Symposium ST04—High Entropy Materials—From Fundamentals to Potential Applications

This talk explores the structural diversity that can be achieved in high entropy alloys and multiphase composites developed through a combination of concepts for designing chemically complex alloys and metallic glasses using rapid quenching and annealing or severe plastic deformation for tuning phase formation and microstructure development. The role of length-scale modulation and phase transformation upon heating or loading will be critically assessed with respect to structural stability and mechanical behavior. Examples for changes in deformation mechanism, e.g. from crack-controlled to dislocation-dominated deformation, twinning or cooperative deformation of shear bands and interfacial sliding, will be presented and discussed as ways to control strength, ductility and fracture toughness in a wide range. Besides, also examples for developing novel nanostructured and ultrafine-grained complex materials via composition and process control will be given, attempting to derive guidelines for how to tune the microstructure and properties of non-equiatomic chemically complex alloys with optimized properties.

Discontinuous deformation or serrated plastic deformation, at temperatures close to 0 K, has formerly been reported in some metals and alloys. Based on the previous reports, concentrated substitutional FCC solid solutions are expected to show this phenomenon in an intense fashion. This would correspondingly provide the conditions to most effectively evaluate the phenomenon. To that end CoCrNi and CoCrFeMnNi were tested and observed to exhibit very intense serrated plastic behavior during deformation near 0 K [Tirunilai et al. Acta Materialia 200 (2020) 980-991]. CoCrFeMnNi, was especially interesting, as it showed low temperature serrations at a higher temperature than previously reported for any other metal or alloy. While previous reports have put forth theories on the cause for serrations, the reports fail to characterize serration trends and make evaluations with respect to active deformation mechanisms. Presently, in order to understand and characterize this serrated plastic deformation, (i) general deformation characteristics at temperatures near 0 K have to be understood, (ii) the influence of the deformation mechanisms seen at these temperatures (dislocation based deformation, deformation twinning and epsilon martensite formation) have to be evaluated and (iii) the serrated plastic deformation has to evaluated based on the influence of temperature and deformation. This was done using the alloys CoNi, CoCrNi and CoCrFeMnNi.
(i) The initial microstructure of the alloys in question was evaluated using XRD and SEM. Subsequently, the specimens were subjected to macroscopic tensile tests at different temperatures in the range between 295 and 4.2 K. Using SEM and TEM, deformation twinning was identified in CoCrNi and CoCrFeMnNi. Additionally, martensite was indexed post deformation in CoCrNi, but not in CoCrFeMnNi, contrary to the expectation based on SFE – temperature relation [Huang et al. Scripta Materialia 108 (2015) 44-47]. However, it was clear that in both these alloys deformation twinning was the primary contributor to strengthening.
(ii) Deformation twinning and martensitic transformations are associated with instability in single crystals and are influential in high temperature serrated plastic deformation. However, tensile tests conducted on CoCrFeMnNi at different temperatures indicate that no new deformation mechanism can be attributed as the cause for serrations. Additional tests on martensite forming CoCrNi and non-twinning CoNi verify the lack of influence of both, deformation twinning as well as martensite formation.
(iii) Serration intensity trends, measured as serration stress amplitude, were evaluated at different temperatures as well as in the pre-deformed condition. Correspondingly, the current results are consistent with the basis proposed by Seeger [Seeger in Fisher et al., Dislocations and Mechanical Properties of Crystals, Wiley, Ney York (1956)], according to which the serrations were a result of ‘avalanche slip’ of dislocations piled up at Lomer-Cottrell (LC) locks. This theory proposes a basis for the phenomenon, but the current work establishes a qualitative model that validates both present results as well as those in former publications.

Multi-principal element alloys (MPEAs) or Complex Concentrated Alloys (CCA), including high-entropy alloys (HEAs) are designed with multiple principal elements of equal or near equal molar ratios. The strength of MPEAs can be further enhanced by refining the microstructure into the nanocrystalline state using severe plastic deformation (SPD) techniques. In this study, the influence of thermal treatment on the microstructure and hardness of nanocrystalline MPEAs processed by SPD was investigated. The SPD process was carried out using high-pressure torsion (HPT) technique up to ten turns at room temperature. The effect of heat treatment was studied from room temperature up to 1000K using differential scanning calorimetry (DSC). It was found that a single phase HfNbTiZr MPEA transformed into multiple phases at elevated temperatures. On the other hand, CoCrFeNi MPEA remained single phase solid solution throughout the annealing process. The microstructures and the chemical compositions of the different phases were examined by transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS). In addition, X-ray diffraction line profile analysis (XLPA) technique was used to monitor the evolution of the crystallite size and the dislocation density of CoCrFeNi, as well as to identify the different decomposed phases in the nanocrystalline HfNbTiZr MPEA. The average hardness of the annealed samples was also measured and correlated to the microstructure. This study demonstrated a comparative analysis of the results obtained in these alloys.

High entropy alloys are next generation potential materials which have the calibre of performing as a structural material. High entropy alloys show improved properties sue to several underlying effects such as: high configurational entropy, lattice distortion, sluggish diffusion and cocktail effect. They exhibit strength-ductility synergy which is an important aspect which is a paradox in conventional materials. Recent works on high entropy alloys span from thermomechanical processing of the same to sever plastic deformation in order to enhance their mechanical performance. The severe plastic deformation induces fine grain structure making the material possess delayed failure. Metallic sheets have wide range of applications starting from large body structures to acting as small components in aerospace and automobile sectors. Sheet forming along with a high performance ensures a high-quality product. The sheet possessing ultrafine grains as well as a gradient microstructure and texture will enable better mechanical behaviour. Multilayered sheets are a method to achieve the above attributes, hence we propose to design this by accumulative roll bonding.
This work presents the processing of hard cantor alloy into ultrafine grained multilayered sheet using hot accumulative roll bonding (ARB) to study its microstructural and texture evolution. The Cantor alloy FeCrCoMnNi was cast and cold rolled to obtain a sheet of thickness of 0.4 mm followed by annealing. The sheet was characterized and studied for its microstructure and annealing texture, along with its mechanical properties. This sheet was then accumulatively roll bonded with a sheet of same alloy at 450 C by imparting a reduction of 50% in each pass upto 3^rd pass using a cladding process. The ARB processed multilayer sheet was investigated for microstructure, bulk texture and microtexture. The strain gradient induced during accumulative roll bonding is instrumental in creating a gradient microstructure and texture along the thickness of the multi-layered sheet. Electron back scattered diffraction will be helpful in predicting the grain structure and the local strain in the deformed material.

