The palladium-hydrogen system is a prototype for hydrogen-metal interactions and underpins technologies such as hydrogen storage, catalysis and purification. Yet its nanoscale behaviour – where surface and interface energetics, elastic coherency strain and size-dependent thermodynamics govern phase separation – has eluded accurate atomistic simulation. Empirical potentials misrepresent the energetics of interstitial hydrogen, while existing machine-learning models are restricted to bulk phases at low-hydrogen environments. Here we introduce an atomic cluster expansion (ACE) for Pd-H that reproduces formation energies, phonon spectra, elastic constants, hydrogen migration barriers and surface adsorption with near-DFT accuracy, benchmarked directly against neutron-scattering, high-pressure and lattice-expansion experiments. Its near-linear scaling and CPU efficiency make molecular dynamics of PdH_x nanoparticles exceeding 28,000 atoms (∼12 nm in diameter) tractable over nanosecond timescales. These simulations resolve, at the atomic scale, the kinetic separation of α- and β-PdH_x into a core-shell architecture, reproduce the experimentally observed size dependence of the lattice parameter, and uncover a pronounced hydrogen-induced lowering of the nanoparticle melting temperature. The potential brings experimentally relevant scales of metal-hydride dynamics within quantitative reach.

ABSTRACT The activity of compositionally complex electrocatalysts depends on their surface composition, which can be different from the volume composition. In solid solutions, surface segregation under vacuum can be estimated based on the surface energy of the constituent elements. Upon exposure to ambient conditions, the surface reactivity of the elements, particularly their tendency to oxidize, is also important. Here, we investigate differences between the surface and volume composition of a model noble metal system, Ag‐Au‐Pd‐Pt, fabricated by co‐sputter deposition in the form of thin‐film materials libraries (MLs), spanning a compositional range of Ag 12‐55 Au 7‐50 Pd 6‐60 Pt 7‐58. The volume compositions of 684 measurement areas of these libraries were determined with energy dispersive X‐ray spectroscopy (EDX). For each library, a set of nine selected areas was additionally measured by X‐ray photoelectron spectroscopy (XPS), to determine the surface compositions, i.e., the first few nanometers of the films. The XPS data reveal near‐surface segregation of Ag up to 8 at.% and Pt depletion of similar magnitude. The results were further validated by large‐scale molecular dynamics/Monte‐Carlo simulations using accurate machine learning interatomic potentials (MLIP), providing theoretical insights of surface segregation under vacuum conditions across the quaternary composition space.

This study investigates the early stages of precipitation in Al–Zn–Mg alloys using an atomic cluster expansion (ACE) interatomic potential, with a focus on the atomic structure and stability of GP zones. Formation energies of candidate solute clusters and precipitate variants are evaluated by static calculations, and precipitation is further explored via large-scale atomisitc simulations of supersaturated solid solutions. The simulations reproduce spherical GP-I zones built from high-symmetry blocks with Zn atoms frequently shifting toward interstitial positions. The formed GP-I zones consist of a Zn-rich core surrounded by a Mg-enriched interfacial region, resulting in an average Zn/Mg ratio of approximately 1.5 for the precipitates. The simulation results indicate that increasing temperature promotes the dissolution (reversion) of pre-existing GP-I zones instead of their gradual transformation into more stable precipitates. Upon dissolution at elevated temperature and in the presence of vacancies, stable vacancy/divacancy-solute complexes are formed, highlighting the key role of vacancy-solute interactions in early clustering and aging response.

We develop and benchmark a general-purpose machine-learned interatomic potential for the Fe-O-H ternary system, based on the Atomic Cluster Expansion. Following our approach developed for the Fe-O system, magnetism is explicitly treated by the model in an Ising-like manner. This allows efficient incorporation of magnetic degrees of freedom, making the potential applicable to large-scale atomistic calculations. We demonstrate the capability of the model to accurately describe a wide range of properties and capture basic mechanisms underlying hydrogen-based reduction of iron oxides, interaction of water with iron and hydrogen embrittlement of metallic iron.

