Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy

Machine Learning-Enabled Tomographic Imaging of Chemical Short-Range Atomic Ordering

In solids, chemical short-range order (CSRO) refers to the self-organization of atoms of certain species occupying specific crystal sites. CSRO is increasingly being envisaged as a lever to tailor the mechanical and functional properties of materials. Yet quantitative relationships between properties and the morphology, number density, and atomic configurations of CSRO domains remain elusive. Herein, it is showcased how machine learning-enhanced atom probe tomography (APT) can mine the near-atomically resolved APT data and jointly exploit the technique's high elemental sensitivity to provide a 3D quantitative analysis of CSRO in a CoCrNi medium-entropy alloy. Multiple CSRO configurations are revealed, with their formation supported by state-of-the-art Monte-Carlo simulations. Quantitative analysis of these CSROs allows establishing relationships between processing parameters and physical properties. The unambiguous characterization of CSRO will help refine strategies for designing advanced materials by manipulating atomic-scale architectures.

Antiferromagnetism and Phase Stability of CrMnFeCoNi High-Entropy Alloy

It has long been suspected that magnetism could play a vital role in the phase stability of multicomponent high-entropy alloys. However, the nature of the magnetic order, if any, has remained elusive. Here, by using elastic and inelastic neutron scattering, we demonstrate evidence of antiferromagnetic order below ∼80  K and strong spin fluctuations persisting to room temperature in a single-phase face-centered cubic (fcc) CrMnFeCoNi high-entropy alloy. Despite the chemical complexity, the magnetic structure in CrMnFeCoNi can be described as γ-Mn-like, with the magnetic moments confined in alternating (001) planes and pointing toward the ⟨111⟩ direction. Combined with first-principles calculation results, it is shown that the antiferromagnetic order and spin fluctuations help stabilized the fcc phase in CrMnFeCoNi high-entropy alloy.

Comprehensive analysis of ordering in CoCrNi and CrNi2 alloys

Chemical Short-Range Order (CSRO) has attracted recent attention from many researchers, creating intense debates about its impact on material properties. The challenges lie in confirming and quantifying CSRO, as its detection proves exceptionally demanding, contributing to conflicting data in the literature regarding its true effects on mechanical properties. Our work uses high-precision calorimetric data to unambiguously prove the existence and, coupled with atomistic simulations, quantify the type of CSRO. This methodology allows us to propose a mechanism for its formation and destruction based on the heat evolution during thermal analysis and facilitates a precise identification of local ordering in CoCrNi alloys. Samples of CoCrNi (Co33Cr33Ni33) and CrNi2 (Cr33Ni66) alloys are fabricated in varying ordered states, extensively characterized via synchrotron X-ray diffraction, X-ray absorption spectroscopy, and transmission electron microscopy. Samples with considerably different ordered states are submitted to tensile tests with in-situ synchrotron X-ray diffraction. We demonstrate, despite inducing varied CSRO levels in CoCrNi, no significant alterations in overall mechanical behavior emerge. However, the CrNi2 alloy, which undergoes long-range ordering, experiences significant shifts in yield strength, ultimate tensile stress and ductility.

Quantifying short-range order using atom probe tomography

Medium- and high-entropy alloys are an emerging class of materials that can exhibit outstanding combinations of strength and ductility for engineering applications. Computational simulations have suggested the presence of short-range order (SRO) in these alloys, and recent experimental evidence is also beginning to emerge. Unfortunately, the difficulty in quantifying the SRO under different heat treatment conditions has generated much debate on the atomic preferencing and implications of SRO on mechanical properties. Here we develop an approach to measure SRO using atom probe tomography. This method balances the limitations of atom probe tomography with the threshold values of SRO to map the regimes where the required atomistic neighbourhood information is preserved and where it is not. We demonstrate the method with a case study of the CoCrNi alloy and use this to monitor SRO changes induced by heat treatments. These species-specific SRO measurements enable the generation of computational simulations of atomic neighbourhood models that are equivalent to the experiment and can contribute to the further understanding and design of medium- and high-entropy alloys and other materials systems where SRO may occur.

Multiple origins of extra electron diffractions in fcc metals

Diffuse intensities in the electron diffraction patterns of concentrated face-centered cubic solid solutions have been widely attributed to chemical short-range order, although this connection has been recently questioned. This article explores the many nonordering origins of commonly reported features using a combination of experimental electron microscopy and multislice diffraction simulations, which suggest that diffuse intensities largely represent thermal and static displacement scattering. A number of observations may reflect additional contributions from planar defects, surface terminations incommensurate with bulk periodicity, or weaker dynamical effects.

Tailoring local chemical fluctuation of high-entropy structures in thermoelectric materials

In high-entropy materials, local chemical fluctuation from multiple elements inhabiting the same crystallographic site plays a crucial role in their unique properties. Using atomic-resolution chemical mapping, we identified the respective contributions of different element characteristics on the local chemical fluctuation of high-entropy structures in thermoelectric materials. Electronegativity and mass had a comparable influence on the fluctuations of constituent elements, while the radius made a slight contribution. The local chemical fluctuation was further tailored by selecting specific elements to induce large lattice distortion and strong strain fluctuation to lower lattice thermal conductivity independent of increased entropy. The chemical bond fluctuation induced by the electronegativity difference had a noticeable contribution to the composition-dependent lattice thermal conductivity in addition to the known fluctuations of mass and strain field. Our findings provide a fundamental principle for tuning local chemical fluctuation and lattice thermal conductivity in high-entropy thermoelectric materials.

