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The discovery of complex concentrated alloys has unveiled materials with diverse atomic environments, prompting the exploration of solute segregation beyond dilute alloys. Data-driven methods offer promising for modeling segregation in such chemically complex environments, and are employed in this study to understand segregation behavior of a refractory complex concentrated alloy, NbMoTaW. A flexible methodology is developed that uses composable computational modules, with different arrangements of these modules employed to obtain site availabilities at absolute zero and the corresponding density of states beyond the dilute limit, resulting in an extremely large dataset containing 10 million data points. The artificial neural network developed here can rely solely on descriptions of local atomic environments to predict behavior at the dilute limit with very small errors, while the addition of negative segregation instance classification allows any solute concentration from zero up to the equiatomic concentration for ternary or quaternary alloys to be modeled at room temperature. The machine learning model thus achieves a significant speed advantage over traditional atomistic simulations, being four orders of magnitude faster, while only experiencing a minimal reduction in accuracy. This efficiency presents a powerful tool for rapid microstructural and interfacial design in unseen domains. Scientifically, our approach reveals a transition in the segregation behavior of Mo from unfavorable in simple systems to favorable in complex environments. Additionally, increasing solute concentration was observed to cause anti-segregation sites to begin to fill, challenging conventional understanding and highlighting the complexity of segregation dynamics in chemically complex environments.

Grain boundary (GB) segregation models are derived for multi-principal element and high-entropy alloys (MPEAs and HEAs). Differing from classical models where one component is taken as solvent and others are considered solutes, these models are referenced to the bulk composition to enable improved treatments of MPEAs and HEAs with no principal components. An ideal solution model is first formulated and solved to obtain analytical expressions that predict GB segregation and GB energy in MPEAs and HEAs. A regular solution model is further derived. The GB composition calculated using the simple analytical expression derived in this study and data from the Materials Project agree well with a prior sphosipcated atomistic simulation for NbMoTaW. The simplicity of the derived analytical expressions makes them useful for not only conveniently predicting GB segregation trends in HEAs, but also analyzing nascent interfacial phenomena in composionally complex GBs. As an application example, the derived models are used to further formulate a set of useful equations to elucidate an emergent concept of high-entropy grain boundaries (HEGBs).

Grain boundary structural transitions can lead to significant changes in the properties and performance of materials. In multi-principal element alloys, understanding these transitions becomes complex due to phenomena such as local chemical ordering and multi-component segregation. Using atomistic simulations, we explore a metastable-to-equilibrium grain boundary structural transition in NbMoTaW. The transition, characterized by structural disordering and reduced free volume, shows high sensitivity to its local chemical environment. Most notably, the transition temperature range of the alloy is more than twice that of a pure metal. Differences in composition between coexisting metastable and equilibrium structures highlight the change in local site availability due to structural relaxation. Further examination of grain boundaries with fixed chemical states at varying temperatures reveals that the amount of segregation significantly influences the onset temperature yet has minimal effect on the transition width. These insights underscore the profound effects of chemical complexity and ordering on grain boundary transitions in complex concentrated alloys, marking a meaningful advancement in our understanding of grain boundary behavior at the atomic level.

Tailoring microstructures represents a daunting goal in materials science. Here, an innovative proposition is to utilize grain boundary (GB) complexions (a.k.a. interfacial phases) to manipulate microstructural evolution, which is challenging to control via only temperature and doping. Herein, we use ZnO as a model system to tailor microstructures using applied electric fields as a new knob to control GB structures locally via field-driven stoichiometry (defects) polarization. Specifically, continuously graded microstructures are created under applied electric fields. By employing aberration-corrected scanning transmission electron microscopy (AC STEM) in conjunction with density functional theory (DFT) and ab initio molecular dynamics (AIMD), we discover cation-deficient, oxygen-rich GBs near the anode with enhanced GB diffusivities. In addition, the field-driven redistribution of cation vacancies is deduced from a defect chemistry model, and subsequently verified by spatially resolved photoluminescence spectroscopy. This bulk stoichiometry polarization leads to preferential formation of cation-deficient (oxidized) GBs near the anode to gradually promote grain growth towards the anode. This mechanism can be utilized to create continuously graded microstructures without abnormal grain growth typically observed in prior studies. This study exemplifies a case of tailoring microstructural evolution via altering GB complexions locally with applied electric fields, and it enriches fundamental GB science.

Compositionally complex ceramics (CCCs), including high-entropy ceramics (HECs) as a subclass, offer new opportunities of materials discovery beyond the traditional methodology of searching new stoichiometric compounds. Herein, we establish new strategies of tailoring CCCs via a seamless combination of (1) non-equimolar compositional designs and (2) controlling microstructures and interfaces. Using oxide solid electrolytes for all-solid-state batteries as an exemplar, we validate these new strategies via discovering a new class of compositionally complex perovskite oxides (CCPOs) to show the possibility of improving ionic conductivities beyond the limit of conventional doping. As an example (amongst the 28 CCPOs examined), we demonstrate that the ionic conductivity can be improved by >60% in (Li0.375Sr0.4375)(Ta0.375Nb0.375Zr0.125Hf0.125)O3-{\delta}, in comparison with the state-of-art (Li0.375Sr0.4375)(Ta0.75Zr0.25)O3-{\delta} (LSTZ) baseline, via maintaining comparable electrochemical stability. Furthermore, the ionic conductivity can be improved by another >70% via grain boundary (GB) engineering, achieving >270% of the LSTZ baseline. This work suggests transformative new strategies for designing and tailoring HECs and CCCs, thereby opening a new window for discovering materials for energy storage and many other applications.

