Understanding how grain boundaries mediate fracture remains a critical challenge in designing ductile, high-performance refractory alloys. Here, we extend the Rice-Thomson criterion to account for the angle between cracks and the impinging grain boundaries (GBs), capturing the competition between intergranular fracture and dislocation-mediated plasticity. Using machine learning interatomic potentials, we performed molecular statics simulations to probe fracture mechanisms in nanocrystalline NbMoTaW and Nb45Ta25Ti15Hf15, each with two different grain sizes, revealing trends consistent with experimental observations and the extended Rice model. Comparison with averaged R-curves for bulk samples demonstrates that GBs enhance ductility in Nb45Ta25Ti15Hf15 in both grain sizes investigated. In contrast, GBs only locally improve fracture resistance in NbMoTaW when cracks are temporarily pinned at GBs inclined at high angles from the crack, but generally promote brittle intergranular fracture. These contrasting behaviors are attributed to differences in GB cohesion, reflecting clear alloying trends that align with ab-initio calculations and trends observed experimentally. Our results bridge classical fracture theory, atomistic simulations, and experimental observations, providing a comprehensive understanding of the fracture mechanisms in nanocrystalline refractory complex concentrated alloys.

Solute-intercalation-induced phase separation creates spatial heterogeneities in host materials, a phenomenon ubiquitous in batteries, hydrogen storage, and other energy devices. Despite many efforts, probing intercalation processes at the atomic scale has been a significant challenge. By utilizing liquid-phase transmission electron microscopy (TEM), we study hydrogen (de)intercalation in palladium nanocrystals as a model system and have achieved unprecedented atomic-resolution imaging of hydrogen intercalation wave dynamics. Our observations reveal that intercalation wave mechanisms, instead of shrinking-core mechanisms, prevail at ambient temperature for palladium nanocubes ranging from ∼60 nm down to ∼10 nm. Systematic image analysis uncovers the atomic evolution of the hydrogen intercalation wave, transitioning from nonplanar and inclined boundaries to those closely aligned with {100} planes. Our kinetic Monte Carlo simulations demonstrate that the observed intercalation wave dynamics correspond to sorption pathways minimizing the lattice mismatch strain at the phase boundary. Unveiling the atomic intercalation pathways holds profound implications for engineering intercalation-mediated devices and advancements in energy sciences.

We propose an approach to simulating the dynamic evolution and transport of charged point defects within and through the oxide scales that form during corrosion. The method follows the cluster dynamics formalism widely adopted for radiation damage in solids, which can apply in both quasi-static and far from equilibrium conditions, such as in radiation environments. By treating each charged defect as a cluster of an atomic defect and associated unit charges, the proposed model flexibly allows charge state transitions and shifts in the Fermi level by absorption and emission of charge carriers from point defects in a reaction network with rates constrained by local equilibrium. Applying this model to hematite predicts changes in self-diffusion and oxidation kinetics in irradiation environments, surprisingly showing reduced oxidation rates in many conditions, despite enhanced self-diffusion. The origin of this effect lies in a change in Fermi level induced by excess vacancies formed under irradiation, which in turn suppresses the transport of cation interstitials which facilitate hematite growth.

Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride (PdHx) nanocrystals are an ideal model system for studying solute-induced phase transformations, where elastic energy from lattice mismatch between α-PdHx and β-PdHx phases is often considered a key to determining the transformation pathways. α/β-PdHx interfacial elastic energy is affected by the confined geometry of a nanocrystal. However, how nanocrystal geometry influences phase transformation pathways is largely unknown. Using in situ liquid phase transmission electron microscopy, we directly visualize hydrogenation in Pd nanocrystals with two geometries, a nanocube and a hexagonal nanoplate. Both follow similar sequences of an initially curved nucleus, interface flattening, and reverse-stage nucleation; however, their evolving α/β-PdHx interfaces exhibit geometry-dependent crystallographic alignments. In nanocubes, {100}-aligned configurations conform to static elastic energy ordering, representing a pathway that maintains a local mechanical equilibrium, whereas nanoplates display both {110}- and {211}-aligned interfaces. Theoretical simulations show that geometry determines the accessibility of alternative phase transformation pathways as the system is driven far from equilibrium during hydrogenation. These findings identify geometry as a fundamental parameter for directing phase transformation pathways, offering design principles for accessing atypical configurations and improving properties of intercalation-based devices.

