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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Rethinking the magnetic properties of lepidocrocite: A density functional theory and cluster expansion study

The iron oxyhydroxide lepidocrocite (g-FeOOH) is an abundant mineral critical to a number of chemical and technological applications. Of particular interest is the ground state and nite temperature magnetic order, and the subsequent impact this has upon crystal properties. The magnetic properties, investigated in this work are governed primarily through superexchange interactions, and have been calculated using density functional theory and cluster expansion methods. Quantication of these exchange terms has facilitated the determination of the ground state magneto-crystalline structure and subsequent calculation of its lattice constants, elastic moduli, cohesive enthalpy, and electronic density of states. Further, using a collinear magnetic conguration model, the magnetic heat capacity versus temperature has been studied and the Neel temperature obtained.

Pope, Daniel J.↗
DOE OSTI2021

Performant implementation of the atomic cluster expansion

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗
DOE OSTI2021

Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Cluster Expansion Analysis of Atomic Order in Li-Ion Battery Cathode Material LiCo y Ni 1-y O 2

A modified cluster-expansion treatment was developed recently to analyze atomic order in LiCo y Ni 1-y O 2 , a model cathode material for Li-ion batteries. In this treatment, referred to as a “spin-atom” cluster expansion, the occupant of a lattice site is identified by its spin state as well as its atomic species. Further, Effective Cluster Interaction (ECI) coefficients are derived from a large training data set (i.e., the set of atomic arrangements for which DFT calculations are performed) which is filtered by an anomaly detection algorithm to eliminate poorly converged DFT calculations. The cluster expansion incorporates Li-Ni (LN) exchange as well as intralayer Co-Ni (CN) exchange. Monte Carlo simulations based on the cluster expansion were applied to the Ni-rich part of the phase diagram. The simulations predict a miscibility gap between y = 0.05 and y = 0.65.

25 ENERGY STORAGE↗
DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Approaches for handling high-dimensional cluster expansions of ionic systems

Disordered multicomponent systems attract great interest due to their engineering design flexibility and subsequent rich space of properties. However, detailed characterization of the structure and atomic correlations remains challenging and hinders full navigation of these complex spaces. A lattice cluster expansion is one tool to obtain configurational and energetic resolution. While in theory a cluster expansion can be applied to any system of any dimensionality, the method has primarily been used in binary systems or ternary alloys. Here we apply cluster expansions in high-component ionic systems, setting up the largest cluster expansion ever attempted to our knowledge. In doing so, we address and discuss challenges specific to high-component ionic systems, namely charge state assignments, structural relaxations, and rank-deficient systems. We introduce practical procedures to make the fitting and analysis of complex systems tractable, providing guidance for future computational studies of disordered ionic systems.

25 ENERGY STORAGE↗
DOE OSTI2022

Quantifying Errors in Effective Cluster Interactions of Lattice Gas Cluster Expansions

The promise of lattice gas (LG) cluster expansions (CEs) is that they can describe a given system property to any level of accuracy since the orthogonal “cluster basis functions” span the complete space of available configurations. Such an approach can be constructed to an arbitrarily large surface of a finite number of distinct adsorption sites. Unfortunately, this is only true for the case of an ideal, fixed lattice decorated with components at precise lattice points (the lattice “sites”) with no distortions or relaxations subsequently allowed. Since most systems, and surfaces specifically, do not conform to such an ideal set of constraints, errors in LG CEs must be expected or CE convergence severely hampered. Beyond this, numerical errors in the provided data can complicate the proper construction of a truly predictive and/or physically significant CE. In this work, we show here how reliance on typical statistical tools like confidence intervals cannot be expected to provide an accurate representation of the uncertainty of effective cluster interactions (ECIs) in the CE due to the nature of the target ab initio data and the nature of CEs themselves. We develop a method for estimating these errors that does not rely on statistical assumptions about the model or data. We then use these ECI errors to quantify fundamental consequences on the uncertainty of ECIs in CEs built from O/Fe(100) data whose surface and adsorbates have been allowed to relax in a typical manner and from O/Fe(100) data whose surface and adsorbates are fixed in ideal lattice positions. We also quantify the effect of using a different density functional theory exchange–correlation functional, using these ECI errors to assess the significance in any deviations. In both cases, our method is shown to have remarkable utility in the quantification of errors in the ECIs of CEs. While we stick to the lattice gas convention in this work, the method is equally applicable to the Ising convention or, in principle, any linear model of sufficient complexity.

