We build random forests models to predict elastic properties and mechanical hardness of a compound, using only its chemical formula as input. The model training uses over 10,000 target compounds and 60 features based on stoichiometric attributes, elemental properties, orbital occupations, and ionic bonding levels. Using the models, we construct triangular graphs for B-C-N compounds to map out their bulk and shear moduli, as well as hardness values. The graphs indicate that a 1:1 B-N ratio can lead to various superhard compositions. We also validate the machine learning results by evolutionary structure prediction and density functional theory. Our study shows that BC$_{10}$N, B$_4$C$_5$N$_3$, and B$_2$C$_3$N exhibit dynamically stable phases with hardness values $>40$GPa, which are potentially new superhard materials that could be synthesized by low-temperature plasma methods.
The basic known and hypothetic one- and two-element phases of the B-C-N-O system (both superhard phases having diamond and boron structures and precursors to synthesize them) are described. The attention has been given to the structure, basic mechanical properties, and methods to identify and characterize the materials. For some phases that have been recently described in the literature the synthesis conditions at high pressures and temperatures are indicated.
We search for new superhard B-N-O compounds with an iterative machine learning (ML) procedure, where ML models are trained using sample crystal structures from evolutionary algorithm. We first use cohesive energy to evaluate the thermodynamic stability of varying B$_x$N$_y$O$_z$ compositions, and then gradually focus on compositional regions with high cohesive energy and high hardness. The results converge quickly after a few iterations. Our resulting ML models show that B$_{x+2}$N$_{x}$O$_{3}$ compounds with $x \geq 3$ (like B$_5$N$_3$O$_3$, B$_6$N$_4$O$_3$, etc.) are potentially superhard an…
Good agreement was found between experimental Vickers hardnesses, $H_\text{v}$, of a wide range of materials and those calculated by three macroscopic hardness models that employ the shear and/or bulk moduli obtained from: (i) first principles via AFLOW-AEL (AFLOW Automatic Elastic Library), and (ii) a machine learning (ML) model trained on materials within the AFLOW repository. Because $H_\text{v}^\text{ML} $ values can be quickly estimated, they can be used in conjunction with an evolutionary search to predict stable, superhard materials. This methodology is implemented in the XtalOpt evolut…
Through machine learning force field accelerated structure search combined with first-principles calculations, we have studied the structures of new C-N compounds with different stoichiometric ratios, and found twelve new superhard C-N compounds, the energies of these structures are similar to c-C3N4 , which is possibly synthesized by high pressure experiment, the XRD of Pa-3(C4N) P3(C4N) and C2/m(C2N) are consistent with previous experimental data and can be used as the structural candidate. According to the macro hardness model, they are all superhard structures, with Vickers hardness over 4…
We have developed a method for prediction of the hardest crystal structures in a given chemical system. It is based on the evolutionary algorithm USPEX (Universal Structure Prediction: Evolutionary Xtallography) and electronegativity-based hardness model that we have augmented with bond-valence model and graph theory. These extensions enable correct description of the hardness of layered, molecular, and low-symmetry crystal structures. Applying this method to C and TiO2, we have (i) obtained a number of low-energy carbon structures with hardness slightly lower than diamond and (ii) proved that…
Boron suboxide B6O, the hardest known oxide, has an R-3m crystal structure (α-B6O) that can be described as an oxygen-intercalated structure of α-boron, or, equivalently, as a cubic close packing of B12 icosahedra with two oxygen atoms occupying all octahedral voids in it. Here we show a new ground state of this compound at ambient conditions, Cmcm-B6O (\b{eta}-B6O), which in all quantum-mechanical treatments that we tested (GGA, LDA, and hybrid functional HSE06) comes out to be slightly but consistently more stable. Increasing pressure and temperature further stabilize it with respect to the …
In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, that has been performed for diamond and…
The pressure-induced transformation of diatomic nitrogen into non-molecular polymeric phases may produce potentially useful high-energy-density materials. We combine first-principles calculations with structure searching to predict a new class of nitrogen-rich boron nitrides with a stoichiometry of B3N5 that are stable or metastable relative to solid N2 and h-BN at ambient pressure. The most stable phase at ambient pressure has a layered structure (h-B3N5) containing hexagonal B3N3 layers sandwiched with intercalated freely rotating N2 molecules. At 15 GPa, a three-dimensional C2221 structure …
We present a systematic search for low-energy metastable superhard carbon allotropes by using the recently developed evolutionary metadynamics technique. It is known that cold compression of graphite produces an allotrope at 15-20 GPa. Here we look for all low-enthalpy structures accessible from graphite. Starting from 2H- or 3R-graphite and applying the pressure of 20 GPa, a large variety of intermediate $sp^3$ carbon allotropes were observed in evolutionary metadynamics simulation. Our calculation not only found all the previous proposed candidates for `superhard graphite', but also predicte…
By electron and X-ray diffraction we establish that the CrB$_4$ compound discovered over 40 years ago crystallizes in the $oP10$ (\emph{Pnnm}) structure, in disagreement with previous experiments but in agreement with a recent first-principles prediction. The 3D boron network in the new structure is a distorted version of the rigid carbon $sp^3$ network proposed recently for the high-pressure C$_4$ allotrope. According to our density functional theory calculations and the analysis of the bonding, CrB$_4$ is a potentially superhard material. In fact, the calculated weakest shear and tensile str…
A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62 GPa, which has reignited extensive interests on whether transition metal borides (TRBs) compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent FeB bonding. Meanwhile, we extensively investig…
In the present paper we performed the analysis of available data on structural, thermodynamic and mechanical properties of B6O. Although the compound is known for half a century and has been extensively studied, many properties of this boron-rich solid remain unknown or doubtful. Semi-empirical analysis of our experimental and literature data allowed us to choose the best values of main thermodynamic and mechanical characteristics among previously reported data, to predict the thermoelastic equation of state of B6O, and dependence of its hardness on non-stoichiometry and temperature.