Recent reports suggest that interstitial solute additions to body-centered cubic (bcc) high-entropy alloys (HEAs) may enhance their mechanical properties. However, details of interactions between interstitial atoms and dislocations in these HEAs remain incompletely understood. Using first-principles calculations, we examine the energetics of C, N, and O interstitial solutes in elemental bcc metals and NbTaTiHfZr, focusing on their segregation in screw dislocation cores. We examine two types of core sites and show that the low-energy configuration and associated segregation energy depend on the transition metal group. In NbTaTiHfZr, we find that chemical complexity substantially suppresses interstitial segregation in dislocation cores, as fluctuations in bulk solute energies induce energetically favorable sites that disfavor segregation to core sites. Local chemical order further enhances this effect by promoting solute clustering away from dislocation cores. These findings reveal fundamental differences between the behavior of interstitial atoms in elemental metals and HEAs, with implications for high-temperature plasticity and dynamic strain aging.

A simple Rice-Ashby type model for ductile–brittle transition temperature (DBTT) of body-centered cubic (bcc) complex concentrated alloys (structures) is presented. The effect of accumulation of dislocation density on DBTT is also analyzed. The model results are compared with experimental yield stress vs. temperature data for four complex concentrated alloys: Nb45Ta25Ti15Hf15 (NTTH), MoNbTaW, HfNbTaTiZr, NbTiZr and two pure bcc metals, Fe and W. It is shown that the DBTT behavior of these alloys and pure metals are in agreement with the simple ductility model presented in this manuscript. The DBTT model presented in this manuscript along with yield strength models for bcc complex concentrated alloys described in the literature should serve as a useful guide for designing such alloys with good high temperature strength and significant room temperature ductility.

Transformation-and twinning-induced plasticity (TRIP and TWIP) have been reported to contribute to the low-temperature deformation of some body-centered cubic (bcc) multi-principal element alloys (MPEAs) containing large fractions of group IV transition metals. The influence of interstitial solutes on the mechanisms underlying these forms of plasticity, however, remains unclear. Using first-principles calculations, we study the effects of interstitial O atoms on the relative stability of bcc and aphases and on unstable and twin boundary stacking fault energy profiles in a representative bcc MPEA with high group-IV elemental fraction: NbTaTiHf. We find that O additions generally promote the relaxation of aconfigurations back to their parent bcc structure, therefore inhibiting atransformation. Calculations of the Rice parameter for bulk bcc and aphases, as well as bcc-ainterfaces, further show that aformation is a potent embrittlement factor, an effect that is enhanced by O additions, suggesting that the formation of bcc-ainterfaces is energetically preferred over the formation of the bulk aphase. By contrast, the Rice parameter for twin boundaries indicates that these interfaces do not embrittle the material, even with O atoms at twin boundaries, providing a more favorable pathway for plastic deformation compared to atransformation.

The refractory medium-entropy alloy (RMEA) Nb45Ta25Ti15Hf15 exhibits exceptional tensile ductility and fracture toughness at ambient temperature, but its engineering applications are limited by a lack of high temperature strength. Using a machine-learning interatomic potential (MLIP) with near-density functional theory (DFT) accuracy, we conducted molecular dynamics (MD) and statics simulations of the behavior of dislocations with both screw and edge characters. We also analyze experimentally measured yield strengths using the Rao-Suzuki model and the Maresca-Curtin model modified to include a temperature-dependent shear modulus and a bulk modulus-dependent misfit volume, thereby uncovering the mechanisms underlying the yielding of this RMEA. Compared with the published experimental yield strength, the models parameterized by the MLIP effectively reproduce the experimental results over a wide temperature range. The models and MD simulations indicate that yielding is governed by screw dislocations, with dipole dragging as the dominant mechanism. In MD simulations, we observed a potential softening mechanism not considered by the Rao-Suzuki screw model: slow migration of interstitial jogs along the dislocation core, which could lead to the annihilation of vacancy and interstitial jog pairs by their combination.

Molecular dynamics techniques are used to investigate {1012} and {1121} twin thickening processes through spontaneous formation of twinning disconnections (TD) under applied shear deformation with a constant strain rate, based on an embedded atom method potential model of Zr. The observed stress responses and twin boundary structure changes verify that both twins thicken through TD formation. However, the thickening processes of {1012} and {1121} twins show significant differences. While {1012} TD loops were observed to form and expand during the twin thickening process, the {1121} twin boundary exhibits a more structurally disordered interface throughout the simulation, and no sharp boundary corresponding to a {1121} TD 'loop' can be identified. Moreover, the {1121} twin requires a much lower critical shear stress for twin thickening, approximately 10% of that for the {1012} twin. The low critical shear stress of {1121} twin thickening also indicates that these twins should grow easily once nucleated. To the extent that these results apply to hexagonal-close-packed (HCP) materials more generally, promotion of {1121} twin nucleation may be an effective way to enhance twinning deformation and twin boundary-related work hardening in HCP materials, with the potential to manipulate the balance between strength and ductility.