Quantifying chemical short-range order in metallic alloys

Metallic alloys often form phases-known as solid solutions-in which chemical elements are spread out on the same crystal lattice in an almost random manner. The tendency of certain chemical motifs to be more common than others is known as chemical short-range order (SRO), and it has received substantial consideration in alloys with multiple chemical elements present in large concentrations due to their extreme configurational complexity (e.g., high-entropy alloys). SRO renders solid solutions "slightly less random than completely random," which is a physically intuitive picture, but not easily quantifiable due to the sheer number of possible chemical motifs and their subtle spatial distribution on the lattice. Here, we present a multiscale method to predict and quantify the SRO state of an alloy with atomic resolution, incorporating machine learning techniques to bridge the gap between electronic-structure calculations and the characteristic length scale of SRO. The result is an approach capable of predicting SRO length scale in agreement with experimental measurements while comprehensively correlating SRO with fundamental quantities such as local lattice distortions. This work advances the quantitative understanding of solid-solution phases, paving the way for the rigorous incorporation of SRO length scales into predictive mechanical and thermodynamic models.

Hidden structures: a driving factor to achieve low thermal conductivity and high thermoelectric performance

The long-range periodic atomic arrangement or the lack thereof in solids typically dictates the magnitude and temperature dependence of their lattice thermal conductivity (κlat). Compared to crystalline materials, glasses exhibit a much-suppressed κlat across all temperatures as the phonon mean free path reaches parity with the interatomic distances therein. While the occurrence of such glass-like thermal transport in crystalline solids captivates the scientific community with its fundamental inquiry, it also holds the potential for profoundly impacting the field of thermoelectric energy conversion. Therefore, efficient manipulation of thermal transport and comprehension of the microscopic mechanisms dictating phonon scattering in crystalline solids are paramount. As quantized lattice vibrations (i.e., phonons) drive κlat, atomistic insights into the chemical bonding characteristics are crucial to have informed knowledge about their origins. Recently, it has been observed that within the highly symmetric 'averaged' crystal structures, often there are hidden locally asymmetric atomic motifs (within a few Å), which exert far-reaching influence on phonon transport. Phenomena such as local atomic off-centering, atomic rattling or tunneling, liquid-like atomic motion, site splitting, local ordering, etc., which arise within a few Å scales, are generally found to drastically disrupt the passage of heat carrying phonons. Despite their profound implication(s) for phonon dynamics, they are often overlooked by traditional crystallographic techniques. In this review, we provide a brief overview of the fundamental aspects of heat transport and explore the status quo of innately low thermally conductive crystalline solids, wherein the phonon dynamics is majorly governed by local structural phenomena. We also discuss advanced techniques capable of characterizing the crystal structure at the sub-atomic level. Subsequently, we delve into the emergent new ideas with examples linked to local crystal structure and lattice dynamics. While discussing the implications of the local structure for thermal conductivity, we provide the state-of-the-art examples of high-performance thermoelectric materials. Finally, we offer our viewpoint on the experimental and theoretical challenges, potential new paths, and the integration of novel strategies with material synthesis to achieve low κlat and realize high thermoelectric performance in crystalline solids via local structure designing.

Dislocation flow turbulence simultaneously enhances strength and ductility

Multi-principal element alloys (MPEAs) exhibit outstanding strength attributed to the complex dislocation dynamics as compared to conventional alloys. Here, we develop an atomic-lattice-distortion-dependent discrete dislocation dynamics framework consisted of random field theory and phenomenological dislocation model to investigate the fundamental deformation mechanism underlying massive dislocation motions in body-centered cubic MPEA. Amazingly, the turbulence of dislocation speed is identified in light of strong heterogeneous lattice strain field caused by short-range ordering. Importantly, the vortex from dislocation flow turbulence not only acts as an effective source to initiate dislocation multiplication but also induces the strong local pinning trap to block dislocation movement, thus breaking the strength-ductility trade-off.

Dynamic Nanoindentation and Short-Range Order in Equiatomic NiCoCr Medium-Entropy Alloy Lead to Novel Density Wave Ordering

Chemical short-range order is believed to be a key contributor to the exceptional properties of multicomponent alloys. However, its direct validation and confirmation has been highly elusive in most compounds. Recent studies for equiatomic NiCoCr alloys have shown that thermal treatments (i.e., annealing and aging) may facilitate and manipulate such ordering. In this work, by using molecular simulations, we show that nanomechanical probes, such as nanoindentation, may be utilized toward further manipulation of chemical short-range order, providing explicit validation pathways. By using well established interatomic potentials, we perform hybrid molecular-dynamics-Monte Carlo at room temperature to demonstrate that particular dwell nanoindentation protocols can lead, through thermal Monte Carlo equilibration, to local reorganization under the indenter tip, toward a density-wave stripe pattern. We characterize the novel density-wave structures, which are highly anisotropic and dependent on local, nanoindentation-induced stress concentrations, and we show how they deeply originate from intrinsic features of interelemental interactions. Furthermore, we show that these novel patterns consistently scale with the incipient plastic zone, under the indenter tip, justifying their observation at experimentally feasible nanoindentation depths.

Deformation mechanisms in high entropy alloys: a minireview of short-range order effects

The complex atomic scale structure of high entropy alloys presents new opportunities to expand the deformation theories of mechanical metallurgy. In this regard, solute-defect interactions have emerged as critical piece in elucidating the operation of deformation mechanisms. While notable progress has been made in understanding solute-defect interactions for random solute arrangements, recent interest in high entropy alloys with short-range order adds a new layer of structural complexity for which a cohesive picture has yet to emerge. To this end, this minireview synthesizes the current understanding of short-range order effects on defect behavior through an examination of the key recent literature. This analysis centers on the nanoscale metallurgy of deformation mechanisms, with the order-induced changes to the relevant defect energy landscapes serving as a touchstone for discussion. The topics reviewed include dislocation-mediated strengthening, twinning and phase transformation-based mechanisms, and vacancy-mediated processes. This minireview concludes with remarks on current challenges and opportunities for future efforts.

