Structural transformations in carbon under extreme pressure: Beyond diamond

Phase Transition in Silicon from Machine Learning Informed Metadynamics

Investigating reconstructive phase transitions in large-sized systems requires a highly efficient computational framework with computational cost proportional to the system size. Traditionally, widely used frameworks such as density functional theory (DFT) have been prohibitively expensive for extensive simulations on large systems that require long-time scales. To address this challenge, this study employed well-trained machine learning potential to simulate phase transitions in a large-size system. This work integrates the metadynamics simulation approach with machine learning potential, specifically deep potential, to enhance computational efficiency and accelerate the study of phase transition and consequent development of grains and dislocation defects in a system. The new method is demonstrated using the phase transitions of bulk silicon under high pressure. This approach has revealed the transition path and formation of polycrystalline silicon systems under specific stress conditions, demonstrating the effectiveness of deep potential-driven metadynamics simulations in gaining insights into complex material behaviors in large-sized systems.

Extreme Metastability of Diamond and its Transformation to the BC8 Post-Diamond Phase of Carbon

Diamond possesses exceptional physical properties due to its remarkably strong carbon-carbon bonding, leading to significant resilience to structural transformations at very high pressures and temperatures. Despite several experimental attempts, synthesis and recovery of the theoretically predicted post-diamond BC8 phase remains elusive. Through quantum-accurate multimillion atom molecular dynamics (MD) simulations, we have uncovered the extreme metastability of diamond at very high pressures, significantly exceeding its range of thermodynamic stability. We predict the post-diamond BC8 phase to be experimentally accessible only within a narrow high pressure-temperature region of the carbon phase diagram. The diamond to BC8 transformation proceeds through premelting followed by BC8 nucleation and growth in the metastable carbon liquid. We propose a double-shock compression pathway for BC8 synthesis, which is currently being explored in experiments at the National Ignition Facility.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Theoretical methods for structural phase transitions in elemental solids at extreme conditions: statics and dynamics

In recent years, theoretical studies have moved from a traditionally supporting role to a more proactive role in the research of phase transitions at high pressures. In many cases, theoretical prediction leads the experimental exploration. This is largely owing to the rapid progress of computer power and theoretical methods, particularly the structure prediction methods tailored for high-pressure applications. This review introduces commonly used structure searching techniques based on static and dynamic approaches, their applicability in studying phase transitions at high pressure, and new developments made toward predicting complex crystalline phases. Successful landmark studies for each method are discussed, with an emphasis on elemental solids and their behaviors under high pressure. The review concludes with a perspective on outstanding challenges and opportunities in the field.

Nucleating a Different Coordination in a Crystal under Pressure: A Study of the B1-B2 Transition in NaCl by Metadynamics

Here we propose an NPT metadynamics simulation scheme for pressure-induced structural phase transitions, using coordination number and volume as collective variables, and apply it to the reconstructive structural transformation B1-B2 in NaCl. By studying systems with size up to 64 000 atoms we reach a regime beyond collective mechanism and observe transformations proceeding via nucleation and growth. We also reveal the crossover of the transition mechanism from Buerger-like for smaller systems to Watanabe-Tolédano for larger ones. The scheme is likely to be applicable to a broader class of pressure-induced structural transitions, allowing study of complex nucleation effects and bringing simulations closer to realistic conditions.

Metastability of diamond ramp-compressed to 2 terapascals

Carbon is the fourth-most prevalent element in the Universe and essential for all known life. In the elemental form it is found in multiple allotropes, including graphite, diamond and fullerenes, and it has long been predicted that even more structures can exist at pressures greater than those at Earth's core^1-3. Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets^4,5. By compressing solid carbon to 2 terapascals (20 million atmospheres; more than five times the pressure at Earth's core) using ramp-shaped laser pulses and simultaneously measuring nanosecond-duration time-resolved X-ray diffraction, we found that solid carbon retains the diamond structure far beyond its regime of predicted stability. The results confirm predictions that the strength of the tetrahedral molecular orbital bonds in diamond persists under enormous pressure, resulting in large energy barriers that hinder conversion to more-stable high-pressure allotropes^1,2, just as graphite formation from metastable diamond is kinetically hindered at atmospheric pressure. This work nearly doubles the highest pressure at which X-ray diffraction has been recorded on any material.

