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Results for “First-principles statistical mechanics”

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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7 records
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2024

Thermodynamically informed priors for uncertainty propagation in first-principles statistical mechanics

Here, this work demonstrates how first-principles statistical mechanics approaches within a Bayesian framework can quantify and propagate uncertainties to downstream thermodynamic calculations. To address the issue of Bayesian prior selection, knowledge of 0 K ground states in the material system of interest is incorporated into the prior. The effectiveness of this framework is shown by creating a phase diagram for the fcc zirconium nitride system, including confidence intervals on order-disorder transition temperatures.

Bayesian methods↗
DOE OSTI2025

First-Principles Statistical Mechanics Study of Magnetic Fluctuations and Order–Disorder in the Spinel LiNi 0.5 Mn 1.5 O 4 Cathode

While significant magnetic interactions exist in lithium transition metal oxides, commonly used as Li-ion cathodes, the interplay between magnetic couplings, disorder, and redox processes remains poorly understood. In this work, we focus on the high-voltage spinel LiNi 0.5 Mn 1.5 O 4 (LNMO) cathode as a model system on which to apply a computational framework that uses first principles-based statistical mechanics methods to predict the finite temperature magnetic properties of materials and provide insights into the complex interplay between magnetic and chemical degrees of freedom. Density functional theory calculations on multiple distinct Ni–Mn orderings within the LNMO system, including the ordered ground-state structure (space group P4332), reveal a preference for a ferrimagnetic arrangement of the Ni and Mn sublattices due to strong antiferromagnetic superexchange interactions between neighboring Mn 4+ and Ni 2+ ions and ferromagnetic Mn–Mn and Ni–Ni couplings, as revealed by magnetic cluster expansions. These results are consistent with qualitative predictions using the Goodenough-Kanamori-Anderson rules. Simulations of the finite temperature magnetic properties of LNMO are conducted using Metropolis Monte Carlo. We find that a “semiclassical” Monte Carlo sampling method based on the Heisenberg Hamiltonian accurately predicts experimental magnetic transition temperatures observed in magnetometry measurements. This study highlights the importance of a robust computational toolkit that accurately captures the complex chemomagnetic interactions and predicts finite temperature magnetic behavior to help analyze experimental magnetic and magnetic resonance spectroscopy data acquired ex situ and operando.

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

Chemomechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemomechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. Furthermore, this has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain.

Materials Science↗
DOE OSTI2025

Time-domain theory of transient heat conduction in the local limit

Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics. Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic-scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function $\overleftrightarrow{𝑍}$⁡(𝑡) defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Molecular dynamics simulation of hydrodynamic transport coefficients in plasmas

Molecular dynamics simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green–Kubo formalism over a broad range of Coulomb coupling strength, 0.01 ≤ Γ ≤ 140. Emphasis is placed on testing standard results of the Chapman–Enskog solution in the weakly coupled regime (Γ ≪ 1) using these first-principles simulations. As expected, the results show good agreement for Γ ≲ 0.1. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green–Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal, and thermoelectric coefficients computed in the Chapman–Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime (Γ ≫ 1). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.

Electrical conductivity↗