On-the-fly training of polynomial machine learning potentials in computing lattice thermal conductivity.

The application of first-principles calculations for predicting lattice thermal conductivity (LTC) in crystalline materials, in conjunction with the linearized phonon Boltzmann equation, has gained increasing popularity. In this calculation, the determination of force constants through first-principles calculations is critical for accurate LTC predictions. For material exploration, performing first-principles LTC calculations in a high-throughput manner is now expected, although it requires significant computational resources. To reduce computational demands, we integrated polynomial machine learning potentials on-the-fly during the first-principles LTC calculations. This paper presents a systematic approach to first-principles LTC calculations. We designed and optimized an efficient workflow that integrates multiple modular software packages. We applied this approach to calculate LTCs for 103 compounds of wurtzite, zinc blende, and rocksalt types to evaluate the performance of the polynomial machine learning potentials in LTC calculations. We demonstrate a significant reduction in the computational resources required for the LTC predictions.

Combination of recommender system and single-particle diagnosis for accelerated discovery of novel nitrides.

Discovery of new compounds from wide chemical space is attractive for materials researchers. However, theoretical prediction and validation experiments have not been systematically integrated. Here, we demonstrate that a new combined approach is powerful in significantly accelerating the discovery rate of new compounds, which should be useful for exploration of a wide chemical space in general. A recommender system for chemically relevant composition is constructed by machine learning of Inorganic Crystal Structure Database using chemical compositional descriptors. Synthesis and identification experiments are made at the chemical compositions with high recommendation scores by the single-particle diagnosis method. Two new compounds, La4Si3AlN9 and La26Si41N80O, and two new variants (isomorphic substitutions) of known compounds, La7Si6N15 and La4Si5N10O, are successfully discovered. Finally, density functional theory calculations are conducted for La4Si3AlN9 to confirm the energetic and dynamical stability and to reveal its atomic arrangement.

Enumeration of nonequivalent substitutional structures using advanced data structure of binary decision diagram.

A derivative structure is a nonequivalent substitutional atomic configuration derived from a given primitive cell. The enumeration of derivative structures plays an essential role in searching for the ground states in multicomponent systems. However, it is computationally difficult to enumerate derivative structures if the number of derivative structures of a target system becomes huge. In this study, we introduce a novel compact data structure of the zero-suppressed binary decision diagram (ZDD) for enumerating derivative structures much more efficiently. We show its simple applications to the enumeration of structures derived from the face-centered cubic and hexagonal close-packed lattices in binary, ternary, and quaternary systems. The present ZDD-based procedure should contribute to computational approaches based on derivative structures in physics and materials science.

Linearized machine-learning interatomic potentials for non-magnetic elemental metals: Limitation of pairwise descriptors and trend of predictive power.

Machine-learning interatomic potential (MLIP) has been of growing interest as a useful method to describe the energetics of systems of interest. In the present study, we examine the accuracy of linearized pairwise MLIPs and angular-dependent MLIPs for 31 elemental metals. Using all of the optimal MLIPs for 31 elemental metals, we show the robustness of the linearized frameworks, the general trend of the predictive power of MLIPs, and the limitation of pairwise MLIPs. As a result, we obtain accurate MLIPs for all 31 elements using the same linearized framework. This indicates that the use of numerous descriptors is the most important practical feature for constructing MLIPs with high accuracy. An accurate MLIP can be constructed using only pairwise descriptors for most non-transition metals, whereas it is very important to consider angular-dependent descriptors when expressing interatomic interactions of transition metals.

Compositional descriptor-based recommender system for the materials discovery.

Structures and properties of many inorganic compounds have been collected historically. However, it only covers a very small portion of possible inorganic crystals, which implies the presence of numerous currently unknown compounds. A powerful machine-learning strategy is mandatory to discover new inorganic compounds from all chemical combinations. Herein we propose a descriptor-based recommender-system approach to estimate the relevance of chemical compositions where crystals can be formed [i.e., chemically relevant compositions (CRCs)]. In addition to data-driven compositional similarity used in the literature, the use of compositional descriptors as a prior knowledge is helpful for the discovery of new compounds. We validate our recommender systems in two ways. First, one database is used to construct a model, while another is used for the validation. Second, we estimate the phase stability for compounds at expected CRCs using density functional theory calculations.

Prediction of Low-Thermal-Conductivity Compounds with First-Principles Anharmonic Lattice-Dynamics Calculations and Bayesian Optimization.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here, we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice-dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them even have an electronic band gap <1 eV, which makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which the chemistry of materials is required to be optimized.

Structure search method for atomic clusters based on the dividing rectangles algorithm.