Novel superhard materials, especially those with superior thermal and chemical stability, are needed to replace diamond. Carbon nitrides (C-N), which are likely to possess these charac- teristics and have even been expected to be harder than diamond, are excellent candidates. Here we report three new superhard and thermodynamically stable carbon nitride phases. Based on a systematic evolutionary structure searches, we report a complete phase diagram of the C-N system at 0-300 GPa and analyze the hardest metastable structures. Surprising- ly, we find that at zero pressure, the earlier proposed …
We present an evolutionary construction technique of formation energy convex hull to search for thermodynamically stable compounds. In this technique, candidates with a wide variety of chemical compositions and crystal structures are created by systematically applying evolutionary operators, "mating", "mutation", and "adaptive mutation", to two target compounds, and the convex hull is directly updated through the evolution. We applied the technique to carbon-hydrogen binary system at 10 GPa and obtained 15 hydrocarbons within the convex hull distance less than 0.5 mRy/atom: graphane, polybutad…
Modern high-performance permanent magnets are made from alloys of rare earth and transition metal elements, and large magnetization is achieved in the alloys with high concentration of transition metals. We applied evolutionary search scheme based on first-principles calculations to the Y-Co-B system and predicted 37 cobalt-rich compounds with high probability of being stable. Focusing on remarkably cobalt-rich compounds, YCo$_{16}$ and YCo$_{20}$, we found that, although they are metastable phases, the phase stability is increased with increase of temperature due to the contribution of vibrat…
Nitrides, carbides and borides of transition metals are an attractive class of hard materials. Our recent preliminary explorations of the binary chemical compounds indicated that chromium-based materials are among the hardest transition metal compounds. Motivated by this, here we explore in detail the binary Cr-B, Cr-C and Cr-N systems using global optimization techniques. Calculated enthalpy of formation and hardness of predicted materials were used for Pareto optimization to define the hardest materials with lowest energy. Our calculations recover all numerous known stable compounds (except …
New candidate ground states at 1:4, 1:2, and 1:1 compositions are identified in the well-known Fe-B system via a combination of ab initio high-throughput and evolutionary searches. We show that the proposed oP12-FeB2 stabilizes by a break up of 2D boron layers into 1D chains while oP10-FeB4 stabilizes by a distortion of a 3D boron network. The uniqueness of these configurations gives rise to a set of remarkable properties: oP12-FeB2 is expected to be the first semiconducting metal diboride and oP10-FeB4 is shown to have the potential for phonon-mediated superconductivity with a Tc of 15-20 K.
Ab-initio insights into the structural, elastic, bonding, and thermophysical properties of UHx (x = 1, 2, 3, 5, 6, 7, 8) under pressure: possible relevance to high-Tc superconductivity
Martin-Luther-Universität Halle-Wittenberg（马丁·路德·哈勒-维腾贝格大学）；University of Coimbra（科英布拉大学）；Friedrich-Schiller-Universität Jena（弗里德里希·席勒·耶拿大学）
Crystal-graph attention networks have emerged recently as remarkable tools for the prediction of thermodynamic stability and materials properties from unrelaxed crystal structures. Previous networks trained on two million materials exhibited, however, strong biases originating from underrepresented chemical elements and structural prototypes in the available data. We tackled this issue computing additional data to provide better balance across both chemical and crystal-symmetry space. Crystal-graph networks trained with this new data show unprecedented generalization accuracy, and allow for re…
We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable crystal structure and a number of low-energy metastable structures for a given compound at any P-T conditions without requiring any experimental input. Extremely high success rate has been observed in a few tens of tests done so far, including ionic, covalent, metallic, and molecular structures with up to 40 atoms in the unit cell. We have been able to resolve so…
Using ab initio evolutionary simulations, we explore all the possible stoichiometries for Mg-O system at pressures up to 850 GPa. In addition to MgO, our calculations find that two extraordinary compounds MgO2 and Mg3O2 become thermodynamically stable at 116 GPa and 500 GPa, respectively. Detailed chemical bonding analysis shows large charge transfer in all magnesium oxides. MgO2 contains peroxide ions [O-O]2-, while non-nuclear electron density maxima play the role of anions in the electride compound Mg3O2. The latter compound is calculated to have a much narrower band gap compared to MgO and…
Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed "crystal structure prediction problem", and recently developed evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary Xtallography) made an important progress in solving it, enabling efficient and reliable prediction of structures with up to ~40 atoms in the unit cell using ab initio methods. Here we review this methodology, as well as rec…
Metal oxyfluorides constitute a broad group of chemical compounds with rich spectrum of crystal structures and properties. Here we predict, based on evolutionary algorithm approach, the crystal structure and selected properties of Ag$_2$OF$_2$. This system may be considered as the 1 to 1 adduct of AgF$_2$ (i.e. an antiferromagnetic charge transfer positive U insulator) and AgO (i.e. a disproportionated negative U insulator). We analyze oxidation states of silver in each structure, possible magnetic interactions, as well as energetic stability. Prospect is outlined for synthesis of polytypes of…
Evolutionary structure searches are used to predict a new class of compounds in the lithium--rich region of the lithium/hydrogen phase diagram under pressure. First principles computations show that LimH, 4<m<9, are stabilized with respect to LiH and Li between 50-100 GPa. The building block of all of the lithium subhydrides is an Li8H cluster, which can be thought of as a superalkali. The geometries and electronic structures of these phases is analogous to that of the well-known alkali metal suboxides.
