arXiv subjects

Anirudh Raju Natarajan

Publications and source records attributed to Anirudh Raju Natarajan.

15 recordsLinked to original sources

arXiv2026

Beyond special quasirandom structures: free energies from energy cumulants

Predicting the finite-temperature stability of a disordered phase requires its free energy. It is traditionally approximated by combining the energy of a special quasirandom structure (a small cell mimicking a random alloy) with the ideal configurational entropy. This approximation neglects the short-range order that develops on cooling. In this study, we show that the conventional approximation is the first term of an infinite expansion of the free energy in energy cumulants. Higher-order cumulants are estimated from energies of random arrangements, without Monte Carlo or molecular dynamics. In a nine-element refractory system, adding the second cumulant reduced free energy errors by about an order of magnitude. The expansion gives phase diagrams with order--disorder transitions, defect concentrations, and short-range order. To demonstrate its utility, we used a foundation interatomic potential to screen lithium-excess rocksalt oxides across 26 elements for synthesizable disordered phases rich in the Li$_4$ clusters needed for lithium percolation. The approach applies to any lattice and chemistry, and brings disordered phases within reach of routine screening.

cond-mat.mtrl-sci↗

arXiv2026

Diffusion coefficients of multi-principal element alloys from first principles

Vacancy-mediated diffusion in multi-principal element alloys (MPEAs) remains poorly understood. Existing computational methods face challenges in connecting electronic structure to macroscopic transport coefficients due to the large number of chemical elements. To address this, we introduce the embedded local cluster expansion (eLCE), which bridges first-principles calculations with kinetic Monte Carlo simulations to compute the matrix of multicomponent diffusion coefficients. Applying this approach to refractory MPEAs in the V-Cr-Nb-Mo-Ta-W system, we evaluate the complete mobility and diffusion tensors of a six-component alloy at finite temperatures. We find that local kinetic barriers, rather than thermodynamics or vacancy correlation factors, primarily control diffusion in these materials. Whether diffusion is sluggish or anti-sluggish depends on the mean vacancy migration barrier relative to the rule-of-mixtures estimate and on the availability of percolating pathways of fast-diffusing species. We use this insight to screen the senary composition space and identify compositions with anti-sluggish diffusion. This study presents a predictive, first-principles approach for computing non-dilute transport coefficients and designing MPEAs with targeted transport properties.

cond-mat.mtrl-sci↗

arXiv2026

Benchmarking average atom potentials derived from atomic cluster expansions

Average atom (A-atom) potentials provide a mean-field description of a chemically disordered alloy and are used to predict the properties of solid solutions without short-range order. Such potentials are usually averaged from an existing interatomic potential and are therefore only as accurate as the parent model. Accurate interatomic potentials are themselves difficult to parameterize and can require large training datasets. Here we benchmark a recently developed formalism that computes an exact A-atom potential directly from a linear atomic cluster expansion (ACE). We first fit a linear ACE to Fe-W data generated with an embedded atom method (EAM) potential. The resulting A-atom potential reproduces the properties of the disordered phase computed from an explicit random supercell and from a conventional A-atom potential averaged from the same EAM potential. We then fit a linear ACE to energies and forces computed from electronic structure calculations for about 1500 small Mo-Nb structures with an average of 7 atoms per structure. The A-atom potential derived from this ACE reproduces the DFT elastic constants, lattice parameter, mixing enthalpy, and Bain path of special quasirandom structures. Of the three chemical site bases, only the occupation basis also reproduces the DFT surface energies of the alloy. For Mo-Nb, the A-atom potential also predicts that the ideal solution entropy outweighs the destabilizing vibrational contribution to the finite-temperature free energy of the disordered phase. These benchmarks show that the properties of disordered alloys can be recovered from small training datasets when the chemical site basis is chosen carefully.

cond-mat.mtrl-sci↗

arXiv2026

Chemical site bases and average-atom potentials for the atomic cluster expansion

Interatomic potentials are central tools in the atomistic modeling of materials. The atomic cluster expansion (ACE) parameterizes such potentials from ab initio data, conventionally encoding the chemical degrees of freedom with a one-hot representation that yields chemically stratified models. The alternative chemical representations used in on-lattice configurational cluster expansions have not been assessed for interatomic potentials. Here we revisit the multicomponent ACE for an arbitrary chemical site basis. We then establish an exact analytical mapping between a fitted linear ACE and the average-atom potential that describes a perfectly random alloy. We benchmark potentials built on the occupational, Chebyshev, and conventional ACE bases against solute binding and vacancy formation energies in Mg-Nd, and against the mixing enthalpies of the Mo-Nb and Cr-W solid solutions. When training data are scarce, the occupational basis converges fastest and offers the best control over targeted material properties, while the conventional and Chebyshev bases face challenges in reproducing these properties. The occupational basis likewise yields the most reliable average-atom description of disordered alloy thermodynamics. In the large-data limit the three bases perform identically. The chemical basis is therefore a design choice that governs data efficiency. Its explicit treatment opens a route to average-atom potentials for the thermodynamic, mechanical, and kinetic properties of concentrated alloys.

