This work aims to predict the microstructure of recrystallized medium and high-entropy alloys (MEAs and HEAs) with a face-centered cubic structure, in particular the density of annealing twins and their thickness. Eight MEAs and five HEAs from the Cr-Mn-Fe-Co-Ni system are considered, which have been cast, homogenized, cold-worked and recrystallized to obtain different grain sizes. This work thus provides a database that could be used for data mining to take twin boundary engineering for alloy development to the next level. Since the stacking fault energy is known to strongly affect recrystallized microstructures, the latter was determined at 293 K using the weak beam dark-field technique and compared with ab initio simulations, which additionally allowed to calculate its temperature dependence. Finally, we show that all these data can be rationalized based on theories and empirical relationships that were proposed for pure metals and binary Cu-based alloys.

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.

Explicit anharmonicity, defined as the vibrational contribution beyond the quasiharmonic approximation, is qualitatively different between the group V and group VI bcc refractory elements. Group V elements show a small and mostly negative anharmonic entropy, whereas group VI elements have a large positive anharmonic entropy, strongly increasing with temperature. Here, we explain this difference utilizing highly accurate anharmonic free energies and entropies from ab initio calculations for Nb and Ta (group V), and Mo and W (group VI). The numerically calculated entropies are in agreement with prior experimental data. The difference in behavior between the two sets of elements arises not from their high-temperature behavior but rather from the 0K quasiharmonic reference state. We understand this by analyzing the 0K and the high-temperature phonon density of states and the electronic density of states. The qualitative difference disappears when the anharmonicity is instead referenced with a high-temperature effective harmonic potential. However, even for an optimized effective harmonic reference, the remaining effective anharmonicity is significant. The reason is that the anharmonicity in the bcc systems - carried by asymmetric distributions in the nearest neighbors - can never be accounted for by a harmonically restricted potential.

In multicomponent materials, short-range order (SRO) is the development of correlated arrangements of atoms at the nanometer scale. Its impact in compositionally complex materials has stimulated an intense debate within the materials science community. Understanding SRO is critical to control the properties of technologically relevant materials, from metallic alloys to functional ceramics. In contrast to long-range order, quantitative characterization of the nature and spatial extent of SRO evades most of the experimentally available techniques. Simulations at the atomistic scale have full access to SRO but face the challenge of accurately sampling high-dimensional configuration spaces to identify the thermodynamic and kinetic conditions at which SRO is formed and what impact it has on material properties. Here we highlight recent progress in computational approaches, such as machine learning-based interatomic potentials, for quantifying and understanding SRO in compositionally complex materials. We briefly recap the key theoretical concepts and methods.

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.

We present the magnetic Moment Tensor Potentials (mMTPs), a class of machine-learning interatomic potentials, accurately reproducing both vibrational and magnetic degrees of freedom as provided, e.g., from first-principles calculations. The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space. The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron, with applications to phonon calculations for different magnetic states, and molecular-dynamics simulations with fluctuating magnetic moments.

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.

We present an analysis of temperature-dependent atomic short-range ordering and phase stability of the face-centered cubic CrCoNi medium-entropy alloy employing a combination of ab initio calculations and on-lattice machine learning interatomic potentials. Temperature-dependent properties are studied with canonical Monte Carlo simulations. At around 975 K a phase transition into an ordered Cr(Ni,Co)2 phase (MoPt2-type) is found. This hitherto not reported state has an ordering energy twice as large than the ordered structures previously suggested. We show that magnetism is not responsible for the observed chemical ordering.

Multi-principal-component alloys have attracted great interest as a novel paradigm in alloy design, with often unique properties and a vast compositional space auspicious for materials discovery. High entropy alloys (HEAs) belong to this class and are being investigated for prospective nuclear applications with reported superior mechanical properties including high-temperature strength and stability compared to conventional alloys. Computational materials design has the potential to play a key role in screening such alloys, yet for high-temperature properties, challenges remain in finding an appropriate balance between accuracy and computational cost. Here we develop an approach based on density-functional theory (DFT) and thermodynamic integration aided by machine learning based interatomic potential models to address this challenge. We systematically evaluate and compare the efficiency of computing the full free energy surface and thermodynamic properties up to the melting point at different stages of the thermodynamic integration scheme. Our new approach provides a ×4 speed-up with respect to comparable free energy approaches at the level of DFT, with errors on high-temperature free energy predictions less than 1 meV/atom. Calculations are performed on an equiatomic HEA, TaVCrW - a low-activation composition and therefore of potential interest for next generation fission and fusion reactors.

High-entropy alloys are solid solutions of multiple principal elements that are capable of reaching composition and property regimes inaccessible for dilute materials. Discovering those with valuable properties, however, too often relies on serendipity, because thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. We propose an active learning strategy to accelerate the design of high-entropy Invar alloys in a practically infinite compositional space based on very sparse data. Our approach works as a closed-loop, integrating machine learning with density-functional theory, thermodynamic calculations, and experiments. After processing and characterizing 17 new alloys out of millions of possible compositions, we identified two high-entropy Invar alloys with extremely low thermal expansion coefficients around 2 × 10-6 per degree kelvin at 300 kelvin. We believe this to be a suitable pathway for the fast and automated discovery of high-entropy alloys with optimal thermal, magnetic, and electrical properties.

