A simple fitting approach is used for modeling the compressive yield strength of body centered cubic (bcc) solid solution high entropy alloys in Al-Hf-Nb-Mo-Ta-Ti-V-Zr system. It is proposed that the yield strength could be modeled by a polynomial where the experimental data can be used for finding the polynomial coefficients. The results show that the proposed polynomial could model the yield strength of solid solution alloys relatively well. The developed polynomial is used for predicting the strength of RHEAs in Hf-Mo-Nb-Ta-Ti-V-Zr system. It is observed that the yield strength of alloys within this system increases with the additions of Mo and Zr and decreases with the addition of Ti. Furthermore, the model predicts that the yield strength increases with increasing the value of parameters valence electron concentration (VEC) and atomic size difference (ASD). Although the developed polynomial does not consider the mechanisms involved in the strengthening of alloys, it can be considered as a straightforward method for assessing the strength of solid solution RHEAs.
We report on the production and characterization of a high-entropy alloy in the refractory Zr-Nb-Ti-V-Hf system. Equiatomic ingots were produced by arc and levitation melting, and were subsequently homogenized by high-temperature annealing. We obtained a coarse-grained, single-phase high-entropy alloy, with a homogeneous distribution of the constituting elements. The phase is a chemically disordered solid solution, based on a bcc lattice with a lattice parameter of 0.336(5) nm.
Developing ductile refractory BCC alloys has remained a challenge. The intrinsic ductility (D) of an alloy is the ratio of surface energy ($γ_s$) and unstable stacking fault energy ($γ_{usfe}$). Lowering the valence electron concentration has been shown to improve the intrinsic ductility of refractory alloys. However, Re has been widely used to ductilize W, contrary to the low valency criteria suggested in the literature. Here we use density functional theory to calculate the enthalpy of formation, $γ_{usfe}$ and $γ_s$ of Group IV, V, VI elements and their 25 equiatomic binary alloys in BCC cr…
New approaches for the design of alloy systems with multiprincipal elements is recently researched in refractory materials field. However, most research aimed at arc melting process with weakness of coarsening of grains and inhomogeneous microstructure of segregation of elements during the cooling. This study aims to design and fabricate high-entropy alloy with powder metallurgy. In this study, a refractory high entropy alloys with composition near AlMo0.5NbTa0.5TiZr were produced by powder metallurgy. The alloy consists of two body-centered cubic (BCC) phases. One phase was disordered BCC enr…
Developing a single-phase and nanograined refractory high-entropy alloy ZrHfNbTaW with ultrahigh hardness by phase transformation via high-pressure torsion
From electronic-structure-based thermodynamic linear-response, we establish chemical ordering behavior in complex solid solutions versus how Gibbs' space is traversed -- applying it on prototype refractory A2 Ta-Nb-Mo-W high-entropy alloys. Near ideal stoichiometry, this alloy has anomalous, intricate chemical ordering tendencies, with long-ranged chemical interactions that produce competing short-range order (SRO) with a crossover to spinodal segregation. This atypical SRO arises from canonical band behavior that, with alloying, create features near the Fermi-surface (well-defined even with d…
The fracture properties of as-cast TiVNbTa, a refractory high-entropy alloy (RHEA), were investigated using four-point bending tests from -139C to 20C under a strain-rate of 10-3 s-1. From those tests and fractography, the conditional fracture toughness values and the brittle-to-ductile transition temperature were obtained. The brittle-to-ductile transition temperature was between -47C to -27C, which gives an estimated activation energy value of 0.52+-0.09 eV for the alloy. This study provides a preliminary understanding of the nature of dislocation motion in a relatively ductile RHEA.
