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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Phase stability in the Hf-N and Zr-N systems

Hf and Zr nitrides are promising compounds for many technologically important areas, including high-temperature structural applications, quantum computing, and solar and optical applications. Here, this article reports on a comprehensive first-principles statistical mechanics study of phase stability in the Hf-N and Zr-N binary systems. A high solubility of nitrogen in the hcp forms of Hf and Zr is predicted. The rocksalt forms of HfN and ZrN can also tolerate a high degree of off-stoichiometry through the introduction of nitrogen and metal vacancies. The Hf-N binary favors a family of stacking faulted parent crystal structures at intermediate nitrogen concentrations that host a unique form of short-range order among nitrogen interstitials and vacancies. These phases can accommodate some degree of configurational entropy and remain ordered to temperatures as high as 1200 K.

Monte Carlo methods↗
DOE OSTI2026

Phase diagram of magnetic shape memory alloy Ni 50 Mn $50–x$ In $x$ , 0 < $x$ , 25 from first principles, via spin cluster expansion and phonon vibrational entropies

The metamagnetic shape memory Heusler alloy Ni 50 Mn $50–x$ In $x$ exhibits a rich phase diagram featuring competing magnetic states, coupled magnetic–structural phase transitions, and strong compositional sensitivity. Existing first-principles approaches struggletocapturetheintertwinedchemical, magnetic, andvibrationaleffectsinthesealloys, necessitating a more integrated modeling framework. We develop a spin cluster expansion (spin-CE) framework augmented by a quasi-harmonic phonon model to capture both configurational (chemical and magnetic) and vibrational contributions to the free energy of Ni 50 Mn $50–x$ In $x$ over the full compositional range 0 ≤ x ≤25. The spin-CE includes both chemical clusters and composition-dependent Ising spin interactions, with parameters fit to a first-principles density functional theory (DFT) dataset. Using this approach, we predict the complete magnetostructural phase diagram and transformation temperatures of Ni 50 Mn $50–x$ In $x$ across the composition space. We find that vibrational entropy alone is insufficient to reproduce the martensitic transformation in the magnetic shape memory alloy regime, highlighting the essential role of magnetism. Incorporating both magnetic and vibrational contributions allows us to reproduce all experimentally known phases, including the disappearance of the stable martensite phase at a critical In concentration and the Curie temperature of the austenite phase. The method also captures the transition with increasing In in martensite from antiferromagnetic to ferromagnetic order and predicts re-entrant ferromagnetism, though the latter occurs at higher In content than reported experimentally. We discuss possible sources of this discrepancy and highlight the broader applicability of the method to other magnetostructurally complex materials, where it may offer mechanistic insight and predictive design capabilities.

Cluster expansion↗
DOE OSTI2024

Heterostructural Alloy Phase Diagram for (Cd 1-x Zn x ) 3 As 2

Alloying the topological semimetal Cd 3 As 2 with Zn 3 As 2 provides a potential route for controlling the electronic properties. We predict the alloy phase diagram from first-principles calculations, considering that both end members have a crystal structure derived from the antifluorite lattice, but with different arrangements of the unoccupied cation sites. To overcome the limitations of the regular solution approximation and to include short-range order effects, we perform Monte Carlo simulations, parameterize the temperature dependence of the mixing enthalpy ΔH m , and perform thermodynamic integration of the free energy. The resulting phase diagram exhibits features that are unique to heterostructural alloy systems and provides computational predictions of solubility limits and composition ranges that are stable against spinodal decomposition.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Ligand Hole Driven Metal–Insulator Transition Exemplified in a Layered Transition Metal Oxide

