Articles in the Spotlight

High-Entropy High-Hardness Metal Carbides Discovered by Entropy Descriptors

Pranab Sarker, Tyler Harrington, Cormac Toher, Corey Oses, Mojtaba Samiee, Jon-Paul Maria, Donald W. Brenner, Kenneth S. Vecchio, and Stefano Curtarolo

High-entropy materials have attracted considerable interest due to the combination of useful properties and promising applications. Predicting their formation remains the major hindrance to the discovery of new systems. Here we propose a descriptor—entropy forming ability—for addressing synthesizability from first principles. The formalism, based on the energy distribution spectrum of randomized calculations, captures the accessibility of equally-sampled states near the ground state and quantifies configurational disorder capable of stabilizing high-entropy homogeneous phases. The methodology is applied to disordered refractory 5-metal carbides—promising candidates for high-hardness applications. The descriptor correctly predicts the ease with which compositions can be experimentally synthesized as rock-salt high-entropy homogeneous phases, validating the ansatz, and in some cases, going beyond intuition. Several of these materials exhibit hardness up to 50% higher than rule of mixtures estimations. The entropy descriptor method has the potential to accelerate the search for high-entropy systems by rationally combining first principles with experimental synthesis and characterization.

Universal Fragment Descriptors for Predicting Properties of Inorganic Crystals

Olexandr Isayev, Corey Oses, Cormac Toher, Eric Gosset, Stefano Curtarolo and Alexander Tropsha

Although historically materials discovery has been driven by a laborious trial-and-error process, knowledge-driven materials design can now be enabled by the rational combination of Machine Learning methods and materials databases. Here, data from the AFLOW repository for ab initio calculations is combined with Quantitative Materials Structure-Property Relationship models to predict important properties: metal/insulator classification, band gap energy, bulk/shear moduli, Debye temperature and heat capacities. The prediction’s accuracy compares well with the quality of the training data for virtually any stoichiometric inorganic crystalline material, reciprocating the available thermomechanical experimental data. The universality of the approach is attributed to the construction of the descriptors: Property-Labelled Materials Fragments. The representations require only minimal structural input allowing straightforward implementations of simple heuristic design rules.

Spectral Descriptors for Bulk Metallic Glasses Based on the Thermodynamics of Competing Crystalline Phases

Eric Perim, Dongwoo Lee, Yanhui Liu, Cormac Toher, Pan Gong, Yanglin Li, W. Neal Simmons, Ohad Levy, Joost J. Vlassak, Jan Schroers, and Stefano Curtarolo

Metallic glasses attract considerable interest due to their unique combination of superb properties and processability. Predicting their formation from known alloy parameters remains the major hindrance to the discovery of new systems. Here, we propose a descriptor based on the heuristics that structural and energetic ‘confusion’ obstructs crystalline growth, and demonstrate its validity by experiments on two well-known glass-forming alloy systems. We then develop a robust model for predicting glass formation ability based on the geometrical and energetic features of crystalline phases calculated ab initio in the AFLOW framework. Our findings indicate that the formation of metallic glass phases could be much more common than currently thought, with more than 17% of binary alloy systems potential glass formers. Our approach pinpoints favourable compositions and demonstrates that smart descriptors, based solely on alloy properties available in online repositories, offer the sought-after key for accelerated discovery of metallic glasses.