Two new, low activation high entropy alloys (HEAs) TiVZrTa and TiVCrTa are studied for use as in-core, structural nuclear materials for in-core nuclear applications. Low-activation is a desirable property for nuclear reactors, in an attempt to reduce the amount of high level radioactive waste upon decommissioning, and for consideration in fusion applications.The alloy TiVNbTa is used as a starting composition to develop two new HEAs; TiVZrTa and TiVCrTa. The new alloys exhibit comparable indentation hardness and modulus, to the TiVNbTa alloy in the as-cast state. After heavy ion implantation t…
Generative deep learning is powering a wave of new innovations in materials design. In this article, we discuss the basic operating principles of these methods and their advantages over rational design through the lens of a case study on refractory high-entropy alloys for ultra-high-temperature applications. We present our computational infrastructure and workflow for the inverse design of new alloys powered by these methods. Our preliminary results show that generative models can learn complex relationships in order to generate novelty on demand, making them a valuable tool for materials info…
EXAFS analysis of pure elements, binary and ternary equiatomic refractory alloys within the Nb-Zr-Ti-Hf-Ta system is performed at the Nb and Zr K-edges to analyze the evolution of the chemical local environment and the lattice distortion. A good mixing of the elements is found at the atomic scale. For some compounds, a distribution of distances between the central atom and its neighbors suggests a distortion of the structure. Finally, analysis of the Debye-Waller parameters show some correlation with the lattice distortion parameter $δ^2$, and allows to quantify experimentally the static disor…
Nickel-based superalloys and near-equiatomic high-entropy alloys containing Molybdenum are known for higher temperature strength and corrosion resistance. Yet, complex solid-solution alloys offer a huge design space to tune for optimal properties at slightly reduced entropy. For refractory Mo-W-Ta-Ti-Zr, we showcase KKR electronic-structure methods via the coherent-potential approximation to identify alloys over 5-dimensional design space with improved mechanical properties and necessary global (formation enthalpy) and local (short-range order) stability. Deformation is modeled with classical …
Energy efficiency is motivating the search for new high-temperature metals. Some new body-centered-cubic random multicomponent "high entropy alloys (HEAs)" based on refractory elements (Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr) possess exceptional strengths at high temperatures but the physical origins of this outstanding behavior are not known. Here we show, using integrated neutron-diffraction (ND), high-resolution transmission electron microscopy (HRTEM), and theory, that the high strength and strength retention of a NbTaVTi alloy and a new high-strength/low-density CrMoNbV alloy are attributable to edge d…
The high entropy alloy containing refractory metals Mo-Nb-Ta-W has a body centered cubic structure, which is not surprising given the complete mutual solubility in BCC solid solutions of all pairs of the constituent elements. However, first principles total energy calculations for the binaries reveal a set of distinct energy minimizing structures implying the likelihood of chemically ordered low temperature phases. We apply a hybrid Monte Carlo and molecular dynamics method to evaluate the temperature-dependent chemical order. At 300K a cesium-chloride ordering emerges between mixed (Nb,Ta) si…
Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Meanwhile, further optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging, which would require systematic predictions of the correlated alloy properties across a vast compositional space. In the present work, we performed first-principles calculations with the special quasi-random structure (SQS) method to predict the unstable stacking fault energy ($γ_{usf}$) of the $(1…
Stacking fault energy (SFE) is an essential parameter for characterizing mechanical properties. However, in high entropy alloys (HEAs), the local chemical environment varies significantly across different stacking fault planes, resulting in a substantial fluctuation of SFE values rather than a unique value, which prohibits the prediction of the local SFE. Herein, we proposed an effective descriptor based on the local concentration ratio near stacking fault to quantitatively predict the local SFE of refractory HEAs. We find that the role of a given element in determining SFE strongly depends on…
In the quest of new materials that can withstand severe irradiation and mechanical extremes for advanced applications (e.g. fission reactors, fusion devices, space applications, etc), design, prediction and control of advanced materials beyond current material designs become a paramount goal. Here, though a combined experimental and simulation methodology, the design of a new nanocrystalline refractory high entropy alloy (RHEA) system is established. Compositions of this alloy, assessed under extreme environments and in situ electron-microscopy, revealed both high mechanical strength and therm…
Enhanced Elevated-Temperature Strength in Refractory Complex Concentrated Alloys via Temperature-Induced Transition from Screw-to-Edge Dislocation Control