High entropy alloys (HEA) are materials with an increasing number of technological applications. Among them, the Cantor Alloy, FeMnCoCrNi, shows desirable mechanical properties at normal loading conditions. In this study we focus on the performance of the Cantor alloy at ultrahigh deformation rates of shock waves.
Intense shock waves may lead to spallation of the sample. In this study we perform molecular dynamics simulations of shock-induced spallation and compare our results with experiments using laser shocks and scanning transmission electrion microscopy of the unloaded samples. Our molecular dynamics simulations were carried out with three different piston velocities, which allow us to gather more information and compare the data about the influence of the velocity on a
microscale. Both experiments and simulations show a high spall strength which would be beneficial for certain applications, with experiments giving 12 GPa at 10⁷s^-1 and MD 30 GPa at 10⁹s^-1. Post-mortem analysis of the experimental samples show nanotwins near the spall plane, while MD simulations show a highly dissordered region giving rise to void nucleation and spall.

In recent years, the transition from high-entropy alloys to high-entropy ceramics^[1] (e.g. high-entropy oxides, oxyfluorides, fluorides, etc.) has paved the way for a completely new field of materials and applications. The strong structure/property relationships and the unique possibility to tailor the compositions of high-entropy materials make them ideal candidates when aiming to prepare novel materials with adjustable properties for a variety of different applications.
Here, the utilization of several different high-entropy ceramics in the electrochemical sector will be presented. Conversion battery anodes and cathodes could be prepared using high-entropy oxides and fluorides, offering unexpected properties and advantages compared to conventional materials, which make them interesting for further research.^[2] It could be shown that the high entropy plays a decisive role regarding the performance of the electrodes and serves as an “adjusting screw” when the material is tailored towards a desired property. High-entropy insertion and intercalation materials could also be synthesized by introducing high-entropy oxyfluorides and layered high-entropy structures, respectively.^[3,4] Moreover, high-entropy oxides and high-entropy metal organic frameworks were applied to design post-Li battery electrodes for Na insertion. These materials do stand out due to their high reversibility and high accessible C-rates over reversible de/sodiation. Finally, the utilization of high-entropy molybdates and fluorides as catalysts for oxygen evolution reactions will shortly be demonstrated.^[5]

[1] C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo, J.-P. Maria, Nat. Commun. 2015, 6, 8485.
[2] A. Sarkar, L. Velasco, D. Wang, Q. Wang, G. Talasila, L. de Biasi, C. Kübel, T. Brezesinski, S. S. Bhattacharya, H. Hahn, B. Breitung, Nat. Commun. 2018, 9, 3400.
[3] Q. Wang, A. Sarkar, D. Wang, L. Velasco, R. Azmi, S. S. Bhattacharya, T. Bergfeldt, A. Düvel, P. Heitjans, T. Brezesinski, H. Hahn, B. Breitung, Energy Environ. Sci. 2019, 12, 2433.
[4] J. Wang, Y. Cui, Q. Wang, K. Wang, X. Huang, D. Stenzel, A. Sarkar, R. Azmi, T. Bergfeldt, S. S. Bhattacharya, R. Kruk, H. Hahn, S. Schweidler, T. Brezesinski, B. Breitung, Sci. Rep. 2020, 10, 18430.
[5] D. Stenzel, I. Issac, K. Wang, R. Azmi, R. Singh, J. Jeong, S. Najib, S. S. Bhattacharya, H. Hahn, T. Brezesinski, S. Schweidler, B. Breitung, Inorg. Chem. 2021, 60, 115.

In recent years, transition metal oxides (TMOs) have gained increasing interest in the field of rechargeable energy storage materials. One of the reasons is that often TMOs have a large theoretical specific capacity > 1000 mAh/g, which is attributed to the conversion reaction mechanism with its multi-electron redox processes during cycling.¹ This makes TMOs promising anode materials compared to graphite (theoretical capacity = 372 mAh/g). However, conventional TMOs suffer from rapid capacity degradation due to severe structural changes (large volume changes) during cycling.
Our recent studies show that transition metal-based high entropy oxide (TM-HEOs) (CoCuMgNiZn)₁O₁ exhibit reversible long-term lithium storage properties. The cycling stability might be attributed to an entropy stabilizing effect, additionally, it turned out that the electrochemical behavior of the TM-HEO is strongly influenced by each of the metal cations present. This makes it possible to change the electrochemical properties by simply changing the elemental composition.^2,3 Furthermore, using operando XRD and SAED, it was shown that, unlike conventional TMOs, the entropy-stabilized crystal structure serves as a kind of host matrix for the conversion reaction and that it is retained even in the fully lithiated state. The operando gassing study further showed that similar cycling performance and stability was obtained for cells with EC and FEC containing electrolytes. The gas analyses showed that H₂ and C₂H₄ were the main gas species during cycling. After the first cycle, especially the evolution rate of C₂H₄ decreased significantly, indicating the formation of a stable SEI layer on the HEO particles and emphasizing further the unique entropy-stabilized mechanism.⁴ In addition, further preliminary electrochemical studies show the successful use of TM-HEO as anode material in coin-type and pouch-type full cells. The cells were found to provide an initial specific discharge capacity of 446 mAh/g, which was maintained at 300 and 256 mAh/g after 50 and 100 cycles, respectively.⁵

(1) Qian, Y.; Niehoff, P.; Zhou, D.; Adam, R.; Mikhailova, D.; Pyschik, M.; Börner, M.; Klöpsch, R.; Rafaja, D.; Schumacher, G.; Ehrenberg H.; Winter M.; Schappacher F. J. Mater. Chem. A 2017, 5, 6556–6568.
(2) Sarkar, A.; Velasco, L.; Wang, D.; Wang, Q.; Talasila, G.; de Biasi, L.; Kübel, C.; Brezesinski, T.; Bhattacharya, S. S.; Hahn, H.; Breitung B. Nat. Commun. 2018, 9, 3400.
(3) Sarkar, A.; Wang, Q.; Schiele, A.; Chellali, M. R.; Bhattacharya, S. S.; Wang, D.; Brezesinski, T.; Hahn, H.; Velasco, L.; Breitung, B. Adv. Mater. 2019, 31, 1806236.
(4) Breitung, B.; Wang, Q.; Schiele, A.; Tripković, D.; Sarkar, A.; Velasco, L.; Wang, D.; Bhattacharya, S. S.; Hahn, H.; Brezesinski, T. Batter. Supercaps 2020, 3, 1–10.
(5) Wang, Q.; Sarkar, A.; Li, Z.; Lu, Y.; Velasco, L.; Bhattacharya, S. S.; Brezesinski, T.; Hahn, H.; Breitung, B. Electrochem. commun. 2019, 100, 121–125.

