Study of polymerization of high-pressure nitrogen by ab initio molecular dynamics.

We study properties of nitrogen at high pressure and temperature (100-120 GPa, 2000-3000 K) where molecular and polymeric phases compete both in solid and liquid phase. We employ ab initio MD simulations with the SCAN functional and study the pressure-induced polymerization in liquid nitrogen for system sizes up to 288 atoms in order to reduce finite-size effects. The transition is studied upon both compression and decompression, and at 3000 K, it is found to take place between 110 and 115 GPa, coming close to experimental data. We also simulate the molecular crystalline phase close to the melting line and analyze its structure. We show that the molecular crystal in this regime is highly disordered, in particular, due to pronounced orientational and also translational disorder of the molecules. Its short-range order and vibrational density of states are very close to those of the molecular liquid revealing that the system likely represents a plastic crystal with high entropy.

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.

High-Pressure Structural Evolution of Disordered Polymeric CS2.

Carbon disulfide is an archetypal double-bonded molecule belonging to the class of group IV-group VI, AB2 compounds. It is widely believed that, upon compression to several GPa at room temperature and above, a polymeric chain of type (-(C═S)-S-)n, named Bridgman's black polymer, will form. By combining optical spectroscopy and synchrotron X-ray diffraction data with ab initio simulations, we demonstrate that the structure of this polymer is different. Solid molecular CS2 polymerizes at ∼10-11 GPa. The polymer is disordered and consists of a mixture of 3-fold (C3) and 4-fold (C4) coordinated carbon atoms with some C═C double bonds. The C4/C3 ratio continuously increases upon further compression to 40 GPa. Upon decompression, structural changes are partially reverted, while the sample also undergoes partial disproportionation. Our work uncovers the nontrivial high-pressure structural evolution in one of the simplest molecular systems exhibiting molecular as well as polymeric phases.

Pressure-induced amorphization and existence of molecular and polymeric amorphous forms in dense SO2.

We report here the pressure-induced amorphization and reversible structural transformation between two amorphous forms of SO2: molecular amorphous and polymeric amorphous, with the transition found at 26 GPa over a broad temperature regime, 77 K to 300 K. The transformation was observed by both Raman spectroscopy and X-ray diffraction in a diamond anvil cell. The results were corroborated by ab initio molecular dynamics simulations, where both forward and reverse transitions were detected, opening a window to detailed analysis of the respective local structures. The high-pressure polymeric amorphous form was found to consist mainly of disordered polymeric chains made of three-coordinated sulfur atoms connected via oxygen atoms, with few residual intact molecules. This study provides an example of polyamorphism in a system consisting of simple molecules with multiple bonds.

Synthesis and Raman spectroscopy of a layered SiS2 phase at high pressures.

Dichalcogenides are known to exhibit layered solid phases, at ambient and high pressures, where 2D layers of chemically bonded formula units are held together by van der Waals forces. These materials are of great interest for solid-state sciences and technology, along with other 2D systems such as graphene and phosphorene. SiS2 is an archetypal model system of the most fundamental interest within this ensemble. Recently, high pressure (GPa) phases with Si in octahedral coordination by S have been theoretically predicted and also experimentally found to occur in this compound. At variance with stishovite in SiO2, which is a 3D network of SiO6 octahedra, the phases with octahedral coordination in SiS2 are 2D layered. Very importantly, this type of semiconducting material was theoretically predicted to exhibit continuous bandgap closing with pressure to a poor metallic state at tens of GPa. We synthesized layered SiS2 with octahedral coordination in a diamond anvil cell at 7.5-9 GPa, by laser heating together elemental S and Si at 1300-1700 K. Indeed, Raman spectroscopy up to 64.4 GPa is compatible with continuous bandgap closing in this material with the onset of either weak metallicity or of a narrow bandgap semiconductor state with a large density of defect-induced, intra-gap energy levels, at about 57 GPa. Importantly, our investigation adds up to the fundamental knowledge of layered dichalcogenides.