08 HYDROGEN↗
DOE OSTI2022

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria: A DFT cluster expansion study

Magnetic contributions have the potential to significantly influence predicted phase stability within alloy and mineral mixing phase diagrams, yet have been historically challenging to incorporate due to a significant increase to phase space sampling. Here, in this work, we employ a computational protocol that includes spin orientation as an additional configurational component within multi-component cluster expansions between magnetic and non-magnetic metal oxide alloys [calculated using density functional theory (DFT) and the generalized gradient approximation]. This approach was used to determine the effect of magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria from first principles. Two-component cluster expansions of the magnetic components of eskolaite and hematite were first performed showing the ability of this method to properly calculate their respective magnetic properties. Two-component cluster expansions were then performed for non-magnetic Al(III) and ferromagnetic Cr(III) and Fe(III), and phase diagrams were calculated for later comparison. Finally, a non-magnetic Al(III) and “up” and “down” magnetic configurations for anti-ferromagnetic Cr(III) and Fe(III) were performed. Magnetic contributions to the calculated phase diagram for the corundumeskolaite system were shown to be inconsequential but are vital for accurate determination of the corundum-hematite solvus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A generalized and adaptable tensor-contraction-based cluster expansion formalism for multicomponent solids

Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has served as the standard workaround to improve computational efficiency. However, the standard CE technique is difficult to extend to exotic and/or low-symmetry lattices, often implemented via iteration over particular cluster types, which must be enumerated per lattice structure. In this work, we introduce the tensor cluster expansion (TCE), implemented in the open-source code tce-lib, which maps correlation functions to mixed tensor contractions, eliminating the need to iterate over cluster types and additionally making the calculation of correlation functions well-suited for massively parallel architectures like GPUs. We show that local interaction energies are an immediate consequence of the TCE formalism, yielding nearly $\mathcal{O}$(1) energy difference calculations. We then use this formalism to fit CE models for the TaW and CoNiCrFeMn systems, and use these models to respectively compute the enthalpy of mixing curve and Cowley short-range order parameters, showing excellent agreement with ground truth data.

Cluster expansion↗
DOE OSTI2020

Prediction of the Al-rich part of the Al-Cu phase diagram using cluster expansion and statistical mechanics

In this work, the thermodynamic properties of α-Al and other phases (GP zones, θ'', θ' and θ) in the Al-rich part of the Al-Cu system have been obtained by means of the cluster expansion formalism in combination with statistical mechanics. This information was used to build the Al-rich part of the Al-Cu phase-diagram taking into account vibrational entropic contributions for θ', as those of the other phases were negligible. The simulation predictions of the phase boundaries between α-Al and either θ'', θ' or θ phases as a function of temperature are in good agreement with experimental data and extend the phase boundaries to a wider temperature range. The DFT calculations reveal the presence of a number of metastable Guinier-Preston-zone type configurations that may coexist with α-Al and θ'' at low temperatures. They also demonstrate that θ' is the stable phase below 550K but it is replaced by θ above this temperature due to the vibrational entropic contribution to the Gibbs energy of θ'. This work shows how the combination of cluster expansion and statistical mechanics can be used to expand our knowledge of the phase diagram of metallic alloys and to provide Gibbs free energies of different phases that can be used as input in mesoscale simulations of precipitation.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A systematic analysis of phase stability in refractory high entropy alloys utilizing linear and non-linear cluster expansion models

We report that obtaining surrogate models for various types of materials has long been a goal of computational material scientists and physicists, as they allow the calculation of thermodynamic quantities and properties of interest far more efficiently than DFT. Many surrogate models, including interatomic potentials generated by machine learning algorthims and cluster expansions, rely on incorporating many-body interactions such as three-body or four-body interactions. When utilizing machine learning algorithms for interatomic potentials, it is common to start with two-body interactions and systematically include three- and four-body clusters to improve the fit, stopping when including the additional clusters does not measurably change the predictive power of the model. In cluster expansions for FCC and related lattices, it is often enough to include mostly two-body interactions and a handful of three-body interactions. However, it remains to be seen whether those will be enough in the case of lattices with a lower packing fraction, such as BCC.