Besides revealing excellent mechanical properties, compositionally complex alloys are also very promising candidates for applications in heterogeneous catalysis. The opportunity provided by the tremendously large composition phase space to explore new materials and tune the materials properties in the materials design cycle is, however, intrinsically coupled with the challenge of controlling surface segregation, which is generally more severe in multicomponent alloys as compared to simpler systems. We demonstrate this by computing the surface phase diagram of two candidate compositionally complex catalysts. Significant surface segregation is found even at very high temperature and this can strongly affect the catalytic properties of these alloys. We explain the observed phase stabilities in terms of segregation energies and rationalize the segregation trends with canonical models. Finally, we propose a set of descriptors accessible with first-principles calculations that allows to quickly incorporate the evaluation of the segregation during the alloy design process.

The interface method is a well established approach for predicting melting points of materials using interatomic potentials. However, applying the interface method is tedious and involves significant human intervention. The whole procedure involves several successive tasks: estimate a rough melting point, set up the interface structure, run molecular dynamic calculations and analyze the data. Loop calculations are necessary if the predicted melting point is different from the estimated one by more than a certain convergence criterion, or if full melting/solidification occurs. In this case monitoring the solid–liquid phase transition in the interface structure becomes critical. As different initial random seeds for the molecular dynamic simulations within the interface method induce slightly different melting points, a few ten or hundred interface method calculations with different random seeds are necessary for performing a statistical analysis on these melting points. Considering all these technical details, the work load for manually executing and combining the various involved scripts and programs quickly becomes prohibitive. To simplify and automatize the whole procedure, we have implemented the interface method into pyiron (http://pyiron.org). Our fully automatized procedure allows to efficiently and precisely predict melting points of stable unaries represented by arbitrary potentials with only two user-specified parameters (interatomic potential file and element). For metastable or dynamically unstable unary phases, the crystal structure needs to be provided as an additional parameter. We have applied our automatized approach on fcc Al, Ni, dynamically unstable bcc Ti and hcp Mg and employed a large set of available interatomic potentials. Melting points for classical interatomic potentials of these metals have been obtained with a numerical precision well below 1 K.

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.

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.

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).

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.

Since its first emergence in 2004, the high-entropy alloy (HEA) concept has aimed at stabilizing single- or dual-phase multi-element solid solutions through high mixing entropy. Here, this strategy is changed and renders such massive solid solutions metastable, to trigger spinodal decomposition for improving the alloys’ magnetic properties. The motivation for starting from a HEA for this approach is to provide the chemical degrees of freedom required to tailor spinodal behavior using multiple components. The key idea is to form Fe-Co enriched regions which have an expanded volume (relative to unconstrained Fe-Co), due to coherency constraints imposed by the surrounding HEA matrix. As demonstrated by theory and experiments, this leads to improved magnetic properties of the decomposed alloy relative to the original solid solution matrix. In a prototype magnetic FeCoNiMnCu HEA, it is shown that the modulated structures, achieved by spinodal decomposition, lead to an increase of the Curie temperature by 48% and a simultaneous increase of magnetization by 70% at ambient temperature as compared to the homogenized single-phase reference alloy. The findings thus open a pathway for the development of advanced functional HEAs.

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.

Precipitation strengthening has been the basis of physical metallurgy since more than 100 years owing to its excellent strengthening effects. This approach generally employs coherent and nano-sized precipitates, as incoherent precipitates energetically become coarse due to their incompatibility with matrix and provide a negligible strengthening effect or even cause brittleness. Here we propose a shear band-driven dispersion of nano-sized and semicoherent precipitates, which show significant strengthening effects. We add aluminum to a model CoNiV medium-entropy alloy with a face-centered cubic structure to form the L2₁ Heusler phase with an ordered body-centered cubic structure, as predicted by ab initio calculations. Micro-shear bands act as heterogeneous nucleation sites and generate finely dispersed intragranular precipitates with a semicoherent interface, which leads to a remarkable strength-ductility balance. This work suggests that the structurally dissimilar precipitates, which are generally avoided in conventional alloys, can be a useful design concept in developing high-strength ductile structural materials.

Negative stacking fault energies (SFEs) are found in face-centered cubic high-entropy alloys with excellent mechanical properties, especially at low temperatures. Their roles remain elusive due to the lack of in situ observation of nanoscale deformation. Here, the polymorphism of Shockley partials is fully explored, assisted by a new method. We show negative SFEs result in novel partial pairs as if they were in hexagonal close-packed alloys. The associated yield stresses are much higher than those for other mechanisms at low temperatures. This generalizes the physical picture for all negative-SFE alloys.