Nanocrystalline alloys (nanoalloys) are prone to grain growth. It is known that grain boundary segregation and precipitation can stabilize nanoalloys, but the stabilization becomes less effective at high temperatures and adding grain growth inhibitors often reduces sinterability. Herein, we have simultaneously achieved improved sinterability and exceptional high-temperature stability for a class of MoNbTaTiW-based refractory high-entropy nanoalloys (RHENs). Bulk pellets of RHENs were fabricated through planetary ball milling and spark plasma sintering, achieving 93-96% relative densities with 50-100 nm grain sizes for three compositions. For example, Mo17.8Nb17.8Ta17.8Ti17.8W17.8Ni6Zr5 sintered at 1300 {\deg}C attained ~96% relative density with ~55 nm mean grain size. Moreover, these RHENs exhibited exceptional stability at 1300 {\deg}C. Both Ti17.8Nb17.8Mo17.8Ta17.8W17.8Ni6Zr5 and Mo18.8Nb18.8Ta18.8Ti18.8W18.8Ni6 retained <150 nm grain sizes with >96% of the theoretical densities after five hours annealing at 1300 {\deg}C. Notably, the addition of Ni, a well-known sintering aid for activated sintering of refractory metals such as W and Mo, in high-entropy MoNbTaTiW can promote sintering while maintaining high-temperature stability against rapid grain growth, which can be explained by hypothesized effects of high-entropy grain boundaries. These RHENs possess some of the highest temperature stability achieved for nanoalloys and ultrafine-grained metals.

Refractory multi-principal element alloys exhibiting promising mechanical properties such as excellent strength retention at elevated temperatures have been attracting increasing attention. Although their inherent chemical complexity is considered a defining feature, a challenge arises in predicting local chemical ordering, particularly in grain boundary regions with enhanced structural disorder. In this study, we use atomistic simulations of a large group of bicrystal models to sample a wide variety of interfacial sites (grain boundary) in NbMoTaW and explore emergent trends in interfacial segregation and the underlying structural and chemical driving factors. Sampling hundreds of bicrystals along the [001] symmetric tilt axis and analyzing more than one hundred and thirty thousand grain boundary sites with a variety of local atomic environments, we uncover segregation trends in NbMoTaW. While Nb is the dominant segregant, more notable are the segregation patterns that deviate from expected behavior and mark situations where local structural and chemical driving forces lead to interesting segregation events. For example, incomplete depletion of Ta in low-angle boundaries results from chemical pinning due to favorable local compositional environments associated with chemical short-range ordering. Finally, machine learning models capturing and comparing the structural and chemical features of interfacial sites are developed to weigh their relative importance and contributions to segregation tendency, revealing a significant increase in predictive capability when including local chemical information. Overall, this work, highlighting the complex interplay between local grain boundary structure and chemical short-range ordering, suggest tunable segregation and chemical ordering by tailoring grain boundary structure in multi-principal element alloys.

Solar thermochemical hydrogen generation (STCH) is a promising approach for eco-friendly H2 production, but conventional STCH redox compounds often suffer from thermodynamic and kinetic limitations with limited tunability. Expanding from the nascent high-entropy ceramics field, this study explores a new class of compositionally complex perovskite oxides (La0.8Sr0.2)(Mn(1-x)/3Fe(1-x)/3CoxAl(1-x)/3)O3 for STCH. In situ X-ray diffraction demonstrates the phase stability during redox cycling and in situ X-ray photoelectron spectroscopy shows preferential redox of Co. The extent of reduction increases, but the intrinsic kinetics decreases, with increased Co content. Consequently, (La0.8Sr0.2)(Mn0.2Fe0.2Co0.4Al0.2)O3-{\delta} achieves an optimal balance between the thermodynamics and kinetics properties. The combination of a moderate enthalpy of reduction, high entropy of reduction, and preferable surface oxygen exchange kinetics enables a maximum H2 yield of 395 +- 11 {\mu}mol g-1 in a short 1-hour redox duration. Entropy stabilization expectedly contributes to the structure stability during redox without phase transformation, which enables an exceptional STCH stability for >50 cycles under harsh interrupted conditions. The underlying redox mechanism is further elucidated by the density functional theory based parallel Monte Carlo computation, which represents a new computation paradigm first established here. This study suggests a new class of non-equimolar compositionally complex ceramics for STCH and chemical looping.

Do high-entropy alloys and ceramics have their grain boundary (GB) counterparts? As the concept of high-entropy grain boundaries (HEGBs) was initially proposed in 2016, this article provides the first complete and rigorous discussion of the underlying interfacial thermodynamics. A simplified segregation model can illustrate both GB and bulk high-entropy effects, which reduce GB energy with increasing temperature for saturated multicomponent (conventional and high-entropy) alloys. HEGBs can be utilized to stabilize nanocrystalline alloys at high temperatures via thermodynamic and kinetic effects. GB structural disordering and transitions offer further opportunities to attain higher effective GB entropies. Future perspective is discussed.