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Cluster expansion of multicomponent ionic systems with controlled accuracy: importance of long-range interactions in heterovalent ionic systems.

We have been examining factors determining the accuracy of cluster expansion (CE), which is used in combination with many density functional theory (DFT) calculations. With the exception of multicomponent metallic or isovalent ionic systems, the contributions of long-range effective cluster interactions (ECIs) to configurational energetics are not negligible, which is ascribed to long-range electrostatic interactions. The truncation of ECIs in such systems leads to systematic errors. A typical problem with such errors can be seen in Monte Carlo simulations, since simulation supercells composed of a larger number of atoms than those of the input DFT structures are used. The prediction errors for long-period structures beyond the cell size of the input DFT structures in addition to those for short-period structures within the cell size of the input DFT structures need to be carefully examined to control the accuracy of CE. In this study, we quantitatively discuss the contribution of the truncation of long-range ECIs to the accuracy of CE. Two types of system, namely a point-charge spinel lattice and a real MgAl2O4 spinel crystal, are examined. The prediction error of the long-period structures can be improved both by increasing the number of pairs and by also considering the effective screened electrostatic energy.

First-principles molecular dynamics study for average structure and oxygen diffusivity at high temperature in cubic Bi2O3.

Bismuth oxide, Bi(2)O(3), has a cubic structure (δ-phase) at high temperature. High oxygen conductivity of δ-Bi(2)O(3) should be closely related to disordering of the oxygen sublattice. In order to reconstruct the disordered structure in the crystal using first-principles molecular dynamics (FPMD), a sufficiently long simulation time is essentially required. In this study, the FPMD simulation up to 1 ns is performed with special interest given to the convergence of the average structure and the oxygen diffusivity with respect to the simulation time. The obtained average structure and the oxygen diffusivity are in good agreement with those obtained by experimental analysis.

Phase relationships and structures of inorganic crystals by a combination of the cluster expansion method and first principles calculations.

Properties of crystalline solutions are generally dependent not only on their chemical composition but also on the configurations of solute atoms and/or point defects. Quantitative knowledge of the configuration-dependent properties is therefore essential for materials design. The cluster expansion (CE) method has been widely used to describe the configurational properties. Increases in computational power and advances in numerical techniques enable us to perform a large set of systematic first principles calculations based on density functional theory (DFT) to be combined with CE calculations. In this paper, our procedure of CE with optimal selections of clusters and DFT structures is described. Two examples of such calculations are then shown. One is the cation arrangement in a series of spinel oxides. The other is arrangement of the oxygen vacancy in a series of tin sub-dioxides.

Native defects in oxide semiconductors: a density functional approach.

We report a semilocal and hybrid Hartree-Fock density functional study of native defects in three oxide semiconductors: ZnO, SrTiO(3), and SnO. The defect that is responsible for the n-type conductivity of ZnO has been debated, in which the O vacancy, Zn interstitial, their complexes, and residual H impurity are considered candidates. Our results indicate that the O vacancy induces a deep and localized in-gap state, whereas the Zn interstitial is a shallow donor and hence can be a source of the carriers. In view of the formation energies, the O vacancy is likely to form with a substantial concentration under O-poor conditions, but the Zn interstitial is unlikely. We thus propose that the O vacancy is relevant to the nonstoichiometry of ZnO and that a source other than the native defects, such as the H impurity, needs to be considered for the n-type conductivity. For SrTiO(3), the O vacancy and its complexes have been regarded as the origins of some of the remarkable electrical and optical properties. We suggest significant roles of the Ti antisite for a new insight into the defect-induced properties. Two types of Ti antisite, both of which are off-centered from the Sr site but toward different directions, exhibit low formation energies under Ti-rich conditions as does the O vacancy. They can explain optical properties such as visible-light emission, deep-level absorption, and the ferroelectricity observed in reduced SrTiO(3). As an example of p-type conductors, SnO has been investigated with a focus on the acceptor-like native defects. Under O-rich conditions, the Sn vacancy and O interstitial are found to be energetically favorable. The Sn vacancy induces shallow acceptor levels and can therefore be a source of carriers. The O interstitial shows no in-gap levels and hence it is inactive in terms of the carrier generation and compensation. However, this defect is a key to the understanding of the structures of intermediate compounds between SnO and SnO(2).

Structure and stability of a homologous series of tin oxides.

The structures and stabilities of a series of nonstoichiometric SnO2-x compounds, which are yet unknown experimentally, are predicted using the cluster expansion technique combined with first-principles calculations. A homologous series of Sn(n+1)O(2n) in which oxygen vacancies are layered on (101) planes of the rutile lattice is discovered. The homologous crystals are composed of divalent and quadrivalent Sn atoms. No trivalent Sn atoms are formed.