Solid-state batteries can be built based on thiophosphate electrolytes such as β-Li₃PS₄. For the preparation of these solid electrolytes, various solvent-based routes have been reported. For recycling of end-of-life solid-state batteries based on such thiophosphates, we consider the development of dissolution and recrystallization strategies for the recovery of the model compound β-Li₃PS₄. We show that recrystallization can only be performed in polar, slightly protic solvents such as N-methylformamide (NMF). The recrystallization is comprehensively studied, showing that it proceeds via an intermediate phase with composition Li₃PS₄·2NMF, which is structurally characterized. This phase has a high resistivity for the transport of lithium ions and must be removed in order to obtain a recrystallized product with a conductivity similar to the pristine material. Moreover, the recrystallization from solution results in an increase of the amorphous phase fraction next to crystalline β-Li₃PS₄

Complex concentrated alloys (CCAs) with a face-centered-cubic (FCC) structure exhibit remarkable mechanical properties, introducing the expansion of compositional space in alloy design for structural materials. The formation of a single solid-solution phase is enabled by configuring various 3d-transition elements, while doping other elements even of a small portion generally leads to the formation of brittle intermetallic compounds. Herein, we demonstrate through a systematic investigation of single FCC (CoNi)_100-xMo_x alloys that a wide range of refractory element Mo can simultaneously improve the strength and ductility while sustaining the solid-solution structure. The addition of Mo with a larger atomic size than those of 3d-transition elements introduces severe lattice distortion in the FCC lattice and causes grain-boundary segregation enriched by Mo atoms. In addition, increasing Mo content effectively reduces the stacking fault energy (SFE). The increased lattice distortion with Mo content enhances the solid-solution strengthening of the alloys. Besides, along with reduced SFE and stabilization of the dislocation emission site by grain-boundary segregation, this elevated solid-solution strengthening increases grain-boundary strengthening, reaching a yield strength of ∼1 GPa. Moreover, the reduction of SFE with increasing Mo results in the transition of dislocation substructures and the refinement of deformation twins, allowing for enhanced strain-hardening capability and thus ∼1.3 GPa tensile strength and ∼50% ductility. Such compositive and synergetic effects of refractory element Mo enable the CCAs with a single FCC solid solution to overcome the strength and ductility trade-off.

High- and medium-entropy alloys (HEAs and MEAs) possess high solid-solution strength. Numerous investigations have been conducted on its impact on yield strength, however, there are limited reports regarding the relation between solid-solution strengthening and strain-hardening rate. In addition, no attempt has been made to account for the dislocation-mediated plasticity; most works focused on twinning- or transformation-induced plasticity (TWIP or TRIP). In this work we reveal the role of solid-solution strengthening on the strain-hardening rate via systematically investigating evolutions of deformation structures by controlling the Cr/V ratio in prototypical V_1-xCr_xCoNi alloys. Comparing the TWIP of CrCoNi with the dislocation slip of V_0.4Cr_0.6CoNi, the hardening rate of CrCoNi was superior to slip-band refinements of V_0.4Cr_0.6CoNi due to the dynamic Hall-Petch effect. However, as V content increased further to V_0.7Cr_0.3CoNi and VCoNi, their rate of slip-band refinement in V_0.7Cr_0.3CoNi and VCoNi with high solid-solution strength surpassed that of CrCoNi. Although it is generally accepted in conventional alloys that deformation twinning results in a higher strain-hardening rate than dislocation-mediated plasticity, we observed that the latter can be predominant in the former under an activated huge solid-solution strengthening effect. The high solid-solution strength lowered the cross-slip activation and consequently retarded the dislocation rearrangement rate, i.e., the dynamic recovery. This delay in the hardening rate decrease, therefore, increased the strain-hardening rate, results in an overall higher strain-hardening rate of V-rich alloys.

Physical properties of ten single-phase FCC Cr_xMn₂₀Fe₂₀Co₂₀Ni_40-x high-entropy alloys (HEAs) were investigated for 0 ≤ x ≤ 26 at%. The lattice parameters of these alloys were nearly independent of composition while solidus temperatures increased linearly by ∼30 K as x increased from 0 to 26 at.%. For x ≥ 10 at.%, the alloys are not ferromagnetic between 100 and 673 K and the temperature dependencies of their coefficients of thermal expansion and elastic moduli are independent of composition. Magnetic transitions and associated magnetostriction were detected below ∼200 K and ∼440 K in Cr₅Mn₂₀Fe₂₀Co₂₀Ni₃₅ and Mn₂₀Fe₂₀Co₂₀Ni₄₀, respectively. These composition and temperature dependencies could be qualitatively reproduced by ab initio simulations that took into account a ferrimagnetic ↔ paramagnetic transition. Transmission electron microscopy revealed that plastic deformation occurs initially by the glide of perfect dislocations dissociated into Shockley partials on {111} planes. From their separations, the stacking fault energy (SFE) was determined, which decreases linearly from 69 to 23 mJ·m⁻² as x increases from 14 to 26 at.%. Ab initio simulations were performed to calculate stable and unstable SFEs and estimate the partial separation distances using the Peierls-Nabarro model. While the compositional trends were reasonably well reproduced, the calculated intrinsic SFEs were systematically lower than the experimental ones. Our ab initio simulations show that, individually, atomic relaxations, finite temperatures, and magnetism strongly increase the intrinsic SFE. If these factors can be simultaneously included in future computations, calculated SFEs will likely better match experimentally determined SFEs.