Grain boundaries (GBs) can be treated as two-dimensional (2-D) interfacial phases (also called 'complexions') that can undergo interfacial phase-like transitions. As bulk phase diagrams and calculation of phase diagram (CALPHAD) methods are a foundation for modern materials science, we propose to extend them to GBs to have equally significant impacts. This perspective article reviews a series of studies to compute the GB counterparts to bulk phase diagrams. First, a phenomenological interfacial thermodynamic model was developed to construct GB lambda diagrams to forecast high-temperature GB disordering and related trends in sintering and other properties for both metallic and ceramic materials. In parallel, an Ising-type lattice statistical thermodynamic model was utilized to construct GB adsorption diagrams, which predicted first-order GB adsorption (a.k.a. segregation) transitions and critical phenomena. These two simplified thermodynamic models emphasize on the GB structural (disordering) and chemical (adsorption) aspects, respectively. Subsequently, hybrid Monte Carlo and molecular dynamics atomistic simulations were used to compute more rigorous and accurate GB 'phase' diagrams. Computed GB diagrams of thermodynamic and structural properties were further extended to include mechanical properties. Moreover, machine learning was combined with atomistic simulations to predict GB properties as functions of four independent compositional variables and temperature in a 5-D space for a given GB in high-entropy alloys or as functions of five GB macroscopic (crystallographic) degrees of freedom (DOFs) plus temperature and composition for a binary alloy in a 7-D space. Relevant other studies are examined. Future perspective and outlook, including two emerging fields of high-entropy grain boundaries (HEGBs) and electrically (or electrochemically) induced GB transitions, are discussed.

This invited talk will review a series of our recent studies on high-entropy ceramics (HECs) and compositionally complex ceramics (CCCs) and discuss the future perspective. Various single-phase equimolar quinary (five-component) HECs, e.g., MB2, MB, M3B4, MB4, and MB6 borides, MSi2 and M3Si5 silicides, perovskite, fluorite, and pyrochlore oxides, and (intermetallic) aluminides have been fabricated. We further proposed to extend HECs to CCCs to include non-equimolar compositions and further consider short- and long-range orders, which reduce configurational entropies but offer additional dimensions and opportunities to tailor and improve various properties. We also reported the first dual-phase HECs/CCCs. Using compositionally complex fluorite-based oxides (CCFBOs, which can possess fluorite or defect fluorite, pyrochlore, weberite, fergusonite, and bixbyite phases) as the model systems, we have recently discovered long- and short- range orders, composition- and redox-induced order-disorder transitions (ODTs), and ultrahigh-entropy weberite and fergusonite phases in several 10- to 21-component systems.

Interfacial segregation and chemical short-range ordering influence the behavior of grain boundaries in complex concentrated alloys. In this study, we use atomistic modeling of a NbMoTaW refractory complex concentrated alloy to provide insight into the interplay between these two phenomena. Hybrid Monte Carlo and molecular dynamics simulations are performed on columnar grain models to identify equilibrium grain boundary structures. Our results reveal extended near-boundary segregation zones that are much larger than traditional segregation regions, which also exhibit chemical patterning that bridges the interfacial and grain interior regions. Furthermore, structural transitions pertaining to an A2-to-B2 transformation are observed within these extended segregation zones. Both grain size and temperature are found to significantly alter the widths of these regions. Analysis of chemical short-range order indicates that not all pairwise elemental interactions are affected by the presence of a grain boundary equally, as only a subset of elemental clustering types are more likely to reside near certain boundaries. The results emphasize the increased chemical complexity that is associated with near-boundary segregation zones and demonstrate the unique nature of interfacial segregation in complex concentrated alloys.

We report on high-order harmonic generation in the two-band superconductor MgB$_2$ driven by intense terahertz electromagnetic pulses. Third- and fifth-order harmonics are resolved in time domain and investigated as a function of temperature and in applied magnetic fields crossing the superconducting phase boundary. The high-order harmonics in the superconducting phase reflects nonequilibrium dynamics of the superconducting order parameter in MgB$_2$, which is probed via nonlinear coupling to the terahertz field. The observed temperature and field dependence of the nonlinear response allows to establish the superconducting phase diagram., Comment: 9 pages, 5 figures

Oxide solid electrolytes (OSEs) have the potential to achieve improved safety and energy density for lithium-ion batteries, but their high grain-boundary (GB) resistance is a general bottleneck. In the most well studied perovskite OSE, Li3xLa2/3-xTiO3 (LLTO), the ionic conductivity of GBs is about three orders of magnitude lower than that of the bulk. In contrast, the related Li0.375Sr0.4375Ta0.75Zr0.25O3 (LSTZ0.75) perovskite exhibits low GB resistance for reasons yet unknown. Here, we used aberration-corrected scanning transmission electron microscopy and spectroscopy, along with an active learning moment tensor potential, to reveal the atomic scale structure and composition of LSTZ0.75 GBs. Vibrational electron energy loss spectroscopy is applied for the first time to characterize the otherwise unmeasurable Li distribution in GBs of LSTZ0.75. We found that Li depletion, which is a major reason for the low GB ionic conductivity of LLTO, is absent for the GBs of LSTZ0.75. Instead, the low GB resistivity of LSTZ0.75 is attributed to the formation of a unique defective cubic perovskite interfacial structure that contained abundant vacancies. Our study provides insights into the atomic scale mechanisms of low GB resistivity and sheds light on possible paths for designing OSEs with high total ionic conductivity.