Creating new layered structures at high pressures: SiS2.

Old and novel layered structures are attracting increasing attention for their physical, electronic, and frictional properties. SiS2, isoelectronic to SiO2, CO2 and CS2, is a material whose phases known experimentally up to 6 GPa exhibit 1D chain-like, 2D layered and 3D tetrahedral structures. We present highly predictive ab initio calculations combined with evolutionary structure search and molecular dynamics simulations of the structural and electronic evolution of SiS2 up to 100 GPa. A highly stable CdI2-type layered structure, which is octahedrally coordinated with space group surprisingly appears between 4 and up to at least 100 GPa. The tetrahedral-octahedral switch is naturally expected upon compression, unlike the layered character realized here by edge-sharing SiS6 octahedral units connecting within but not among sheets. The predicted phase is semiconducting with an indirect band gap of about 2 eV at 10 GPa, decreasing under pressure until metallization around 40 GPa. The robustness of the layered phase suggests possible recovery at ambient pressure, where calculated phonon spectra indicate dynamical stability. Even a single monolayer is found to be dynamically stable in isolation, suggesting that it could possibly be sheared or exfoliated from bulk -SiS2.

Structural transformation between long and short-chain form of liquid sulfur from ab initio molecular dynamics.

We present results of ab initio molecular dynamics study of the structural transformation occurring in hot liquid sulfur under high pressure, which corresponds to the recently observed chain-breakage phenomenon and to the electronic transition reported earlier. The transformation is temperature-induced and separates two distinct polymeric forms of liquid sulfur: high-temperature form composed of short chain-like fragments with open endings and low-temperature form with very long chains. We offer a structural description of the two liquid forms in terms of chain lengths, cross-linking, and chain geometry and investigate several physical properties. We conclude that the transformation is accompanied by changes in energy (but not density) as well as in diffusion coefficient and electronic properties­semiconductor-metal transition. We also describe the analogy of the investigated process to similar phenomena that take place in two other chalcogens selenium and tellurium. Finally, we remark that the behavior of heated liquid sulfur at ambient pressure might indicate a possible existence of a critical point in the low-pressure region of sulfur phase diagram.

Transformation pathways in high-pressure solid nitrogen: from molecular N2 to polymeric cg-N.

The transformation pathway in high-pressure solid nitrogen from N2 molecular state to polymeric cg-N phase was investigated by means of ab initio molecular dynamics and metadynamics simulations. In our study, we observed a transformation mechanism starting from molecular Immm phase that initiated with formation of trans-cis chains. These chains further connected within layers and formed a chain-planar state, which we describe as a mixture of two crystalline structures--trans-cis chain phase and planar phase, both with Pnma symmetry. This mixed state appeared in molecular dynamics performed at 120 GPa and 1500 K and in the metadynamics run at 110 GPa and 1500 K, where the chains continued to reorganize further and eventually formed cg-N. During separate simulations, we also found two new phases--molecular P2(1)/c and two-three-coordinated chain-like Cm. The transformation mechanism heading towards cg-N can be characterized as a progressive polymerization process passing through several intermediate states of variously connected trans-cis chains. In the final stage of the transformation chains in the layered form rearrange collectively and develop new intraplanar as well as interplanar bonds leading to the geometry of cg-N. Chains with alternating trans and cis conformation were found to be the key entity--structural pattern governing the dynamics of the simulated molecular-polymeric transformation in compressed nitrogen.

Systematic comparison of crystalline and amorphous phases: Charting the landscape of water structures and transformations.

Systematically resolving different crystalline phases starting from the atomic positions, a mandatory step in algorithms for the prediction of structures or for the simulation of phase transitions, can be a non-trivial task. Extending to amorphous phases and liquids which lack the discrete symmetries, the problem becomes even more difficult, involving subtle topological differences at medium range that, however, are crucial to the physico-chemical and spectroscopic properties of the corresponding materials. Typically, system-tailored order parameters are devised, like global or local symmetry indicators, ring populations, etc. We show that a recently introduced metric provides a simple and general solution to this intricate problem. In particular, we demonstrate that a map can be traced displaying distances among water phases, including crystalline as well as amorphous states and the liquid, consistently with experimental knowledge in terms of phase diagram, structural features, and preparation routes.