Modeling Off-Stoichiometry Materials with a High-Throughput Ab-Initio Approach

Kesong Yang, Corey Oses, and Stefano Curtarolo

Predicting material properties of off-stoichiometry systems remains a long-standing and formidable challenge in rational materials design. A proper analysis of such systems by means of a supercell approach requires the exhaustive consideration of all possible superstructures, which can be a time-consuming process. On the contrary, the use of quasirandom approximants, although very computationally effective, implicitly bias the analysis toward disordered states with the lowest site correlations. Here, we propose a novel framework designed specifically to investigate stoichiometrically driven trends of disordered systems (i.e., having partial occupation and/or disorder in the atomic sites). At the heart of the approach is the identification and analysis of unique supercells of a virtually equivalent stoichiometry to the disordered material. We employ Boltzmann statistics to resolve system-wide properties at a high-throughput (HT) level. To maximize efficiency and accessibility, we integrated the method within the automatic HT computational framework AFLOW. As proof of concept, we apply our approach to three systems of interest, a zinc chalcogenide (ZnS1−xSex), a wide-gap oxide semiconductor (MgxZn1−xO), and an iron alloy (Fe1−xCux), at various stoichiometries. These systems exhibit properties that are highly tunable as a function of composition, characterized by optical bowing and linear ferromagnetic behavior. Not only are these qualities successfully predicted, but additional insight into underlying physical mechanisms is revealed.

Entropy-Stabilized Oxides

Christina M. Rost, Edward Sachet, Trent Borman, Ali Moballegh, Elizabeth C. Dickey, Dong Hou, Jacob L. Jones, Stefano Curtarolo, and Jon-Paul Maria

Configurational disorder can be compositionally engineered into mixed oxide by populating a single sublattice with many distinct cations. The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways. Here, through rigorous experiments, a simple thermodynamic model, and a five-component oxide formulation, we demonstrate beyond reasonable doubt that entropy predominates the thermodynamic landscape, and drives a reversible solid-state transformation between a multiphase and single-phase state. In the latter, cation distributions are proven to be random and homogeneous. The findings validate the hypothesis that deliberate configurational disorder provides an orthogonal strategy to imagine and discover new phases of crystalline matter and untapped opportunities for property engineering.

Seminal AFLOW Publications

AFLOW: An Automatic Framework for High-Throughput Materials Discovery

Stefano Curtarolo, Wahyu Setyawan, Gus L.W. Hart, Michal Jahnatek, Roman V. Chepulskii, Richard H. Taylor, Shidong Wang, Junkai Xue, Kesong Yang, Ohad Levy, Michael J. Mehl, Harold T. Stokes, Denis O. Demchenko, Dane Morgan

Recent advances in computational materials science present novel opportunities for structure discovery and optimization, including uncovering of unsuspected compounds and metastable structures, electronic structure, surface, and nano-particle properties. The practical realization of these opportunities requires systematic generation and classification of the relevant computational data by high-throughput methods. In this paper we present Aflow (Automatic Flow), a software framework for high-throughput calculation of crystal structure properties of alloys, intermetallics and inorganic compounds. The Aflow software is available for the scientific community on the website of the materials research consortium, Its geometric and electronic structure analysis and manipulation tools are additionally available for online operation at the same website. The combination of automatic methods and user online interfaces provide a powerful tool for efficient quantum computational materials discovery and characterization.

AFLOWLIB.ORG: A Distributed Materials Properties Repository from High-Throughput ab initio Calculations

Stefano Curtarolo, Wahyu Setyawan, Shidong Wang, Junkai Xue, Kesong Yang, Richard H. Taylor, Lance J. Nelson, Gus L.W. Hart, Stefano Sanvito, Marco Buongiorno-Nardelli, Natalio Mingo, Ohad Levy

Empirical databases of crystal structures and thermodynamic properties are fundamental tools for materials research. Recent rapid proliferation of computational data on materials properties presents the possibility to complement and extend the databases where the experimental data is lacking or difficult to obtain. Enhanced repositories that integrate both computational and empirical approaches open novel opportunities for structure discovery and optimization, including uncovering of unsuspected compounds, metastable structures and correlations between various characteristics. The practical realization of these opportunities depends on a systematic compilation and classification of the generated data in addition to an accessible interface for the materials science community. In this paper we present an extensive repository,, comprising phase-diagrams, electronic structure and magnetic properties, generated by the high-throughput framework AFLOW. This continuously updated compilation currently contains over 150,000 thermodynamic entries for alloys, covering the entire composition range of more than 650 binary systems, 13,000 electronic structure analyses of inorganic compounds, and 50,000 entries for novel potential magnetic and spintronics systems. The repository is available for the scientific community on the website of the materials research consortium,