Hexagonal Close-Packed (HCP) alloys are used in structural materials applications for extreme environments such as those involving cryogenic conditions, or for nuclear cladding. However, the alloy design space explored for HCP compositionally complex alloys, namely High-Entropy or Medium-Entropy Alloys (hereafter referred to as HEAs) has been limited. Here, we propose the Ti-Zr-Hf ternary system as an ideal model for developing single-phase HCP HEAs and systematically investigate its composition-microstructure-property relationships. CALPHAD thermodynamic calculations predicted, and experimental results confirmed, that a stable single-phase HCP solid solution forms over a wide compositional range. The as-cast microstructure exhibited a systematic evolution dictated primarily by Hf content: high-Hf content alloys formed coarse dendritic structures via diffusion-dominant transformations, whereas low-Hf alloys formed fine acicular structures through diffusionless martensitic transformations. This change with Hf content is rationalized by a compositional dependence of the Continuous Cooling Transformation (CCT) kinetics. Nanoindentation revealed a strong solid-solution strengthening effect, with hardness generally increasing from 4.3 GPa in Ti-rich compositions to 5.5 GPa in high Hf-content alloys. Notably, the equiatomic TiZrHf alloy demonstrated an exceptional synergy of high yield strength (1140 MPa) and superior ductility (elongation >16%). Post-deformation analysis revealed that this is governed by the Twinning-Induced Plasticity (TWIP) effect, via the activation of {10-12} extension twins, confirmed by a characteristic misorientation angle of ∼86° across twin boundaries. Comparing alloys of contrasting c/a ratio at fixed Ti content further revealed a transition from twinning- and stacking-fault-mediated plasticity to confined planar slip, consistent with the reduced {10-12} twinning shear and enhanced slip accessibility that accompany a higher c/a ratio; the as-cast morphology, by contrast, modulates the magnitude of the work-hardening response rather than the operative deformation mode. This work establishes the Ti-Zr-Hf system as a cornerstone for developing high-performance HCP HEAs.

The CALPHAD framework provides a rigorous basis for thermodynamic modeling, yet its ability to predict new chemistries is restricted by limited data and by functional forms that rely heavily on composition alone. Here, we show that machine learning (ML) can address these challenges through a hybrid strategy that learns Redlich-Kister (RK) interaction coefficients directly from physically informed elemental descriptors. Using formation energies of 14-element FCC alloys generated by a universal machine-learning interatomic potential (MLIP), we benchmark three classes of models: (1) composition-based RK and ML models, (2) descriptor-based ML models, and (3) a combined ML-augmented RK approach (ML4RK). Leave-one-element-out tests highlight complementary strengths. RK models, class (1), remain the most data-efficient when binary information is available, while descriptor-based ML models, class (2), enable genuine zero-shot extrapolation to elements absent from the training set. By embedding elemental descriptors into the RK framework, the hybrid approach unifies these regimes and enables prediction of interaction parameters for otherwise unknown or data-scarce binaries, class (3). This work demonstrates a physically grounded and data-efficient route to extend CALPHAD models by combining the transferability of ML with the physical grounding, interpretability, data efficiency, and robustness of thermodynamic formalisms.

Phase-field simulations of liquid metal dealloying (LMD) can capture complex microstructural evolutions but can be prohibitively expensive for large domains and long time horizons. In this paper, we introduce a fully convolutional, conditionally parameterized U-Net surrogate designed to extrapolate far beyond its training data in both space and time. The architecture integrates convolutional self-attention, physically informed padding, and a flood-fill corrector method to maintain accuracy under extreme extrapolation, while conditioning on simulation parameters allows for flexible time-step skipping and adaptation to varying alloy compositions. To remove the need for costly solver-based initialization, we couple the surrogate with a conditional diffusion model that generates synthetic, physically consistent initial conditions. We train our surrogate on simulations generated over small domain sizes and short time spans, but, by taking advantage of the convolutional nature of U-Nets, we are able to run and extrapolate surrogate simulations for longer time horizons than what would be achievable with classic numerical solvers. Across multiple alloy compositions, the framework is able to reproduce the LMD physics accurately. It predicts key quantities of interest and spatial statistics with relative errors typically below 5

Molten fluoride salts such as Li 2 BeF 4 (FLiBe) are used in molten salt reactors, fluoride-salt-cooled high-temperature reactors and fusion reactors as a fuel solvent, coolant and/or tritium breeding medium. In engineered systems that use molten salt, solid-state material will be present during melting and freezing scenarios, and therefore the temperature-dependent properties of the solid and solid/liquid phase transition merit investigation. To observe the behavior of the solid state of Li 2 BeF 4 from room temperature to melting, this work used neutron and X-ray diffraction to measure the changes in the lattice parameters and volume of the crystalline unit cell and compared the results with prior low-temperature data for solid Li 2 BeF 4 . From neutron diffraction data it is also possible to identify anisotropy: centimetre-scaled crystals align preferentially with the a axes parallel to the direction of freezing front propagation, and the c axes expand 54% more than the a axes. This work provides the lattice constants as a function of temperature, quantifies the thermal expansion, and determines the equation describing the change in density for solid Li 2 BeF 4 from room temperature to 459°C to be ρ solid (kg m −3 ) = 2182 (3) − 0.115 (2) T (°C) and the volume expansion upon melting to be less than 5%. This density changes depending on molecular weight and enrichment.

