arXiv subjects

Yann L. Müller

Publications and source records attributed to Yann L. Müller.

4 recordsLinked to original sources

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

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↗