University of California, Davis（加州大学戴维斯分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
Refractory high-entropy alloys (RHEAs) are a promising class of alloys that show elevated-temperature yield strengths and have potential to use as high-performance materials in gas turbine engines. However, exploring the vast RHEA compositional space experimentally is challenging, and only a small fraction of this space has been explored to date. The work demonstrates the development of a state-of-the-art machine learning (ML) predictive framework coupled with optimization methods to intelligently explore the vast compositional space and drive the search in a direction that improves high-tempe…
Refractory high entropy alloys containing elements from the Ti, V and Cr columns of the periodic table form body centered cubic (BCC) structures. Elements from the Ti column are noteworthy because they take the BCC structure at high temperature but undergo a shear instability and transform to the hexagonal (HCP) structure at low temperature. We show that the instability of these elements impacts the properties of the HEAs that contain them. In particular, the shear moduli are greatly reduced, causing increased dynamic contributions to lattice distortion. Relatively large size differences betwe…
Determinants of Self-Interstitial Energetics in Refractory High-Entropy Alloys
Key Laboratory of Automobile Materials (Jilin University), Ministry of Education, Department of Materials Science and Engineering, Jilin University（吉林大学汽车材料教育部重点实验室，材料科学与工程学院）
The ability to predict the composition- and temperature-dependent stability of refractory complex concentrated alloys (RCCAs) is vital to the design of high-temperature structural alloys. Here, we present a model based on first-principles calculations to predict the thermodynamic stability of multicomponent equimolar solid solutions in a high-throughput manner and apply it to screen over 20,000 compositions. We develop a database that contains pairwise mixing enthalpy of 17 refractory metals using density-functional theory (DFT)-based total energy calculations. To these, we fit thermodynamic s…
Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while nonlinear elasticity describes the response to finite deformations. It was previously shown that uniaxial strain along [100] drives refractory metals and alloys towards mechanical instabilities. These include an extensional instability, and a symmetry-breaking orthorhombic distortion caused by a Jahn-Teller-Peierls instability that splays the cubic lattice vect…
Whereas exceptional mechanical and radiation performances have been found in the emergent medium- and high-entropy alloys (MEAs and HEAs), the importance of their complex atomic environment, reflecting diversity in atomic size and chemistry, to defect transport has been largely unexplored at the atomic level. Here we adopt a local structure approach based on the atomic pair distribution function measurements in combination with density functional theory calculations to investigate a series of body-centered cubic (BCC) MEAs and HEAs. Our results demonstrate that all alloys exhibit local lattice…
Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a tot…
Cracking the case: fluctuations enhance ductility in refractory alloys
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Laboratory of materials design and simulation (MADES), Institute of Materials, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院材料研究所材料设计与模拟实验室）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院新型材料计算设计与发现国家中心）；EMPA - Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术研究院）；Laboratory for Multiscale Modeling in Mechanics (LAMMM), Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院机械工程学院多尺度力学建模实验室）；School of Engineering, Brown University, Providence, RI 02906 USA（布朗大学工程学院）
Phase diagrams supported by density functional theory methods can be crucial for designing high-entropy alloys that are subset of multi-principal$-$element alloys. We present phase and property analysis of quinary (MoW)$_{x}$Zr$_{y}$(TaTi)$_{1-x-y}$ refractory high-entropy alloys from combined Calculation of Phase Diagram (CALPHAD) and density-functional theory results, supplemented by molecular dynamics simulations. Both CALPHAD and density-functional theory analysis of phase stability indicates a Mo-W-rich region of this quinary has a stable single-phase body-centered-cubic structure. We rep…
University of California, Irvine（加州大学尔湾分校）；University of New Mexico（新墨西哥大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Massachusetts Institute of Technology（麻省理工学院）；University of California, San Diego（加州大学圣地亚哥分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；Stony Brook University（石溪大学）；University of Arizona（亚利桑那大学）；Los Alamos National Lab（洛斯阿拉莫斯国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
In this study Mo-Nb-Ta-W refractory high-entropy alloys (R-HEAs) have been studied for their phase stability for a wide temperature range (100 K to 2000 K). The equilibrium thermodynamic phases are determined by the changes in enthalpy and entropy. The enthalpy changes at any temperature are simulated by embedded atom method (EAM) potential based hybrid Monte Carlo molecular dynamics (MC/MD) simulations. Configurational entropy was calculated by quasichemical method. The EAM potentials were all calculated based on the physical input parameters of elements like atomic volume, cohesive energy, e…
