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Refractory high entropy alloys (HEA), such as BCC NbMoTaW, represent a promising materials class for next-generation high-temperature applications, due to their extraordinary mechanical properties. A characteristic feature of HEAs is the formation of single-phase solid solutions. For BCC NbMoTaW, recent computational studies revealed, however, a B2(Mo,W;Nb,Ta)-ordering at ambient temperature. This ordering could impact many materials properties, such as thermodynamic, mechanical, or diffusion properties, and hence be of relevance for practical applications. In this work, we theoretically address how the B2-ordering impacts thermodynamic properties of BCC NbMoTaW and how the predicted ordering temperature itself is affected by vibrations, electronic excitations, lattice distortions, and relaxation energies.

Refractory high entropy alloys feature outstanding properties making them a promising materials class for next-generation high-temperature applications. At high temperatures, materials properties are strongly affected by lattice vibrations (phonons). Phonons critically influence thermal stability, thermodynamic and elastic properties, as well as thermal conductivity. In contrast to perfect crystals and ordered alloys, the inherently present mass and force constant fluctuations in multi-component random alloys (high entropy alloys) can induce significant phonon scattering and broadening. Despite their importance, phonon scattering and broadening have so far only scarcely been investigated for high entropy alloys. We tackle this challenge from a theoretical perspective and employ ab initio calculations to systematically study the impact of force constant and mass fluctuations on the phonon spectral functions of 12 body-centered cubic random alloys, from binaries up to 5-component high entropy alloys, addressing the key question of how chemical complexity impacts phonons. We find that it is crucial to include both mass and force constant fluctuations. If one or the other is neglected, qualitatively wrong results can be obtained such as artificial phonon band gaps. We analyze how the results obtained for the phonons translate into thermodynamically integrated quantities, specifically the vibrational entropy. Changes in the vibrational entropy with increasing the number of elements can be as large as changes in the configurational entropy and are thus important for phase stability considerations. The set of studied alloys includes MoTa, MoTaNb, MoTaNbW, MoTaNbWV, VW, VWNb, VWTa, VWNbTa, VTaNbTi, VWNbTaTi, HfZrNb, HfMoTaTiZr. High entropy alloys: Theoretical perspectives on phonons In contrast to conventional alloys, high entropy alloys possess five or more equiatomic elemental species within a single lattice, resulting in some extraordinary physical properties. All these properties are linked to the lattice vibrations, i.e. phonons, indicating the importance of modelling of phonon excitations and their interactions. A team led by Fritz Körmann at Netherlands’ Delft University of Technology and Yuji Ikeda at Kyoto University in Japan performed first-principles calculations on 12 different refractory alloys to address the key question of how the chemical complexity impacts phonons. Results show that both atomic mass and force constants contribute to the phonon energies, and changes in the vibrational entropy with more elements could be comparable to the configurational entropy. Research into the computationally designed phonon broadening may open an avenue towards tailored high temperature high entropy alloys.

Cluster expansions have proven a very useful tool to model thermodynamics and kinetics of substitutional alloys in metallic, ionic, and even covalently bonded systems. Cluster expansions are usually obtained with the structure inversion method in which the energies, or other relevant property, of a set of structures are used to obtain expansion coefficients. The expansion coefficients are multipliers of correlation functions which pertain to clusters of sites on the parent lattice. There are significant practical issues associated with obtaining a cluster expansion, such as selecting which structures and especially which correlation functions are required for an adequate description of the energy. While these issues are significant for binary alloys, they become much more daunting when dealing with multicomponent alloys. Moreover, oftentimes interest is not limited to the energetics of the thermodynamic equilibrium state, but the evolution of quenched alloys with time is just as important. The treatment of diffusion within the context of cluster expansions is then another challenge. The article describes a formal method for utilizing cluster expansions for transition states as occur during vacancy mediated diffusion in substitutional alloys. The methods are illustrated with some applications to the prediction of initial coherent precipitates in Al-Cu and Al-Mg-Si alloys.

The human brain is capable of learning tasks sequentially mostly without forgetting. However, deep neural networks (DNNs) suffer from catastrophic forgetting when learning one task after another. We address this challenge considering a class-incremental learning scenario where the DNN sees test data without knowing the task from which this data originates. During training, Continual Prune-and-Select (CP&S) finds a subnetwork within the DNN that is responsible for solving a given task. Then, during inference, CP&S selects the correct subnetwork to make predictions for that task. A new task is learned by training available neuronal connections of the DNN (previously untrained) to create a new subnetwork by pruning, which can include previously trained connections belonging to other subnetwork(s) because it does not update shared connections. This enables to eliminate catastrophic forgetting by creating specialized regions in the DNN that do not conflict with each other while still allowing knowledge transfer across them. The CP&S strategy is implemented with different subnetwork selection strategies, revealing superior performance to state-of-the-art continual learning methods tested on various datasets (CIFAR-100, CUB-200-2011, ImageNet-100 and ImageNet-1000). In particular, CP&S is capable of sequentially learning 10 tasks from ImageNet-1000 keeping an accuracy around 94% with negligible forgetting, a first-of-its-kind result in class-incremental learning. To the best of the authors’ knowledge, this represents an improvement in accuracy above 10% when compared to the best alternative method.