The interplay of cooperative Jahn–Teller (JT) distortions and charge-disproportionation (CD) with a strong electronic correlation in transition metal oxides leads to structural symmetry breaking. Both JT and CD often manifest in the form of significant modifications in electronic and structural properties such as band splitting, metal–insulator transitions (MIT), and enhanced electron lattice interactions. Notably, the charge-disproportionation is a key electronic feature that drives the MIT. Here, we demonstrate and quantify it using first-principles calculations combining density-functional theory, dynamical mean-field theory, and spin–lattice Monte Carlo simulations. Taking Ca 2 FeMnO 6 as a prototypical example of a correlated oxide, our ab initio study shows that MIT in Ca 2 FeMnO 6 arises from the partial localization of oxygen ligand holes at alternate Fe sites that control both charge and magnetic ordering. Interestingly, the band gap was found to be fundamentally controlled by the strength of the charge-transfer energy and not by the Mott–Hubbard interactions. The novel physics and insights presented in this work reveal promising routes for tuning the electronic functionality in transition-metal oxides.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic Modeling of Complex Solid Solutions in the Lu-H-N System via Graph Neural Network Accelerated Monte Carlo Simulations

Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂⁡(10 2 ) ⁢GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂⁡(10 0 ) ⁢GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.

Monte Carlo methods↗
DOE OSTI2025

Melting curves of atomic hydrogen and deuterium calculated using path-integral Monte Carlo

We calculate the melting line of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. Here, the resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

08 HYDROGEN↗
DOE OSTI2025

CASM Monte Carlo: Calculations of the thermodynamic and kinetic properties of complex multicomponent crystals

Monte Carlo techniques play a central role in statistical mechanics approaches that connect macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo techniques for the study of multicomponent crystalline materials within the Clusters Approach to Statistical Mechanics (CASM) software suite, and demonstrates their use in model systems to calculate free energies and kinetic coefficients, study phase transitions, and construct phase diagrams from first principles. Many crystal structures are complex, with multiple sublattices occupied by differing sets of chemical species, along with the presence of vacancies or interstitial species. This imposes constraints on concentration variables, the form of thermodynamic potentials, and the values of kinetic transport coefficients. The framework used by CASM to formulate thermodynamic potentials and kinetic transport coefficients accounting for arbitrarily complex crystal structures is presented and demonstrated with examples of increasing complexity. Additionally, an overview of the capabilities of the CASM software specific to Monte Carlo methods is given, and a new CASM software package is introduced, casm-flow, which helps automate the setup, submission, management, and analysis of Monte Carlo simulations.

Cluster expansion↗
DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗
NASA NTRS2026

Diffusion Quantum Monte Carlo Calculation of the Austenite and Martensite Phases of NiTi

NiTi is a promising material for smart and active technologies due to its exhibition of the shape memory effect, superelasticity, and biocompatibility. The shape memory effect is tied to the reversible transition between the austenite and martensite phases. A major research direction is to alloy NiTi with Zr, Hf, Pd, Pt, etc., in order to tune the martensitic transition temperature (MTT). Modeling the MTT from first principles is challenging because the lattice dynamics is complicated by anharmonicity and various low-energy structures. Using density functional theory, the energy difference between the austenite and martensite phases of NiTi varies by up to 100 meV/atom depending on the choice of density functional, which is of the same order of the energy difference itself. Consequently, free energy calculations with different functionals can result in estimates of the MTT that vary by several hundred K. Using diffusion quantum Monte Carlo, we calculated the energy difference between the B2 and B19' structures of NiTi to be 70.9 +- 2.5 meV/atom.

Kevin K Ly↗
DOE OSTI2024

Toward first principles-based simulations of dense hydrogen

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g., planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange–correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principles PIMC as well as in DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions that are based on first principles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Simulated structure and thermodynamics of decagonal Al-Co-Cu quasicrystals

Atomic structures of Al-Co-Cu decagonal quasicrystals (dQCs) are investigated using empirical oscillating pair potentials (EOPP) in molecular dynamic (MD) simulations that we enhance by Monte Carlo (MC) swapping of chemical species and replica exchange. Predicted structures exhibit planar decagonal tiling patterns and are periodic along the perpendicular direction. We then recalculate the energies of promising structures using first-principles density functional theory (DFT), along with energies of competing phases. We find that our τ -inflated sequence of QC approximants (QCAs) are energetically unstable at low temperature by at least 3 meV/atom. Extending our study to finite temperatures by calculating harmonic vibrational entropy, as well as anharmonic contributions that include chemical species swaps and tile flips, our results suggest that the quasicrystal phase is entropically stabilized at temperatures in the range 600-800 K and above. It decomposes into ordinary (though complex) crystal phases at low temperatures, including a partially disordered B2-type phase. We discuss the influence of density and composition on QC phase stability; we compare the structural differences between Co-rich and Cu-rich quasicrystals; and we analyze the role of entropy in stabilizing the quasicrystal, concluding with a discussion of the possible existence of “high entropy” quasicrystals. Published by the American Physical Society 2024