Achieving high strength and ductility is a common goal in structural alloy design. Body-centered cubic high-entropy alloys (HEAs) commonly highlight the conflict between these properties, with stronger alloys being brittle and vice versa. Recent reports suggest interstitial solutes can be used to overcome this trade-off, in some cases providing both strength and ductility enhancements. This effect has been correlated with interstitial cluster formation, although the conditions favoring their formation remain incompletely understood. Using first-principles calculations of solution energies and diffusivities, we provide insights into thermodynamic and kinetic factors favoring interstitial solute clusters. Among C, N and O solutes, O interstitials display most desirable diffusion kinetics. Further, the results highlight the importance of local composition fluctuations in the HEAs to enable the formation of clusters of appreciable size. The results are explained in terms of bonding and distortion trends across solutes and HEA compositions to provide guidelines for alloy design.

Phase-field models of liquid metal dealloying (LMD) can resolve rich microstructural dynamics but become intractable for large domains or long time horizons. We present a conditionally parameterized, fully convolutional U-Net surrogate that generalizes far beyond its training window in both space and time. The design integrates convolutional self-attention and physics-aware padding, while parameter conditioning enables variable time-step skipping and adaptation to diverse alloy systems. Although trained only on short, small-scale simulations, the surrogate exploits the translational invariance of convolutions to extend predictions to much longer horizons than traditional solvers. It accurately reproduces key LMD physics, with relative errors typically under 5

Despite over a century of studies, fundamental questions remain about the processes governing crystal nucleation from melts or solutions. Research over the past three decades has presented mounting evidence for kinetic pathways of crystal nucleation that are more complex than envisioned by the simplest forms of classical theory. Such observations have been presented for colloidal and elemental systems with covalent and metallic bonding. Despite the technological and geochemical importance of molten salts, similar studies for these ionically bonded systems are currently lacking. Here we develop a machine learning interatomic potential for a model ionic system: LiF. The potential features quantum-level accuracy for both liquid and multiple solid polymorphs over wide temperature and pressure ranges and accurately reproduces experimentally measured properties. Thanks to the efficiency of the potential, which enables microsecond-scale molecular dynamics simulations, induction times for nucleation of LiF solids from their melts are computed over a range of undercoolings. With the aid of a set of robust local order parameters established here, the simulations reveal that homogeneous crystal nucleation in undercooled melts preferentially initiates from liquid regions showing slow dynamics and high bond orientational order simultaneously, and the second-shell order of both precritical nuclei and the surface of postcritical nuclei is dominated by hexagonal close packing and body-centered cubic local structure, even though the nucleus core is dominated by face-centered cubic structure corresponding to the stable rocksalt crystal structure. Finally, we establish a connection between the crystallization pathway and the equilibrium crystal-melt interface structure.

The segregation energy of oxygen interstitial solutes to grain boundaries (GBs) in hexagonal close-packed (HCP) titanium is investigated through atomistic simulations based on a machine-learning interatomic potential (MLIP). The Ti-O MLIP is developed for titanium with interstitial oxygen solutes up to a concentration of 20 at.%. It is based on the formalism of the atomic cluster expansion (ACE), trained on an extensive dataset of density functional theory calculations exploring over 200,000 atomic environments for Ti and O interstitials. The ACE MLIP is used to compute oxygen GB segregation energies in 4685 different symmetric tilt GBs with [0001], [1100] and [1210] tilt axes. The segregation energies span a range of -0.2 eV to 2.0 eV, and over 90% of the 4685 GBs display one or more sites with negative (attractive) segregation energies. The lowest-energy sites are found to be those with coordination numbers and Voronoi indices most similar to that of the equilibrium octahedral site in the bulk HCP Ti structure. We further explore the efficacy of crystal-graph convolutional neural network ML models for predicting segregation energies based solely on information about the local atomic environment.

Correction for “Atomate2: modular workflows for materials science” by Alex M. Ganose et al., Digital Discovery, 2025, 4, 1944–1973, https://doi.org/10.1039/D5DD00019J.