The AFLOW Standard for High-Throughput Materials Science Calculations

Camilo E. Calderon, Jose J. Plata, Cormac Toher, Corey Oses, Ohad Levy, Marco Fornari, Amir Natan, Michael J. Mehl, Gus Hart, Marco Buongiorno Nardelli, Stefano Curtarolo

The Automatic-Flow (AFLOW) standard for the high-throughput construction of materials science electronic structure databases is described. Electronic structure calculations of solid state materials depend on a large number of parameters which must be understood by researchers, and must be reported by originators to ensure reproducibility and enable collaborative database expansion. We therefore describe standard parameter values for k-point grid density, basis set plane wave kinetic energy cut-off, exchange–correlation functionals, pseudopotentials, DFT+U parameters, and convergence criteria used in AFLOW calculations.

AFLUX: The LUX Materials Search API for the AFLOW Data Repositories

Frisco Rose, Cormac Toher, Eric Gossett, Corey Oses, Marco Buongiorno Nardelli, Marco Fornari, Stefano Curtarolo

Automated computational materials science frameworks rapidly generate large quantities of materials data for accelerated materials design. In order to take advantage of these large databases, users should have the ability to efficiently search and extract the desired data. Therefore, we have extended the data-oriented AFLOW-repository Application-Program-Interface (API) (Comput. Mater. Sci. 93, 178 (2014)) to enable programmatic access to search queries. A Uniform Resource Identifier (URI)-based search API is proposed for the construction of complex queries for remote creation and retrieval of customized data sets. It is expected that the new language, AFLUX, from “Automatic Flow of LUX (light)”, will enable remote search operations on the AFLOW set of computational materials science data repositories. In addition, AFLUX facilitates the verification and validation of the data in the AFLOW repositories.

The AFLOW Fleet for Materials Discovery

Cormac Toher, Corey Oses, David Hicks, Eric Gossett, Frisco Rose, Pinku Nath, Demet Usanmaz, Denise C. Ford, Eric Perim, Camilo E. Calderon, Jose J. Plata, Yoav Lederer, Michal Jahnátek, Wahyu Setyawan, Shidong Wang, Junkai Xue, Kevin Rasch, Roman V. Chepulskii, Richard H. Taylor, Geena Gomez, Harvey Shi, Andrew R. Supka, Rabih Al Rahal Al Orabi, Priya Gopal, Frank T. Cerasoli, Laalitha Liyanage, Haihang Wang, Ilaria Siloi, Luis A. Agapito, Chandramouli Nyshadham, Gus L. W Hart, Jesús Carrete, Fleur Legrain, Natalio Mingo, Eva Zurek, Olexandr Isayev, Alexander Tropsha, Stefano Sanvito, Robert M. Hanson, Ichiro Takeuchi, Michael J. Mehl, Aleksey N. Kolmogorov, Kesong Yang, Pino D’Amico, Arrigo Calzolari, Marcio Costa, Riccardo De Gennaro, Marco Buongiorno Nardelli, Marco Fornari, Ohad Levy, Stefano Curtarolo

The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data-driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first-principles calculations and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational modules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermomechanical properties, and more. The AFLOW data repository is publicly accessible online at, with more than 1.8 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available.

High-Throughput Electronic Band Structure Calculations: Challenges and Tools

Wahyu Setyawan, Stefano Curtarolo

The article is devoted to the discussion of the high-throughput approach to band structures calculations. We present scientific and computational challenges as well as solutions relying on the developed framework (Automatic Flow, AFLOW/ACONVASP). The key factors of the method are the standardization and the robustness of the procedures. Two scenarios are relevant: (1) independent users generating databases in their own computational systems (off-line approach) and (2) teamed users sharing computational information based on a common ground (on-line approach). Both cases are integrated in the framework: for off-line approaches, the standardization is automatic and fully integrated for the 14 Bravais lattices, the primitive and conventional unit cells, and the coordinates of the high symmetry k-path in the Brillouin zones. For on-line tasks, the framework offers an expandable web interface, where the user can prepare and set up calculations following the proposed standard. Few examples of band structures are included. LSDA+U parameters (U, J) are also presented for Nd, Sm, and Eu.