Tailoring Local Chemical Ordering via Elemental Tuning in High-Entropy Alloys

Due to the large multi-elemental space desired for property screening and optimization, high-entropy alloys (HEAs) hold greater potential over conventional alloys for a range of applications, such as structural materials, energy conversion, and catalysis. However, the relationship between the HEA composition and its local structural/elemental configuration is not well understood, particularly in noble-metal-based HEA nanomaterials, hindering the design and development of nano-HEAs in energy conversion and catalysis applications. Herein, we determined precise atomic-level structural and elemental arrangements in model HEAs composed of RhPtPdFeCo and RuPtPdFeCo to unveil their local characteristics. Notably, by changing just one constituent element in the HEA (Rh to Ru), we found dramatic changes in the elemental arrangement from complete random mixing to a local single elemental ordering feature. Additionally, we demonstrate that the local ordering in RuPtPdFeCo can be further controlled by varying the Ru concentration, allowing us to toggle between local Ru clustering and distinct heterostructures in multicomponent systems. Overall, our study presents a practical approach for manipulating local atomic structures and elemental arrangements in noble-metal-based HEA systems, which could provide in-depth knowledge to mechanistically understand the functionality of noble-metal-based HEA nanomaterials in practical applications.

Porosity modeling in a TiNbTaZrMo high-entropy alloy for biomedical applications

High-entropy alloys (HEAs) have attracted great attention for many biomedical applications. However, the nature of interatomic interactions in this class of complex multicomponent alloys is not fully understood. We report, for the first time, the results of theoretical modeling for porosity in a large biocompatible HEA TiNbTaZrMo using an atomistic supercell of 1024 atoms that provides new insights and understanding. Our results demonstrated the deficiency of using the valence electron count, quantification of large lattice distortion, validation of mechanical properties with available experimental data to reduce Young's modulus. We utilized the novel concepts of the total bond order density (TBOD) and partial bond order density (PBOD) via ab initio quantum mechanical calculations as an effective theoretical means to chart a road map for the rational design of complex multicomponent HEAs for biomedical applications.

Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys

Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy1-8, catalysis9-14 and other fields15-18. One of the core hypotheses of M/HEAs is lattice distortion5,19,20, which has been investigated by different numerical and experimental techniques21-26. However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies27, atomistic simulations28-30, energy dispersive spectroscopy31,32 and electron diffraction33,34, which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes7,32,34 and diffuse electron reflections may originate from planar defects instead of local chemical order35. Here we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography36 and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, the first experimental observation of correlating local chemical order with structural defects in any material. We expect that this work will not only expand our fundamental understanding of this important class of materials but also provide the foundation for tailoring M/HEA properties through engineering lattice distortion and local chemical order.

Sub-Ångstrom-scale structural variations in high-entropy oxides

High-entropy oxides (HEOs) are a special class of materials that utilize the concept of high-entropy alloys (HEAs) with five or more elements randomly distributing at a single sublattice in near-equiatomic proportions. HEOs have been attracting increasing attention owing to their many outstanding physical and chemical properties. However, unlike HEAs, for which local chemical compositions, order/disorder behaviors, and property-structure relationships have been comprehensively investigated, detailed information on the atomic-scale chemical and structural features and their correlations with functionalities in HEOs so far is still not sufficient. Herein, we select four typical HEOs with pyrochlore, spinel, perovskite and rock-salt type structures, and directly observe and quantify sub-Ångstrom-scale structure variations in different manners by means of advanced aberration-corrected scanning transmission electron microscopy techniques. Visualization and quantification of local structural variations and lattice distortions in the current work may show a valuable example for future investigations on local fluctuating structures and their relationships with properties in more systems of HEOs.

Quantitative three-dimensional imaging of chemical short-range order via machine learning enhanced atom probe tomography

Chemical short-range order (CSRO) refers to atoms of specific elements self-organising within a disordered crystalline matrix to form particular atomic neighbourhoods. CSRO is typically characterized indirectly, using volume-averaged or through projection microscopy techniques that fail to capture the three-dimensional atomistic architectures. Here, we present a machine-learning enhanced approach to break the inherent resolution limits of atom probe tomography enabling three-dimensional imaging of multiple CSROs. We showcase our approach by addressing a long-standing question encountered in body-centred-cubic Fe-Al alloys that see anomalous property changes upon heat treatment. We use it to evidence non-statistical B2-CSRO instead of the generally-expected D03-CSRO. We introduce quantitative correlations among annealing temperature, CSRO, and nano-hardness and electrical resistivity. Our approach is further validated on modified D03-CSRO detected in Fe-Ga. The proposed strategy can be generally employed to investigate short/medium/long-range ordering phenomena in different materials and help design future high-performance materials.

