thermodynamically stable phases of carbon at multiterapascal pressures

Phases of carbon are studied up to pressures of 1 petapascal (PPa) using first-principles density-functional-theory methods and a structure searching algorithm. Our extensive search over the potential energy surface supports the sequence of transitions diamond → BC8 → simple cubic under increasing pressure found in previous theoretical studies. At higher pressures we predict a soft-phonon driven transition to a simple hexagonal structure at 6.4 terapascals (TPa), and further transitions to the face centered cubic electride structure at 21 TPa, a double hexagonal close packed structure at 270 TPa, and the body centered cubic structure at 650 TPa.

Ultrafast melting of carbon induced by intense proton beams

Laser-produced proton beams have been used to achieve ultrafast volumetric heating of carbon samples at solid density. The isochoric melting of carbon was probed by a scattering of x rays from a secondary laser-produced plasma. From the scattering signal, we have deduced the fraction of the material that was melted by the inhomogeneous heating. The results are compared to different theoretical approaches for the equation of state which suggests modifications from standard models.

Structure of liquid metals by ab initio molecular-dynamics simulations

How the study of liquid metals has progressed in the past three decades is summarized briefly from a personal point of view. It is emphasized that, by ab initio molecular-dynamics (MD) simulations, we can now obtain the electronic states as well as the structure of liquid metals at the same time and therefore we can understand the characteristic features of the microscopic atomic structure and bonding states in real space. As examples we show the results of our ab initio MD simulations for liquid phosphorus, liquid tellurium and liquid carbon at high pressures.

Diamond at 800 GPa

A new compression technique, which enables the study of solids into the TPa regime, is described and used to ramp (or quasi-isentropically) compress diamond to a peak pressure of 1400 GPa. Diamond stress versus density data are reported to 800 GPa and suggest that the diamond phase is stable and has significant material strength up to at least this stress level. Data presented here are the highest ramp compression pressures by more than a factor of 5 and the highest-pressure solid equation-of-state data ever reported.

Phase-ordering kinetics of the liquid-liquid transition in single-component molecular liquids

Recently it has been revealed that even a single-component liquid can have more than two liquid states. The transition between these liquid states is called the "liquid-liquid transition." Most known liquid-liquid transitions occur at temperatures and pressures which are difficult to access experimentally, so the physical nature of the transition, particularly the kinetics, has remained elusive. However, the recent discovery of liquid-liquid transitions in molecular liquids opens up a possibility to study the kinetics in detail. Here, we report the first phase field simulation on the kinetics of a liquid-liquid transition and its direct comparison with experimental results of the molecular liquids. Both nucleation-growth-type and spinodal-decomposition-type liquid-liquid transformation observed experimentally are well reproduced by numerical simulation based on a two-order-parameter model of liquid that regards the liquid-liquid transition as the cooperative formation of locally favored structures. Thus, phase field calculations may allow us to predict the kinetics of liquid-liquid transitions and the resulting spatiotemporal change of various physical properties of the liquid, such as density and refractive index.

Laser-shock compression of diamond and evidence of a negative-slope melting curve

Diamond is the only known high-pressure structure of carbon. In spite of its fundamental and planetary importance, the stability domain of this strong covalent material is largely unknown. After decades of experimental efforts, evidence was obtained that the diamond-liquid melting line has a positive slope above the graphite-diamond-liquid triple point. At higher pressure, theoretical studies have suggested that the melting curve of diamond should have a maximum, owing to a loss of stability of the sp3 hybridization in the fluid phase. Accurate Hugoniot data of diamond exist up to 590 GPa (ref. 6). Higher-pressure measurements along the diamond Hugoniot have recently been achieved by laser shocks, showing that diamond probably melts to a conducting fluid. We report here laser-shock Hugoniot data across the melting transition. The shocked diamond crystal begins to melt around 750 GPa. Furthermore, a negative volume discontinuity at melting is observed. This requires a negative melting slope and thus supports the existence of a maximum on the diamond melting curve. These melting data allow us to test various calculations of the phase diagram of carbon at very high pressure. Finally, the stability domain of the diamond crystal is now constrained in a relevant region for Uranus-like planetary interiors.

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.

Modeling the phase diagram of carbon

We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respectively. The graphite-diamond transition line that we computed is in good agreement with experimental data, confirming the accuracy of the employed empirical potential. On the basis of the computed slope of the graphite melting line, we rule out the hotly debated liquid-liquid phase transition of carbon. Our simulations allow us to give accurate estimates of the location of the diamond melting curve and of the graphite-diamond-liquid triple point.

Shock compressing diamond to a conducting fluid

Laser generated shock reflectance data show that diamond undergoes a continuous transition from optically absorbing to reflecting between Hugoniot pressures 600<P(H)<1000 GPa. The data are consistent with diamond having a thermal population of carriers at P(H) approximately 600 GPa, undergoing band overlap metallization at P(H) approximately 1000 GPa and melting at 800<P(H)<1000 GPa. The results agree well with an equation of state model that predicts that elemental carbon remains solid throughout the interior of Neptune.

Hugoniot data for carbon at megabar pressures

We present an experimental point for the carbon equation of state (EOS) at megabar pressures, obtained by laser-driven shock waves. The rear side emissivity of "two-materials two-steps" targets (Al-C) was recorded with space and time resolution and, by applying the impedance mismatch method, allowed a direct determination of relative EOS points. Experiments were performed at the PALS and LULI laboratories using carbon samples with two different values of initial density, in order to explore a wider region of the phase diagram. Previously unreached pressures were obtained. The results are compared with previous experiments and with available theoretical models and seem to show a high compressibility of carbon at megabar pressures.

General view of a liquid-liquid phase transition

We present a general view of a liquid-liquid phase transition, based on a simple physical picture that there is "cooperative medium-range bond ordering" for any liquids. Contrary to the common belief, we argue that liquid is not homogeneous and in any liquid there exist locally favored structures, which are frustrated with normal-liquid structures. The cooperative excitation of locally favored structures leads to a gas-liquid-like critical point of bond ordering. This picture naturally leads to the conclusion that liquid-liquid transition is not specific to special materials, but can in principle exist in any liquids. Our model suggests a new possibility that (i) even an ordinary molecular liquid can have a hidden liquid-liquid phase transition and (ii) it may be the origin of a second amorphous phase (e.g., "glacial phase") and critical-like, large-scale fluctuations ("Fischer clusters") observed in supercooled molecular liquids.