cond-mat.mtrl-sci↗

arXiv2026

First-principles calculations of the thermodynamic factor of multicomponent alloys

Computing non-dilute diffusion coefficients from Onsager transport coefficients of a multicomponent alloy requires the thermodynamic factor, which measures the curvature of the free energy with respect to composition. As diffusion in metals is mediated by vacancies, the curvature that matters is not that of the vacancy-free alloy, which is straightforward to compute, but that of an alloy carrying a dilute concentration of vacancies. The resulting matrix is nearly singular, and composition fluctuations from which it is obtained converge slowly in Monte Carlo simulations. Here we develop two routes that avoid sampling vacancy composition fluctuations. The first constructs the thermodynamic factor from two quantities, the free-energy curvature of the vacancy-free alloy and the vacancy concentration. The second truncates the semi-grand canonical partition function at a single vacancy and recovers the full thermodynamic factor of the vacancy-containing alloy. The same separation shows that the largest eigenvalue of the diffusion matrix is the vacancy tracer diffusion coefficient for any number of components and any degree of non-ideality, while the remaining eigenvalues scale with the vacancy concentration. Across binary through quinary alloys of the Hf--Mo--Nb--Ti--Zr system, both routes reproduce eigenvalues and eigenvectors of diffusion matrices obtained from fully converged Monte Carlo simulations. The single-vacancy expansion reaches this accuracy with roughly one tenth of the sampling effort. A scaling relation extends both routes to local vacancy chemical potentials away from equilibrium, without additional simulations. These results allow thermodynamic descriptions from atomistic models or CALPHAD assessments to be used directly in mesoscale simulations of mass transport.

cond-mat.mtrl-sci↗

arXiv2026

Cracking the case: fluctuations enhance ductility in refractory alloys

Refractory body-centered cubic (BCC) alloys are attractive candidates for structural applications at extreme temperatures, yet combining room-temperature ductility with high-temperature strength remains the unsolved challenge. Ductility in crystals requires that dislocations emit from a sharp crack tip before brittle cleavage, but continuum theories that treat disordered alloys as chemically homogeneous incorrectly predict brittleness for many experimentally ductile alloys. Here we show that atomic-scale stress fluctuations in disordered alloys create an additional local stress intensity at the crack tip, enabling dislocation loop nucleation below the cleavage threshold. Accounting for these fluctuations yields a local ductility criterion where alloys deemed brittle by conventional fracture mechanics can be intrinsically ductile. Atomistic simulations with machine-learned interatomic potentials and an analytic fracture mechanics model correctly predict composition-driven brittle-to-ductile transitions in binary and ternary Mo-Nb-Ti alloys, in Nb-Ti alloys at 4 K, and in several commercial BCC alloys at room temperature. Guided by this criterion, we predict, fabricate, and test the Hf$_{15}$Mo$_{15}$Nb$_{32}$Ti$_{38}$ alloy, confirming its room-temperature ductility. This fluctuation-driven mechanism provides a quantitative basis for designing ductile multicomponent BCC alloys.

cond-mat.mtrl-sci↗

arXiv2026

pyeCE: A Python Implementation of the Embedded Cluster Expansion

The cluster expansion is a widely used approach for predicting the finite-temperature thermodynamics of alloys from zero-kelvin first-principles calculations, but its conventional formulation becomes intractable for materials with more than three or four chemical species. High-entropy alloys have therefore remained largely out of reach. We present pyeCE, an open-source Python library that implements the embedded cluster expansion (eCE), in which machine learning maps many chemical species onto a smaller set of effective species and thereby limits the growth in the number of cluster functions. pyeCE provides the complete modeling workflow, including the construction of symmetry-adapted descriptors with a learnable per-sublattice chemical embedding, a neural-network energy model, ladder-based training, uncertainty quantification, and finite-temperature simulations through Monte Carlo sampling. Built on the PyTorch and pymatgen libraries, it supports systems with multiple species on multiple sublattices and runs on graphics processing units. We demonstrate the package on two material systems. In the first, a single model spanning the full composition space of a 9-component refractory alloy resolves short-range order and order--disorder behavior. This model enables rapid screening for compositions with strong Cr clustering, a feature linked to the formation of a continuous, corrosion-resistant oxide scale. In the second, a model of hydrogen dissolution in a Mo--Nb--W alloy reproduces the composition dependence of hydrogen uptake and resolves the interstitial environments that hydrogen occupies. The modular design of pyeCE allows it to be extended to problems beyond alloy thermodynamics, including kinetics, defect energetics, and the coupling of chemical order to magnetic and vibrational degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2026