Current deep neural networks (DNNs) are overparameterized and use most of their neuronal connections during inference for each task. The human brain, however, developed specialized regions for different tasks and performs inference with a small fraction of its neuronal connections. We propose an iterative pruning strategy introducing a simple importance-score metric that deactivates unimportant connections, tackling overparameterization in DNNs and modulating the firing patterns. The aim is to find the smallest number of connections that is still capable of solving a given task with comparable accuracy, i.e. a simpler subnetwork. We achieve comparable performance for LeNet architectures on MNIST, and significantly higher parameter compression than state-of-the-art algorithms for VGG and ResNet architectures on CIFAR-10/100 and Tiny-ImageNet. Our approach also performs well for the two different optimizers considered—Adam and SGD. The algorithm is not designed to minimize FLOPs when considering current hardware and software implementations, although it performs reasonably when compared to the state of the art.

In 1970, Hillert and Staffansson published a paper entitled “The Regular Solution Model for Stoichiometric Phases and Ionic Melts”. It was the beginning of the sublattice model that has been a key component in the development of Computational Thermodynamics. This formalism, now often called the Compound Energy Formalism (CEF), has been used to describe a great variety of phases driven by the need for accurate descriptions of thermodynamic phase stability in a wide range of materials involving many elements. The purpose of this paper is to describe the formalism, the physical meaning of its various parameters and the way they can be assessed using experimental and theoretical data. Furthermore, new developments derived from the CEF, such as the Effective Bond Energy Formalism, and other ideas for further development are presented.

The elastic constant tensor of an inorganic compound provides a complete description of the response of the material to external stresses in the elastic limit. It thus provides fundamental insight into the nature of the bonding in the material, and it is known to correlate with many mechanical properties. Despite the importance of the elastic constant tensor, it has been measured for a very small fraction of all known inorganic compounds, a situation that limits the ability of materials scientists to develop new materials with targeted mechanical responses. To address this deficiency, we present here the largest database of calculated elastic properties for inorganic compounds to date. The database currently contains full elastic information for 1,181 inorganic compounds, and this number is growing steadily. The methods used to develop the database are described, as are results of tests that establish the accuracy of the data. In addition, we document the database format and describe the different ways it can be accessed and analyzed in efforts related to materials discovery and design. Design Type(s) observation design Measurement Type(s) elastic constant tensor Technology Type(s) stress-strain methodology Factor Type(s) Machine-accessible metadata file describing the reported data (ISA-Tab format)

The control of carbide formation is crucial for the development of advanced low-alloy steels. Hence, it is of great practical use to know the (de)stabilization of carbides by commonly used alloying elements. Here, we use ab initio density functional theory (DFT) calculations to calculate the stabilization offered by common alloying elements (Al, Si, P, S, Ti, V, Cr, Mn, Ni, Co, Cu, Nb, Mo, and W) to carbides relevant to low-alloy steels, namely cementite Hägg and eta-carbide . All alloying elements are considered on the Fe sites of the carbides, whereas Al, Si, P, and S are also considered on the C sites. To consider the effect of larger supercell size on the results of (de)stabilization, we use both 1 × 1 × 1 and 2 × 2 × 2 supercells in the case of

The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr23−xFexC6 (x = 0–3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M23C6 structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M(4a) M12(48h)) and negatively charged cubo-octahedron (M8(32f) C6(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M23C6 carbides may facilitate further development of high-chromium heat-resistant steels.

Universal machine-learning interatomic potentials (uMLIPs) are emerging as foundation models for atomistic simulation, offering near-ab initio accuracy at far lower cost. Their safe, broad deployment is limited by the absence of reliable, general uncertainty estimates. We present a unified, scalable uncertainty metric, U , built from a heterogeneous ensemble that reuses existing pretrained MLIPs. Across diverse chemistries and structures, U strongly tracks true prediction errors and robustly ranks configuration-level risk. Using U , we perform uncertainty-aware distillation to train system-specific potentials with far fewer labels: for tungsten, we match full density-functional-theory (DFT) training using 4% of the DFT data; for MoNbTaW, a dataset distilled by U supports high-accuracy potential training. By filtering numerical label noise, the distilled models can in some cases exceed the accuracy of the MLIPs trained on DFT data. This framework provides a practical reliability monitor and guides data selection and fine-tuning, enabling cost-efficient, accurate, and safer deployment of foundation models.