Over the past decade, evolutionary algorithms, data mining, and other methods showed great success in solving the main problem of theoretical crystallography: finding the stable structure for a given chemical composition. Here we develop a method that addresses the central problem of computational materials science: the prediction of material(s), among all possible combinations of all elements, that possess the best combination of target properties. This nonempirical method combines our new coevolutionary approach with the carefully restructured "Mendelevian" chemical space, energy filtering, …
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 compoun…
Hafnium carbides are studied by a systematic search for possible stable stoichiometric compounds in the Hf-C system at ambient pressure using variable-composition ab initio evolutionary algorithm implemented in the USPEX code. In addition to well-known HfC, we predicted two additional compounds Hf3C2 and Hf6C5. The structure of Hf6C5 with space group C2/m contains 11 atoms in the primitive cell and this prediction revives the earlier proposal by A. I. Gusev. The stable structure of Hf3C2 also has space group C2/m, and is more energetically favorable than the Immm, P-3m1, P2 and C2221 structure…
The Li-Sn binary system has been the focus of extensive research because it features Li-rich alloys with potential applications as battery anodes. Our present re-examination of the binary system with a combination of machine learning and ab initio methods has allowed us to screen a vast configuration space and uncover a number of overlooked thermodynamically stable alloys. At ambient pressure, our evolutionary searches identified a new stable Li$_3$Sn phase with a large BCC-based hR48 structure and a possible high-T LiSn$_4$ ground state. By building a simple model for the observed and predict…
BaBiO3 is a well-known example of a 3D charge density wavecompound, in which the CDW behavior is induced by charge disproportionation at the Bi site. At ambient pressure, this compound is a charge-ordered insulator, but little is known about its high-pressure behavior. In this work, we study from first-principles the high-pressure phase diagram of BaBiO3 using phonon modes analysis and evolutionary crystal structure prediction. We show that charge disproportionation is very robust in this compound and persists up to 100 GPa. This causes the system to remain insulating up to the highest pressur…
We have performed first-principles evolutionary searches for all stable titanium nitrides and have found, in addition to the well-known rocksalt-type TiN, new ground states Ti$_3$N$_2$, Ti$_4$N$_3$, Ti$_6$N$_5$ at atmospheric pressure, and Ti$_2$N and TiN$_2$ at higher pressures. The latest nitrogen-rich structure presents encapsulated N$_2$ dumbbells with a N-N distance of 1.348 Å at 60 GPa and TiN$_2$ is predicted to be mechanically stable (quenchable). Our calculations of the mechanical properties (bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and hardness) are in excellent…
Adaptive fine-tuning of foundation models for crystal structure prediction: Discovery of high-pressure phases in the CaFeNi system
Joint Institute for Nuclear Research（苏联联合核研究所）；Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences（俄罗斯科学院韦列夏金高压物理研究所）；Vatolin Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences（俄罗斯科学院乌拉尔分支瓦托林冶金研究所）；Ural Federal University（乌拉尔联邦大学）
The discovery of new multicomponent inorganic compounds can provide direct solutions to many scientific and engineering challenges, yet the vast size of the uncharted material space dwarfs current synthesis throughput. While the computational crystal structure prediction is expected to mitigate this frustration, the NP-hardness and steep costs of density functional theory (DFT) calculations prohibit material exploration at scale. Herein, we introduce SPINNER, a highly efficient and reliable structure-prediction framework based on exhaustive random searches and evolutionary algorithms, which is…
Prediction of the stable crystal structure for multinary (ternary or higher) compounds with unexplored compositions demands fast and accurate evaluation of free energies in exploring the vast configurational space. The machine-learning potential such as the neural network potential (NNP) is poised to meet this requirement but a dearth of information on the crystal structure poses a challenge in choosing training sets. Herein we propose constructing the training set from densityfunctional-theory (DFT) based dynamical trajectories of liquid and quenched amorphous phases, which does not require a…