Two new high-entropy ceramics (HECs) in the weberite and fergusonite structures, along with unexpected formation of ordered pyrochlore phases with ultrahigh-entropy compositions and an abrupt pyrochlore-weberite transition, are discovered in a 21-component oxide system. While the Gibbs phase rule allows 21 equilibrium phases, nine out of the 13 compositions examined possess single HEC phases (with ultrahigh ideal configurational entropies: ~2.7kB per cation or higher on one sublattice in most cases). Notably, (15RE1/15)(Nb1/2Ta1/2)O4 possess a single monoclinic fergusonite (C2/c) phase and (15RE1/15)3(Nb1/2Ta1/2)1O7 form a single orthorhombic (C2221) weberite phase, where 15RE1/15 represents Sc1/15Y1/15La1/15Pr1/15Nd1/15Sm1/15Eu1/15Gd1/15Tb1/15Dy1/15Ho1/15Er1/15Tm1/15Yb1/15Lu1/15. Moreover, a series of eight (15RE1/15)2+x(Ti1/4Zr1/4Ce1/4Hf1/4)2-2x(Nb1/2Ta1/2)xO7 specimens all exhibit single phases, where a pyrochlore-weberite transition occurs within 0.75 < x < 0.8125. This cubic-to-orthorhombic transition does not change the temperature-dependent thermal conductivity appreciably, as the amorphous limit may have already been achieved in the ultrahigh-entropy 21-component oxides. These discoveries expand the diversity and complexity of HECs, towards many-component compositionally complex ceramics (CCCs) and ultrahigh-entropy ceramics.

This study discovers a reversible order-disorder transition (ODT) in a 10-cation compositionally complex ceramic, (Nd0.15Pr0.15Dy0.8Ho0.8Er0.8Ti0.2Yb0.1Hf0.1Zr0.1Nb0.8)O7-delta, induced via annealing in oxidized vs. reduced environments at 1600C. Notably, the 10-cation oxide remains a homogenous single-phase high-entropy solid solution before and after the ODT in the pyrochlore vs. fluorite structure that can be quenched. In-situ neutron diffraction reveals the oxygen vacancy formation and atomic displacement during this ODT. The temperature dependence of thermal conductivity is altered by the ODT. This study reveals a new pathway to induce ODT via a redox transition to tailor the properties of compositionally complex fluorite-based oxides.

A new type of compositionally complex (medium- or high-entropy) M5Si3 silicides is synthesized. Both (V1/5Cr1/5Nb1/5Ta1/5W1/5)5Si3 and (Ti1/5Zr1/5Nb1/5Mo1/5Hf1/5)5Si3 form single-phase homogenous solid solutions. Notably, (V1/5Cr1/5Nb1/5Ta1/5W1/5)5Si3 forms the hexagonal gamma (D88) phase, while all its five constituent binary silicides, V5Si3, Cr5Si3, Nb5Si3, Ta5Si3, and W5Si3, are stable in the tetragonal alpha (D8l) or beta (D8m) phases. Annealing at 1600C demonstrates that this hexagonal gamma phase is stable. Comparison of the experimental and calculated X-ray diffraction patterns, Rietveld refinements, and analysis of aberration-corrected scanning transmission electron microscopy high-angle annular dark-field images suggest cation ordering, which reduces the configurational entropy. This work expands the field of high-entropy and compositional complex ceramics by not only discovering a new compositional complex silicide phase but also demonstrating the cation ordering and unusual phase stability. These compositionally complex silicides can be combined with refractory high-entropy alloys to make the high-entropy counterparts to the Nb-silicide and Mo-Si-B composites.

Grain boundaries have been shown to dramatically influence the behavior of relatively simple materials such as monatomic metals and binary alloys. The increased chemical complexity associated with multi-principal element alloys is hypothesized to lead to new grain boundary phenomena. To explore the relationship between grain boundary structure and chemistry in these materials, hybrid molecular dynamics/Monte Carlo simulations of a faceted {\Sigma}11 <110> tilt boundary, chosen to sample both high- and low-energy boundary configurations, are performed in face-centered cubic CrFeCoNiCu and CrFeCoNi equiatomic alloys. Unexpected enrichment of Fe is discovered in the face-centered cubic regions adjacent to the interface and found to be correlated with a structurally-distinct region of reduced atomic volume. Comparison with the boundary of the same type in monatomic Cu demonstrates that altered near-boundary regions exist in simpler systems as well, with the chemical complexity of the multi-principal element alloys highlighting its existence and importance.

Machine learning (ML) models utilizing structure-based features provide an efficient means for accurate property predictions across diverse chemical spaces. However, obtaining equilibrium crystal structures typically requires expensive density functional theory (DFT) calculations, which limits ML-based exploration to either known crystals or a small number of hypothetical crystals. Here, we demonstrate that the application of Bayesian optimization with symmetry constraints using a graph deep learning energy model can be used to perform "DFT-free" relaxations of crystal structures. Using this approach to significantly improve the accuracy of ML-predicted formation energies and elastic moduli of hypothetical crystals, two novel ultra-incompressible hard materials MoWC2 (P63/mmc) and ReWB (Pca21) were identified and successfully synthesized via in-situ reactive spark plasma sintering from a screening of 399,960 transition metal borides and carbides. This work addresses a critical bottleneck to accurate property predictions for hypothetical materials, paving the way to ML-accelerated discovery of new materials with exceptional properties.

Computing the grain boundary (GB) counterparts to bulk phase diagrams represents an emerging research direction. Using a classical embrittlement model system Ga-doped Al alloy, this study demonstrates the feasibility of computing temperature- and composition-dependent GB diagrams to represent not only equilibrium thermodynamic and structural characters, but also mechanical properties. Specifically, hybrid Monte Carlo and molecular dynamics (MC/MD) simulations are used to obtain the equilibrium GB structure as a function of temperature and composition. Simulated GB structures are validated by aberration-corrected scanning transmission electron microscopy. Subsequently, MD tensile tests are performed on the simulated equilibrium GB structures. GB diagrams are computed for not only GB adsorption and structural disorder, but also interfacial structural and chemical widths, MD ultimate tensile strength, and MD tensile toughness. This study suggests a research direction to investigate GB composition-structure-property relationships via computing GB diagrams of thermodynamic, structural, and mechanical (or potentially other) properties.

