Layer-by-layer phase transformation in Ti3O5 revealed by machine-learning molecular dynamics simulations.

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive phase transitions are usually slow due to the large energy barrier. Nevertheless, the reconstructive phase transformation from ß- to λ-Ti3O5 exhibits an ultrafast and reversible behavior. Despite extensive studies, the underlying microscopic mechanism remains unclear. Here, we discover a kinetically favorable in-plane nucleated layer-by-layer transformation mechanism through metadynamics and large-scale molecular dynamics simulations. This is enabled by developing an efficient machine learning potential with near first-principles accuracy through an on-the-fly active learning method and an advanced sampling technique. Our results reveal that the ß-λ phase transformation initiates with the formation of two-dimensional nuclei in the ab-plane and then proceeds layer-by-layer through a multistep barrier-lowering kinetic process via intermediate metastable phases. Our work not only provides important insight into the ultrafast and reversible nature of the ß-λ transition, but also presents useful strategies and methods for tackling other complex structural phase transitions.

Unlocking the mysterious polytypic features within vaterite CaCO3.

Calcium carbonate (CaCO3), the most abundant biogenic mineral on earth, plays a crucial role in various fields such as hydrosphere, biosphere, and climate regulation. Of the four polymorphs, calcite, aragonite, vaterite, and amorphous CaCO3, vaterite is the most enigmatic one due to an ongoing debate regarding its structure that has persisted for nearly a century. In this work, based on systematic transmission electron microscopy characterizations, crystallographic analysis and machine learning aided molecular dynamics simulations with ab initio accuracy, we reveal that vaterite can be regarded as a polytypic structure. The basic phase has a monoclinic lattice possessing pseudohexagonal symmetry. Direct imaging and atomic-scale simulations provide evidence that a single grain of vaterite can contain three orientation variants. Additionally, we find that vaterite undergoes a second-order phase transition with a critical point of ~190 K. These atomic scale insights provide a comprehensive understanding of the structure of vaterite and offer advanced perspectives on the biomineralization process of calcium carbonate.

Phase Transition between Crystalline Variants of Ordinary Ice.

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

A combined molecular dynamics and experimental study of two-step process enabling low-temperature formation of phase-pure α-FAPbI3.

It is well established that the lack of understanding the crystallization process in a two-step sequential deposition has a direct impact on efficiency, stability, and reproducibility of perovskite solar cells. Here, we try to understand the solid-solid phase transition occurring during the two-step sequential deposition of methylammonium lead iodide and formamidinium lead iodide. Using metadynamics, x-ray diffraction, and Raman spectroscopy, we reveal the microscopic details of this process. We find that the formation of perovskite proceeds through intermediate structures and report polymorphs found for methylammonium lead iodide and formamidinium lead iodide. From simulations, we discover a possible crystallization pathway for the highly efficient metastable α phase of formamidinium lead iodide. Guided by these simulations, we perform experiments that result in the low-temperature crystallization of phase-pure α-formamidinium lead iodide.

Ab initio phase diagram and nucleation of gallium.

Elemental gallium possesses several intriguing properties, such as a low melting point, a density anomaly and an electronic structure in which covalent and metallic features coexist. In order to simulate this complex system, we construct an ab initio quality interaction potential by training a neural network on a set of density functional theory calculations performed on configurations generated in multithermal-multibaric simulations. Here we show that the relative equilibrium between liquid gallium, α-Ga, ß-Ga, and Ga-II is well described. The resulting phase diagram is in agreement with the experimental findings. The local structure of liquid gallium and its nucleation into α-Ga and ß-Ga are studied. We find that the formation of metastable ß-Ga is kinetically favored over the thermodinamically stable α-Ga. Finally, we provide insight into the experimental observations of extreme undercooling of liquid Ga.

Temperature Dependence of Homogeneous Nucleation in Ice.

Ice nucleation is a process of great relevance in physics, chemistry, technology, and environmental sciences; much theoretical effort has been devoted to its understanding, but it still remains a topic of intense research. We shed light on this phenomenon by performing atomistic based simulations. Using metadynamics and a carefully designed set of collective variables, reversible transitions between water and ice are able to be simulated. We find that water freezes into a stacking disordered structure with the all-atom transferable intermolecular potential with 4 points/ice (TIP4P/ice) model, and the features of the critical nucleus of nucleation at the microscopic level are revealed. We have also estimated the ice nucleation rates along with other nucleation parameters at different undercoolings. Our results are in agreement with recent experimental and other theoretical works, and they confirm that nucleation is preceded by a large increase in tetrahedrally coordinated water molecules.