Huang, Yang (ORCID:0009000045917347)↗
NASA NTRS2019

The Effects of High-Temperature Fractional Crystallization on Calcium Isotopic Composition

We report Ca isotope fractionation among a co-genetic suite of samples from the Mauritanian Guelb el Azib ultramafic-mafic-anorthosite complex (GAC), which represents the fractional crystallization sequence of an igneous magma chamber. We investigate how the composition of an evolving crystallizing liquid and the resultant mineralogy of co-crystallizing assemblages affects inter-phase Ca isotope fractionation. Because the GAC is an Archean metamorphosed complex, we first investigate the resistance of the Ca isotope signature to secondary hydrothermal alteration and to metamorphism. While we cannot conclude here that Ca isotopes are undisturbed at the mineral scale, we show that they are preserved at the bulk rock scale. This is adequate for our study where several samples are almost monomineralic at the bulk scale level. The δ(exp 44/40)Ca (relative to NIST standard SRM 915a) of GAC layers range from −1.53 to 1.61‰, with the earliest-formed ultramafic cumulate layer being isotopically heaviest and the later, more felsic layers being isotopically lighter. For the first time, we show that plagioclase is much more enriched in light Ca isotopes compared to olivine and (Ca-) pyroxene. Monte Carlo simulations suggest that Ca isotopes are fractionated among co-existing silicate minerals during fractional crystallization, possibly in relation with the residual liquid composition. In qualitative agreement with computational models based on first principles lattice dynamics, we observe that Ca isotope fractionation is mineralogically controlled and importantly, that the degree of fractionation can vary according to the CaO composition of the residual liquid. While previous studies have aimed to understand partial melting as a source of Ca isotope fractionation, our results suggest that fractional crystallization is also a source of Ca isotope variability among co-genetic samples.

Maria C. Valdes↗
NASA NTRS2001

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗
DOE OSTI2025

A Machine Learning Framework for Modeling Ensemble Properties of Atomically Disordered Materials

Atomic disorder can strongly influence material properties such as charge transport, optical response, and catalytic activity. However, efficiently modeling these disorder effects remains challenging for first-principles methods due to the cost of sampling large configurational spaces and computing complex physical quantities. Recent advances of machine learning techniques, particularly graph neural networks (GNNs), has enabled the efficient and accurate predictions of complex material properties, offering promising tools for studying disordered systems. In this work, we present a general machine-learning-assisted computational framework that integrates equivariant GNNs with Monte Carlo simulations to compute the thermodynamic and ensemble-averaged functional properties of disordered materials. Using the surface-termination-disordered MXene monolayer Ti 3 C 2 T 2–x as a representative system, we find that electrical conductivity exhibits an emergent peak near the order–disorder phase transition temperature due to the interplay between electron scattering and doping. In contrast, optical conductivity remains largely insensitive to local atomic disorder and reflects the global surface chemical composition. These results highlight the role of atomic disorder in affecting material properties and demonstrate the potential of our approach for statistically modeling disorder effects in a wide range of materials such as high-entropy alloys and spin liquids.