Identification of Phase Transitions and Metastability in Dynamically Compressed Antimony Using Ultrafast X-Ray Diffraction

Ultrafast x-ray diffraction at the LCLS x-ray free electron laser has been used to resolve the structural behavior of antimony under shock compression to 59 GPa. Antimony is seen to transform to the incommensurate, host-guest phase Sb-II at ∼11  GPa, which forms on nanosecond timescales with ordered guest-atom chains. The high-pressure bcc phase Sb-III is observed above ∼15  GPa, some 8 GPa lower than in static compression studies, and mixed Sb-III/liquid diffraction are obtained between 38 and 59 GPa. An additional phase which does not exist under static compression, Sb-I^{'}, is also observed between 8 and 12 GPa, beyond the normal stability field of Sb-I, and resembles Sb-I with a resolved Peierls distortion. The incommensurate Sb-II high-pressure phase can be recovered metastably on release to ambient pressure, where it is stable for more than 10 ns.

Short-wavelength free-electron laser sources and science: a review

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.

Graphene and nano-diamond synthesis in expansions of molten liquid carbon

Despite their widespread use in high-pressure experiments, little is known about the physical and chemical properties of carbon-containing materials as they expand and cool to ambient conditions. As a result, interpretation of experiments can rely on use of unconstrained models with poor accuracy for the ensuing equation of state properties and final chemical products. To this end, we use quantum simulations to study the free expansion and cooling of carbon from metallic liquid states achieved during shock compression. Expansions from three different sets of shock conditions yielded of a variety of chain and ring structures. We then quantify the relative amounts of graphite-like and diamond-like particles formed during cooling and equilibration. We observe that for all cases, graphene sheets are the majority product formed with more extreme initial conditions producing increasingly larger amounts of diamond particles. Our results can address key needs for future meso-scale models of experiments, where knowledge of material properties and chemical end products can have a pronounced effect on interpreting experimental observables.

Ramp compression of diamond to five terapascals

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

Phase transformation of cadmium sulfide under high temperature and high pressure conditions

Cadmium sulfide (CdS) is one of the most significant wide band gap semiconductors, and knowledge of the phase transformation of CdS under high temperature and pressure is especially important for its applications. The pressure-temperature phase diagram and the phase transformation pathways of CdS have been investigated by using density functional theory combined with quasiharmonic approximation. Our results indicated that under ambient conditions, wz-CdS is a stable phase, while under high temperature and pressure, rs-CdS becomes the stable phase. It is also found that zb-CdS is an intermediate phase in transforming from rs-CdS to wz-CdS. Therefore, although there are no zb-CdS phase regions in the CdS pressure-temperature phase diagram, zb-CdS can be found in some prepared experiments.

Ramp compression of diamond to five terapascals

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

Single photon energy dispersive x-ray diffraction

With the pressure range accessible to laser driven compression experiments on solid material rising rapidly, new challenges in the diagnosis of samples in harsh laser environments are emerging. When driving to TPa pressures (conditions highly relevant to planetary interiors), traditional x-ray diffraction techniques are plagued by increased sources of background and noise, as well as a potential reduction in signal. In this paper we present a new diffraction diagnostic designed to record x-ray diffraction in low signal-to-noise environments. By utilising single photon counting techniques we demonstrate the ability to record diffraction patterns on nanosecond timescales, and subsequently separate, photon-by-photon, signal from background. In doing this, we mitigate many of the issues surrounding the use of high intensity lasers to drive samples to extremes of pressure, allowing for structural information to be obtained in a regime which is currently largely unexplored.

Stable all-nitrogen metallic salt at terapascal pressures

The phase diagram and equation of state of dense nitrogen are of interest in understanding the fundamental physics and chemistry under extreme conditions, including planetary processes, and in discovering new materials. We predict several stable phases of nitrogen at multi-TPa pressures, including a P4/nbm structure consisting of partially charged N(2)(δ+) pairs and N(5)(δ-) tetrahedra, which is stable in the range 2.5-6.8 TPa. This is followed by a modulated layered structure between 6.8 and 12.6 TPa, which also exhibits a significant charge transfer. The P4/nbm metallic nitrogen salt and the modulated structure are stable at high pressures and temperatures, and they exhibit strongly ionic features and charge density distortions, which is unexpected in an element under such extreme conditions and could represent a new class of nitrogen materials. The P-T phase diagram of nitrogen at TPa pressures is investigated using quasiharmonic phonon calculations and ab initio molecular dynamics simulations.

Room-temperature structures of solid hydrogen at high pressures

By employing first-principles metadynamics simulations, we explore the 300 K structures of solid hydrogen over the pressure range 150-300 GPa. At 200 GPa, we find the ambient-pressure disordered hexagonal close-packed (hcp) phase transited into an insulating partially ordered hcp phase (po-hcp), a mixture of ordered graphene-like H(2) layers and the other layers of weakly coupled, disordered H(2) molecules. Within this phase, hydrogen remains in paired states with creation of shorter intra-molecular bonds, which are responsible for the very high experimental Raman peak above 4000 cm(-1). At 275 GPa, our simulations predicted a transformation from po-hcp into the ordered molecular metallic Cmca phase (4 molecules/cell) that was previously proposed to be stable only above 400 GPa. Gibbs free energy calculations at 300 K confirmed the energetic stabilities of the po-hcp and metallic Cmca phases over all known structures at 220-242 GPa and >242 GPa, respectively. Our simulations highlighted the major role played by temperature in tuning the phase stabilities and provided theoretical support for claimed metallization of solid hydrogen below 300 GPa at 300 K.