Improving collective variables: The case of crystallization.

Several enhanced sampling methods, such as umbrella sampling or metadynamics, rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis; the other is based on a variational approach to conformational dynamics and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. Wherever the different metastable states are well-separated, the method based on linear discriminant analysis, based on its harmonic version, is to be preferred because simpler to implement and less computationally demanding. The variational approach, however, has the potential to discover the existence of different metastable states.

Combining Metadynamics and Integrated Tempering Sampling.

The simulation of rare events is one of the key problems in atomistic simulations. Toward its solution, a plethora of methods have been proposed. Here we combine two such methods: metadynamics and integrated tempering sampling. In metadynamics, the fluctuations of a carefully chosen collective variable are amplified, while in integrated tempering sampling the system is pushed to visit an approximately uniform interval of energies and allows exploring a range of temperatures in a single run. We describe our approach and apply it to the two prototypical systems a SN2 chemical reaction and to the freezing of silica. The combination of metadynamics and integrated tempering sampling leads to a powerful method. In particular in the case of silica we have measured more than 1 order of magnitude acceleration.

Molecular dynamics simulations of liquid silica crystallization.

Silica is one of the most abundant minerals on Earth and is widely used in many fields. Investigating the crystallization of liquid silica by atomic simulations is of great importance to understand the crystallization mechanism; however, the high crystallization barrier and the tendency of silica to form glasses make such simulations very challenging. Here we have studied liquid silica crystallization to ß-cristobalite with metadynamics, using X-ray diffraction (XRD) peak intensities as collective variables. The frequent transitions between solid and liquid of the biased runs demonstrate the highly successful use of the XRD peak intensities as collective variables, which leads to the convergence of the free-energy surface. By calculating the difference in free energy, we have estimated the melting temperature of ß-cristobalite, which is in good agreement with the literature. The nucleation mechanism during the crystallization of liquid silica can be described by classical nucleation theory.

Diverse Chemistry of Stable Hydronitrogens, and Implications for Planetary and Materials Sciences.

Nitrogen hydrides, e.g., ammonia (NH3), hydrazine (N2H4) and hydrazoic acid (HN3), are compounds of great fundamental and applied importance. Their high-pressure behavior is important because of their abundance in giant planets and because of the hopes of discovering high-energy-density materials. Here, we have performed a systematic investigation on the structural stability of N-H system in a pressure range up to 800 GPa through evolutionary structure prediction. Surprisingly, we found that high pressure stabilizes a series of previously unreported compounds with peculiar structural and electronic properties, such as the N4H, N3H, N2H and NH phases composed of nitrogen backbones, the N9H4 phase containing two-dimensional metallic nitrogen planes and novel N8H, NH2, N3H7, NH4 and NH5 molecular phases. Another surprise is that NH3 becomes thermodynamically unstable above ~460 GPa. We found that high-pressure chemistry of hydronitrogens is much more diverse than hydrocarbon chemistry at normal conditions, leading to expectations that N-H-O and N-H-O-S systems under pressure are likely to possess richer chemistry than the known organic chemistry. This, in turn, opens a possibility of nitrogen-based life at high pressure. The predicted phase diagram of the N-H system also provides a reference for synthesis of high-energy-density materials.

Prediction of novel stable compounds in the Mg-Si-O system under exoplanet pressures.