An active learning approach to train machine-learning interatomic potentials (moment tensor potentials) for multicomponent alloys to ab initio data is presented. Employing this approach, the disordered body-centered cubic (bcc) TiZrHfTax system with varying Ta concentration is investigated via molecular dynamics simulations. Our results show a strong interplay between elastic properties and the structural ω phase stability, strongly affecting the mechanical properties. Based on these insights we systematically screen composition space for regimes where elastic constants show little or no temperature dependence (elinvar effect).

Multi-principal element alloys usually exhibit outstanding strength and toughness at cryogenic temperatures, especially in CrMnFeCoNi and CrCoNi alloys. These remarkable cryogenic properties are attributed to the occurrence of deformation twins, and it is envisaged that a reduced stacking fault energy (SFE) transforms the deformation mechanisms into advantageous properties at cryogenic temperatures. A recently reported high-strength VCoNi alloy is expected to exhibit further notable cryogenic properties. However, no attempt has been made to investigate the cryogenic properties in detail as well as the underlying deformation mechanisms. Here, the effects of cryogenic temperature on the tensile and impact properties are investigated, and the underlying mechanisms determining those properties are revealed in terms of the temperature dependence of the yield strength and deformation mechanism. Both the strength and ductility were enhanced at 77 K compared to 298 K, while the Charpy impact toughness gradually decreased with temperature. The planar dislocation glides remained unchanged at 77 K in contrast to the CrMnFeCoNi and CrCoNi alloys resulting in a relatively constant and slightly increasing SFE as the temperature decreased, which is confirmed via ab initio simulations. However, the deformation localization near the grain boundaries at 298 K changed into a homogeneous distribution throughout the whole grains at 77 K, leading to a highly sustained strain hardening rate. The reduced impact toughness is directly related to the decreased plastic zone size, which is due to the reduced dislocation width and significant temperature dependence of the yield strength.

Interstitial alloying has become an important pillar in tuning and improving the materials properties of high-entropy alloys, e.g., enabling interstitial solid-solution hardening and for tuning the stacking fault energies. In this work we performed ab initio calculations to evaluate the impact of interstitial alloying with nitrogen on the fcc–hcp phase stability for the prototypical CrMnFeCoNi alloy. The N solution energies are broadly distributed and reveal a clear correlation with the local environments. We show that N addition stabilizes the fcc phase of CrMnFeCoNi and increases the stacking fault energy.

Complex concentrated alloys (CCAs) are of growing interest due to their outstanding mechanical properties that exceed the property limits of conventional alloys. Whereas the superior properties are often attributed to severe lattice distortion, to date it is not clear what controls the lattice distortion and how it affects the mechanical properties of CCAs. In this work, we study the element-resolved local lattice distortion (ELLD) in CCAs of 3d transition-metal elements (3d CCAs) by the extended X-ray absorption fine structure experiment and the density-functional theory calculations. We show that ELLD is primarily dependent upon charge transfer among elements and affects the properties through atomic-level pressure and orbital transition. The ELLD provides a qualitative measure of the effective atomic size for explaining element-specific properties and macroscopic properties.

Recent experiments show that the chemical composition of body-centered cubic (bcc) refractory high entropy alloys (HEAs) can be tuned to enable transformation-induced plasticity (TRIP), which significantly improves the ductility of these alloys. This calls for an accurate and efficient method to map the structural stability as a function of composition. A key challenge for atomistic simulations is to separate the structural transformation between the bcc and the ω phases from the intrinsic local lattice distortions in such chemically disordered alloys. To solve this issue, we develop a method that utilizes a symmetry analysis to detect differences in the crystal structures. Utilizing this method in combination with ab initio calculations, we demonstrate that local lattice distortions largely affect the phase stability of Ti–Zr–Hf–Ta and Ti–Zr–Nb–Hf–Ta HEAs. If relaxation effects are properly taken into account, the predicted compositions near the bcc–hcp energetic equilibrium are close to the experimental compositions, for which good strength and ductility due to the TRIP effect are observed.