Face-centered cubic (fcc) high-entropy alloys (HEAs) can display exceptional combinations of strength, tensile ductility and fracture toughness, properties that can be further enhanced at cryogenic temperatures. Body-centered cubic (bcc) refractory HEAs, conversely, can display exceptional strength and compressive ductility at elevated temperatures, but are often compromised by poor lower-temperature behavior. We examine here the damage-tolerance of these two classes of multiple principal-element alloys, and show that whereas some of the fcc HEAs exhibit the highest fracture toughness on record, the bcc HEAs can display extremely low toughness (and ductility) when subject to tensile loading. We further examine the role of short-range order (SRO) in these two alloy classes, theoretically using DFT-based Monte-Carlo and Molecular Dynamics simulations and experimentally using energy-filtered TEM and 4D-STEM techniques. Whereas atomistic simulations predict the existence of SRO in fcc and bcc HEAs, together with its influence on plastic deformation behavior, e.g., slip behavior, dislocation mobility, etc., direct experimental evidence is difficult. We believe that we have unequivocal evidence for SRO in fcc HEAs, with an understanding of the role of magnetically-driven ordering in CrCoNi-based systems; studies for the bcc systems, however, are still in process. Our emphasis now is on defining the mechanistic role and quantitative effect on mechanical properties, with respect to how SRO can affect the strength, strain-hardening, ductility and toughness.

Due to their multi-component nature, preferential chemical ordering, which is otherwise known as short-range order, has been proposed in various concentrated alloys. Short-range order can be caused by various origins such as magnetic frustration, strong electronic interaction, and the formation of complexes with interstitial elements. Here we present a first systematic study of the methods to control the degree of SROs and the resultant mechanical properties in 3d transition metal-based complex concentrated alloys (3d CCAs). Theory-based proposals for the effects of short-range order will be discussed via the in-situ deformation studies using various scanning electron microscopy techniques. Our findings call for revisiting the classical understanding of the deformation behavior of 3d CCAs taking into account chemically ordered configuration effects.

Traditionally, alloying has involved the addition of relatively small concentrations of foreign elements to a base metal. In recent years, there has been a paradigmatic shift in alloying wherein three or more elements are mixed in near equal fraction to obtain multi-principal element (MPE) alloys. The inclusion of many elements increases the mixing entropy and results in the stabilization of solid solutions and has been shown to improve mechanical and electrochemical properties. This approach has also been extended beyond pure metallic alloys to solid solutions of oxides and carbides with multiple cations. While the combinatorics of cation choice result in large phase spaces of possible MPE alloys, entropic stabilization is limited by its ability to overcome positive mixing enthalpies, i.e., not all MPE alloys will have single phase solid solutions at reasonable synthesis temperatures. A computational model that can predict the stability of MPE alloys based on a limited set of first-principles calculations would be an invaluable tool for rapid screening of promising candidates for subsequent synthesis and characterization. Here, we present a method for calculating the equilibrium phase diagram of N-component MPE alloys. This method combines the mixing enthalpy of equimolar components calculated using density-functional theory with a modified Miedema scheme [1,2] to predict temperatures above which a single-phase solid solution can be stabilized. A functional form for the mixing enthalpy is determined by fitting a (N−1)-dimensional polynomial to the equimolar mixing enthalpies of an N-component MPE alloy and the (N−1)-, … , 2-component alloys of the constituent compounds. By including a contribution from the configurational entropy, (N−1)-dimensional Gibbs free energy surfaces are generated and used to construct phase diagrams. In addition to providing miscibility temperatures for solid solutions, our method can identify regions of metastability and can be used to predict the stability of near-equimolar alloys. Where applicable, stable ordered alloys are also included in our analysis. Results for MPE alloys of refractory metals, oxides, carbides, and transition metal dichalcogenides will be discussed.

Acknowledgments: This work was funded by NSF DMREF-1729787.

1. Boer FR, Perrifor DG, editors. Cohesion in metals. Amsterdam: Elsevier; 1988.
2. Bakker H. In: Enthalpies in alloys, materials science foundations, vol. 1. Netherlands: Trans Tech Publications; 1998. p. 1-78.

We present a bilinear log model for modeling and predicting the temperature-dependent strength properties of high-entropy alloys (HEAs). We have applied the model to prediction of the ultimate strength of HEAs and evaluated its effectiveness for 21 compositions. We model the logarithm of the yield or ultimate strength vs. temperature in terms of two linear regimes, a low-temperature and a high-temperature regime with a break temperature, T_break, in between. We present a global optimization approach for simultaneously optimizing the parameters of the bilinear model over the low-temperature and high-temperature regimes and for accurately estimating T_break. We consider the break temperature an important parameter for the design of materials with attractive high-temperature properties, one warranting inclusion in alloy specifications. For reliable operation, the operating temperature for the corresponding alloys may need to stay below T_break. Previous models for the temperature dependence of the yield strength of alloys only accounted for a single exponential. Hence, there was no break temperature.
The bilinear log model is founded on physical interpretations provided in a 2019 Acta Materialia paper by Senkov, Gorsse and Miracle titled “High Temperature Strength of Refractory Complex Concentrated Alloys”. Here, the authors show that, once above T_break, materials lose strengths rapidly due to rapid diffusion leading to easy dislocation motion and dissolution of strengthening phases (if any). According to Senkov et al., the diffusion processes required to initiate phase transformations generally become noticeable at temperatures T > 0.4 T_m, where T_m represents the melting temperature, while at T < 0.4 T_m the phase transformations are kinetically restricted. In case of the low-temperature regime, atoms cannot move out of the lattice, and no phase transformations can take place. This is the case for low-entropy alloys (LEAs), medium-entropy alloys (MEAs), and HEAs, and serves to explain the two exponentials. A solid-solution strengthening model by Rao et al. does not take into account diffusion effects and agrees well with the experimental data only at relatively low temperatures, where diffusion-controlling deformation mechanisms can be ignored. Then, as the temperature increases, the chemical bonds between the elements become softer. The diffusion-controlled regime generally occurs above ~ 0.5 - 0.6 T_m. It can be distinguished from the low-temperature regime by a more rapid drop in strength with increasing temperature, because dislocations are able to move more easily around obstacles.
We then investigate the suitability of our bilinear regression model to commercial alloys, including Ni-based superalloys. Anomalous yield stress behavior is common among superalloys strengthened by L12 order intermetallics. We analyze suitability of our bilinear model for predicting the yield strength of commercial alloys, with or without evidence of the anomalous yield stress phenomenon. We compare and contrast our observations with the physical interpretations of Senkov et al., per the 2019 paper in Acta Materialia.