The Mg-Si-O system is the major Earth and rocky planet-forming system. Here, through quantum variable-composition evolutionary structure explorations, we have discovered several unexpected stable binary and ternary compounds in the Mg-Si-O system. Besides the well-known SiO2 phases, we have found two extraordinary silicon oxides, SiO3 and SiO, which become stable at pressures above 0.51 TPa and 1.89 TPa, respectively. In the Mg-O system, we have found one new compound, MgO3, which becomes stable at 0.89 TPa. We find that not only the (MgO)x · (SiO2)y compounds, but also two (MgO3)x · (SiO3)y compounds, MgSi3O12 and MgSiO6, have stability fields above 2.41 TPa and 2.95 TPa, respectively. The highly oxidized MgSi3O12 can form in deep mantles of mega-Earths with masses above 20 M⊕ (M⊕:Earth's mass). Furthermore, the dissociation pathways of pPv-MgSiO3 are also clarified, and found to be different at low and high temperatures. The low-temperature pathway is MgSiO3 ⇒ Mg2SiO4 + MgSi2O5 ⇒ SiO2 + Mg2SiO4 ⇒ MgO + SiO2, while the high-temperature pathway is MgSiO3 ⇒ Mg2SiO4 + MgSi2O5 ⇒ MgO + MgSi2O5 ⇒ MgO + SiO2. Present results are relevant for models of the internal structure of giant exoplanets, and for understanding the high-pressure behavior of materials.

A novel phase of beryllium fluoride at high pressure.

A previously unknown thermodynamically stable high-pressure phase of BeF2 has been predicted using the evolutionary algorithm USPEX. This phase occurs in the pressure range 18-27 GPa. Its structure has C2/c space group symmetry and contains 18 atoms in the primitive unit cell. Given the analogy between BeF2 and SiO2, silica phases have been investigated as well, but the new phase has not been observed to be thermodynamically stable for this system. However, it is found to be metastable and to have comparable energy to the known metastable phases of SiO2, suggesting a possibility of its synthesis.

Variable-composition structural optimization and experimental verification of MnB3 and MnB4.

In combination with variable-composition evolutionary algorithm calculations and first-principles calculations, we have systematically searched for all the stable compounds and their crystal structures in the extensively investigated binary Mn-B system. Our results have uncovered four viable ground-state compounds, with Mn2B, MnB, and MnB4, and previously never reported MnB3 and two metastable compounds, MnB2 and Mn3B4. Our calculations demonstrate that the early characterized mC10 structure of MnB4 showed dynamic instability with large imaginary phonon frequencies and, instead, a new mP20 structure is predicted to be stable both dynamically and thermodynamically, with a considerable energy gain and no imaginary phonon frequencies. The new MnB3 compound crystallizes in the monoclinic mC16 structure which lies 3.2 meV per atom below the MnB (oP8) ↔ MnB4 (mP20) tie-line at T = 0 K. Furthermore, these proposed phases have been verified by our annealed samples after arc-melting synthesis and corresponding powder XRD measurements.

Extra-electron induced covalent strengthening and generalization of intrinsic ductile-to-brittle criterion.

Traditional strengthening ways, such as strain, precipitation, and solid-solution, come into effect by pinning the motion of dislocation. Here, through first-principles calculations we report on an extra-electron induced covalent strengthening mechanism, which alters chemical bonding upon the introduction of extra-valence electrons in the matrix of parent materials. It is responsible for the brittle and high-strength properties of Al(12)W-type compounds featured by the typical fivefold icosahedral cages, which are common for quasicrystals and bulk metallic glasses (BMGs). In combination with this mechanism, we generalize ductile-to-brittle criterion in a universal hyperbolic form by integrating the classical Pettifor's Cauchy pressure with Pugh's modulus ratio for a wide variety of materials with cubic lattices. This study provides compelling evidence to correlate Pugh's modulus ratio with hardness of materials and may have implication for understanding the intrinsic brittleness of quasicrystals and BMGs.

Families of superhard crystalline carbon allotropes constructed via cold compression of graphite and nanotubes.

We report a general scheme to systematically construct two classes of structural families of superhard sp(3) carbon allotropes of cold-compressed graphite through the topological analysis of odd 5+7 or even 4+8 membered carbon rings stemmed from the stacking of zigzag and armchair chains. Our results show that the previously proposed M, bct-C(4), W and Z allotropes belong to our currently proposed families and that depending on the topological arrangement of the native carbon rings numerous other members are found that can help us understand the structural phase transformation of cold-compressed graphite and carbon nanotubes (CNTs). In particular, we predict the existence of two simple allotropes, R and P carbon, which match well the experimental x-ray diffraction patterns of cold-compressed graphite and CNTs, respectively, display a transparent wide-gap insulator ground state and possess a large Vickers hardness comparable to diamond.