High entropy alloys (HEAs) in the hexagonal close-packed (hcp) phase usually show poor mechanical properties. We demonstrate here, by use of ab initio simulations and detailed experimental investigations, that the mechanical properties can be improved by optimizing the microstructure. In particular we design a dual-phase HEA consisting of a body-centered cubic (bcc) matrix and hcp laths, with nanoprecipitates of the ω phase in the Sc-Ti-Zr-Hf-Re system, by controlling the Re content. This dedicated microstructure reveals, already in the as-cast state, high compressive strength and good ductility of 1910 MPa and 8%, respectively. Our study lifts the hcp-based HEAs onto a competitive, technological level.

In conventional metallic materials, strength and ductility are mutually exclusive, referred to as strength-ductility trade-off. Here, we demonstrate an approach to improve the strength and ductility simultaneously by introducing micro-banding and the accumulation of a high density of dislocations in single-phase high-entropy alloys (HEAs). We prepare two compositions (Cr₁₀Mn₅₀Fe₂₀Co₁₀Ni₁₀ and Cr₁₀Mn₁₀Fe₆₀Co₁₀Ni₁₀) with distinctive different stacking fault energies (SFEs) as experimental materials. The strength and ductility of the Cr₁₀Mn₅₀Fe₂₀Co₁₀Ni₁₀ HEA are improved concurrently by grain refinement from 347.5 ± 216.1 µm to 18.3 ± 9.3 µm. The ultimate tensile strength increases from 543 ± 4 MPa to 621 ± 8 MPa and the elongation to failure enhances from 43±2% to 55±1%. To reveal the underlying deformation mechanisms responsible for such a strength-ductility synergy, the microstructural evolution upon loading is investigated by electron microscopy techniques. The dominant deformation mechanism observed for the Cr₁₀Mn₅₀Fe₂₀Co₁₀Ni₁₀ HEA is the activation of micro-bands, which act both as dislocation sources and dislocation barriers, eventually, leading to the formation of dislocation cell structures. By decreasing grain size, much finer dislocation cell structures develop, which are responsible for the improvement in work hardening rate at higher strains (>7%) and thus for the increase in both strength and ductility. In order to drive guidelines for designing advanced HEAs by tailoring their SFE and grain size, we compute the SFEs of Cr₁₀Mn_xFe_70–xCo₁₀Ni10 (10 ≤ x ≤ 60) based on first principles calculations. Based on these results the overall changes on deformation mechanism can be explained by the influence of Mn on the SFE.

Local lattice distortions in a series of body-centered cubic alloys, including refractory high-entropy alloys, are investigated by means of atomic volumes, atomic charges, and atomic stresses defined by the Bader charge analysis based on first-principles calculations. Analyzing the extensive data sets, we find large distributions of these atomic properties for each element in each alloy, indicating a large impact of the varying local chemical environments. We show that these local-environment effects can be well understood and captured already by the first and the second nearest neighbor shells. Based on this insight, we employ linear regression models up to the second nearest neighbor shell to accurately predict these atomic properties. Finally, we find that the elementwise-averaged values of the atomic properties correlate linearly with the averaged valence-electron concentration of the considered alloys.

We reveal the impact of magnetic ordering on stacking fault energy (SFE) and its influence on the deformation mechanisms and mechanical properties in a class of nonequiatomic quinary Mn-containing compositional complex alloys or high entropy alloys (HEAs). By combining ab initio simulation and experimental validation, we demonstrate magnetic ordering as an important factor in the activation and transition of deformation modes from planar dislocation slip to TWIP (twinning-induced plasticity) and/or TRIP (transformation-induced plasticity). A wide compositional space of Cr20MnxFeyCo20Niz(x+y+z=60, at. %) was probed by density-functional theory calculations to search for potential alloys displaying the TWIP/TRIP effects. Three selected promising HEA compositions with varying Mn concentrations were metallurgically synthesized, processed, and probed for microstructure, deformation mechanism, and mechanical property evaluation. The differences in the deformation modes of the probed HEAs are interpreted in terms of the computed SFEs and their dependence on the predicted magnetic state, as revealed by ab initio calculations and validated by explicit magnetic measurements. It is found that the Mn content plays a key role in the stabilization of antiferromagnetic configurations which strongly impact the SFEs and eventually lead to the prevalent deformation behavior.

The field of atomistic simulations of multicomponent materials and high entropy alloys is progressing rapidly, with challenging problems stimulating new creative solutions. In this Perspective, we present three topics that emerged very recently and that we anticipate will determine the future direction of research of high entropy alloys: the usage of machine-learning potentials for very accurate thermodynamics, the exploration of short-range order and its impact on macroscopic properties, and the more extensive exploitation of interstitial alloying and high entropy alloy surfaces for new technological applications. For each of these topics, we briefly summarize the key achievements, point out the aspects that still need to be addressed, and discuss possible future improvements and promising directions.