Much of the outstanding mechanical behavior of High Entropy Alloys (HEAs) in monotonic loading and in fatigue can be attributed to its propensity to strain-harden under large deformation. Such strain-hardening fundamentally arises from interactions between dislocations and twin boundaries. Recent work from our group has shown the role of such slip-twin (also twin-twin) interactions in increasing strain-hardening rates (M. Bönisch, Y. Wu, H. Sehitoglu, Acta Materialia 153 (2018) 391-403), decelerating fatigue-crack growth, their dependence on crystallographic orientation with respect to load (R. Sidharth, W. Abuzaid, H. Sehitoglu, Intermetallics 126 (2020) 106919), and a strong correlation with Burgers vector residuals of slip-twin (or twin-twin) interactions. Although such interactions have been a subject of intensive study via Molecular Dynamics and Dislocation-Dynamics methods, the methods employed are not truly predictive as they rely on some form of empiricism. Tapping the full potential of strain-hardening from High-Entropy Alloys requires an ab-initio understanding of these interactions, one that does not involve any empiricism, captures the orientation-dependence and roots the critical stresses of these interactions in fundamental fault energy parameters such as those parametrizing the Stacking-Fault Energy (SFE) landscape (e.g. intrinsic SFE, unstable SFE). We develop such a predictive framework for Dislocation-Twin-Boundary (D-TB) interactions within Generalized Peierls-Nabarro theory, predicting the critical stress for several dislocation reactions on twin boundaries. From a scientific standpoint, there has been a longstanding knowledge-gap in understanding core-structures of sessile dislocations such as stair-rods on twin boundaries. This gap has been the primary obstacle to modeling such dislocation reactions. We propose a core-structure for such dislocations, illustrating their evolution during their reaction and linking the changing core-width to the observed interaction stresses. The proposed framework establishes the dependence of the critical stresses on fundamental energy barriers of the crystal structure namely the intrinsic SFE, the unstable SFE and the unstable twinning energy. The physical fidelity of the model is validated by comparing against recent experimental data on HEAs showing good agreement, particularly in explaining the orientation-dependent behavior. By applying the model on several FCC materials and preparing Ashby-like plots we explain the reason behind such unseen strain hardening behavior of HEAs to be their critical stresses of D-TB interaction, finding them to be considerably higher than conventional FCC metals and alloys. We forward this predictive framework as a useful tool in designing HEA compositions and polycrystalline textures tailored to push boundaries of strength and toughness.

High entropy materials have shown superior mechanical performances owing to the unique random mixing structure with multielement solid solution strengthening and stabilization. When scale down to nanometers, high entropy nanomaterials are promising for functional applications such as catalysis due to the exposed reactive surfaces. Particularly, the multielement mixing enables continuously tunable surfaces and properties while the high entropy structure provides the critical stability for using in harsh reactive conditions. However, in considering the large multielement compositional space and complex structures, the general synthesis of uniform mixing structure and the rapid screening of high entropy nanomaterials are still extremely challenging.
In this report, we introduce the enabling and controllable thermal shock synthesis of high entropy nanomaterials (including alloys, oxides, and others) and their specific formation guidelines. In addition, the promising of high entropy nanomaterials as highly active and stable catalysts were demonstrated for both thermochemical and electrochemical reactions. Finally, combined with computational guide and high throughput screening, we briefly layout a potential way for accelerated discovery in the rarely explored multidimensional space.

The study explores the boro-carbothermal reduction synthesis of high entropy transition metal diborides via microwave plasma. High entropy diborides are promising materials due to ultra-hardness and resistance to high-temperature oxidation. The use of microwave plasma is a novel approach for high entropy diboride formation that capitalizes on its ability to transfer thermal energy to chemical reactions produced via the low-temperature plasma. Aiming to produce a five-component equimolar diboride, the starting powders consist of metal oxides (HfO₂, TiO₂, ZrO₂, Ta₂O₅, MoO₃) with carbon black blended by high energy ball mill, then combined with boron carbide. By annealing the sample using microwave plasma, both boro-carbothermal reduction and a single-phase high entropy diboride (Hf_0.2, Zr_0.2, Ti_0.2, Ta_0.2, Mo_0.2)B₂ were achieved in a single step.

Metal oxides are promising materials for energy storage applications. For instance, disordered rocksalt types of metal oxides are promising Li-ion battery cathodes. Such materials are always made as a solid solution, in which short-range order (SRO) usually occurs and plays a crucial role on the Li transport properties. In this work, we developed a modeling suite that combines first-principles calculations, cluster expansion Monte Carlo simulations, electron diffraction prediction and Li percolation analyses to understand the evolution of Li transport properties with the increasing entropy. The impact of entropy on transport properties is evaluated from two types of compositional design: 1) Adding more species (such as F) into the anion site while maintaining three or four species on the cation sites; and 2) adding more than seven species on the cation sites. It has been found that the engineering of entropy on an anion site (O site) will lead to diverse evolution of transport properties, which is determined by how cations are mixed. On the other hand, once more than seven species are introduced to the cation site, the SRO generally evolves to be more favorable for Li transport. As a result, our findings lead to two routes of improving Li transport properties. For both directions of compositional engineering, we validated our theoretical predictions with experiments, which also lead to the discovery of new Li cathode materials with much higher capacities and rate capability than other state-of-the-art cathode materials. With the understanding of entropic effect on ionic transport, we hope to provide broader insights into understanding and exploring novel high entropy ceramic materials with extraordinary properties.

High entropy oxides (HEO) are single phase oxides that combine traditionally immiscible metal cations through the increase of configurational entropy, by incorporating five or more cations. In some ways, this mimics a material’s natural tendency to stabilize surfaces by the introduction of point defects to increase configurational possibilities of atoms. Using this concept, we demonstrate that a HEO can be designed with vacancies as an integral component of its structure. In this manner, we design structures with atomic porosities to yield a significantly vacant final product. For this, we utilize conventional alumina as a base, and through solid-state diffusion, induce sub-stoicheometric formations and vacancies as cations are introduced on its surface. The final product, a heterostructure, demonstrates a defined interface and unique vacancies sites that do not exist in conventional alumina-based structures, whether perovskites or spinel, and affords us to design catalytic active sites for tailored reactions. As a demonstration of the utility of this approach, we use the CO oxidation reaction as exemplar. In this case, the designed atomic porosities/vacancies engender oxidation pathways through the Mars Van Krevelen mechanism, which conventionally do not exist in alumina supports. In this manner, we demonstrate the catalytic potential of a highly engineered HEO, yielding a catalyst with performance that rivals the best state-of-the art single atom ceria-based catalysts.