For the first time, a group of CaB6-typed cubic rare earth high-entropy hexaborides have been successfully fabricated into dense bulk pellets (>98.5% in relative densities). The specimens are prepared from elemental precursors via in-situ metal-boron reactive spark plasma sintering. The sintered bulk pellets are determined to be single-phase without any detectable oxides or other secondary phases. The homogenous elemental distributions have been confirmed at both microscale and nanoscale. The Vickers microhardness are measured to be 16-18 GPa at a standard indentation load of 9.8 N. The nanoindentation hardness and Young's moduli have been measured to be 19-22 GPa and 190-250 GPa, respectively, by nanoindentation test using a maximum load of 500 mN. The material work functions are determined to be 3.7-4.0 eV by ultraviolet photoelectron spectroscopy characterizations, which are significantly higher than that of LaB6.

Rare-earth niobates and tantalates possess low thermal conductivities, which can be further reduced in high-entropy compositions. Here, a large number of 40 compositions are synthesized to investigate the origin of low thermal conductivity. Amongst, 29 possess single (nominally cubic) fluorite phases and most of them are new compositionally complex (medium- or high-entropy) compositions. One new finding is that doping 2 % of light element cations can further reduce thermal conductivity. This large data set enables the discovery of a negative correlation between the thermal conductivity and averaged radius ratio of the 3+/5+ cations. While this ratio is still below the threshold for forming long-range ordered weberite phases, this correlation suggests the reduced thermal conductivity is related to short-range weberite order, which is indeed revealed by diffuse scattering in X-ray and neutron diffraction. Specifically, neutron diffraction is used characterize five selected specimens. A better fit to a weberite structure is found at nanoscale (~1 nm). The characteristic length (domain size) is smaller but with stronger short-range ordering in more insulative materials. As it approaches the Ioffe-Regel limit, the phonon limit breaks down and "diffusons" give rise to the observed amorphous-like thermal conductivity. Disordered oxygen sublattices are also confirmed by neutron diffraction.

A systematics of grain boundary (GB) segregation transitions and critical phenomena has been derived to expand the classical GB segregation theory. Using twist GBs as an example, this study uncovers when GB layering vs. prewetting transitions should occur and how they are related to one another. Moreover, a novel descriptor, normalized segregation strength (phi_seg), is introduced. It can represent several factors that control GB segregation, including strain and bond energies, as well as misorientation for small-angle GBs (in a mean-field approximation), which had to be treated separately in prior models. In a strong segregation system with a large phi_seg, first-order layering transitions occur at low temperatures and become continuous above GB roughing temperatures. With reducing phi_seg, the layering transitions gradually merge and finally lump into prewetting transitions without quantized layer numbers, akin to Cahn's critical-point wetting model. Furthermore, GB complexion diagrams with universal characters are constructed as the GB counterpart to the classical exemplar of Pelton-Thompson regular-solution binary bulk phase diagrams.

Electric fields and currents, which are used in innovative materials processing and electrochemical energy conversion, can often alter microstructures in unexpected ways. However, little is known about the underlying mechanisms. Using ZnO-Bi2O3 as a model system, this study uncovers how an applied electric current can change the microstructural evolution through an electrochemically induced grain boundary (GB) transition. By combining aberration-corrected electron microscopy, photoluminescence spectroscopy, first-principles calculations, a generalizable thermodynamic model, and ab initio molecular dynamics, this study reveals that electrochemical reduction can cause a GB disorder-to-order transition to markedly increase GB diffusivities and mobilities. Consequently, abruptly enhanced or abnormal grain growth takes place. These findings advance our fundamental knowledge of GB complexion (phase-like) transitions and electric field effects on microstructural stability and evolution, with broad scientific and technological impacts. A new method to tailor the GB structures and properties, as well as the microstructures, electrochemically can also be envisioned., Comment: 70 pages, 26 (6 main + 20 Supplementary) Figures

Grain boundaries (GBs) can critically influence the microstructural evolution and various materials properties. However, a fundamental understanding of GBs in high-entropy alloys (HEAs) is lacking because of the complex couplings of the segregations of multiple elements and interfacial disordering, which can generate new phenomena and challenge the classical theories. Here, by combining large-scale atomistic simulations and machine learning, we demonstrate the feasibility of predicting the GB properties as functions of four independent compositional degrees of freedoms and temperature in a 5D space. Subsequently, GB counterparts to bulk phase diagrams are constructed for the first time for quinary HEAs. A data-driven discovery further reveals new coupled segregation and disordering effects in HEAs. Notably, an analysis of a large dataset discovers a critical compensation temperature at which the segregations of all elements virtually vanish simultaneously. While the machine learning model can predict GB properties via a black-box approach, a surrogate data-based analytical model (DBAM) is constructed to provide more physics insights and better transferability, with good accuracies. This study not only provides a new paradigm enabling prediction of GB properties in a 5D space, but also uncovers new GB segregation phenomena in HEAs beyond the classical GB segregation models.

