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.

Stability and Semiconducting Behavior of Magnesium Polysulfides by Nonequivalent sp3 Hybridizations.

The Mg/S battery has attracted enormous interest in recent years due to its high theoretical capacity, low cost, and high security. However, the understanding of many intermediate magnesium polysulfides in the Mg/S battery remains elusive. Combining extensive structural search and first-principles calculations, we investigate the phase stability, structural character, and electronic structure of magnesium polysulfides in a wide range from MgS to MgS8. The pyrite-type MgS2 (space group: Pa3̅) is predicted to be stable. Five magnesium polysulfides, MgSx (x = 3, 4, 5, 6, and 8), are found to be metastable, with formation enthalpies slightly above the convex hull. S2 dimer, "V"-like S3, and highly distorted Sx chains are found for the polysulfides with bond lengths close to or slightly longer than S8 and bond angles similar to S8. A wide range of band gaps (0.77-2.82 eV) are revealed for the polysulfides due to the contribution of the nonequivalent sp3 hybridization of the S atoms in Sx2-. Our results can help to further understand the electrochemical process in the Mg/S battery.

Self-Limiting Sub-5 nm Nanodiamonds by Geochemistry-Inspired Synthesis.

Controlling diamond structures with nanometer precision is fundamentally challenging owing to their extreme and far-from-equilibrium synthetic conditions. State-of-the-art techniques, including detonation, chemical vapor deposition, mechanical grinding, and high-pressure-high-temperature synthesis, yield nanodiamond particles with a broad distribution of sizes. Despite many efforts, the direct synthesis of nanodiamonds with precisely controlled diameters remains elusive. Here the geochemistry-inspired synthesis of sub-5 nm nanodiamonds with sub-nanometer size deviation is described. High-pressure-high-temperature treatment of uniform iron carbide nanoparticles embedded in iron oxide matrices yields nanodiamonds with tunable diameters down to 2.13 and 0.22 nm standard deviation. A self-limiting, redox-driven, and diffusion-controlled solid-state reaction mechanism is proposed and supported by in situ X-ray diffraction, ex situ characterizations, and computational modeling. This work provides a unique mechanism for the precise control of nanostructured diamonds under extreme conditions and paves the road for the full realization of their potential in emerging technologies.

Quantum structural fluxion in superconducting lanthanum polyhydride.

The discovery of 250-kelvin superconducting lanthanum polyhydride under high pressure marked a significant advance toward the realization of a room-temperature superconductor. X-ray diffraction (XRD) studies reveal a nonstoichiometric LaH9.6 or LaH10±Î´ polyhydride responsible for the superconductivity, which in the literature is commonly treated as LaH10 without accounting for stoichiometric defects. Here, we discover significant nuclear quantum effects (NQE) in this polyhydride, and demonstrate that a minor amount of stoichiometric defects will cause quantum proton diffusion in the otherwise rigid lanthanum lattice in the ground state. The diffusion coefficient reaches ~10-7 cm2/s in LaH9.63 at 150 gigapascals and 240 kelvin, approaching the upper bound value of interstitial hydrides at comparable temperatures. A puzzling phenomenon observed in previous experiments, the positive pressure dependence of the superconducting critical temperature Tc below 150 gigapascals, is explained by a modulation of the electronic structure due to a premature distortion of the hydrogen lattice in this quantum fluxional structure upon decompression, and resulting changes of the electron-phonon coupling. This finding suggests the coexistence of the quantum proton fluxion and hydrogen-induced superconductivity in this lanthanum polyhydride, and leads to an understanding of the structural nature and superconductivity of nonstoichiomectric hydrogen-rich materials.

Size-Dependent Nucleation in Crystal Phase Transition from Machine Learning Metadynamics.

In this Letter, we present a framework that combines machine learning potential (MLP) and metadynamics to investigate solid-solid phase transition. Based on the spectral descriptors and neural networks regression, we develop a scalable MLP model to warrant an accurate interpolation of the energy surface where two phases coexist. Applying it to the simulation of B4-B1 phase transition of GaN under 50 GPa with different model sizes, we observe sequential change of the phase transition mechanism from collective modes to nucleation and growths. When the size is at or below 128 000 atoms, the nucleation and growth appear to follow a preferred direction. At larger sizes, the nuclei occur at multiple sites simultaneously and grow to microstructures by passing the critical size. The observed change of the atomistic mechanism manifests the importance of statistical sampling with large system size in phase transition modeling.

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.

Design Principles for High-Temperature Superconductors with a Hydrogen-Based Alloy Backbone at Moderate Pressure.