This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government.

High entropy perovskite oxides (HEPOs) with A-, B-, or both-site mixing are promising redox materials to enable solar thermochemical hydrogen (STCH) generations with the improved efficiency, stability, and kinetics. In the STCH process, hydrogen is generated through a two-step cycle, where oxygen vacancies are created at high temperature and filled at low temperature by splitting water and releasing hydrogen. The efficiency of hydrogen production via the STCH process is, therefore, controlled by the difference between oxygen vacancy concentrations (δ) at the two steps, Δδ. We hypothesized the HEPOs can allow more oxygen vacancies (V_O) without a phase transition. Thus, a thorough study on the oxygen vacancy formation in the HEPOs is needed.

In this study, we combined density functional theory (DFT) calculations with statistical thermodynamics to investigate the oxygen vacancy formation and interactions in the randomly mixed systems {A}{B}O_3-δ. This method enabled us to investigate the effects of multi-ions mixing in {A}{B}O_3-δ and to calculate the oxygen vacancy concentrations (δ) and the difference in δ at two stages (Δδ). The δ and Δδ are governed by the chemical potential of oxygen which varies with experimental conditions such as dry, wet, or ideal conditions. We analyzed a set of A-site elements, {Ba, Sr, La, Y, Gd, Nd, Pr, Sm}, and that of B-site elements, {Al, Ga, Mn, Fe, Ni, Co}, in {A}{B}O_3-δ. We further compared the predicted vacancy concentration δ and Δδ with experimental observations in different STCH cycles. The atomistic insight, such as the oxygen formation energy was more sensitive to the charge of the {A} site ion, can be used to guide the design of new HEPO compositions with the improved properties for the STCH production.

The solid-state magnetic refrigeration technique is the convincing alternative reversible technique to replace the conventional gas compression refrigeration method based on the Magnetocaloric effect (MCE). The MCE is the intrinsic property of the magnetic materials. Rare earth (RE) iron garnets are complex ceramic oxides, having the chemical formula A₃B₂C₃O₁₂, (where A = RE³⁺ ion, B and C = Fe³⁺ ions) is suitable for MCE for low temperature. The garnet structure contains three different crystallographic sites, namely, dodecahedral (c), octahedral (a), and tetrahedral (d) site. The magnetic properties in rare-earth garnets arise from the antiferromagnetic exchange interactions of these sites. In Gd₃Fe₅O₁₂, two sublattices of ferric ions couple antiferromagnetically via the superexchange interaction through oxygen anions. The formula unit consists of three Fe³⁺ cations on tetrahedral sites and two Fe³⁺ cations on octahedral sites. The Gd³⁺ ions are also antiferromagnetically coupled to the net moment of the Fe³⁺ ions. Since the Gd³⁺ ions are disordered at room temperature and ordered at low temperature, the moment of Fe³⁺ ions are governed at high temperature, and Gd³⁺ dominates at low temperature. In this temperature range, interactions between neighboring spins and magnetic frustration result in finite entropy. In the present study, Al is doped in Gd₃Fe_5-xAl_xO₁₂ to investigate crystal structure and magnetic properties, including the magnetocaloric effect. Gd₃Fe_5-xAl_xO₁₂; x = 0.0, 0.25, 0.50 and 1.0 samples were synthesized via autocombution method and heat-treated in air at 1100^OC for 12 h. The phase identification and lattice parameter of the powders performed using x-ray diffraction show the presence of high-crystalline single phases garnet (JCPDS-48-0077). With Al³⁺ doping, a gradual shift in the peaks to the left as compared to pure garnet is observed that showed a decrease in lattice parameters from 12.50A to 12.44A due to smaller ionic radii of Al³⁺ ion (0.535 A) replacing Fe³⁺ ions (0.645 A). Magnetic measurements were performed using SQUID magnetometer. Temperature dependence of the zero-field-cooled (ZFC) curve exhibits transition temperature at ∼50 K that is associated with glass transitions. Noticeably, there is a sharp decrease in the FC magnetization below ∼120 K, which coincides with the magnetic ordering temperature of the Gd sub-lattice. Saturation magnetization increased gradually with x content and reached an optimum value 43 emu/g for x=0.5 from 18 emu/g for x = 0.0 and followed by a decrease with x content at 5K. Observed enhanced magnetization for x = 0.5 is due to the optimal distance between Fe⁺³ ions, thus enhancing pair exchange interaction. To evaluate the MCE of the samples, the magnetization isothermal curves were collected at different fixed temperatures ranging from 10 to 250 K and in the field range between 1-3T. The magnetic entropy change(ΔS_M⁾ as a function of the temperature curve shows a broad peak for x = 0.0. The peak position is shifted towards lower temperatures as x increases. This trend is consistent with our observation that the maximum magnetic entropy change (ΔS_M^Max) of the x=0.50 sample at 40K increases abruptly with an applied magnetic field of 3T. The increase in ΔS_M is mainly due to superexchange interaction between Fe–Fe ions and particle size. Arrot plots showed the positive slope of the curve, indicating a second-order phase transition in Al-doped nanoparticles. Cooling efficiency can be calculated from the peak position of ΔS_M^Max called relative cooling power(RCP). RCP values of our nanoparticle samples lie between 5 and 90 Jkg^-1, with 90 Jkg^-1 being the maximum for x = 0.50. These results make our compounds promising materials for magnetic refrigeration technology. Our study suggests that up to a certain level of non-magnetic atom doping, enhancement in MCE is possible. Thus, the proposed compound is cost-effective in terms of reducing the expensive rare-earth element.