Improved thermomechanical properties have been reported for various high-entropy oxides containing typically five metal cations. This study further investigates a series of duodenary (11 metals + oxygen) high-entropy oxides by mixing different fractions of a five-cation fluorite-structured niobate and a seven-cation pyrochlore (both containing Yb) with matching lattice constants. Nine compositions of duodenary high-entropy oxides have been examined. All of them exhibit single high-entropy phases of either disordered fluorite or ordered pyrochlore structure. An order-disorder transition (ODT) is evident with changing composition, accompanied by a reduction in thermal conductivity (k). In comparison with the ODT criteria developed from ternary oxides, these duodenary oxides are more prone to disorder, but the ODT is still controlled by similar factors (but at different thresholds). Interestingly, there are abrupt increases in Young's modulus (E) at low mixing concentrations near both endmembers. The E/k ratios are increased, in comparison with both endmembers. This study suggests a new route to tailor high-entropy ceramics via controlling cation ordering vs. disordering.

Six high-entropy rare earth tetraborides of the tetragonal UB4-prototyped structure have been successfully synthesized for the first time. The specimens are prepared from elemental precursors via high-energy ball mill and in-situ reactive spark plasma sintering. The sintered specimens are >98% in relative densities without detectable oxide impurities (albeit the presence of minor hexaborides in some compositions). No detectable secondary phase is observed in the composition (Y$_{0.2}$Nd$_{0.2}$Sm$_{0.2}$Gd$_{0.2}$Tb$_{0.2}$)B$_{4}$, which is proven homogeneous at both microscale and nanoscale. The Vickers microhardness are determined to be ~13-15 GPa at a standard indentation load of 9.8 N. A scientifically interesting observation is represented by the anisotropic lattice distortion from the rule-of-mixture averages. This work expands the family of high-entropy ceramics via fabricating a new class of high-entropy borides with a unique tetragonal quasi-layered crystal structure.

Single-phase high-entropy monoborides (HEMBs) of the CrB prototype structure have been synthesized for the first time. Reactive spark plasma sintering of ball milled mixtures of elemental precursor powders produced bulk (V0.2Cr0.2Nb0.2Mo0.2Ta0.2)B, (V0.2Cr0.2Nb0.2Mo0.2W0.2)B, and (V0.2Cr0.2Nb0.2Ta0.2W0.2)B HEMB specimens of ~98.3-99.5% relative densities. Vickers hardness was measured to be ~22-26 GPa at an indentation load of 9.8 N and ~32-37 GPa at 0.98 N. In particular, the load-dependent hardness of (V0.2Cr0.2Nb0.2Ta0.2W0.2)B is higher than those of ternary (Ta0.5W0.5)B (already considered as superhard) and hardest reported high-entropy metal diborides, and on a par with the classical superhard boride WB4., Comment: 29 pages, 3 main plus 8 suppl, figures; 1 main plus 2 suppl. tables

Grain boundaries (GBs) often control the processing and properties of polycrystalline materials. Here, a potentially transformative research is represented by constructing GB property diagrams as functions of temperature and bulk composition, also called "complexion diagrams," as a general materials science tool on par with phase diagrams. However, a GB has five macroscopic (crystallographic) degrees of freedom (DOFs). It is essentially a "mission impossible" to construct property diagrams for GBs as a function of five DOFs by either experiments or modeling. Herein, we combine isobaric semi-grand-canonical ensemble hybrid Monte Carlo and molecular dynamics (hybrid MC/MD) simulations with a genetic algorithm (GA) and deep neural network (DNN) models to tackle this grand challenge. The DNN prediction is ~108 faster than atomistic simulations, thereby enabling the construction of the property diagrams for millions of distinctly different GBs of five DOFs. Notably, excellent prediction accuracies have been achieved for not only symmetric-tilt and twist GBs, but also asymmetric-tilt and mixed tilt-twist GBs; the latter are more complex and much less understood, but they are ubiquitous and often limit the performance properties of real polycrystals as the weak links. The data-driven prediction of GB properties as function of temperature, bulk composition, and five crystallographic DOFs (i.e., in a 7D space) opens a new paradigm.

A series of dual-phase high-entropy ultrahigh temperature ceramics (DPHE-UHTCs) are fabricated starting from N binary borides and (5-N) binary carbides powders. >~99% relative densities have been achieved with virtually no native oxides. These DPHE-UHTCs consist of a hexagonal high-entropy boride (HEB) phase and a cubic high-entropy carbide (HEC) phase. A thermodynamic relation that governs the compositions of the HEB and HEC phases in equilibrium is discovered and a thermodynamic model is proposed. These DPHE-UHTCs exhibit tunable grain size, Vickers microhardness, Young' and shear moduli, and thermal conductivity. The DPHE-UHTCs have higher hardness than the weighted linear average of the two single-phase HEB and HEC, which are already harder than the rule-of-mixture averages of individual binary borides and carbides. This study extends the state of the art by introducing dual-phase high-entropy ceramics (DPHECs), which provide a new platform to tailor various properties via changing the phase fraction and microstructure.