Synthesizability, hardness, and stacking order in multicomponent transition metal carbides from machine-learned potentials

Multicomponent transition metal carbides are promising for extreme-environment applications, but identifying compositions that are both synthesizable and hard remains challenging. We fine-tune the MACE machine-learned interatomic potential on approximately 28,000 density functional theory calculations spanning the composition space of groups 4-6 transition metals and carbon to predict the thermodynamic stability and elastic properties of multicomponent carbides. The fine-tuned model achieves formation energy errors of ~ 10 meV/atom for thermodynamically relevant structures with only 20% of the training data. We screen over 1500 equiatomic compositions across rocksalt, hexagonal, and hcp prototypes, combining free energy models with elasticity-based hardness surrogates. Synthesizability predictions at 1500°C agree well with experimental reports for both single-phase and multiphase carbides. The group number of the constituent metals governs both stability and hardness. Free energy contributions from short-range order are small, typically a few meV/atom, indicating that a perfectly disordered solid solution provides a reasonable approximation for high-throughput screening. For compositions mixing group 4/5 and group 6 metals, we identify a new family of stacking-ordered phases with formation energies well below those of disordered rocksalt or hexagonal structures. DFT calculations corroborate these predictions and suggest that stacking-ordered phases should be experimentally accessible in multicomponent carbides. This study provides a framework for screening synthesizable multicomponent materials with target properties, identifies promising carbide compositions across the full nine-component space, and reveals a new class of stacking-ordered carbides accessible only in multicomponent compositions.

cond-mat.mtrl-sci↗

arXiv2026

Machine learning interatomic potentials for solid-state precipitation

Machine learning interatomic potentials (MLIPs) are routinely used to model diverse atomistic phenomena, yet parameterizing them to accurately capture solid-state phase transformations remains difficult. We present error metrics and data-generation schemes designed to streamline the parameterization of MLIPs for modeling precipitation in multi-component alloys. We developed an algorithm that enumerates symmetrically distinct transformation pathways connecting chemical decorations on different parent crystal structures. Additionally, we introduce the weighted Kendall-$τ$ coefficient and its semi-grand canonical generalization as metrics for quantifying MLIP accuracy in predicting low-temperature thermodynamics. We apply these approaches to parameterize an MLIP for a dilute Mg-Nd alloy. The resulting potential reproduces the complex early-stage precipitation behavior observed in experiment. Large-scale atomistic simulations reveal competition between order-disorder and structural transformations. Furthermore, these results suggest a continuous transition between high-symmetry hcp and bcc crystal structures during aging heat treatments.

cond-mat.mtrl-sci↗

arXiv2026

Thermodynamic and electronic properties of rutile Sn$_{1-x}$Ge$_x$O$_2$ alloys from first principles

Rutile Sn$_{1-x}$Ge$_x$O$_{2}$ alloys are promising materials for high-power electronic applications due to their dopability and tunable ultra-wide band gaps. We use first-principles density functional theory and statistical mechanics to investigate the crystallographic, electronic, and thermodynamic properties of rutile $\text{Sn}_{1-x}\text{Ge}_x\text{O}_2$ alloys. We predict that the lattice parameters follow Vegard's law, while band gaps calculated with the hybrid HSE06 functional exhibit strong bowing, consistent with experiment. We also predict that the disordered phase has a large positive mixing enthalpy and a slight tendency for Ge-Sn clustering, indicated by weakly negative short-range order parameters. This large positive mixing enthalpy produces a miscibility gap with a critical temperature above 2300 K, implying that the high Ge and Sn solubilities observed in thin-film synthesis cannot be explained by the incoherent phase diagram alone. We demonstrate that coherency strain during epitaxial growth substantially alters phase stability. Calculations of the coherent spinodal show significant suppression of the miscibility gap, reducing the critical temperature to $\approx 900$ K. These coherent phase boundaries account for the experimentally observed high solubilities at typical growth temperatures. Our results indicate that coherency strain stabilizes these metastable alloys and enables bandgap engineering in this ultrawide-bandgap material system.

