arXiv subjects

Dallas R. Trinkle

Publications and source records attributed to Dallas R. Trinkle.

At least 19 recordsLinked to original sources

arXiv2026

Spin-polarized Energy Density Method from Spin-Density Functional Theory

The energy density method is generalized to include spin polarization with the full formalism derived based on spin-density functional theory, which aims at decomposing the total energy into well-defined atomic energies. The method involves two steps: (1) decomposing the total energy into spin-polarized energy density functions in real space, and (2) integrating these energy densities over chosen gauge-invariant volumes for uniquely defined atomic energies, whose summation over all the atoms restores the DFT total energy up to a constant difference. This method is numerically implemented into the Vienna ab initio simulation package for the projector augmented-wave method, and is showcased with two applications. In the first application, we model the paramagnetic face-centered cubic Fe using spin special quasirandom structures; the spin energies are fit to spin cluster expansions and a deep neural network. In the second application, we calculate the atomic energy distributions of dilute magnetic semiconductor Ni-doped GaN with different dopant distances and spin configurations. This method extracts additional useful information for the study of magnetic systems with density functional theory.

cond-mat.mtrl-sci↗

arXiv2026

Thermodynamics and kinetics of lithium at the silver-lithium battery interface

Silver interlayers have been shown to enable smooth lithium deposition and cycling in anode-free solid-state batteries. Here, we report the atomic structure of the Ag and Li interface, showing that Li preferentially plates as FCC on both the (111) and (100) Ag surfaces. This forms an energetically favorable coherent interface with Ag, while the BCC phase forms a semi-coherent interface due to large lattice mismatch. We also calculate vacancy formation energies and migration energies for Li diffusion through the interface. We show that vacancy formation energies increase at the interface, leading to an energetic driving force for vacancies to diffuse away from the interface. Additionally, the migration barriers for vacancies from the Ag to the Li are small (29 meV), and therefore promote rapid alloying between Ag and Li. Rapid Li diffusion kinetics directly at the interface leads to smooth deposition of Li, reducing the onset of dendrites. However, diffusion in the 2nd and 3rd Li layers is slower compared to bulk FCC or BCC Li, leading to kinetically hindered alloying when multiple layers of pure Li form. The diffusion kinetics for Ag nanoparticles may be improved by alloying with Mg to expand the Ag lattice constant while forming a solid solution with both Ag and Li.

cond-mat.mtrl-sci↗

arXiv2025

Effect of Magneto-Mechanical Synergism in the Process-Structure Correlation in Fe-C Alloys: A Phase-Field Modeling Approach

Applied magnetic fields can alter phase equilibria and kinetics in steels; however, quantitatively resolving how magnetic, chemical, and elastic driving forces jointly influence the microstructure remains challenging. We develop a quantitative magneto-mechanically coupled phase-field model for the Fe-C system that couples a CALPHAD-based chemical free energy with demagnetization-field magnetostatics and microelasticity. The model reproduces single- and multi-particle evolution during the alpha to gamma inverse transformation at 1023 K under external fields up to 20 T, including ellipsoidal morphologies observed experimentally at 8 T. Chemically driven growth is isotropic; a magnetic interaction introduces an anisotropic driving force that elongates gamma precipitates along the field into ellipsoids, while elastic coherency promotes faceting, yielding elongated cuboidal or ``brick-like" particles under combined magneto-elastic coupling. Growth kinetics increase with C content, and decrease with field strength and misfit strain. Multi-particle simulations reveal dipolar interaction-mediated coalescence for field-parallel neighbors and ripening for field-perpendicular neighbors. Incorporating field-dependent diffusivity from experiment slows kinetics as expected; a first-principles-motivated anisotropic diffusivity correction is estimated to be small (<2%). These results establish a process-structure link for magnetically assisted heat treatments of Fe-C alloys and provide guidance for microstructure control via chemo-magneto-mechanical synergism.

cond-mat.mtrl-sci↗

arXiv2025

Energy density and stress fields in quantum systems

There has been an enduring interest and controversy about whether or not one can define physically meaningful energy density and stress fields, $e(\bf{r})$ and $σ_{αβ}(\bf{r})$, since the two forms of the kinetic energy, $\frac{1}{2}|\nabla Ψ|^2$ and $-\frac{1}{2}Ψ\nabla^2 Ψ$, lead to different densities, and analogous issues arise for interactions. This paper considers the ground state of a system of many interacting particles in an external potential, and presents a resolution in steps. 1) For the kinetic energy all effects of exchange and correlation are shown to be unique functions of position $\bf{r}$; all issues of non-uniqueness involve only the density $n(\bf{r})$ and are equivalent to an effective single-particle problem with wavefunction $s(\bf{r}) = \sqrt{n(\bf{r})/N}$. 2) Interactions can be considered as potentials acting on particles or interaction fields, e.g., the Maxwell form in terms of electric fields. In each case, there is a mean field part that is a function of the density and a part due to correlation that is uniquely defined. 3) The final results follow from the nature of energy and stress. Because the energy determines the ground state itself through the variational principle, the kinetic energy must involve $-\frac{1}{2}s\nabla^2 s$ and interactions in terms of potentials. This leads to density functional theory interpreted as energy density $e(\bf{r})$ equilibrated to minimize fluctuations with the same chemical potential at all points $\bf{r}$. However, stress is related to forces, and the only acceptable expressions for the stress field involve the combination $\frac{1}{2}[s\nabla^2 s - |\nabla s|^2]$, and Coulomb interactions in terms of electric fields. Together these results lead to well-defined formulations of energy density and stress fields that are physically motivated and based on a clear set of arguments.