Most compositionally complex materials (CCMs, frequently referred to as high entropy alloys) are metastable and their attractive properties often belong to kinetically trapped states. However, pathways towards lower-free-energy phase states governing long-term stability, can remain hidden because diffusion-controlled atomic redistribution is too slow to be revealed at experimentally accessible timescales. This blind spot is acute in CCM design: enormous compositional spaces are screened for performance, yet the low-temperature kinetics and the associated transformation pathways determining whether that performance persists are rarely considered in material selection. Here we use defect-rich nanoscale volumes coupled with atom-probe tomography to access and reconstruct the hidden phase-evolution pathway in a metastable Ag24Au20Pd50Pt6 electrocatalyst, without relying on elevated temperatures to accelerate the transformation. By varying microstructural starting state, annealing temperature and time, we reveal precipitation of a Pt-rich phase within the fcc matrix, its coarsening and re-homogenization. The Pt-rich phase recurs after homogenization with delayed kinetic accessibility, while prolonged annealing extends the pathway to 300°C. Atomistic simulations independently predict the same Pt-rich phase selection. The transformation is accompanied by a 3.7-fold loss of catalytic activity for hydrogen evolution. These results establish hidden phase-evolution pathways as a materials-design variable: resolving them can guide the selection of metastable CCMs not only for their as-synthesized properties, but also for the phase states and associated functionalities they may access over time.

Predicting the α→ β (grey-to-white) transition temperature in tin presents a longstanding challenge for atomistic simulations, with existing theoretical approaches over- or underestimating the experimental boundary (286 K) by up to several hundred Kelvin. In this work, we construct an Atomic Cluster Expansion (ACE) potential trained on density functional theory data to evaluate the finite-temperature free energies of both phases. Evaluated on the same potential energy surface, the quasi-harmonic approximation predicts a transformation temperature of 377 K, whereas full thermodynamic integration, which accounts for explicit vibrational anharmonicity, yields 288 K. This shift directly quantifies the explicit anharmonic free energy, which is substantial for metallic β-Sn but negligible for semiconducting α-Sn. The anisotropic anharmonicity in β-Sn is corroborated by its excess heat capacity, temperature-driven renormalization of its vibrational spectrum, and deviations of its atomic forces and displacements from the harmonic reference. Our results demonstrate that capturing full lattice anharmonicity is essential for predicting the phase stability of tin, while the absolute transition temperature remains limited by the accuracy of the underlying 0 K energetics.

The palladium-hydrogen system plays a crucial role in catalysis, hydrogen production and storage, hydrogen embrittlement, and sensing technologies. Understanding the transition of palladium nanocrystals (NCs) from the hydrogen-poor (α) phase to the hydrogen-rich (β) phase is crucial for elucidating hydrogen absorption/desorption mechanisms as well as related phenomena such as hydrogen trapping. In this study, we carefully minimized undesired X-ray beam effects and used in situ Bragg coherent diffraction imaging under electrochemical control to map the strain and lattice parameter distribution within individual palladium NCs across electrochemical potentials relevant to hydrogen absorption and desorption. Lattice parameter changes in both α and β phases are tracked, and reversible strain inversion during the α-to-β phase transition is observed. Through strain and reciprocal space analysis and molecular simulations, a model for the α-to-β phase transition is proposed, which includes a hydrogen-saturated subsurface shell, hydrogen depletion from the α phase during β phase nucleation, and propagation of the β phase in a spherical-cap fashion.

We perform nanoindentation simulations for both the prototypical face-centered cubic metal copper and the body-centered cubic metal tungsten with an adaptive-precision description of interaction potentials including different accuracy and computational costs. We combine both a computationally efficient embedded atom method (EAM) potential and a precise but computationally less efficient machine learning potential based on the atomic cluster expansion (ACE) into an adaptive precision (AP) potential tailored for the nanoindentation. The numerically more expensive ACE potential is employed selectively only in regions of the computational cell where high precision is required. The comparison with pure EAM and pure ACE simulations shows that for Cu, all potentials yield similar dislocation morphologies under the indenter with only small quantitative differences. In contrast, markedly different plasticity mechanisms are observed for W in simulations performed with the central-force EAM potential compared to results obtained using the ACE potential. ACE is able to describe accurately the angular character of bonding, which is in W due to its half-filled d band. All ACE-specific mechanisms are reproduced in the AP nanoindentation simulations, however, with a significant speedup of 20-30 times compared to the pure ACE simulations. Hence, the AP potential overcomes the performance gap between the precise ACE and the fast EAM potential by combining the advantages of both potentials.