cond-mat.mtrl-sci↗

arXiv2025

Modeling the Equilibrium Vacancy Concentration in Multi-Principal Element Alloys from First-Principles

Multi-principal element alloys (MPEAs), also known as high-entropy alloys, have garnered significant interest across many applications due to their exceptional properties. Equilibrium vacancy concentrations in MPEAs influence diffusion and microstructural stability in these alloys. However, computing vacancy concentrations from ab-initio methods is computationally challenging due to the vast compositional space of MPEAs and the complexity of the local environment around each vacancy. In this work, we present an efficient approach to connect electronic structure calculations to equilibrium vacancy concentrations in MPEAs through embedded cluster expansions (eCE) and rigorous statistical mechanics methods. Using first-principles calculations and Monte Carlo simulations informed by eCE, we assess the variation in vacancy formation with alloy composition and temperature. Our method is demonstrated on a nine-component MPEA comprised of elements in groups 4, 5, and 6 of the periodic table. Correlations between alloy chemistry, short-range order, and equilibrium vacancy concentrations in alloys containing up to 9 different elements are analyzed. The vacancy concentration of refractory alloys increases with the addition of group 4 elements or elements whose mixing is energetically unfavorable. The insights into vacancy behavior and the efficient computational framework presented in this study serve as a guide for the design of complex concentrated alloys with controlled vacancy concentrations.

cond-mat.mtrl-sci↗

arXiv2025

Constructing multicomponent cluster expansions with machine-learning and chemical embedding

Cluster expansions are commonly employed as surrogate models to link the electronic structure of an alloy to its finite-temperature properties. Using cluster expansions to model materials with several alloying elements is challenging due to a rapid increase in the number of fitting parameters and training set size. We introduce the embedded cluster expansion (eCE) formalism that enables the parameterization of accurate on-lattice surrogate models for alloys containing several chemical species. The eCE model simultaneously learns a low dimensional embedding of site basis functions along with the weights of an energy model. A prototypical senary alloy comprised of elements in groups 5 and 6 of the periodic table is used to demonstrate that eCE models can accurately reproduce ordering energetics of complex alloys without a significant increase in model complexity. Further, eCE models can leverage similarities between chemical elements to efficiently extrapolate into compositional spaces that are not explicitly included in the training dataset. The eCE formalism presented in this study unlocks the possibility of employing cluster expansion models to study multicomponent alloys containing several alloying elements.

cond-mat.mtrl-sci↗

arXiv2020

Linking electronic structure calculations to generalized stacking fault energies in multicomponent alloys

The generalized stacking fault energy is a key ingredient to mesoscale models of dislocations. Here we develop an approach to quantify the dependence of generalized stacking fault energies on the degree of chemical disorder in multicomponent alloys. We introduce the notion of a "configurationally-resolved planar fault" (CRPF) energy and extend the cluster expansion method from alloy theory to express the CRPF as a function of chemical occupation variables of sites surrounding the fault. We apply the approach to explore the composition and temperature dependence of the unstable stacking fault energy (USF) in binary Mo-Nb alloys. First-principles calculations are used to parameterize a formation energy and CRPF cluster expansion. Monte Carlo simulations show that the distribution of USF energies is significantly affected by chemical composition and temperature. The formalism can be applied to any multicomponent alloy and will enable the development of rigorous models for deformation mechanisms in high-entropy alloys.

cond-mat.mtrl-sci↗

arXiv2019

Machine learning the DFT potential energy surface for inorganic halide perovskite CsPbBr$_3$

Structural phase transitions as a function of temperature dictate the structure--functionality relationships in many technologically important materials. Harmonic Hamiltonians have proven successful in predicting the vibrational properties of many materials. However, they are inadequate for modeling structural phase transitions in crystals with potential energy surfaces that are either strongly anharmonic or no\ n-convex with respect to collective atomic displacements or homogeneous strains. In this paper we develop a framework to express highly anharmonic first-principles potential energy surfaces as polynomials of collective cluster deformati\ ons. We further adapt the approach to a nonlinear extension of the cluster expansion formalism through the use of an artificial neural net model. The machine learning models are trained on a large database of first-principles calculations and are shown to reproduce the potential energy surface with l\ ow error.

cond-mat.mtrl-sci↗

arXiv2016

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. Spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.

cond-mat.mtrl-sci↗