On the origin of diffuse intensities in fcc electron diffraction patterns

Interpreting diffuse intensities in electron diffraction patterns can be challenging in samples with high atomic-level complexity, as often is the case with multi-principal element alloys. For example, diffuse intensities in electron diffraction patterns from simple face-centred cubic (fcc) and related alloys have been attributed to short-range order1, medium-range order2 or a variety of different {111} planar defects, including thin twins3, thin hexagonal close-packed layers4, relrod spiking5 and incomplete ABC stacking6. Here we demonstrate that many of these diffuse intensities, including [Formula: see text]{422} and [Formula: see text]{311} in ⟨111⟩ and ⟨112⟩ selected area diffraction patterns, respectively, are due to reflections from higher-order Laue zones. We show similar features along many different zone axes in a wide range of simple fcc materials, including CdTe, pure Ni and pure Al. Using electron diffraction theory, we explain these intensities and show that our calculated intensities of projected higher-order Laue zone reflections as a function of deviation from their Bragg conditions match well with the observed intensities, proving that these intensities are universal in these fcc materials. Finally, we provide a framework for determining the nature and location of diffuse intensities that could indicate the presence of short-range order or medium-range order.

Deformation and failure of the CrCoNi medium-entropy alloy subjected to extreme shock loading

The extraordinary work hardening ability and fracture toughness of the face-centered cubic (fcc) high-entropy alloys render them ideal candidates for many structural applications. Here, the deformation and failure mechanisms of an equiatomic CrCoNi medium-entropyalloy (MEA) were investigated by powerful laser-driven shock experiments. Multiscale characterization demonstrates that profuse planar defects including stacking faults, nanotwins, and hexagonal nanolamella were generated during shock compression, forming a three-dimensional network. During shock release, the MEA fractured by strong tensile deformation and numerous voids was observed in the vicinity of the fracture plane. High defect populations, nanorecrystallization, and amorphization were found adjacent to these areas of localized deformation. Molecular dynamics simulations corroborate the experimental results and suggest that deformation-induced defects formed before void nucleation govern the geometry of void growth and delay their coalescence. Our results indicate that the CrCoNi-based alloys are impact resistant, damage tolerant, and potentially suitable in applications under extreme conditions.

Hydrogen Embrittlement of CrCoNi Medium-Entropy Alloy with Millimeter-Scale Grain Size: An In Situ Hydrogen Charging Study

In this study, we examined the effect of charging current density on the hydrogen embrittlement (HE) of MEA and the associated HE mechanisms using electron backscattered diffraction (EBSD). Results show that MEA is susceptible to HE, but is stronger than as-rolled and 3D-printed Cantor alloy and stainless steel. The HE susceptibility of MEA decreases with increasing current density. Ductile fracture with transgranular dimples switches to intergranular brittle fracture with clear slip bands in the interior of grains. EBSD results uncovered that hydrogen facilitates localized slips and deformation twins. Hydrogen-enhanced localized plasticity and hydrogen decohesion are the possible HE mechanisms.

Detection and impact of short-range order in medium/high-entropy alloys

Medium/High-entropy alloys (MEAs/HEAs) have attracted much attention during the past two decades and have been studied extensively owing to their excellent physical and mechanical properties. These materials form simple lattice structures and thermodynamically favored single-phase solutions. Despite having a single-phase, the local structure of MEAs/HEAs still contain some degree of order. Recently, short-range order (SRO) has been studied to better understand the local structure of MEAs/HEAs and how this order impacts their properties. Efforts to characterize SRO in high-entropy alloys have included non-imaging methods such as X-ray diffraction and X-ray absorption spectroscopy, as well as imaging methods such as transmission electron microscopy-based techniques. In this perspective, structural studies using non-imaging and imaging techniques to investigate SRO in MEAs/HEAs are discussed. Moreover, the impact of SRO on the physical and mechanical properties of MEAs/HEAs is also covered.

Defect modeling and control in structurally and compositionally complex materials

Conventional computational approaches for modeling defects face difficulties when applied to complex materials, mainly due to the vast configurational space of defects. In this Perspective, we discuss the challenges in calculating defect properties in complex materials, review recent advances in computational techniques and showcase new mechanistic insights developed from these methods. We further discuss the remaining challenges in improving the accuracy and efficiency of defect modeling in complex materials, and provide an outlook on potential research directions.

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.

Exceptional fracture toughness of CrCoNi-based medium- and high-entropy alloys at 20 kelvin

CrCoNi-based medium- and high-entropy alloys display outstanding damage tolerance, especially at cryogenic temperatures. In this study, we examined the fracture toughness values of the equiatomic CrCoNi and CrMnFeCoNi alloys at 20 kelvin (K). We found exceptionally high crack-initiation fracture toughnesses of 262 and 459 megapascal-meters ½ (MPa·m ½ ) for CrMnFeCoNi and CrCoNi, respectively; CrCoNi displayed a crack-growth toughness exceeding 540 MPa·m ½ after 2.25 millimeters of stable cracking. Crack-tip deformation structures at 20 K are quite distinct from those at higher temperatures. They involve nucleation and restricted growth of stacking faults, fine nanotwins, and transformed epsilon martensite, with coherent interfaces that can promote both arrest and transmission of dislocations to generate strength and ductility. We believe that these alloys develop fracture resistance through a progressive synergy of deformation mechanisms, dislocation glide, stacking-fault formation, nanotwinning, and phase transformation, which act in concert to prolong strain hardening that simultaneously elevates strength and ductility, leading to exceptional toughness.

Mechanically derived short-range order and its impact on the multi-principal-element alloys

Chemical short-range order in disordered solid solutions often emerges with specific heat treatments. Unlike thermally activated ordering, mechanically derived short-range order (MSRO) in a multi-principal-element Fe₄₀Mn₄₀Cr₁₀Co₁₀ (at%) alloy originates from tensile deformation at 77 K, and its degree/extent can be tailored by adjusting the loading rates under quasistatic conditions. The mechanical response and multi-length-scale characterisation pointed to the minor contribution of MSRO formation to yield strength, mechanical twinning, and deformation-induced displacive transformation. Scanning and high-resolution transmission electron microscopy and the anlaysis of electron diffraction patterns revealed the microstructural features responsible for MSRO and the dependence of the ordering degree/extent on the applied strain rates. Here, we show that underpinned by molecular dynamics, MSRO in the alloys with low stacking-fault energies forms when loaded at 77 K, and these systems that offer different perspectives on the process of strain-induced ordering transition are driven by crystalline lattice defects (dislocations and stacking faults).