Aluminum-magnesium alloys are widely used in engineering, but their susceptibility to hydrogen embrittlement and intergranular corrosion limits their applications. Understanding these phenomena requires accurate atomistic modeling of the ternary Al-Mg-H system, which has been hindered by the lack of reliable interatomic potentials. This work presents a ternary atomic cluster expansion (ACE) potential for Al-Mg-H, trained on an extensive density functional theory dataset using active learning. The ACE potential accurately reproduces a wide range of properties, including defect energetics, phase stability, and diffusion coefficients. Thanks to its outstanding computational efficiency, ACE can be employed in large-scale atomistic simulations that help elucidate the nanoscale mechanisms of hydrogen-related degradation in Al-Mg alloys.

The combined structural and electronic complexity of iron oxides poses many challenges to atomistic modeling. To leverage limitations in terms of the accessible length and time scales, one requires a physically justified interatomic potential which is accurate to correctly account for the complexity of iron-oxygen systems. Such a potential is not yet available in the literature. In this work, we propose a machine-learning potential based on the Atomic Cluster Expansion for modeling the iron-oxygen system, which explicitly accounts for magnetism. We test the potential on a wide range of properties of iron and its oxides, and demonstrate its ability to describe the thermodynamics of systems spanning the whole range of oxygen content and including magnetic degrees of freedom.

Barium titanate (BTO) is a representative perovskite oxide that undergoes three first-order ferroelectric phase transitions related to exceptional functional properties. In this work, we develop two atomic cluster expansion (ACE) models for BTO to reproduce fundamental properties of bulk as well as defective BTO phases. The two ACE models do not target full transferability but rather aim to examine the influence of implicit and explicit treatment of long-range Coulomb interactions. We demonstrate that both models describe equally well the temperature induced phase transitions as well as polarization switching due to applied electric field. Even though the parametrizations are based on a limited number of configurations that are mostly not far away from the equilibrium, the ACE models are able to capture also properties of important crystal defects, such as oxygen vacancies, stacking faults and domain walls. A systematic comparison shows that the phase transitions as well as the fundamental properties of the investigated defects can be described with similar accuracy with or without explicit treatment of charges and Coulomb interactions allowing for efficient short-range machine learning potentials.

Steels are among the technologically and economically most relevant materials. Key innovations in important sectors of human society such as mobility, energy and safety, are currently based on alloying of Fe with other transition-metal elements such as Mn, Cr, or Co. Due to strong impacts and conceptual challenges related to magnetism, however, the fundamental understanding and the ability to computationally design these steels in high-throughput approaches lags behind other classes of alloys. In this article, we will provide a substantial review of the role of magnetism, magnetic excitations and transformations for alloy thermodynamics, point defects, interfaces and kinetics. This will be achieved by combining insights from different methods: Ab initio simulations have the advantage that the magnetic ground state is intrinsic part of the electronic minimization. Due to the coarsening of the many-electron structures and therewith magnetic interactions, tight-binding methods can handle larger system sizes. Effective interaction models provide the freedom to exploit more sophisticated magnetic interactions. The performance of these methods in terms of magnetic properties of Fe alloys will be evaluated by providing state-of-the-art results for their sensitivity to magnetism. Furthermore, dedicated experiments will be discussed to complete the understanding of magnetic effects in Fe alloys and to validate the modeling strategy.

We present a comprehensive and user-friendly framework built upon the pyiron integrated development environment (IDE), enabling researchers to perform the entire Machine Learning Potential (MLP) development cycle consisting of (i) creating systematic DFT databases, (ii) fitting the Density Functional Theory (DFT) data to empirical potentials or MLPs, and (iii) validating the potentials in a largely automatic approach. The power and performance of this framework are demonstrated for three conceptually very different classes of interatomic potentials: an empirical potential (embedded atom method - EAM), neural networks (high-dimensional neural network potentials - HDNNP) and expansions in basis sets (atomic cluster expansion - ACE). As an advanced example for validation and application, we show the computation of a binary composition-temperature phase diagram for Al-Li, a technologically important lightweight alloy system with applications in the aerospace industry.

We elucidated the core structure of screw dislocations in ordered B2 FeCo using a recent magnetic bond-order potential (BOP) [Egorov et al., Phys. Rev. Mater. 7, 044403 (2023)]. We corroborated that dislocations in B2 FeCo exist in pairs separated by antiphase boundaries. The equilibrium separation is about 50 A, which demands large-scale atomistic simulations - inaccessible for density functional theory but attainable with BOP. We performed atomistic simulations of these separated dislocations with BOP and predicted that they reside in degenerate core structures. Also, dislocations induce changes in the local electronic structure and magnetic moments.