Rare earth(RE) iron garnets are complex ceramic oxides, having interesting magnetocaloric properties. The garnet structure contains three different crystallographic sites that hold a wide variety of cations. The magnetic properties in rare-earth garnets arise from the antiferromagnetic exchange interactions. In Gd₃Fe₅O₁₂, two sublattices of ferric ions couple antiferromagnetically via the superexchange interaction through oxygen anions. The formula unit consists of three Fe³⁺ cations on tetrahedral sites and two Fe³⁺ cations on octahedral sites. The Gd³⁺ ions are also antiferromagnetically coupled to the net moment of the Fe³⁺ ions, but this coupling is weaker than that between Fe³⁺ ions. Since the Gd³⁺ ions are disordered at room temperature, the ferrimagnetic properties of the material at high temperatures are governed by the moments of the Fe³⁺ ions. At low temperature, however, the Gd³⁺ lattice becomes ordered and dominates the magnetic properties of the material due to the larger magnetic moment of Gd compared with that of Fe ions. In this temperature range, despite interactions between neighboring spins, magnetic frustration due to the geometric configuration results in a disordered cooperative paramagnetic state with finite entropy. Besides structure, MCE also depends on morphology and defects. The present study investigates MCE in rare-earth-doped Gd_3-xRE_xFe₅O₁₂ where Gd ion is replaced by RE=Dy, Sm, and Nd. Doped Gd_3-xRE_xFe₅O₁₂ samples were synthesized via autocombution method and heat-treated in the air at 1100^OC for 12 h. The influence of replacing Gd³⁺ ions by rare-earth ions (RE3+) ions on the structural, morphology, magnetic, and magnetocaloric properties have been investigated using X-ray diffraction, scanning electron microscopy, and SQUID. The diffraction patterns showed the garnet structure (JCPDS-48-0077) of the cubic group Ia3d with the absence of any impurity phases. The lattice parameter of the powders calculated from the XRD pattern. The analysis of the XRD data confirmed that all compositions are single phase with garnet structure. The Dy doped garnet showed a decrease while Sm and Nd-doped garnet showed an increase in lattice volume. This systemic changes in the lattice volume are the result of the difference in ionic radii of RE ions. The temperature-dependent magnetization of the as-prepared pure phase RE doped samples was measured with field and zero-field cooling(FC and ZFC). Dy doped garnet had transition temperature at 90K, whereas Nd and Sm doped samples showed similar transition temperature with pure garnet. All RE3+ doped samples showed paramagnetic behavior at RT and antiferromagnetic behavior at 5K. The isothermal magnetic entropy changes (ΔS_M) calculated by using Maxwell equation from the isothermal magnetization curves that were collected at different fixed temperatures ranging from 10 to 250 K. -ΔS_M as a function of temperature curve shows a broad peak for x = 0.00. The peak position is independent with applied fields for the same material, whereas the peak shifted as RE³⁺ doped. ΔS_M increased with Dy³⁺ increases, whereas Nd³⁺ showed decreases with x content. For Sm³⁺, x = 0.25 has maximum ΔS_M. This trend is consistent with our observation that the maximum magnetic entropy change (ΔS_M^Max) of the Sm³⁺ (x=0.25) sample at 40K increases abruptly with the applied magnetic field of 3T. The variation in ΔS_M^Max is mainly due to super-exchange interaction between Fe – Fe ions. By doping Dy³⁺, the distance between Fe³⁺ – Fe²⁺ ions decreases, so the exchange interactions and the super-exchange interaction become strong, resulting in the enhance of . Moreover, increased ~ 23% for Dy³⁺ x=0.75 sample and ~ 73% for Sm³⁺ x = 0.25 sample. These values are relatively high and comparable to some noticeable magnetocaloric material. Thus, based on these results, our samples are promising materials for magnetic refrigeration technology.

Microstructural evolution of dynamically recrystallized (DRX) grains and grain boundary sliding (GBS) in the heterogeneous necklace structure of HfNbTaTiZr refractory high entropy alloy (RHEA) was studied systematically during high temperature deformation. Uniaxial compression testing was carried out to different strains at 1000 °C and a strain rate 10⁻³ s⁻¹ . Significant bulging of grain boundaries led initially to the formation of DRX grains. The fraction of DRX grains increased with strain, and typical necklace structures of fine ( d ≤ 1.5 μm) DRX grains formed at strain ε≥ 0.3. The DRX grains showed limited grain growth, and heterogeneous microstructures composed of coarse unrecrystallized regions surrounded by the characteristic DRX necklace structure were formed at larger strains. Interrupted testing with marker grids revealed that DRX grains deformed by a GBS mechanism. The DRX necklace regions connected mesoscopically and also displayed diamond network morphologies, with unique “Y-shaped”, “T-shaped”and “X-shaped” junctions. The formation of different types of junctions were rationalized on the basis of GBS accommodated by local dislocation slip in unrecrystallized regions. The unrecrystallized regions showed preferred <001> / <111> micro-textures, consistent with conventional dislocation slip in the BCC crystals. On the other hand, the newly formed DRX grains initially had similar orientations to those of the parent grains, but they displayed a random texture with increasing strain, as expected from GBS. The randomized texture of DRX grains and the stability of DRX grains size represented GBS in the DRX necklace regions.

Element redistributions after initial oxidation of a Ni₃₈Cr₂₂Fe₂₀Mn₁₀Co₁₀ (at.%) multi-principle element alloy at 120 °C and 300 °C is captured via in situ atom probe tomography. All cations contribute to the oxide in both conditions, consisting of a Cr-rich inner oxide and a Fe, Mn, Co and Ni-rich outer oxide. At lower temperature, Ni tends to be trapped at the outer/inner oxide interface, while Ni enriches at the oxide/metal interface at higher temperature in tandem with Cr metal depletion. These observations confirm oxidation of complex alloys involves the formation of metastable, multi-layered oxide films, with a distinct tendency for solute trapping.

Fatigue failures in engineering structures can cause catastrophic accidents without obvious warning. Thus, a fundamental understanding of cyclic-deformation and fatigue-failure mechanisms is critical for developing fatigue-resistant structural materials. Here we report a ductile multicomponent B2 precipitates-strengthened high-entropy alloy (HEA), which exhibits the outperforming fatigue life, relative to traditional materials, at low strain amplitudes. Its real-time cyclic-deformation mechanisms are revealed by in-situ neutron diffraction, transmission-electron microscopy, crystal-plasticity modeling, and Monte-Carlo simulation. Multiple cyclic-deformation mechanisms, including dislocation slips, multicomponent-precipitation strengthening, deformation twinning, and reversible stress-induced martensitic transformation, are observed in the studied HEA. Its excellent fatigue performance is attributed to the outstanding fatigue-crack-initiation resistance, resulting from the high elasticity, plastic deformability, and martensitic transformation of the B2 phase that leads to the effective load redistribution and strain partitioning with the face-centered-cubic (FCC) matrix. Guided by this study, fatigue-resistant alloys strengthened by ductile multicomponent intermetallic phases can be developed.

