The prediction of stable alloys forming solid-state solutions across large portions of the composition space is a serious theoretical challenge, since one has to evaluate the Gibbs free energy, including both configurational and vibrational contributions. This requires an energy theory capable of extremely high throughput. By taking the Ni-Pd system as prototype, we construct an efficient Jacobi-Legendre machine-learning potential based on density-functional-theory data, which provides accurate energies and forces across the entire composition space. Based on a cluster expansion up to three-body terms and only 873 trainable parameters, this allows us to compute the partition function by directly integrating all accessible microstates, differing for composition, atomic configuration and thermal agitation. We confirm that Ni and Pd are fully miscible, forming an $fcc$ solid-state solution. This is only metastable at room temperature, while becomes thermodynamically stable at around 600~K, with the stability achieved first at the Pd-rich end of the composition range. Interestingly, entropy and heat capacity analysis reveal a competition between the solid-state solution and two intermetallic phases with long-period L1$_0$ structure for NiPd and NiPd$_3$. All in all, our approach offers a powerful and high-throughput workflow for the study of disordered alloys, an approach that can be extended to multi-component systems such as high-entropy alloys.
A machine-learning workflow that couples the crystal generator MatterGen with a fine-tuned MatterSim interatomic potential to expand the candidate phase space and compute temperature-dependent phase stability with accuracy approaching density functional theory is reported.
Chen Su, Jie Lu, Yuchen Fu et al.· Journal of Physical Chemistr...· 0 citations
Phase stability in multicomponent solid solutions depends on configurational entropy beyond the ideal mixing limit, but capturing it together with vibrational entropy within the same atomistic framework remains challenging. Here, we extend non-equilibrium thermodynamic integration to composition-dependent transformations through an alchemical interpolation of the interactions, combined with Monte Carlo identity exchange moves and molecular dynamics that sample the vibrational and non-ideal configurational entropy along the integration path. We apply the framework to the Au-Cu binary alloy using Atomic Cluster Expansion potentials trained on density functional theory data using the LDA, PBE, and r2SCAN functionals, and construct composition-temperature phase diagrams directly from atomistic free energies. We find that explicit configurational sampling lowers the AuCu order-disorder transition temperature predicted by the ACE potential trained on LDA data from approximately 810 K to 710 K, closer to the experimental value of 683 K, and substantially widens the stability range of the solid solution. At the same time, the much larger sensitivity to the exchange-correlation functional shows that this level of agreement should not be interpreted as general predictive accuracy. Non-ideal configurational entropy must therefore be sampled explicitly, alongside a careful choice of functional, for a reliable atomistic description of binary phase diagrams.
Sarath Menon, M. Poul, T. Hickel et al.· 0 citations
High-entropy alloys (HEAs) possess exceptional mechanical properties and thermal stability, yet their vast compositional space and complex atomic arrangements present significant challenges for property prediction and design. To overcome this, we have trained a machine-learned interatomic potential (MLIP) for the AlTiCrMoW HEA using the message-passing atomic cluster expansion (MACE) framework. This new MLIP is trained on a series of high-accuracy density functional theory (DFT) calculations that covers the available configuration space of the HEA. The training set includes key configurations with linear-response-informed short-range ordered configurations, which are generated using a concentration wave analysis within the coherent potential approximation (CPA) and subsequently optimizedd using conventional DFT calculations. Phonon bispersion ands (PDBs) for the HEA are generated using the MACE model, and several physical properties are extracted for the HEA, such as the elastic constants and the bulk modulus. The fine-tuned model reproduces DFT structural and elastic benchmarks with high accuracy, at a significantly reduced computational cost, allowing for larger simulations to be performed, which can more accurately probe the configuration space and composition of the alloy. Here, we perform Monte Carlo based simulations to identify the ordering transition of equiatomic AlTiCrMoW, where we match the experimental value of 1273 K. Vacancy relaxation volumes are investigated for AlTiCrMoW, as an example of a property analysis, which would be computationally intractable via DFT.