Unlike diffusion-mediated chemical short-range orders (SROs) in multi-principal element alloys, diffusionless SROs and their impact on alloys have been elusive. Here, the authors show the formation of strain-induced SROs by crystalline lattice defects, upon external loading at 77 K.

Anomalous size effect on yield strength enabled by compositional heterogeneity in high-entropy alloy nanoparticles

High-entropy alloys (HEAs), although often presumed to be random solid solutions, have recently been shown to display nanometer-scale variations in the arrangements of their multiple chemical elements. Here, we study the effects of this compositional heterogeneity in HEAs on their mechanical properties using in situ compression testing in the transmission electron microscope (TEM), combined with molecular dynamics simulations. We report an anomalous size effect on the yield strength in HEAs, arising from such compositional heterogeneity. By progressively reducing the sample size, HEAs initially display the classical “smaller-is-stronger” phenomenon, similar to pure metals and conventional alloys. However, as the sample size is decreased below a critical characteristic length (~180 nm), influenced by the size-scale of compositional heterogeneity, a transition from homogeneous deformation to a heterogeneous distribution of planar slip is observed, coupled with an anomalous “smaller-is-weaker” size effect. Atomic-scale computational modeling shows these observations arise due to compositional fluctuations over a few nanometers. These results demonstrate the efficacy of influencing mechanical properties in HEAs through control of local compositional variations at the nanoscale.

Compositional heterogeneity in high-entropy alloys (HEAs) has gained lots of attention, but its relation with the properties remains vague. Here the authors report an anomalous size effect on strength by the compositional heterogeneity, which provides new insights in its connection to properties.

Chemical medium-range order in a medium-entropy alloy

High-/medium-entropy alloys (H/MEA) have the inherent local chemical order. Yet, as a structural link between the incipient short-range order and mature long-range counterpart, the chemical medium-range order (CMRO) is conjectural and remains open questions as to if, and what kind of, CMRO would be produced and if CMRO is mechanically stable during plastic deformation. Here, we show compelling evidences for CMRO in an Al_9.5CrCoNi MEA. Specifically, the electron diffraction under both [\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$112$$\end{document}112] and [\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$013$$\end{document}013] zone axis show the definite spots for CMRO of lattice periodicity. CMRO entities are seen directly of medium-ranged in sizes by using dark-field imaging, along with the tendency towards like-pair avoidance and unlike-pair preference based on atomic-resolution EDS mapping. These findings substantiate CMRO with a realistic structural picture in view of crystal periodicity and chemical species occupation, shedding light on understanding the microstructural link at an extended length scale beyond the short-range order.

The existence of chemical medium-range order (CMRO) in high- and medium- entropy alloys remains conjectural. Here the authors show evidences of CMRO by electron diffraction spots of lattice periodicity, observable entities, occupancy of preferential species, and stable sizes upon deformation.

Local chemical fluctuation mediated ultra-sluggish martensitic transformation in high-entropy intermetallics

Superelasticity associated with martensitic transformation has found a broad range of engineering applications, such as in low-temperature devices in the aerospace industry. Nevertheless, the narrow working temperature range and strong temperature sensitivity of the first-order phase transformation significantly hinder the usage of smart metallic components in many critical areas. Here, we scrutinized the phase transformation behavior and mechanical properties of multicomponent B2-structured intermetallic compounds. Strikingly, the (TiZrHfCuNi)_83.3Co_16.7 high-entropy intermetallics (HEIs) show superelasticity with high critical stress over 500 MPa, high fracture strength of over 2700 MPa, and small temperature sensitivity in a wide range of temperatures over 220 K. The complex sublattice occupation in these HEIs facilitates formation of nano-scaled local chemical fluctuation and then elastic confinement, which leads to an ultra-sluggish martensitic transformation. The thermal activation of the martensitic transformation was fully suppressed while the stress activation is severely retarded with an enhanced threshold stress over a wide temperature range. Moreover, the high configurational entropy also results in a small entropy change during phase transformation, consequently giving rise to the low temperature sensitivity of the superelasticity stress. Our findings may provide a new paradigm for the development of advanced superelastic alloys, and shed new insights into understanding of martensitic transformation in general.

Tunable Chemical Disorder in Concentrated Alloys: Defect Physics and Radiation Performance