Recently, various refractory high entropy superalloys, which have unique microstructure containing cuboidal nano-precipitates in BCC high entropy alloy (HEA), reported. They exhibited superior mechanical properties at both ambient and high temperature. However, there are many unsolved issues to attract even greater attention such as precipitation control of unwanted compounds, optimal phase selection between ordered and disordered BCC, and optimization of mechanical properties etc. In the present study, we studied the phase diagram and phase transformations of refractory high entropy superalloy through a bulk combinatorial approach in Ti-Zr-Nb-Ta-Al quaternary HEAs. Microstructural evolution for the non-equiatomic HEA compositions obtained by a bulk combinatorial approach were systematically investigated by considering phase transformation mechanism as well as phase equilibria. This result could provide an effective guideline for tailoring microstructure of HEAs with ordered and disordered BCC phases, and developing a promising high entropy superalloy with customized microstructure for ultra-high temperature structural application.

The lattice distortion is the core effect of HEAs to enhance the strength at room as well as high temperatures. The number of constituent elements with various atomic sizes have the identical possibility to occupy at atom positions of a crystal lattice, which induces a severe distortion of the crystalline lattice. Several studies have attempted to quantitatively measure the lattice distortion with increasing the number of alloying elements, using x-ray diffraction (XRD) and neutron diffraction (ND). However, only limited alloy systems have succeeded to demonstrate the correlation between lattice distortion and mechanical properties. In this study, we have systematically investigated the evolution of lattice distortions for Nb-Ta-Ti-V-Zr systems as function of number of additional elements and its effect on mechanical properties, using experimental [atom-probe-tomography (APT at CNMS), transmission-electron microscopy (TEM)] and modeling methods [density-functional-theory (DFT)]. It is found that lattice distortions have a critical role in improving yield strength.

Recently, BCC high entropy alloys (HEAs) composed by Group-4 to Group-6 elements were reported to exhibit superior mechanical properties up to high temperature above 1273 K comparing conventional Ni-based superalloy. However, RHEAs is their industrial application is limited due to the high melting point and poor ductility in room temperature. In this study, TiVNbTaW RHEA powder with single BCC phase was prepared by high-energy ball milling and the fabricated powder were sintered using spark plasma sintering. Sintered TiVNbTaW high entropy alloy exhibited TRIPLEX nanostructure consisting of (Nb,Ta)-rich BCC, W-rich BCC and TiO FCC phase, which was formed during the sintering process by decomposition of single BCC phase in as-milled powder. Microstructural evolution of TRIPLEX nanostructure was analyzed in terms of metastable thermodynamic equilibrium related with segregation of solutes and diffusion kinetics in a complex multi-principle system. This result could provide an effective guideline for tailoring the nanostructure of RHEAs fabricated by powder metallurgy.

Due to its high melting point, low deuterium/tritium retention, high thermal conductivity and so on, Refractory metals including tungsten(W) has been recognized as the most promising candidate of plasma facing materials (PFMs) for fusion reactors. Moreover, Refractor high entropy alloys (RHEA) is known to exhibit higher strength and thermal conductivity at elevated temperatures than W alloys due to solid solution strengthening as well as high resistivity against neutron irradiation damage.
Meanwhile, copper(Cu) based alloys have been proposed as the heat sink materials behind the plasma facing material due to its excellent thermo-mechanical properties. The joining of W to copper based heat-sink (CuCrZr) remain a main problem in the development of plasma facing component (PFC) due to the large difference in the coefficient of thermal expansion (CTE) between these two materials.
In this research, therefore, we fabricated composites of R-HEA and Cu by liquid metal dealloying (LMD) process. To utilize this technique, we prepared a precursor material which contains elements having positive and negative enthalpy of mixing with Cu simultaneously, and we immersed it into high-temperature liquid copper to form bi-continuous composite material. Finally, we analyze strength and thermal conductivity of the composite systematically. This work will give a guide line for designing PFMs with improved properties.

The plastic deformation behavior of single crystals of the FCC equatomic and non-equiatomic high-entropy alloys of the Cr-Mn-Fe-Co-Ni system has been investigated in a temperature range of 10-1273 K both in tension and compression. Deformation occurs via slip of the {111}<110> system exclusively in the whole temperature range for all alloys investigated. The CRSS values increase with decreasing temperature, especially below room temperature, so that the concept of ‘stress equivalence’ is obeyed. This is a clear indication that the strength of these alloys should be described by a mechanism based on solid-solution hardening. The CRSS values at 10 K seems to be well scaled by the mean-square atomic displacement from the regular FCC lattice points (calculated based on density-functional theory). Deformation twinning occurs in later stages of deformation at low temperatures below room temperature in many of these alloys. The correlation between twinning stress and the stacking-fault energy will be discussed.

Since high entropy alloy (HEA) is constituted with multi-principal elements, it can be understood in a very severe condition of solid solution strengthening (SSS). In particular, the local atomic clusters (LAC), sub-nano scale atomic structure, can be easily formed in HEAs by having preferential bonding among specific elements with thermodynamic stability. Understandably, the LACs can drive HEAs to extreme condition of SSS. Moreover, some former researches have reported that this structure can also affect on the bulk properties of HEAs, such as stacking fault energy (SFE) and so on.
In the present study, we systematically evaluate the influence of LAC formation on the degree of SSS in various CrMnFeCoNi HEAs. The LAC formation was carefully controlled by solidification history intensive structural analysis including APT, EXAFS and so on. Finally, this work will establish a tuning recipe for SSS in HEAs, which uses the sub-nano scale structural information.

Like elements choose to gather together and tend to form chemical short-range ordering in compositionally complex alloys, i.e., high-entropy alloys. The role of chemical short-range ordering in plastic deformation of a CoCrFeNiPd alloy has been studied using in-situ neutron diffraction and small-angle neutron scattering. The FCC single-phase CoCrFeNiPd alloys show much more substantial nanaoscale heterogeneity than CoCrFeNiMn Cantor alloy, indicating the existence of pronounced chemical short-range order. Moreover, lattice strain analysis reveals that the stacking fault probability is much higher in CoCrFeNiPd alloy than that of Cantor alloy due to the increase of stacking falt energy by chemical short-range ordering. Analysis of diffraction and microscopy data confirms that dislocations interations and propagations, rather than stacking faults or twinning, play an essential role at the early stage of plastic deformation in CoCrFeNiPd, leading to higher yield strength without compromising strain hardening and tensile ductility than those in Cantor alloy.