36 MATERIALS SCIENCE↗
DOE OSTI2024

First-principles and cluster expansion study of the effect of magnetism on short-range order in Fe–Ni–Cr austenitic stainless steels

Short-range order (SRO), the regular and predictable arrangement of atoms over short distances, alters the mechanical properties of technologically relevant structural materials such as medium/high entropy alloys and austenitic stainless steels. In this study, we present a generalized spin cluster expansion (CE) model and show that magnetism is a primary factor influencing the level of SRO present in austenitic Fe-Ni-Cr alloys. The spin CE consists of a chemical cluster expansion combined with an Ising model for Fe-Ni-Cr austenitic alloys. It explicitly accounts for local magnetic exchange interactions, thereby capturing the effects of finite temperature magnetism on SRO. Model parameters are obtained by fitting to a first-principles data set comprising both chemically and magnetically diverse FCC configurations. The magnitude of the magnetic exchange interactions are found to be comparable to the chemical interactions. Compared to a conventional implicit magnetism CE built from only magnetic ground state configurations, the spin CE shows improved performance on several experimental benchmarks over a broad spectrum of compositions, particularly at higher temperatures due to the explicit treatment of magnetic disorder. We find that SRO is strongly influenced by alloy Cr content, since Cr atoms prefer to align antiferromagnetically with nearest neighbors but become magnetically frustrated with increasing Cr concentration. Using the spin CE, we predict that increasing the Cr concentration in typical austenitic stainless steels promotes the formation of SRO and increases order-disorder transition temperatures. Furthermore, this study underscores the significance of considering magnetic interactions explicitly when exploring the thermodynamic properties of complex transition metal alloys. It also highlights guidelines for customizing SRO through adjustments of alloy composition.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Atomic cluster expansion potential for large scale simulations of hydrocarbons under shock compression

We present an Atomic Cluster Expansion (ACE) machine learned potential developed for high-fidelity atomistic simulations of hydrocarbons, targeting pressures and temperatures near and above supercritical fluid regimes for molecular fluids. A diverse set of stoichiometries were covered in training, including 1:0 (pure carbon), 1:4 (methane), and 1:1 (benzene), and rich bonding environments sampled at supercritical temperatures, hydrogen rich, reactive mixtures where metastable stoichiometries arise, including 1:2 (ethylene) and 1:3 (ethane). A high-fidelity training database was constructed by performing large-scale quantum molecular dynamic simulations [density functional theory (DFT) MD] of diamond, graphite, methane, and benzene. A novel approach to selecting structures from DFT MD is also presented, which allows for the rapid selection of unique DFT MD frames from complex trajectories. Comparisons to DFT and experimental data demonstrate that the presented ACE potential accurately reproduces isotherms, carbon melting curves, radial distribution functions, and shock Hugoniots for carbon and hydrocarbon systems for pressures up to 100 GPa and temperatures up to 6000 K for hydrocarbon systems and up to 9000 K for pure carbon systems. This work delivers a potential that can be used for accurate, large-scale simulations of shocked hydrocarbons and demonstrates a methodology for fitting and validating machine learning interatomic potentials to complex molecular environments, which can be applied to energetic materials in future works.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Cluster expansion by transfer learning for phase stability predictions

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster expansions provide accurate phase stability predictions but are computationally demanding to parameterize from first principles, especially for structures of low dimension or with a large number of components, such as interfaces or multimetal catalysts. We overcome this trade-off via transfer learning. Using Bayesian inference, we incorporate prior statistical knowledge from machine-learned and physics-based potentials, enabling us to sample the most informative configurations and to efficiently fit first-principles cluster expansions. Furthermore, this algorithm is tested on Pt:Ni, showing robust convergence of the mixing energies as a function of sample size with reduced statistical fluctuations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Shadow Molecular Dynamics and Atomic Cluster Expansions for Flexible Charge Models

Here, a shadow molecular dynamics scheme for flexible charge models is presented where the shadow Born–Oppenheimer potential is derived from a coarse-grained approximation of range-separated density functional theory. The interatomic potential, including the atomic electronegativities and the charge-independent short-range part of the potential and force terms, is modeled by the linear atomic cluster expansion (ACE), which provides a computationally efficient alternative to many machine learning methods. The shadow molecular dynamics scheme is based on extended Lagrangian (XL) Born–Oppenheimer molecular dynamics (BOMD). XL-BOMD provides stable dynamics while avoiding the costly computational overhead associated with solving an all-to-all system of equations, which normally is required to determine the relaxed electronic ground state prior to each force evaluation. To demonstrate the proposed shadow molecular dynamics scheme for flexible charge models using atomic cluster expansion, we emulate the dynamics generated from self-consistent charge density functional tight-binding (SCC-DFTB) theory using a second-order charge equilibration (QEq) model. The charge-independent potentials and electronegativities of the QEq model are trained for a supercell of uranium oxide (UO 2 ) and a molecular system of liquid water. The combined ACE+XL-QEq molecular dynamics simulations are stable over a wide range of temperatures both for the oxide and for the molecular systems and provide a precise sampling of the Born–Oppenheimer potential energy surfaces. Accurate ground Coulomb energies are produced by the ACE-based electronegativity model during an NVE simulation of UO 2 , predicted to be within 1 meV of those from SCC-DFTB on average during comparable simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