High-entropy ceramics (HECs) have quickly gained attention since 2015. To date, nearly all work has focused on five-component, equimolar compositions. This perspective article briefly reviews different families of HECs and selected properties. Following a couple of our most recent studies, we propose a step forward to expand HECs to Compositionally Complex ceramics (CCCs) to include medium-entropy and non-equimolar compositions. Using defective fluorite and ordered pyrochlore oxides as two primary examples, we further consider the complexities of aliovalent cations and anion vacancies as well as ordered structures with two cation sublattices. Better thermally-insulating yet stiff CCCs have been found in non-equimolar compositions with optimal amounts of oxygen vacancies and in ordered pyrochlores with substantial size disorder. It is demonstrated that medium-entropy ceramics (MECs) can prevail over their high-entropy counterparts. The diversifying classes of CCCs provide even more possibilities than HECs to tailor the composition, defects, disorder/order, and, consequently, various properties., Comment: 32 pages, 6 figures

Five single-phase WB2- and MoB2-containing high-entropy borides (HEBs) have been made via reactive spark plasma sintering of elemental boron and metals. A large reactive driving force enables the full dissolution of 10-20 mol. % WB2 to form dense, single-phase HEBs, including (Ti0.2Zr0.2Hf0.2Mo0.2W0.2)B2, (Ti0.2Ta0.2Cr0.2Mo0.2W0.2)B2, (Zr0.2Hf0.2Nb0.2Ta0.2W0.2)B2, and (Zr0.225Hf0.225Ta0.225Mo0.225W0.1)B2; the successful fabrication of such single-phase WB2-containing HEBs has not been reported before. In the processing science, this result serves perhaps the best example demonstrating that the phase formation in high-entropy ceramics can strongly depend on the kinetic route. A scientifically interesting finding is that HEBs containing softer WB2 and/or MoB2 components are significantly harder than (Ti0.2Zr0.2Hf0.2Nb0.2Ta0.2)B2 (with harder binary boride components). This exemplifies that high-entropy ceramics can achieve unexpected properties.

High-entropy ceramics generally exhibit reduced thermal conductivity, but little is known about what controls this suppression and which descriptor can predict it. Herein, 18 medium- and high-entropy pyrochlores were synthesized to measure their thermal conductivity and Young's modulus. Up to 35% reductions in thermal conductivity were achieved with retained moduli, thereby attaining insulative yet stiff properties for potential thermal barrier coating applications. Notably, the measured thermal conductivity correlates well with a modified size disorder parameter. Thus, this modified size disorder parameter is suggested as a useful descriptor for designing thermally-insulative medium- and high-entropy ceramics (broadly defined as "compositionally-complex ceramics").

Using fluorite oxides as an example, this study broadens high-entropy ceramics (HECs) to compositionally-complex ceramics (CCCs) or multi-principal cation ceramics (MPCCs) to include medium-entropy and/or non-equimolar compositions. Nine compositions of compositionally-complex fluorite oxides (CCFOs) with the general formula of (Hf1/3Zr1/3Ce1/3)1-x(Y1/2X1/2)xO2-delta (X = Yb, Ca, and Gd; x = 0.4, 0.148, and 0.058) are fabricated. The phase stability, mechanical properties, and thermal conductivities are measured. Compared with yttria-stabilized zirconia, these CCFOs exhibit increased cubic phase stability and reduced thermal conductivity, while retaining high Young's modulus (~210 GPa) and nanohardness (~18 GPa). Moreover, the temperature-dependent thermal conductivity in the non-equimolar CCFOs shows an amorphous-like behavior. In comparison with their equimolar high-entropy counterparts, the medium-entropy non-equimolar CCFOs exhibit even lower thermal conductivity (k) while maintaining high modulus (E), thereby achieving higher E/k ratios. These results suggest a new direction to achieve thermally-insulative yet stiff CCCs (MPCCs) via exploring non-equimolar and/or medium-entropy compositions., Comment: 39 pages; 8 + 5 figures; Accepted for publications in Journal of the European Ceramic Society (1/7/2020)

High entropy materials, which include high entropy alloys, carbides, and borides, are a topic of substantial research interest due to the possibility of a large number of new material compositions that could fill gaps in application needs. There is a current need for materials exhibiting high temperature stability, particularly oxidation resistance. A systematic understanding of the oxidation behavior in high entropy materials is therefore required. Prior work notes large differences in the thermodynamic favorability between oxides formed upon oxidation of high entropy materials. This work uses both analytical and computational thermodynamic approaches to investigate and quantify the effects of this large variation and the resulting potential for preferential component oxidation in refractory high entropy materials including group IV-, V- and VI-element based alloys and ceramics. Thermodynamic calculations show that a large tendency towards preferential oxidation is expected in these materials, even for elements whose oxides exhibit a small difference in thermodynamic favorability. The effect is reduced in carbides, compared to their alloy counterparts. Further, preferential oxidation in high entropy refractory materials could result in possible destabilization of the solid solution or formation of other, competing phases, with corresponding changes in bulk material properties., Comment: Acta Materialia. (2020). Also see Part II of this work: https://doi.org/10.1016/j.actamat.2020.07.004

High-entropy intermetallic compounds (HEICs) were fabricated by mechanical alloying and spark plasma sintering to fill a knowledge gap between the traditional high-entropy alloys (HEAs) and emerging high-entropy ceramics (HECs). Notably, several four- or five-component equimolar aluminides, such as the B2-phase (Fe1/5Co1/5Ni1/5Mn1/5Cu1/5)Al, have been made into single-phase HEICs for the first time. Thermodynamic modeling and a reversible, temperature-dependent, phase-stability experiment suggest that such B2-phase HEICs are entropy-stabilized phases. The structure of these HEICs resembles that of HECs with high-entropy mixing of four or five elements of nearly equal fractions in one and only one sublattice, but with significant (~10%) anti-site defects (differing from typical HECs). A new phase stability rule for forming single B2-phase HEICs is proposed. Five additional HEICs of predominantly D022 phases have also been made. This study broadens the families of equimolar, single-phase, high-entropy materials that have been successfully fabricated.

