High-entropy high-hardness metal carbides discovered by entropy descriptors

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.Comment: 12 pages, 2 figure

Discovery of high-entropy ceramics via machine learning

AbstractAlthough high-entropy materials are attracting considerable interest due to a combination of useful properties and promising applications, predicting their formation remains a hindrance for rational discovery of new systems. Experimental approaches are based on physical intuition and/or expensive trial and error strategies. Most computational methods rely on the availability of sufficient experimental data and computational power. Machine learning (ML) applied to materials science can accelerate development and reduce costs. In this study, we propose an ML method, leveraging thermodynamic and compositional attributes of a given material for predicting the synthesizability (i.e., entropy-forming ability) of disordered metal carbides. The relative importance of the thermodynamic and compositional features for the predictions are then explored. The approach’s suitability is demonstrated by comparing values calculated with density functional theory to ML predictions. Finally, the model is employed to predict the entropy-forming ability of 70 new compositions; several predictions are validated by additional density functional theory calculations and experimental synthesis, corroborating the effectiveness in exploring vast compositional spaces in a high-throughput manner. Importantly, seven compositions are selected specifically, because they contain all three of the Group VI elements (Cr, Mo, and W), which do not form room temperature-stable rock-salt monocarbides. Incorporating the Group VI elements into the rock-salt structure provides further opportunity for tuning the electronic structure and potentially material performance

First principles computational descriptor for entropy forming ability

Entropy stabilized materials [1], where the mixing of the components is driven by configurational entropy rather than formation enthalpy, are potential candidates for ultra-high temperature applications. The prediction of which compositions will form entropy stabilized materials is difficult since calculating the entropic contribution to the free energy from first principles is computationally expensive. Therefore, we have formulated a descriptor for the synthesizability of disordered materials based on the energy distribution of the thermodynamic density of states (TDOS) for an ensemble of ordered configurations generated using the AFLOW (Automatic FLOW) partial occupation (AFLOW-POCC) methodology [2,3] and calculated with DFT. This descriptor has been used to successfully predict which refractory metal carbide compositions can be experimentally synthesized as single-phase entropy stabilized materials [4]. This work is supported by the U.S. Office of Naval Research MURI program (grant No. N00014-15- 1-2863). [1] C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo, and J.-P. Maria, Entropy Stabilized Oxides, Nat. Commun. 6, 8485 (2015). [2] S. Curtarolo, W. Setyawan, G. L. W. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. J. Mehl, H. T. Stokes, D. O. Demchenko, and D. Morgan, AFLOW: an automatic framework for high-throughput materials discovery, Comput. Mater. Sci. 58, 218-226 (2012). [3] K. Yang, C. Oses, and S. Curtarolo, Modeling off-stoichiometry materials with a high-throughput ab-initio approach, Chem. Mater. 28, 6484-6492 (2016). [4] P. Sarker, T. Harrington, C. Toher, K. Vecchio, and S. Curtarolo, First principles materials design using a spectral descriptor for entropy forming ability, in preparation (2017)

Modelling and synthesis of high-entropy refractory carbides

Bulk samples of equiatomic, hexanery (5-metal), high-entropy refractory carbides were fabricated using a combination of high-energy ball milling (HEBM), spark plasma sintering (SPS), and hot pressing (HP) annealing. To select candidate composition that are likely to form single phase high-entropy materials at lower processing temperatures (\u3c2500°C), a novel, first-principles materials design method was developed. The theory follows that for low temperature single phase formation, the different configurations should have similar energies to increase the number of thermodynamically accessible states. A partial occupation method was implemented within AFLOW to automate the generation and calculation of the different configurations. The energy distributions were then used to construct a descriptor of Entropy Forming Ability (EFA) to predict the formation of high-entropy materials. CALPHAD results were found to agree with the configuration energy range descriptor for each composition, and these carbides exhibited broad, single-phase solubility across each system, making processing possible at reasonable temperatures. Many of the complex carbide compositions, including (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2V0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2W0.2)C, and (Nb0.2Ta0.2Ti0.2V0.2W0.2)C demonstrated virtually single-phase, solid-solution compounds with the NaCl crystal structure as determined by x-ray diffraction (XRD) and energy dispersive x-ray spectroscopy (EDS), while some compositions, including (Hf0.2Mo 0.2Ta0.2W0.2Zr0.2)C and (Hf0.2Mo0.2V0.2W0.2Zr0.2)C, exhibited multiple phases. Results were found to be in good agreement with the ab initio based formulation of entropic stability, where the compositions with the highest EFA values were found to form a single rocksalt structure and compositions with the lower EFA values were found to exhibit multiple phases. Further, among the systems that were found to form single phase materials at 2500°C, artificial segregation was introduced via lower processing temperatures. In these artificially segregated samples, the extent of mixing was analyzed via peak broadening in XRD according to the formulation of Williamson and Hall [1] and compositional mapping in EDS. Results of artificially segregated samples provide continued support for the viability of the EFA formulation, where broadening was found to be more pronounced (i.e. more chemical segregation) in samples that were determined to have a lower EFA value. This work demonstrates the extension of entropic-stabilization into refractory interstitial carbides, paving the way for development of an entirely new class of UHTCs. This work is supported by the U.S. Office of Naval Research MURI program (Grant No. N00014-15- 1-2863). [1] G.. Williamson, W.. Hall, X-ray line broadening from filed aluminium and wolfram, Acta Metall. 1 (1953) 22–31. doi:10.1016/0001-6160(53)90006-6

Fabrication of high-entropy nitrides and carbonitrides

In high-entropy alloys, the use of multiple principle alloying elements is known to entropically stabilize the material. Refractory nitrides and carbides of transition metals are widely known for their ultra high-temperature stability and their high hardness, properties that make them valuable materials for extreme environments, such as coating the exterior of hypersonic flight vehicles and the interior of nuclear reactors. By creating entropy-stabilized complex solid solutions of nitrides and carbides, one can take advantage of the inherent favorable properties of these materials, as well as increased thermal stability and solid solution strengthening. Five-metal systems are chosen using first-principles calculations to describe the energetic distribution of possible atomic configurations, in order to identify systems that are likely to form an entropy-stabilized solid solution. Bulk samples of equiatomic, hexanery (5-metal), high-entropy refractory nitrides and carbonitrides were then fabricated to demonstrate this concept, by using a combination of high-energy ball milling, spark plasma sintering, and hot pressing. The uniformity of the microstructures is characterized, and single-phase solid solutions are achieved, thus demonstrating the ability to entropically stabilize multi-component random mixtures of refractory carbides and nitrides. This work is supported by the U.S. Office of Naval Research MURI program (Grant No. N00014-15- 1-2863

The status of GEO 600

The GEO 600 laser interferometer with 600m armlength is part of a worldwide network of gravitational wave detectors. GEO 600 is unique in having advanced multiple pendulum suspensions with a monolithic last stage and in employing a signal recycled optical design. This paper describes the recent commissioning of the interferometer and its operation in signal recycled mode