The development of advanced structural alloys with performance meeting the requirements of extreme environments in nuclear reactors has been long pursued. In the long history of alloy development, the search for metallic alloys with improved radiation tolerance or increased structural strength has relied on either incorporating alloying elements at low concentrations to synthesize so-called dilute alloys or incorporating nanoscale features to mitigate defects. In contrast to traditional approaches, recent success in synthesizing multicomponent concentrated solid-solution alloys (CSAs), including medium-entropy and high-entropy alloys, has vastly expanded the compositional space for new alloy discovery. Their wide variety of elemental diversity enables tunable chemical disorder and sets CSAs apart from traditional dilute alloys. The tunable electronic structure critically lowers the effectiveness of energy dissipation via the electronic subsystem. The tunable chemical complexity also modifies the scattering mechanisms in the atomic subsystem that control energy transport through phonons. The level of chemical disorder depends substantively on the specific alloying elements, rather than the number of alloying elements, as the disorder does not monotonically increase with a higher number of alloying elements. To go beyond our knowledge based on conventional alloys and take advantage of property enhancement by tuning chemical disorder, this review highlights synergistic effects involving valence electrons and atomic-level and nanoscale inhomogeneity in CSAs composed of multiple transition metals. Understanding of the energy dissipation pathways, deformation tolerance, and structural stability of CSAs can proceed by exploiting the equilibrium and non-equilibrium defect processes at the electronic and atomic levels, with or without microstructural inhomogeneities at multiple length scales. Knowledge of tunable chemical disorder in CSAs may advance the understanding of the substantial modifications in element-specific alloy properties that effectively mitigate radiation damage and control a material's response in extreme environments, as well as overcome strength-ductility trade-offs and provide overarching design strategies for structural alloys.

Martensitic Transformation in Fe_{x}Mn_{80-x}Co_{10}Cr_{10} High-Entropy Alloy

High-entropy alloys and even medium-entropy alloys are an intriguing class of materials in that structure and property relations can be controlled via alloying and chemical disorder over wide ranges in the composition space. Employing density-functional theory combined with the coherent-potential approximation to average over all chemical configurations, we tune free energies between face-centered-cubic and hexagonal-close-packed phases in Fe_{x}Mn_{80-x}Co_{10}Cr_{10} systems. Within Fe-Mn-based alloys, we show that the martensitic transformation and chemical short-range order directly correlate with the face-centered-cubic and hexagonal-close-packed energy difference and stacking-fault energies, which are in quantitative agreement with recent observation of two phase region (face-centered cubic and hexagonal closed pack) in a polycrystalline high-entropy alloy sample at x=40 at.%. Our predictions are further confirmed by single-crystal measurements on a x=40 at.% using transmission-electron microscopy, selective-area diffraction, and electron-backscattered-diffraction mapping. The results herein offer an understanding of transformation-induced or twinning-induced plasticity in this class of high-entropy alloys and a design guide for controlling the physics at the electronic level.

Simultaneously enhancing the ultimate strength and ductility of high-entropy alloys via short-range ordering

Simultaneously enhancing strength and ductility of metals and alloys has been a tremendous challenge. Here, we investigate a CoCuFeNiPd high-entropy alloy (HEA), using a combination of Monte Carlo method, molecular dynamic simulation, and density-functional theory calculation. Our results show that this HEA is energetically favorable to undergo short-range ordering (SRO), and the SRO leads to a pseudo-composite microstructure, which surprisingly enhances both the ultimate strength and ductility. The SRO-induced composite microstructure consists of three categories of clusters: face-center-cubic-preferred (FCCP) clusters, indifferent clusters, and body-center-cubic-preferred (BCCP) clusters, with the indifferent clusters playing the role of the matrix, the FCCP clusters serving as hard fillers to enhance the strength, while the BCCP clusters acting as soft fillers to increase the ductility. Our work highlights the importance of SRO in influencing the mechanical properties of HEAs and presents a fascinating route for designing HEAs to achieve superior mechanical properties.

Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order

Refractory high-entropy alloys (RHEAs) are designed for high elevated-temperature strength, with both edge and screw dislocations playing an important role for plastic deformation. However, they can also display a significant energetic driving force for chemical short-range ordering (SRO). Here, we investigate mechanisms underlying the mobilities of screw and edge dislocations in the body-centered cubic MoNbTaW RHEA over a wide temperature range using extensive molecular dynamics simulations based on a highly-accurate machine-learning interatomic potential. Further, we specifically evaluate how these mechanisms are affected by the presence of SRO. The mobility of edge dislocations is found to be enhanced by the presence of SRO, whereas the rate of double-kink nucleation in the motion of screw dislocations is reduced, although this influence of SRO appears to be attenuated at increasing temperature. Independent of the presence of SRO, a cross-slip locking mechanism is observed for the motion of screws, which provides for extra strengthening for refractory high-entropy alloy system.

Direct observation of chemical short-range order in a medium-entropy alloy

Complex concentrated solutions of multiple principal elements are being widely investigated as high- or medium-entropy alloys (HEAs or MEAs)^1-11, often assuming that these materials have the high configurational entropy of an ideal solution. However, enthalpic interactions among constituent elements are also expected at normal temperatures, resulting in various degrees of local chemical order^12-22. Of the local chemical orders that can develop, chemical short-range order (CSRO) is arguably the most difficult to decipher and firm evidence of CSRO in these materials has been missing thus far^16,22. Here we discover that, using an appropriate zone axis, micro/nanobeam diffraction, together with atomic-resolution imaging and chemical mapping via transmission electron microscopy, can explicitly reveal CSRO in a face-centred-cubic VCoNi concentrated solution. Our complementary suite of tools provides concrete information about the degree/extent of CSRO, atomic packing configuration and preferential occupancy of neighbouring lattice planes/sites by chemical species. Modelling of the CSRO order parameters and pair correlations over the nearest atomic shells indicates that the CSRO originates from the nearest-neighbour preference towards unlike (V-Co and V-Ni) pairs and avoidance of V-V pairs. Our findings offer a way of identifying CSRO in concentrated solution alloys. We also use atomic strain mapping to demonstrate the dislocation interactions enhanced by the CSROs, clarifying the effects of these CSROs on plasticity mechanisms and mechanical properties upon deformation.