Designing electrocatalysts with optimal activity and selectivity relies on a thorough understanding of the surface structure under reaction conditions. In this study, experimental and computational approaches are combined to elucidate reconstruction processes on low-index Pd surfaces during H-insertion following proton electroreduction. While electrochemical scanning tunneling microscopy clearly reveals pronounced surface roughening and morphological changes on Pd(111), Pd(110), and Pd(100) surfaces during cyclic voltammetry, a complementary analysis using inductively coupled plasma mass spectrometry excludes Pd dissolution as the primary cause of the observed restructuring. Large-scale molecular dynamics simulations further show that these surface alterations are related to the creation and propagation of structural defects as well as phase transformations that take place during hydride formation.

The Atomic Cluster Expansion (ACE) provides a formally complete basis for the local atomic environment. ACE is not limited to representing energies as a function of atomic positions and chemical species, but can be generalized to vectorial or tensorial properties and to incorporate further degrees of freedom (DOF). This is crucial for magnetic materials with potential energy surfaces that depend on atomic positions and atomic magnetic moments simultaneously. In this work, we employ the ACE formalism to develop a non-collinear magnetic ACE parametrization for the prototypical magnetic element Fe. The model is trained on a broad range of collinear and non-collinear magnetic structures calculated using spin density functional theory. We demonstrate that the non-collinear magnetic ACE is able to reproduce not only ground state properties of various magnetic phases of Fe but also the magnetic and lattice excitations that are essential for a correct description of finite temperature behavior and properties of crystal defects.

Understanding the competition between brittleness and plasticity in refractory ceramics is of importance for aiding design of hard materials with enhanced fracture resistance. Inspired by experimental observations of crack shielding due to dislocation activity in TiN ceramics [Int J Plast 27 (2011) 739], we carry out comprehensive atomistic investigations to identify mechanisms responsible for brittleness and slip-induced plasticity in Ti-N systems. First, we validate a semi-empirical interatomic potential against density-functional theory results of Griffith and Rice stress intensities for cleavage (KIc) and dislocation emission (KIe) as well as ab initio molecular dynamics mechanical-testing simulations of pristine and defective TiN lattices at temperatures between 300 and 1200 K. The calculated KIc and KIe values indicate intrinsic brittleness, as KIc<<KIe. However, KI-controlled molecular statics simulations - which reliably forecast macroscale mechanical properties through nanoscale modelling - reveal that slip-plasticity can be promoted by a reduced sharpness of the crack and/or the presence of anion vacancies. Classical molecular dynamics simulations of notched Ti-N supercell models subject to tension provide a qualitative understanding of the competition between brittleness and plasticity at finite temperatures. Although crack growth occurs in most cases, a sufficiently rapid accumulation of shear stress at the notch tip may postpone or prevent fracture via nucleation and emission of dislocations. Furthermore, we show that the probability to observe slip-induced plasticity leading to crack-blunting in flawed Ti-N lattices correlates with the ideal tensile/shear strength ratio (Iplast) of pristine Ti-N crystals. We propose that the Iplast descriptor should be considered for ranking the ability of ceramics to blunt cracks via dislocation-mediated plasticity at finite temperatures.

We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parametrized from an exhaustive set of important carbon structures over extended volume and energy ranges, computed using density functional theory (DFT). Rigorous validation reveals that ACE accurately predicts a broad range of properties of both crystalline and amorphous carbon phases while being several orders of magnitude more computationally efficient than available machine learning models. We demonstrate the predictive power of ACE on three distinct applications: brittle crack propagation in diamond, the evolution of amorphous carbon structures at different densities and quench rates, and the nucleation and growth of fullerene clusters under high-pressure and high-temperature conditions.

Diffusion along dislocations, the so-called pipe diffusion (PD), may significantly contribute to self-diffusion in plastically deformed materials. In this work, we carry out a comprehensive investigation of PD mechanisms in several representative body-centered cubic transition metals by means of large-scale atomistic simulations. We find that screw and edge dislocations exhibit distinct intrinsic PD mechanisms associated with dynamical formation and migration of kink pairs and bounded Frenkel pairs, respectively. Different atomic structures of both core types are decisive for the character of the migration events, resulting in a very fast 1D diffusion along the screw dislocations and a slower 3D diffusion along the edge dislocations. The predicted PD coefficients are several orders of magnitude greater than the bulk diffusion coefficients, indicating that the PD contribution needs to be taken into account when interpreting diffusion measurements in deformed bcc metals at temperatures below half of the melting temperature.