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor made in a laboratory, can reach a critical temperature (T_{c}) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary H-based superconductors with alloy backbones. We identify a "fluorite-type" backbone in compositions of the form AXH_{8}, which exhibit high-temperature superconductivity at moderate pressures compared with other reported hydrogen-based superconductors. The Fm3[over ¯]m phase of LaBeH_{8}, with a fluorite-type H-Be alloy backbone, is predicted to be thermodynamically stable above 98 GPa, and dynamically stable down to 20 GPa with a high T_{c}∼185 K. This is substantially lower than the synthesis pressure required by the geometrically similar clathrate hydride LaH_{10} (170 GPa). Our approach paves the way for finding high-T_{c} ternary H-based superconductors at conditions close to ambient pressures.

Quantum and Classical Proton Diffusion in Superconducting Clathrate Hydrides.

The discovery of near room temperature superconductivity in clathrate hydrides has ignited the search for both higher temperature superconductors and deeper understanding of the underlying physical phenomena. In a conventional electron-phonon mediated picture for the superconductivity for these materials, the high critical temperatures predicted and observed can be ascribed to the low mass of the protons, but this also poses nontrivial questions associated with how the proton dynamics affect the superconductivity. Using clathrate superhydride Li_{2}MgH_{16} as an example, we show through ab initio path integral simulations that proton diffusion in this system is remarkably high, with a diffusion coefficient, for example, reaching 6×10^{-6} cm^{2}/s at 300 K and 250 GPa. The diffusion is achieved primarily through proton transfer among interstitial voids within the otherwise rigid Li_{2}Mg sublattice at these conditions. The findings indicate the coexistence of proton quantum diffusion together with hydrogen-induced superconductivity, with implications for other very-high-temperature superconducting hydrides.

Potassium-activated anionic copper and covalent Cu-Cu bonding in compressed K-Cu compounds.

Elemental copper and potassium are immiscible under ambient conditions. It is known that pressure is a useful tool to promote the reaction between two different elements by modifying their electronic structure significantly. Here, we predict the formation of four K-Cu compounds (K3Cu2, K2Cu, K5Cu2, and K3Cu) under moderate pressure through unbiased structure search and first-principles calculations. Among all predicted structures, the simulated x-ray diffraction pattern of K3Cu2 perfectly matches a K-Cu compound synthesized in 2004. Further simulations indicate that the K-Cu compounds exhibit diverse structural features with novel forms of Cu aggregations, including Cu dimers, linear and zigzag Cu chains, and Cu-centered polyhedrons. Analysis of the electronic structure reveals that Cu atoms behave as anions to accept electrons from K atoms through fully filling 4s orbitals and partially extending 4p orbitals. Covalent Cu-Cu interaction is found in these compounds, which is associated with the sp hybridizations. These results provide insights into the understanding of the phase diversity of alkali/alkaline earth and metal systems.

IrN4 and IrN7 as potential high-energy-density materials.

Transition metal nitrides have attracted great interest due to their unique crystal structures and applications. Here, we predict two N-rich iridium nitrides (IrN4 and IrN7) under moderate pressure through first-principles swarm-intelligence structural searches. The two new compounds are composed of stable IrN6 octahedrons and interlinked with high energy polynitrogens (planar N4 or cyclo-N5). Balanced structural robustness and energy content result in IrN4 and IrN7 being dynamically stable under ambient conditions and potentially as high energy density materials. The calculated energy densities for IrN4 and IrN7 are 1.3 kJ/g and 1.4 kJ/g, respectively, comparable to other transition metal nitrides. In addition, IrN4 is predicted to have good tensile (40.2 GPa) and shear strengths (33.2 GPa), as well as adequate hardness (20 GPa). Moderate pressure for synthesis and ambient pressure recoverability encourage experimental realization of these two compounds in near future.

Hydrogen Pentagraphenelike Structure Stabilized by Hafnium: A High-Temperature Conventional Superconductor.

The recent discovery of H_{3}S and LaH_{10} superconductors with record high superconducting transition temperatures T_{c} at high pressure has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we introduce a new class of high T_{c} hydrides with a novel structure and unusual properties. We predict the existence of an unprecedented hexagonal HfH_{10}, with remarkably high value of T_{c} (around 213-234 K) at 250 GPa. As concerns the novel structure, the H ions in HfH_{10} are arranged in clusters to form a planar "pentagraphenelike" sublattice. The layered arrangement of these planar units is entirely different from the covalent sixfold cubic structure in H_{3}S and clathratelike structure in LaH_{10}. The Hf atom acts as a precompressor and electron donor to the hydrogen sublattice. This pentagraphenelike H_{10} structure is also found in ZrH_{10}, ScH_{10}, and LuH_{10} at high pressure, each material showing a high T_{c} ranging from 134 to 220 K. Our study of dense superhydrides with pentagraphenelike layered structures opens the door to the exploration of a new class of high T_{c} superconductors.