Theoretical investigation of planar square carbon allotrope and its hydrogenation

Using density functional theory we investigate a novel carbon allotrope 'SqC': a square planar material that can be more than tetracoordinated. Carbon atoms in this 2D square Bravais lattice form an unusual five-center four-electron bond with neighboring four carbon atoms (tetracoordination). Such an electron-deficient bonding leaves an empty orbital which enables penta- or hexa-coordinated carbon atom. Indeed, our simulations demonstrate such penta- and hexa-coordinated configurations upon partial and complete hydrogenation, respectively. Surprisingly, in all the forms SqC shows the metallic character. SqC has the binding energy of 6.7 eV and it also satisfies the Born stability criteria. Yet our phonon calculations show that it may only be considered as quasi-stable.

Superhard F-carbon predicted by ab initio particle-swarm optimization methodology

A simple (5 + 6 + 7)-sp(3) carbon (denoted as F-carbon) with eight atoms per unit cell predicted by a newly developed ab initio particle-swarm optimization methodology on crystal structure prediction is proposed. F-carbon can be seen as the reconstruction of AA-stacked or 3R-graphite, and is energetically more stable than 2H-graphite beyond 13.9 GPa. Band structure and hardness calculations indicate that F-carbon is a transparent superhard carbon with a gap of 4.55 eV at 15 GPa and a hardness of 93.9 GPa at zero pressure. Compared with the previously proposed Bct-, M- and W-carbons, the simulative x-ray diffraction pattern of F-carbon also well matches the superhard intermediate phase of the experimentally cold-compressed graphite. The possible transition route and energy barrier were observed using the variable cell nudged elastic band method. Our simulations show that the cold compression of graphite can produce some reversible metastable carbons (e.g. M- and F-carbons) with energy barriers close to diamond or lonsdaleite.

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.

Persistence and eventual demise of oxygen molecules at terapascal pressures

Computational searches for structures of solid oxygen under high pressures in the multi-TPa range are carried out using density-functional-theory methods. We find that molecular oxygen persists to about 1.9 TPa at which it transforms into a semiconducting square-spiral-like polymeric structure (I4(1)/acd) with a band gap of ~3.0 eV. Solid oxygen forms a metallic zigzag chainlike structure (Cmcm) at about 3.0 TPa, but the chains in each layer gradually merge as the pressure is increased and a structure of Fmmm symmetry forms at about 9.3 TPa in which each atom has four nearest neighbors. The superconducting properties of molecular oxygen do not vary much with compression, although the structure becomes more symmetric. The electronic properties of oxygen have a complex evolution with pressure, swapping between insulating, semiconducting, and metallic.

High-pressure phases of hydrogen cyanide: formation of hydrogenated carbon nitride polymers and layers and their electronic properties

We have performed a set of first-principles simulations to consider the possible phase transitions in molecular crystals of HCN under high pressure. Our calculations reveal several transition paths from the orthorhombic phase to tetragonal and then to triclinic phases. The transitions from the orthorhombic to the tetragonal phases are of the second order, whereas those from the tetragonal to the triclinic phases turn out to be of the first-order type and characterized by an abrupt decrease in volume. Our calculations show that, by adjustment of the temperature and pressure of the HCN molecular crystal, novel layered and polymeric crystals with insulating, semiconducting or metallic properties can be found. Based on our simulation results, two different crystal formation mechanisms are deduced. The stabilities of the predicted structures at ambient pressure are further assessed by performing phonon or MD simulations. In addition, the electron transport properties of the predicted polymers are obtained using the non-equilibrium Green's function technique combined with density functional theory. The results show that the polymers have metallic-like I-V characteristics.

Structural prediction and phase transformation mechanisms in calcium at high pressure

High-pressure phase transformations of Ca are studied using the metadynamics method to explore the anharmonic free-energy surface, together with a genetic algorithm structural search method to identify lowest enthalpy structures. Disagreement between theory and experiment regarding the structure of Ca in the pressure range 32-119 GPa is partially resolved by the demonstration of different phase transition behavior at 300 K from that at low temperatures. A new lowest enthalpy I4(1)/amd structure is obtained with both methods with an estimated superconducting critical temperature in agreement with experiment.