In-situ synchrotron high-energy X-ray diffraction and small-angle neutron scattering have been employed to study the kinetics of static structure and magnetic structure evolution in a high-entropy Fe-Er-Ho-Tm-Y-Dy-Nb-B metallic glass with an anomalous exothermic phenomenon upon heating. Our experimental evidence reveals that the high-entropy glassy alloy of a calorimetric anomaly would undergo a liquid-liquid phase transition accompanied by structure changes on medium-range ordering in the supercooled liquid region. Moreover, there is an increase of magnetic correlation length with the enhanced connectivity of medium-range ordering, resulting in the higher saturation magnetization for the sample after the liquid-liquid phase transition. Our results may help build a correlation between the medium-range order and the magnetic structures in soft-magnetic high-entropy metallic glasses.

High- and medium-entropy alloys are presumed to form a stable single phase of a random solid solution due to the high configurational entropy and are reported to have novel mechanical properties where they hold decent combinations of strength and toughness even under extreme conditions. One of the critical factors in designing HEA and MEA is to ensure stability of the solid solution, which typically is metastable unless the heat treatment temperature is sufficiently high to ignore the enthalpy term. Therefore, solid solution of HEA or MEA cannot be designed based on entropy alone, but the extent of enthalpy affecting solid solution stability should also be considered. In addition, atomic interactions affecting the short-range order and stacking fault energy can largely affect the expected mechanical properties. In this study, non-equiatomic NiCoCr HEA alloy is chosen to study the effect of composition on the mechanical properties using combinatorial high throughput method. Thin film composition library was fabricated via co-sputtering at different processing temperatures. Chemical mapping of the composition library indicated formation of NiCoCr with composition range of Ni varies from 18 to 51 at.%, Co from 19 to 59 at.%, Cr from 20 to 56 at.%, and x-ray diffraction was performed to analyze the phases. Measurement of Young’s modulus and hardness was performed using nanoindentation methods, where thin film model was used to accurately determine the mechanical properties of the NiCoCr thin film by removing substrate effects. This study is first to report a high throughput method involving a thin film combinatorial method in studying the effect of composition of NiCoCr on the mechanical properties via nanoindentation.

While refractory high-entropy alloys (HEAs) exhibit exceptional mechanical properties, insights into the underlying microstructures are limited—experimental data appear scarce relative to the vast composition space. Here, we present a high-throughput first-principles study of Mo-V-Nb-Ti-Zr, a refractory HEA known for its high-temperature strength and biomechanical compatibility. Using cluster expansion and Monte-Carlo simulations, we compute the temperature dependence of the microstructures across the whole composition space. We demonstrate that as the high-temperature solid solution cools, Zr preferably segregates from Mo and V (rather than from Nb and Ti), leading to secondary phases that are enriched in Zr with randomly dispersed Nb and Ti. Across compositions, the segregation is more pronounced for a higher segregation T_c, which increases with higher Mo and V contents. We elucidate the origins of the phase separation and elemental distribution via tracing the short-range ordering tendency of the different elemental pairs. Not only do our results reproduce numerous sets of experimental observations within a consistent framework, they also provide predictions for much of the compositional space lacking experimental data. Finally, using the segregation T_c, we discuss the phase stability of solid solutions and identify compositions for which solid solution formation is prohibited. Our work provides the much needed insights into the HEA's microstructures, guiding future experiments in the design of HEAs with superior mechanical properties.

High Entropy Alloys (HEA) form a fascinating class of materials with various technological applications arising from their interesting properties. Due to the complex nature of these systems, a detailed and reliable exposition of nanoscale structure-property correlations via full atomistic simulations is a considerable challenge.
In this work, we generate robust parametrized Embedded Atom Method (EAM) potentials and critically compare it with a generalized Machine Learning-based Moment Tensor potential for predictions of mechanical properties in the Fe-Ni-Co-Cr-Cu alloy system. These potentials are fit to results from detailed ab inito Molecular Dynamics (AIMD) simulations yielding energies, stresses and atomic positions under various conditions (varying temperature, strains and defects), with the advantage of using the same DFT training set for both the classical EAM potential, and the Machine Learning Interatomic Potential. Model structures in training include constituent unaries, equiatomic binaries and ternaries and a few non-equiatomic compositions of the quinary alloy. We show that although the EAM potential for the alloy is able to capture the static structural properties and near-equilibrium dynamic properties well, the MTP potential with active learning of the potential resulting from on-the-fly calculations of atomic trajectories, yields superior results even for far-from-equilibrium dynamic conditions such as high-strain rate tension and compression. This modeling protocol serves as a high-fidelity approach for large-scale atomistic simulations of structure-property correlations in HEAs.

Deformability of high entropy alloys (HEAs) has been shown to strongly depend on their stacking fault energy (SFE). Reducing the SFE of HEAs can lead to enhanced twin susceptibility, which can ultimately lead to improved deformability of the alloys. CoCrFeMnNi shows good deformability at room temperature, which is attributed to low SFE. We observe that SFE of CoCrFeMnNi is lower than SFE of each of its constituent elements. This hints towards a way of lowering the SFE of BCC metals (which are less deformable than FCC alloys), by alloying them to from multi principal component alloys. To predict effect of alloying elements reliably, first-principle density functional theory (DFT) technique is used.

Special quasi-random structure (SQS) supercells are widely used to calculate the SFE of HEAs. Such SQS attempt to mimic random occupancy of each lattice site by constituent elements in the bulk, we call this approach as “bulk-SQS” method. This approach does not guarantee same stoichiometry in each plane as in the bulk, which results in large variation in calculated SFE depending on type and number of atoms in the two planes being sheared.

Here we propose a new “bilayer-SQS (bSQS)” methodology to reliably calculate the SFE of HEAs. Instead of considering the correlation in the entire volume of the supercell, in bSQS method, the correlations are considered only in the two neighboring planes. First, a bilayer, i.e. SQS with 2 planes (in which SFE need to be calculated) is generated with the same chemical composition as the alloy. This bSQS is then repeated 5 times to get 10 slip planes in the supercell. A minimum of 10Å of vacuum is added to prevent the effect of neighboring faults due to the periodic boundary condition.

The bSQS methodology gives the same SFE value irrespective of which slip plane is sheared. We also optimize the minimum number of slip planes and the minimum number of atoms per plane required to reliably calculate the SFE of HEAs. The SFE values are said to be converged when the values from two consecutive atoms per plane supercells are within 1meV/atom (which is typical DFT error). This gives us the minimum number of atoms required in the supercell to get a reliable SFE value. In present work, the bSQS methodology is used to calculate the SFE of {110}<111>, of Ti, Zr, Hf, Nb, Ta, and their equiatomic binaries, ternaries and quaternaries.