Nitrogen in black phosphorus structure.

Group V elements in crystal structure isostructural to black phosphorus with unique puckered two-dimensional layers exhibit exciting physical and chemical phenomena. However, as the first element of group V, nitrogen has never been found in the black phosphorus structure. Here, we report the synthesis of the black phosphorus-structured nitrogen at 146 GPa and 2200 K. Metastable black phosphorus-structured nitrogen was retained after quenching it to room temperature under compression and characterized in situ during decompression to 48 GPa, using synchrotron x-ray diffraction and Raman spectroscopy. We show that the original molecular nitrogen is transformed into extended single-bonded structure through gauche and trans conformations. Raman spectroscopy shows that black phosphorus-structured nitrogen is strongly anisotropic and exhibits high Raman intensities in two A g normal modes. Synthesis of black phosphorus-structured nitrogen provides a firm base for exploring new type of high-energy-density nitrogen and a new direction of two-dimensional nitrogen.

Formation of Stable Compounds of Potassium and Iron under Pressure.

We predict stable stoichiometric potassium-iron (K-Fe) intermetallic compounds at high pressures from first principles. Thermodynamic stability, crystal structures, and bonding properties of these compounds are also investigated. The dynamic stability of the predicted structures is established through phonon calculations while mechanical stability is established through Born-Huang stability criteria. Our results reveal that potassium and iron can form intermetallic compounds that are stabilized by high pressure and energy reordering of atomic orbital through electron transfer. A K-rich K-Fe compound is predicted to undergo structural phase transformations under pressure where clustering of K atoms is observed to precede transformation into the Fe-rich phase above 120 GPa. The elastic velocities and the densities predicted for various K-Fe compounds suggest that they may explain a potassium-containing Earth's core.

Pressure-induced structural transformations and new polymorphs in BiVO4.

BiVO4 has attracted much attention in recent years due to its active photocatalytic and microwave dielectric properties. BiVO4 exhibits a rich structural polymorphism, and its properties strongly depend on the crystalline phase. Therefore, it is of great importance to achieve an easy control of its crystalline phase. In the present work, phase stability and vibrational properties of fergusonite- and zircon-type BiVO4 are investigated up to 41.6 GPa by in situ synchrotron X-ray diffraction (XRD), Raman spectroscopy, and first principles calculation. Upon compression, although having different initial structures, both types of BiVO4 consecutively transform to scheelite- and ß-fergusonite structures. For the first time reported for BiVO4, the ß-fergusonite structure is determined using first principles computational techniques and from refinement of the XRD data. Along the way, one new phase of BiVO4 is theoretically predicted at higher pressures. Moreover, both the fergusonite-to-scheelite and scheelite-to-ß-fergusonite transitions are reversible, while the zircon-to-scheelite transition is irreversible. A large volume collapse is observed associated with each phase transition, and the equations of state for different types of BiVO4 have been determined. These results provide new insights into the relationship between different structural types in the AVO4 family.

o-C240: a new sp3-dominated allotrope of carbon.

We report a new allotrope of carbon predicted from first principles simulations. This allotrope is formed in a simulated conversion of two-dimensional polymeric C60 precursor subjected to uniaxial compression at high temperature. The structure is made up of 240 carbon atoms in an orthorhombic unit cell (termed as o-C240) having a mixed sp2/sp3 hybridization with the ratio of about 1:5. o-C240 is stable at ambient condition and exhibits superior mechanical performance including optimum Vickers hardness (45 GPa) and fracture toughness (4.10 MPa m1/3), outperforming most of widely used hard ceramics. The electronic structure reveals semiconducting ground state with an indirect band gap of 1.72 eV. The simple reaction pathway could accelerate discovery of this allotrope in laboratory, and the simultaneous occurrence of high fracture toughness, superhardness and semiconductivity is expected to find applications for this material.

Superconducting Zirconium Polyhydrides at Moderate Pressures.

Highly compressed hydrides have been at the forefront of the search for high-Tc superconductivity. The recent discovery of record-high Tc's in H3S and LaH10±x under high pressure fuels the enthusiasm for finding good superconductors in similar hydride groups. Guided by first-principles structure prediction, we successfully synthesized ZrH3 and Zr4H15 at modest pressures (30-50 GPa) in diamond anvil cells by two different reaction routes: ZrH2 + H2 at room temperature and Zr + H2 at ∼1500 K by laser heating. From the synchrotron X-ray diffraction patterns, ZrH3 is found to have a Pm3̅n structure corresponding to the familiar A15 structure, and Zr4H15 has an I4̅3d structure isostructural to Th4H15. Electrical resistance measurement and the dependence of Tc on the applied magnetic field of the sample showed the emergence of two superconducting transitions at 6.4 and 4.0 K at 40 GPa, which correspond to the two Tc's for ZrH3 and Zr4H15.