Severe lattice distortion is a core effect in the design of multiprincipal element alloys with the aim to enhance yield strength, a key indicator in structural engineering. Yet, the yield strength values of medium- and high-entropy alloys investigated so far do not substantially exceed those of conventional alloys owing to the insufficient utilization of lattice distortion. Here it is shown that a simple VCoNi equiatomic medium-entropy alloy exhibits a near 1 GPa yield strength and good ductility, outperforming conventional solid-solution alloys. It is demonstrated that a wide fluctuation of the atomic bond distances in such alloys, i.e., severe lattice distortion, improves both yield stress and its sensitivity to grain size. In addition, the dislocation-mediated plasticity effectively enhances the strength–ductility relationship by generating nanosized dislocation substructures due to massive pinning. The results demonstrate that severe lattice distortion is a key property for identifying extra-strong materials for structural engineering applications.

To facilitate the understanding of Invar effects and design of FeNiCo-base Invar alloys characterized by low thermal expansion coefficient (TEC), we investigated the magnetic and thermal expansion behavior of an equiatomic prototype medium entropy alloy FeNiCo and a non-equiatomic (super Invar)Fe₆₃Ni₃₂Co₅ (at. %)reference alloy by means of experiments and ab initio calculations. Both alloys consist of a single face-centered cubic phase with fully recrystallized microstructure in the homogenized state. Large spontaneous volume magnetostriction is observed in both alloys below their respective Curie temperatures. The Invar effect in the non-equiatomic Fe₆₃Ni₃₂Co₅ alloy is of step-type with nearly zero TEC over a wide temperature range (from room temperature to 120 °C)below its Curie temperature. The equiatomic FeNiCo alloy shows a peak-type Invar effect in a very narrow temperature range (from ∼675 °C to ∼730 °C)with relatively low TECs. The equiatomic FeNiCo alloy shows both higher saturation magnetization and Curie temperature than the non-equiatomic Fe₆₃Ni₃₂Co₅ alloy. The relationships among magnetic behavior, spontaneous volume magnetostriction and Invar effects for a wider array of metallic alloys are discussed mainly based on Masumoto's rule combined with Wohlfarth's itinerant electron theory. An Invar alloy search map is constructed based on the present results and available literature data to visualize the relationships among saturation magnetization, Curie temperature and thermal expansion coefficient for a wide range of Invar alloys. Based on this treasure map a design route for further developments of new Invar alloys by tuning their magnetic properties is discussed.

Quantitative and well-targeted design of modern alloys is extremely challenging due to their immense compositional space. When considering only 50 elements for compositional blending the number of possible alloys is practically infinite, as is the associated unexplored property realm. In this paper, we present a simple property-targeted quantitative design approach for atomic-level complexity in complex concentrated and high-entropy alloys, based on quantum-mechanically derived atomic-level pressure approximation. It allows identification of the best suited element mix for high solid-solution strengthening using the simple electronegativity difference among the constituent elements. This approach can be used for designing alloys with customized properties, such as a simple binary NiV solid solution whose yield strength exceeds that of the Cantor high-entropy alloy by nearly a factor of two. This study provides general design rules that enable effective utilization of atomic level information to reduce the immense degrees of freedom in compositional space without sacrificing physics-related plausibility.

Multicomponent alloys with multiple principal elements including high entropy alloys (HEAs) and compositionally complex alloys (CCAs) are attracting rapidly growing attention. The endless possibilities to explore new alloys and the hope for better combinations of materials properties have stimulated a remarkable number of research works in the last years. Most of these works have been based on experimental approaches, but ab initio calculations have emerged as a powerful approach that complements experiment and serves as a predictive tool for the identification and characterization of promising alloys. The theoretical ab initio modeling of phase stabilities and mechanical properties of multi-principal element alloys by means of density functional theory (DFT) is reviewed. A general thermodynamic framework is laid down that provides a bridge between the quantities accessible with DFT and the targeted thermodynamic and mechanical properties. It is shown how chemical disorder and various finite-temperature excitations can be modeled with DFT. Different concepts to study crystal and alloy phase stabilities, the impact of lattice distortions (a core effect of HEAs), magnetic transitions, and chemical short-range order are discussed along with specific examples. Strategies to study elastic properties, stacking fault energies, and their dependence on, e.g., temperature or alloy composition are illustrated. Finally, we provide an extensive compilation of multi-principal element alloys and various material properties studied with DFT so far (a set of over 500 alloy-property combinations).