MXene↗
NASA NTRS1997

A Comprehensive Reliability Methodology for Assessing Risk of Reusing Failed Hardware Without Corrective Actions with and Without Redundancy

This paper deals with the development of a reliability methodology to assess the consequences of using hardware, without failure analysis or corrective action, that has previously demonstrated that it did not perform per specification. The subject of this paper arose from the need to provide a detailed probabilistic analysis to calculate the change in probability of failures with respect to the base or non-failed hardware. The methodology used for the analysis is primarily based on principles of Monte Carlo simulation. The random variables in the analysis are: Maximum Time of Operation (MTO) and operation Time of each Unit (OTU) The failure of a unit is considered to happen if (OTU) is less than MTO for the Normal Operational Period (NOP) in which this unit is used. NOP as a whole uses a total of 4 units. Two cases are considered. in the first specialized scenario, the failure of any operation or system failure is considered to happen if any of the units used during the NOP fail. in the second specialized scenario, the failure of any operation or system failure is considered to happen only if any two of the units used during the MOP fail together. The probability of failure of the units and the system as a whole is determined for 3 kinds of systems - Perfect System, Imperfect System 1 and Imperfect System 2. in a Perfect System, the operation time of the failed unit is the same as that of the MTO. In an Imperfect System 1, the operation time of the failed unit is assumed as 1 percent of the MTO. In an Imperfect System 2, the operation time of the failed unit is assumed as zero. in addition, simulated operation time of failed units is assumed as 10 percent of the corresponding units before zero value. Monte Carlo simulation analysis is used for this study. Necessary software has been developed as part of this study to perform the reliability calculations. The results of the analysis showed that the predicted change in failure probability (P(sub F)) for the previously failed units is as high as 49 percent above the baseline (perfect system) for the worst case. The predicted change in system P(sub F) for the previously failed units is as high as 36% for single unit failure without any redundancy. For redundant systems, with dual unit failure, the predicted change in P(sub F) for the previously failed units is as high as 16%. These results will help management to make decisions regarding the consequences of using previously failed units without adequate failure analysis or corrective action.

Putcha, Chandra S.↗
DOE OSTI2025

Perspective on Many-Body Methods for Molecular Polaritonic Systems

Recent advances in strong light–matter interactions have revealed a wealth of new physical phenomena in molecules embedded in optical cavities, including modified chemical reactivity, altered excitation spectra, and novel quantum correlations. To describe these effects from first-principles, the field of ab initio quantum electrodynamics (QED) has emerged as a compelling extension of quantum chemistry that treats electronic and photonic degrees of freedom on equal footing. In this Perspective, we review the growing landscape of many-body QED methods, including Hartree–Fock, density functional theory (QEDFT), time-dependent DFT (QED-TDDFT), configuration interaction (QED-CI), complete active space (QED-CASSCF), coupled cluster (QED-CC), quantum Monte Carlo (QED-QMC), and density matrix renormalization group (QED-DMRG), highlighting recent developments and implementations. We further explore real-time methods, gradient and Hessian formalisms, and the integration of nonadiabatic nuclear dynamics. Applications range from benchmark simulations of polaritonic chemistry to quantum simulations on emerging quantum hardware. We conclude by outlining future directions for theory development and interdisciplinary efforts at the interface of quantum chemistry, condensed matter, and quantum optics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Design principles for energy transfer in the photosystem II supercomplex from kinetic transition networks

Photosystem II (PSII) has the unique ability to perform water-splitting. With light-harvesting complexes, it forms the PSII supercomplex (PSII-SC) which is a functional unit that can perform efficient energy conversion, as well as photoprotection, allowing photosynthetic organisms to adapt to the naturally fluctuating sunlight intensity. Achieving these functions requires a collaborative energy transfer network between all subunits of the PSII-SC. In this work, we perform kinetic analyses and characterise the energy landscape of the PSII-SC with a structure-based energy transfer model. With first passage time analyses and kinetic Monte Carlo simulations, we are able to map out the overall energy transfer network. We also investigate how energy transfer pathways are affected when individual protein complexes are removed from the network, revealing the functional roles of the subunits of the PSII-SC. In addition, we provide a quantitative description of the flat energy landscape of the PSII-SC. We show that it is a unique landscape that produces multiple kinetically relevant pathways, corresponding to a high pathway entropy. These design principles are crucial for balancing efficient energy conversion and photoprotection.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Finite-element-based simulations of electrodes for CO 2 cascade reduction reactions

The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