High-temperature shape memory loss in nitinol: a first principles study.

We have performed first-principles calculations to investigate the possibility of shape memory loss in a member of the binary smart alloy family - NiTi. A detailed analysis of the transition kinetics and dynamical pathway reveals the possibility of the B19' phase of NiTi losing its shape memory when subjected to high stress conditions and is heated above a critical temperature, Tc. The B19' phase is predicted to transform to P1[combining macron]-NiTi, which is also predicted to be dynamically stable and temperature-quench recoverable. It is found that the B2(B33) → B19' transition is dominated by the ß shearing mode with pronounced distortion in the (001) planes and significant volume reduction. Furthermore, the B19' → P1[combining macron] transition is dominated by the γ shearing mode with pronounced distortion in the (010) planes and slight volume expansion. The cumulative effect of both processes activates the lowering and eventual breaking of symmetry in the precursor phases and drives the permanent deformation and shape memory loss. We further show that the P1[combining macron]-NiTi structure is stabilized (over B19' structure) by kinetics. The findings of this study will stimulate further studies on how to retain and improve the shape memory feature in NiTi and other binary smart alloys to prevent property failure when used in the fabrication of devices operated in the high temperature and pressure regime.

Mechanism for the Structural Transformation to the Modulated Superconducting Phase of Compressed Hydrogen Sulfide.

A comprehensive description of crystal and electronic structures, structural transformations, and pressure-dependent superconducting temperature (Tc) of hydrogen sulfide (H2S) compressed from low pressure is presented through the analysis of the results from metadynamics simulations. It is shown that local minimum metastable crystal structures obtained are dependent on the choice of pressure-temperature thermodynamic paths. The origin of the recently proposed 'high-Tc' superconducting phase with a modulated structure and a diffraction pattern reproducing two independent experiments was the low pressure Pmc21 structure. This Pmc21 structure is found to transform to a Pc structure at 80 K and 80 GPa which becomes metallic and superconductive above 100 GPa. This structure becomes dynamically unstable above 140 GPa beyond which phonon instability sets in at about a quarter in the Γ to Y segment. This explains the transformation to a 1:3 modulation structure at high pressures proposed previously. The pressure trend of the calculated Tc for the Pc structure is consistent with the experimentally measured 'low-Tc phase'. Fermi surface analysis hints that pressurized hydrogen sulfide may be a multi-band superconductor. The theoretical results reproduced many experimental characteristics, suggesting that the dissociation of H2S is unrequired to explain the superconductivity of compressed H2S at any pressure.

B1-B2 phase transition mechanism and pathway of PbS under pressure.

Experimental studies at finite Pressure-Temperature (P-T) conditions and a theoretical study at 0 K of the phase transition in lead sulphide (PbS) have been inconclusive. Many studies that have been done to understand structural transformation in PbS can broadly be classified into two main ideological streams-one with Pnma and another with Cmcm orthorhombic intermediate phase. To foster better understanding of this phenomenon, we present the result of the first-principles study of phase transition in PbS at finite temperature. We employed the particle swarm-intelligence optimization algorithm for the 0 K structure search and first-principles metadynamics simulations to study the phase transition pathway of PbS from the ambient pressure, 0 K Fm-3m structure to the high-pressure Pm-3m phase under experimentally achievable P-T conditions. Significantly, our calculation shows that both streams are achievable under specific P-T conditions. We further uncover new tetragonal and monoclinic structures of PbS with space group P21/c and I41/amd, respectively. We propose the P21/c and I41/amd as a precursor phase to the Pnma and Cmcm phases, respectively. We investigated the stability of the new structures and found them to be dynamically stable at their stability pressure range. Electronic structure calculations reveal that both P21/c and I41/amd phases are semiconducting with direct and indirect bandgap energies of 0.69(5) eV and 0.97(3) eV, respectively. In general, both P21/c and I41/amd phases were found to be energetically competitive with their respective orthorhombic successors.

Synthesis of Xenon and Iron-Nickel Intermetallic Compounds at Earth's Core Thermodynamic Conditions.

Using in situ synchrotron x-ray diffraction and Raman spectroscopy in concert with first principles calculations we demonstrate the synthesis of stable Xe(Fe,Fe/Ni)_{3} and XeNi_{3} compounds at thermodynamic conditions representative of Earth's core. Surprisingly, in the case of both the Xe-Fe and Xe-Ni systems Fe and Ni become highly electronegative and can act as oxidants. The results indicate the changing chemical properties of elements under extreme conditions by documenting that electropositive at ambient pressure elements could gain electrons and form anions.