Magnetically driven short-range order can explain anomalous measurements in CrCoNi

The presence, nature, and impact of chemical short-range order in the multi-principal element alloy CrCoNi are all topics of current interest and debate. First-principles calculations reveal that its origins are fundamentally magnetic, involving repulsion between like-spin Co-Cr and Cr-Cr pairs that is complemented by the formation of a magnetically aligned sublattice of second-nearest-neighbor Cr atoms. Ordering models following these principles are found to predict otherwise anomalous experimental measurements concerning both magnetization and atomic volumes across a range of compositions. In addition to demonstrating the impact of magnetic interactions and resulting chemical rearrangement, the possible explanation of experiments would imply that short-range order of this type is far more prevalent than previously realized.

Short-Range Order in GeSn Alloy

Group IV alloys have been long viewed as homogeneous random solid solutions since perceiving them as Si-compatible, direct-band gap semiconductors 30 years ago. Such a perception underlies the understanding, interpretation, and prediction of alloys' properties. However, as the race to create scalable and tunable device materials enters a composition domain far beyond the alloys' equilibrium solubility, a fundamental question emerges as to how random these alloys truly are. Here, we show, by combining statistical sampling and large-scale ab initio calculations, that GeSn alloy, a promising group IV alloy for mid-infrared technology, exhibits a clear short-range order for solute atoms within its entire composition range. Such a short-range order is further found to substantially affect the electronic properties of GeSn. We demonstrate that the proper inclusion of this short-range order through canonical sampling can lead to a significant improvement over previous predictions on alloy's band gaps by showing an excellent agreement with experiments within the entire studied composition range. Our finding thus not only calls for an important revision of the current structural model for group IV alloy but also suggests that short-range order may generically exist in different types of alloys.

A structural modeling approach to solid solutions based on the similar atomic environment

A solid solution is one of the important ways to enhance the structural and functional performance of materials. In this work, we develop a structural modeling approach to solid solutions based on the similar atomic environment (SAE). We propose a similarity function associated with any type of atom cluster to describe quantitatively the configurational deviation from the desired solid-solution structure that is fully disordered or contains short-range order (SRO). In this manner, the structural modeling for solid solutions is transferred to a minimization problem in the configuration space. Moreover, we strive to enhance the practicality of this approach. The approach and implementation are demonstrated by cross validations with the special quasi-random structure method. We apply the SAE method to the typical quinary CoCrFeMnNi high-entropy alloy, continuous binary Ta-W alloy, and ternary CoCrNi medium-entropy alloy with SRO as prototypes. In combination with ab initio calculations, we investigate the structural properties and compare the calculation results with experiments.

Effect of Stacking Fault Energy on Microstructure and Texture Evolution during the Rolling of Non-Equiatomic CrMnFeCoNi High-Entropy Alloys

The evolution of microstructure and texture in three non-equiatomic CrMnFeCoNi high-entropy alloys (HEAs) with varying stacking fault energy (SFE) has been studied in up to 90% rolling reductions at both room and cryogenic temperature. All the HEAs deform by dislocation slip and additional mechanical twinning at intermediate and shear banding at high rolling strains. The microstructure is quite heterogeneous and, with strain, becomes highly fragmented. During rolling, a characteristic brass-type texture develops. Its strength increases with a decreasing SFE and the lowering of the rolling temperature. The texture evolution is discussed with regard to planar slip, mechanical twinning, and shear banding.

Yield strength and misfit volumes of NiCoCr and implications for short-range-order

The face-centered cubic medium-entropy alloy NiCoCr has received considerable attention for its good mechanical properties, uncertain stacking fault energy, etc, some of which have been attributed to chemical short-range order (SRO). Here, we examine the yield strength and misfit volumes of NiCoCr to determine whether SRO has measurably influenced mechanical properties. Polycrystalline strengths show no systematic trend with different processing conditions. Measured misfit volumes in NiCoCr are consistent with those in random binaries. Yield strength prediction of a random NiCoCr alloy matches well with experiments. Finally, we show that standard spin-polarized density functional theory (DFT) calculations of misfit volumes are not accurate for NiCoCr. This implies that DFT may be inaccurate for other subtle structural quantities such as atom-atom bond distance so that caution is required in drawing conclusions about NiCoCr based on DFT. These findings all lead to the conclusion that, under typical processing conditions, SRO in NiCoCr is either negligible or has no systematic measurable effect on strength.

Can Ordered Precursors Promote the Nucleation of Solid Solutions?

Crystallization often proceeds through successive stages that lead to a gradual increase in organization. Using molecular simulation, we determine the nucleation pathway for solid solutions of copper and gold. We identify a new nucleation mechanism (liquid→L1_{2} precursor→solid solution) involving a chemically ordered intermediate that is more organized than the end product. This nucleation pathway arises from the low formation energy of L1_{2} clusters which, in turn, promote crystal nucleation. We also show that this mechanism is composition dependent since the high formation energy of other ordered phases precludes them from acting as precursors.

Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways

High-entropy and medium-entropy alloys are presumed to have a configurational entropy as high as that of an ideally mixed solid solution (SS) of multiple elements in near-equal proportions. However, enthalpic interactions inevitably render such chemically disordered SSs rare and metastable, except at very high temperatures. Here we highlight the wide variety of local chemical ordering (LCO) that sets these concentrated SSs apart from traditional solvent-solute ones. Using atomistic simulations, we reveal that the LCO of the multi-principal-element NiCoCr SS changes with alloy processing conditions, producing a wide range of generalized planar fault energies. We show that the LCO heightens the ruggedness of the energy landscape and raises activation barriers governing dislocation activities. This influences the selection of dislocation pathways in slip, faulting, and twinning, and increases the lattice friction to dislocation motion via a nanoscale segment detrapping mechanism. In contrast, severe plastic deformation reduces the LCO towards random SS.

