Simulating short-range order in compositionally complex materials.

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.

Machine learning-enabled high-entropy alloy discovery.

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.

Shear band-driven precipitate dispersion for ultrastrong ductile medium-entropy alloys.

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.

Hidden Effects of Negative Stacking Fault Energies in Complex Concentrated Alloys.

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.

Engineering atomic-level complexity in high-entropy and complex concentrated alloys.

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.

Ultrastrong Medium-Entropy Single-Phase Alloys Designed via Severe Lattice Distortion.

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.

Anomalous Phonon Lifetime Shortening in Paramagnetic CrN Caused by Spin-Lattice Coupling: A Combined Spin and Ab Initio Molecular Dynamics Study.

We study the mutual coupling of spin fluctuations and lattice vibrations in paramagnetic CrN by combining atomistic spin dynamics and ab initio molecular dynamics. The two degrees of freedom are dynamically coupled, leading to nonadiabatic effects. Those effects suppress the phonon lifetimes at low temperature compared to an adiabatic approach. The dynamic coupling identified here provides an explanation for the experimentally observed unexpected temperature dependence of the thermal conductivity of magnetic semiconductors above the magnetic ordering temperature.

Impact of Chemical Fluctuations on Stacking Fault Energies of CrCoNi and CrMnFeCoNi High Entropy Alloys from First Principles.

Medium and high entropy alloys (MEAs and HEAs) based on 3d transition metals, such as face-centered cubic (fcc) CrCoNi and CrMnFeCoNi alloys, reveal remarkable mechanical properties. The stacking fault energy (SFE) is one of the key ingredients that controls the underlying deformation mechanism and hence the mechanical performance of materials. Previous experiments and simulations have therefore been devoted to determining the SFEs of various MEAs and HEAs. The impact of local chemical environment in the vicinity of the stacking faults is, however, still not fully understood. In this work, we investigate the impact of the compositional fluctuations in the vicinity of stacking faults for two prototype fcc MEAs and HEAs, namely CrCoNi and CrMnFeCoNi by employing first-principles calculations. Depending on the chemical composition close to the stacking fault, the intrinsic SFEs vary in the range of more than 150 mJ/m 2 for both the alloys, which indicates the presence of a strong driving force to promote particular types of chemical segregations towards the intrinsic stacking faults in MEAs and HEAs. Furthermore, the dependence of the intrinsic SFEs on local chemical fluctuations reveals a highly non-linear behavior, resulting in a non-trivial interplay of local chemical fluctuations and SFEs. This sheds new light on the importance of controlling chemical fluctuations via tuning, e.g., the annealing condition to obtain the desired mechanical properties for MEAs and HEAs.

Operando Phonon Studies of the Protonation Mechanism in Highly Active Hydrogen Evolution Reaction Pentlandite Catalysts.

Synthetic pentlandite (Fe4.5Ni4.5S8) is a promising electrocatalyst for hydrogen evolution, demonstrating high current densities, low overpotential, and remarkable stability in bulk form. The depletion of sulfur from the surface of this catalyst during the electrochemical reaction has been proposed to be beneficial for its catalytic performance, but the role of sulfur vacancies and the mechanism determining the reaction kinetics are still unknown. We have performed electrochemical operando studies of the vibrational dynamics of pentlandite under hydrogen evolution reaction conditions using 57Fe nuclear resonant inelastic X-ray scattering. Comparing the measured Fe partial vibrational density of states with density functional theory calculations, we have demonstrated that hydrogen atoms preferentially occupy substitutional positions replacing pre-existing sulfur vacancies. Once all vacancies are filled, the protonation proceeds interstitially, which slows down the reaction. Our results highlight the beneficial role of sulfur vacancies in the electrocatalytic performance of pentlandite and give insights into the hydrogen adsorption mechanism during the reaction.

Computationally-driven engineering of sublattice ordering in a hexagonal AlHfScTiZr high entropy alloy.

Multi-principle element alloys have enormous potential, but their exploration suffers from the tremendously large range of configurations. In the last decade such alloys have been designed with a focus on random solid solutions. Here we apply an experimentally verified, combined thermodynamic and first-principles design strategy to reverse the traditional approach and to generate a new type of hcp Al-Hf-Sc-Ti-Zr high entropy alloy with a hitherto unique structure. A phase diagram analysis narrows down the large compositional space to a well-defined set of candidates. First-principles calculations demonstrate the energetic preference of an ordered superstructure over the competing disordered solid solutions. The chief ingredient is the Al concentration, which can be tuned to achieve a D019 ordering on the hexagonal lattice. The computationally designed D019 superstructure is experimentally confirmed by transmission electron microscopy and X-ray studies. Our scheme enables the exploration of a new class of high entropy alloys.

Impact of magnetic fluctuations on lattice excitations in fcc nickel.

The spin-space averaging formalism is applied to compute atomic forces and phonon spectra for magnetically excited states of fcc nickel. Transverse and longitudinal magnetic fluctuations are taken into account by a combination of magnetic special quasi random structures and constrained spin-density-functional theory. It turns out that for fcc Ni interatomic force constants and phonon spectra are almost unaffected by both kinds of spin fluctuations. Given the computational expense to simulate coupled magnetic and atomic fluctuations, this insight facilitates computational modeling of magnetic alloys such as Ni-based superalloys.