Novel metastable metallic and semiconducting germaniums.

Group-IVa elements silicon and germanium are known for their semiconducting properties at room temperature, which are technologically critical. Metallicity and superconductivity are found at higher pressures only, Ge ß-tin (tI4) being the first high-pressure metallic phase in the phase diagram. However, recent experiments suggest that metallicity in germanium is compatible with room conditions, calling for a rethinking of our understanding of its phase diagram. Missing structures can efficiently be identified based on structure prediction methods. By means of ab initio metadynamics runs we explored the lower-pressure region of the phase diagram of germanium. A monoclinic germanium phase (mC16) with four-membered rings, less dense than diamond and compressible into ß-tin phase (tI4) was found. Tetragonal bct-5 appeared between diamond and tI4. mC16 is a narrow-gap semiconductor, while bct-5 is metallic and potentially still superconducting in the very low pressure range. This finding may help resolving outstanding experimental issues.

Constant pressure molecular dynamics simulations for ellipsoidal, cylindrical and cuboidal nano-objects based on inertia tensor information.

We present an extension to a constant-pressure molecular dynamics method for ellipsoidal finite systems that allows one to deal with nano-objects of cylindrical and cuboidal shapes. The method is based on the inclusion of a pressure x volume term in the system Lagrangian, where the volume is defined as a function of the eigenvalues of the inertia tensor. We illustrate how such a method works for selected systems, including CdSe nanocrystals and nanorods, carbon nanotubes and NaCl nanocrystals over a range of pressures. We also assess its performance in comparison with the use of an auxiliary pressure transmitting medium.

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.

Structural transformations in carbon under extreme pressure: beyond diamond.

High-pressure structural transformations of carbon at terapascal pressures are studied using metadynamics and ab initio methods. Diamond transforms to a mechanically stable cubic structure (P4(1)32) at 2.5 TPa and 300 K. At 4000 K and 2 TPa, simple cubic carbon SC1 (Pm-3m) is obtained from cubic diamond. The high-pressure tetrahedrally coordinated BC8 (Ia-3) structure of carbon is obtained by decompression of the SC1 structure at 1 TPa and 5000 K. At 3000 K, with decompression of SC1 carbon to 1 TPa, two new metastable tetrahedrally coordinated structures form, MP8 (P2/c) and OP8 (Pccn) with higher density than that of cubic diamond. The results show the presence of strong kinetic effects and suggest that phase transformations and structures of carbon at extreme pressures are more complex than previously thought.

Pressure-induced structural phase transitions in CdSe: a metadynamics study.

We present a computational study of pressure-induced structural phase transitions in bulk CdSe. Thanks to the use of the metadynamics technique we were able to observe the phase transitions at room temperature close to the experimental transition pressure. We discuss the transition mechanisms from four-coordinated wurtzite and zinc blende to six-coordinated rock salt, as well as the reverse transitions, where we found a mixed wurtzite/zinc blende stacking.

High-pressure polymeric phases of carbon dioxide.

Understanding the structural transformations of solid CO(2) from a molecular solid characterized by weak intermolecular bonding to a 3-dimensional network solid at high pressure has challenged researchers for the past decade. We employ the recently developed metadynamics method combined with ab initio calculations to provide fundamental insight into recent experimental reports on carbon dioxide in the 60-80 GPa pressure region. Pressure-induced polymeric phases and their transformation mechanisms are found. Metadynamics simulations starting from the CO(2)-II (P4(2)/mnm) at 60 GPa and 600 K proceed via an intermediate, partially polymerized phase, and finally yield a fully tetrahedral, layered structure (P-4m2). Based on the agreement between calculated and experimental Raman and X-ray patterns, the recently identified phase VI [Iota V, et al. (2007) Sixfold coordinated carbon dioxide VI. Nature Mat 6:34-38], assumed to be disordered stishovite-like, is instead interpreted as the result of an incomplete transformation of the molecular phase into a final layered structure. In addition, an alpha-cristobalite-like structure (P4(1)2(1)2), is predicted to be formed from CO(2)-III (Cmca) via an intermediate Pbca structure at 80 GPa and low temperatures (<300 K). Defects in the crystals are frequently observed in the calculations at 300 K whereas at 500 to 700 K, CO(2)-III transforms to an amorphous form, consistent with experiment [Santoro M, et al. (2006) Amorphous silica-like carbon dioxide. Nature 441:857-860], but the simulation yields additional structural details for this disordered solid.