Multi-principal-element alloys have been assumed to have the configurational entropy of an ideal solution. Here, the authors use atomistic simulations to show that instead NiCoCr exhibits local chemical order, raising the activation barriers of dislocation activities to elevate mechanical strength.

Lattice Distortion and Phase Stability of Pd-Doped NiCoFeCr Solid-Solution Alloys

In the present study, we have revealed that (NiCoFeCr)_100−xPd_x (x= 1, 3, 5, 20 atom%) high-entropy alloys (HEAs) have both local- and long-range lattice distortions by utilizing X-ray total scattering, X-ray diffraction, and extended X-ray absorption fine structure methods. The local lattice distortion determined by the lattice constant difference between the local and average structures was found to be proportional to the Pd content. A small amount of Pd-doping (1 atom%) yields long-range lattice distortion, which is demonstrated by a larger (200) lattice plane spacing than the expected value from an average structure, however, the degree of long-range lattice distortion is not sensitive to the Pd concentration. The structural stability of these distorted HEAs under high-pressure was also examined. The experimental results indicate that doping with a small amount of Pd significantly enhances the stability of the fcc phase by increasing the fcc-to-hcp transformation pressure from ~13.0 GPa in NiCoFeCr to 20–26 GPa in the Pd-doped HEAs and NiCoFeCrPd maintains its fcc lattice up to 74 GPa, the maximum pressure that the current experiments have reached.

Core Electrons in the Electronic Stopping of Heavy Ions

Electronic stopping power in the keV/Å range is accurately calculated from first principles for high atomic-number projectiles and the effect of core states is carefully assessed. The energy loss to electrons in self-irradiated nickel is studied using real-time time-dependent density functional theory. Different core states are explicitly included in the simulations to understand their involvement in the dissipation mechanism. The core electrons of the projectile are found to open additional dissipation channels as the projectile velocity increases. Almost all of the energy loss is accounted for, even for high projectile velocities, when core electrons as deep as 2s^{2}2p^{6} are explicitly treated. In addition to their expected excitation at high velocities, a flapping dynamical response of the projectile core electrons is observed at intermediate velocities. The empirical reference data are well reproduced in the projectile velocity range of 1.0-12.0 a.u. (1.5-210 MeV).

Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys

High-entropy alloys (HEAs) are an intriguing new class of metallic materials due to their unique mechanical behavior. Achieving a detailed understanding of structure-property relationships in these materials has been challenged by the compositional disorder that underlies their unique mechanical behavior. Accordingly, in this work, we employ first-principles calculations to investigate the nature of local chemical order and establish its relationship to the intrinsic and extrinsic stacking fault energy (SFE) in CrCoNi medium-entropy solid-solution alloys, whose combination of strength, ductility, and toughness properties approaches the best on record. We find that the average intrinsic and extrinsic SFE are both highly tunable, with values ranging from -43 to 30 mJ⋅m^-2 and from -28 to 66 mJ⋅m^-2, respectively, as the degree of local chemical order increases. The state of local ordering also strongly correlates with the energy difference between the face-centered cubic (fcc) and hexagonal close-packed (hcp) phases, which affects the occurrence of transformation-induced plasticity. This theoretical study demonstrates that chemical short-range order is thermodynamically favored in HEAs and can be tuned to affect the mechanical behavior of these alloys. It thus addresses the pressing need to establish robust processing-structure-property relationships to guide the science-based design of new HEAs with targeted mechanical behavior.

Influence of Annealing on Microstructure and Mechanical Properties of a Nanocrystalline CrCoNi Medium-Entropy Alloy

An equiatomic CrCoNi medium-entropy alloy was subjected to high-pressure torsion. This process led to a refinement of the microstructure to a grain size of about 50 nm, combined with a strong increase in the materials hardness. Subsequently, the thermodynamic stability of the medium entropy alloy was evaluated by isothermal and isochronal heat treatments. Annealed samples were investigated by scanning and transmission electron microscopy as well as X-ray diffraction, and were subjected to tensile tests to establish microstructure-property relationships. Furthermore, a comparison of mechanical properties with a grade 316L stainless steel was performed in order to evaluate if the CrCoNi alloy is competitive with commercially available structural materials in the nanocrystalline state. A minority phase embedded in the face-centered cubic matrix of the CrCoNi alloy could be observed in multiple annealed states, as well as the as-received and high-pressure torsion processed material. For 200 h of annealing at 500 °C, it was determined that the minority phase has a hexagonal-closed-packed crystal structure. A possible explanation for the formation of the phase is a preferential segregation of Co to stacking faults.

Local structure and defects in ion irradiated KTaO3

The modification of the local structure in cubic perovskite KTaO₃ irradiated with 3 MeV and 1.1 GeV Au ions is studied by Raman and x-ray absorption spectroscopy, complemented by density functional theory (DFT) calculations. In the case of irradiation with 3 MeV Au ions where displacement cascade processes are dominant, the Ta L₃-edge x-ray absorption measurements suggest that a peak corresponding to the Ta-O bonds in the TaO₆ octahedra splits, which is attributed to the formation of Ta_K antisite defects that are coupled with oxygen vacancies, V _O. This finding is consistent with the DFT calculations. Under irradiation with 1.1 GeV ions, the intense ionization and electronic energy deposition lead to a blue shift and an intensity reduction of active Raman bands. In the case of sequential irradiations, extended x-ray absorption fine structure measurements reveal a decrease in concentration of coupled Ta_K-V _O defects under subsequent irradiation with 1.1 GeV Au ions.