Joseph E. Arnold, C. D. Woodgate, Roohollah Hafizi et al.· PHYSICAL REVIEW MATERIALS· 0 citations
We present a high-dimensional neural network potential (HDNNP) for the martensitic phase of the NiTi shape-memory alloy trained to density functional theory (DFT) data. A central aspect of this work is the systematic validation of the potential with respect to the underlying DFT reference method for key properties governing structural evolution, including equilibrium crystal structures, elastic constants, generalized-stacking fault energies, and vibrational spectra. The HDNNP accurately describes the relative stability of the B19$^\prime$ and B33 phases, including subtle energy differences on the order of meV/atom. The predicted stacking-fault energy landscape is strongly anisotropic and reveals a preferential shear pathway, providing atomistic insight into deformation and twinning mechanisms. Finite-temperature molecular dynamics simulations further enable the investigation of unconstrained structural evolution as a function of temperature. Overall, the developed HDNNP provides a robust basis for atomistic simulations of the complex structural and functional behavior of martensitic NiTi systems containing hundreds of thousands of atoms on nanosecond time scales.
P. Jaroš, Petr Sedlák, Petr Šesták et al.· 0 citations
High-entropy alloys (HEAs) exhibit exceptional structural and functional properties arising from their complex local chemical environments, and their vast compositional space offers considerable flexibility to further tune and optimize these properties. Atomistic simulations based on density functional theory (DFT) have played a central role in elucidating the thermodynamic, mechanical, magnetic, and defect-related properties of HEAs. However, DFT simulations are severely limited by the intrinsic chemical and configurational complexity of these alloys, particularly because reliable predictions require extensive statistical sampling over chemically diverse configurations and access to extended spatial and temporal scales. In this review, we summarize recent advances in atomistic simulations of HEAs, with particular emphasis on machine learning interatomic potentials (MLIPs), which extend beyond conventional DFT approaches. We discuss how MLIPs enable statistically robust simulations with near-DFT accuracy while dramatically reducing computational cost, thereby allowing explicit treatment of chemical short-range order, vibrational contributions to Gibbs energies, point defects, diffusion, dislocation behavior, grain boundaries, and hydrogen absorption in chemically complex alloys. Particular attention is devoted to the role of local chemical environments, many-body interactions, and configurational sampling in determining HEA properties. We further review recent developments in universal/foundation MLIPs trained on chemically diverse datasets and discuss their potential for rapid and transferable atomistic simulations of HEAs across broad compositional and configurational spaces. We discuss current limitations and open challenges, including transferability to highly distorted defect configurations, treatment of magnetic and charge degrees of freedom, incorporation of finite-temperature excitations, and construction of representative training datasets for chemically and structurally complex systems. This review aims to provide a comprehensive perspective on the ongoing transition from conventional DFT-based simulations toward scalable, statistically rigorous, and predictive atomistic modeling frameworks for HEAs and related compositionally complex materials.
Yuji Ikeda, Xiang Xu, Pranav Kumar et al.· Journal of Materials Science· 0 citations
The vast compositional space of high-entropy alloys (HEA) holds promise for next-generation functional materials, yet its exploration is stifled by a combinatorial bottleneck: conventional first-principles accuracy is computationally prohibitive for complex disordered lattices, while black-box machine learning (ML) lacks physical interpretability. We overcome this by establishing a minimal-supercell principle, demonstrating that the magnetostructural behaviour is an emergent feature of local atomic environments rather than long-range configurations. This enables a physics-informed ML framework that inverts the conventional screening approach, transitioning from limited local identification to global design-space mapping, reducing computational time by 40 – 60% without compromising accuracy. Applying this framework to MM’X family uncovers a fundamental design dichotomy: mean electronic descriptors govern baseline phase stability, while dispersion descriptors, specifically the magnetic-moment dispersion, drive the critical transformation response. This analysis reveals an intrinsic stability-performance trade-off, where the disorder required to maximise the transformation driving force inevitably penalises thermodynamic stability. By quantifying this Pareto frontier, we propose a hierarchical tuning strategy that decouples phase transition temperature from hysteresis, providing a scalable paradigm to transform HEA exploration from serendipitous discovery into rational design.
Zhe Cui, C. Romero-Muñiz, J. Law et al.· Nature Communications· 0 citations