Influence of temperature and anisotropic pressure on the phase transitions in alpha-cristobalite.

The role of temperature and anisotropy of the applied load in the pressure-induced transformations of alpha-cristobalite is investigated by means of first principles molecular dynamics combined with the metadynamics algorithm for the study of solid-solid phase transitions. We reproduce the transition to alpha-PbO2 as found in experiments and we observe that the transition paths are qualitatively different and yield different products when a nonhydrostatic load is applied, giving rise to a new class of metastable structures with mixed tetrahedral and octahedral coordination.

Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential.

We study in a systematic way the complex sequence of the high-pressure phases of silicon obtained upon compression by combining an accurate high-dimensional neural network representation of the density-functional theory potential-energy surface with the metadynamics scheme. Starting from the thermodynamically stable diamond structure at ambient conditions we are able to identify all structural phase transitions up to the highest-pressure fcc phase at about 100 GPa. The results are in excellent agreement with experiment. The method developed promises to be of great value in the study of inorganic solids, including those having metallic phases.

Crystal structure transformations in SiO2 from classical and ab initio metadynamics.

Silica is the main component of the Earth's crust and is also of great relevance in many branches of materials science and technology. Its phase diagram is rather intricate and exhibits many different crystalline phases. The reported propensity to amorphization and the strong influence on the outcome of the initial structure and of the pressurization protocol indicate the presence of metastability and large kinetic barriers. As a consequence, theory is also faced with great difficulties and our understanding of the complex transformation mechanisms is still very sketchy despite a large number of simulations. Here, we introduce a substantial improvement of the metadynamics method, which finally brings simulations in close agreement with experiments. We unveil the subtle and non-intuitive stepwise mechanism of the pressure-induced transformation of fourfold-coordinated alpha-quartz into sixfold-coordinated stishovite at room temperature. We also predict that on compression fourfold-coordinated coesite will transform into the post-stishovite alpha-PbO2-type phase. The new method is far more efficient than previous methods, and for the first time the study of complex structural phase transitions with many intermediates is within the reach of molecular dynamics simulations. This insight will help in designing new experimental protocols capable of steering the system towards the desired transition.

Anisotropy of Earth's D'' layer and stacking faults in the MgSiO3 post-perovskite phase.

The post-perovskite phase of (Mg,Fe)SiO3 is believed to be the main mineral phase of the Earth's lowermost mantle (the D'' layer). Its properties explain numerous geophysical observations associated with this layer-for example, the D'' discontinuity, its topography and seismic anisotropy within the layer. Here we use a novel simulation technique, first-principles metadynamics, to identify a family of low-energy polytypic stacking-fault structures intermediate between the perovskite and post-perovskite phases. Metadynamics trajectories identify plane sliding involving the formation of stacking faults as the most favourable pathway for the phase transition, and as a likely mechanism for plastic deformation of perovskite and post-perovskite. In particular, the predicted slip planes are {010} for perovskite (consistent with experiment) and {110} for post-perovskite (in contrast to the previously expected {010} slip planes). Dominant slip planes define the lattice preferred orientation and elastic anisotropy of the texture. The {110} slip planes in post-perovskite require a much smaller degree of lattice preferred orientation to explain geophysical observations of shear-wave anisotropy in the D'' layer.