A high-entropy metal disilicide, (Mo0.2Nb0.2Ta0.2Ti0.2W0.2)Si2, has been successfully synthesized. X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), and electron backscatter diffraction (EBSD) collectively show the formation of a single high-entropy silicide phase. This high-entropy (Mo0.2Nb0.2Ta0.2Ti0.2W0.2)Si2 possesses a hexagonal C40 crystal structure with ABC stacking sequence and a point group of P6222. This discovery expands the known families of high-entropy materials from metals, oxides, borides, carbides, and nitrides to a silicide, for the first time to our knowledge, as well as demonstrating that a new, non-cubic, crystal structure (with lower symmetry) can be made into high-entropy. This (Mo0.2Nb0.2Ta0.2Ti0.2W0.2)Si2 exhibits high nanohardness of 16.7 +- 1.9 GPa and Vickers hardness of 11.6 +- 0.5 GPa. Moreover, it has a low thermal conductivity of 6.9 +- 1.1 W m-1 K-1, which is approximately one order of magnitude lower than that of the widely-used tetragonal MoSi2 and ~1/3 of those reported values for the hexagonal NbSi2 and TaSi2 with the same crystal structure., Comment: 18 pages; 5 + 1 figures

Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth has remained ambiguous for more than 60 years. The models for grain growth, based on the classically linear relationship between the grain boundary migration and capillary driving force, generally predict normal grain growth. Quantitative model for abnormal grain growth is lacking despite decades of efforts. Here, we present a unified model to reveal quantitatively how grain growth evolves, which predicts the normal, abnormal and stagnant behaviors of grain growth in polycrystalline materials. Our model indicates that the relationship between grain boundary migration and capillary driving force is generally nonlinear, but will switch to be the classically linear relationship in a specific case. Furthermore, the grain growth experiments observed in polycrystalline SrTiO3 demonstrates the validity of the unified model. Our study provides a unified, quantitative model to understand and predict grain growth in polycrystalline materials, and thus offers helpful guides for the microstructural design to optimize the properties of polycrystalline materials.

An algorithm implemented in an open-source python library was developed for building periodic coincidence site lattice (CSL) grain boundary models in a universal fashion. The software framework aims to generate tilt and twist grain boundaries from cubic and tetragonal crystals for ab-initio and classical atomistic simulation. This framework has two useful features: i) it can calculate all the CSL matrices for generating CSL from a given Sigma ({\Sigma}) value and rotation axis, allowing the users to build the specific CSL and grain boundary models; ii) it provides a convenient command line tool to enable high-throughput generation of tilt and twist grain boundaries by assigning an input crystal structure, {\Sigma} value, rotation axis, and grain boundary plane. The developed algorithm in the open-source python library is expected to facilitate studies of grain boundary in materials science. The software framework is available on the website: aimsgb.org., Comment: 13 pages, 7 figures, 1 table

In recent years, efficient inter-atomic potentials approaching the accuracy of density functional theory (DFT) calculations have been developed using rigorous atomic descriptors satisfying strict invariances, for example, to translation, rotation, permutation of homonuclear atoms, among others. In this work, we generalize the spectral neighbor analysis potential (SNAP) model to bcc-fcc binary alloy systems. We demonstrate that machine-learned SNAP models can yield significant improvements even over well-established, high-performing embedded atom method (EAM) and modified EAM (MEAM) potentials for fcc Cu and Ni. We also report on the development of a SNAP model for the fcc Ni-bcc Mo binary system by machine learning a carefully-constructed large computed data set of elemental and intermetallic compounds. We demonstrate that this binary Ni-Mo SNAP model can achieve excellent agreement with experiments in the prediction of Ni-Mo phase diagram as well as near-DFT accuracy in the prediction of many key properties such as elastic constants, formation energies, melting points, etc., across the entire binary composition range. In contrast, the existing Ni-Mo EAM has significant errors in the prediction of the phase diagram and completely fails in binary compounds. This work provides a systematic model development process for multicomponent alloy systems, including an efficient procedure to optimize the hyper-parameters in the model fitting, and paves the way to long-time, large-scale simulations of such systems., Comment: 6 figures

DC flash sintering of both pure and 0.5 mol. % Bi2O3-doped ZnO at a relatively high activating field of 300 V/cm has been investigated. It is demonstrated that even high-purity ZnO single crystals can "flash" at 870C. In comparison, flash sintering occurs at a substantially lower onset temperature of 550C in ZnO powder specimens, indicating the important roles of surfaces and/or grain boundaries. A model has been developed to forecast the thermal runaway conditions and the predictions are in excellent agreements with the observed onset flash temperatures, attesting that the flash starts as a thermal runaway in at least these ZnO based systems. Interestingly, enhanced grain growth is observed at the anode side of the pure ZnO specimens with an abrupt change in the grain sizes, indicating the occurrence of electric-potential-induced abnormal grain growth. With a large current density, the growth of aligned hexagonal single-crystalline rods toward the anode direction is evident in the ZnO powder specimen. Moreover, Bi2O3 doping defers the onset of flash sintering, which can be explained from the formation of space charges at grain boundaries, and it homogenizes the microstructure due to a liquid-phase sintering effect. The key scientific contributions of this study include the development of a model to predict the thermal runaway conditions that are coincident with the observed onset flash sintering temperatures, the clarification of how flash starts in ZnO based specimens, and the observation and explanation of diversifying phenomena of sintering and microstructural development under applied electric currents., Comment: 36 pages