cond-mat.mtrl-sci↗

arXiv2025

Explainable Machine Learning for Oxygen Diffusion in Perovskites and Pyrochlores

Explainable machine learning can help to discover new physical relationships for material properties. To understand the material properties that govern the activation energy for oxygen diffusion in perovskites and pyrochlores, we build a database of experimental activation energies and apply a grouping algorithm to the material property features. These features are then used to fit seven different machine learning models. An ensemble consensus determines that the most important features for predicting the activation energy are the ionicity of the A-site bond and the partial pressure of oxygen for perovskites. For pyrochlores, the two most important features are the A-site $s$ valence electron count and the B-site electronegativity. The most important features are all constructed using the weighted averages of elemental metal properties, despite weighted averages of the constituent binary oxides being included in our feature set. This is surprising because the material properties of the constituent oxides are more similar to the experimentally measured properties of perovskites and pyrochlores than the features of the metals that are chosen. The easy-to-measure features identified in this work enable rapid screening for new materials with fast oxide-ion diffusivity.

cond-mat.mtrl-sci↗

arXiv2025

Investigating the effects of local environment on nitrogen vacancies in high entropy metal nitrides

High entropy metal nitrides are an important material class in a variety of applications, and the role of nitrogen vacancies is of great importance for understanding their stability and mechanical properties. We study six different high entropy nitrides with eight different metal species to build a predictive model of the nitrogen vacancy formation energy. We construct sets of supercells that maximize the number of unique nitrogen environments for a given chemistry, and then use density-functional theory to calculate the energy density for all nitrogen sites, and the vacancy formation energies for the highest, lowest, and a median subset based on the energy densities. The energy density of nitrogen sites correlates with the vacancy formation energies, for binary, ternary and high entropy nitrides. A linear regression model predicts the vacancy formation energies using only the nearest-neighbor composition; across our eight metals, we find the largest vacancy formation energies next to Hf, then Zr, Ti, V, Cr, Ta, Nb, and the lowest near Mo. Additionally, we see that binary nitride data shows qualitatively similar vacancy formation energy trends for high entropy nitrides; however, the binary data alone is insufficient to predict the complex nitride behavior. Our model is both predictive and easily interpretable, and correlates with experimental data.

cond-mat.mtrl-sci↗

arXiv2025

External magnetic field suppression of carbon diffusion in iron

External magnetic fields reduce diffusion of carbon in BCC iron, but the physical mechanism is not understood. Using DFT calculations with magnetic moments sampled from a Heisenberg model, we calculate diffusivities of carbon in iron at high temperatures and with field. Our model reproduces the measured suppression of diffusivity from field. We find that increasing magnetic disorder flattens the electron density of states compared with the ferromagnetic case, which distorts the octahedral cages around carbon, lowering the activation barrier to diffusion; an applied field reverses these trends.

cond-mat.mtrl-sci↗

arXiv2025

Computing ternary liquid phase diagrams: Fe-Cu-Ni

We compute the phase separation of the immiscible liquid alloy Fe-Cu-Ni. Our computational approach uses a virtual semigrand canonical Widom approach to determine differences in excess chemical potentials between different species. Using an embedded atom potential for Fe-Cu-Ni, we simulate liquid states over a range of compositions and temperatures. This raw data is then fit to Redlich-Kister polynomials for the Gibbs free energy with a simple temperature dependence. Using the analytic form, we can determine the phase diagram for the ternary liquid, compute the miscibility gap and spinodal decomposition as a function of temperature for this EAM potential. In addition, we compute density as a function of composition and temperature, and predict pair correlation functions. We use static structure factors to estimate the second derivative of the Gibbs free energy (the $S^0$ method) and compare with our fit Gibbs free energy. Finally, using a nonequilibrium Hamiltonian integration method, we separately compute absolute Gibbs free energies for the pure liquid states; this shows that our endpoints are accurate to within 1 meV for our ternary Gibbs free energy, as well as the absolute Gibbs free energy for the ternary liquid.

cond-mat.mtrl-sci↗

arXiv2025

Core Energies in Isolated Edge and Mixed Dislocations in BCC Fe from First-principles Energy Density Method

We use first-principles spin-polarized energy density method (EDM) to calculate the atomic energies in isolated $a_0[100](010)$ edge, $a_0[100](011)$ edge, $\frac{a_0}{2}[\bar1\bar11](1\bar10)$ edge and $\frac{a_0}{2}[111](1\bar10)$ $71^\circ$ mixed dislocations in body-centered cubic (BCC) Fe. The distribution of atomic energies shows the energetic effects of slip, including non-linear displacements in and near the core, and the elastic field further away. The EDM atomic energies agree well with anisotropic elasticity predictions in the elastic region, while they deviate in the core region due to failure of linear elasticity, and the energy deviation quantifies the core widths. Dislocation line energies are obtained by partial sums of the atomic energies within distance $r$ of the dislocation center; the core energy is extracted from the large $r$ behavior. We compare our results with an EAM and a GAP potential, showing that while both potentials produce core structures similar to DFT predictions, the GAP potential has a closer match with DFT and EDM in core energies.

cond-mat.mtrl-sci↗

arXiv2024

Quantifying the contributions to diffusion in complex materials

Using machine learning with a variational formula for diffusivity, we recast diffusion as a sum of individual contributions to diffusion--called "kinosons"--and compute their statistical distribution to model a complex multicomponent alloy. Calculating kinosons is orders of magnitude more efficient than computing whole trajectories, and elucidates kinetic mechanisms for diffusion. The distribution of kinosons with temperature leads to new accurate analytic models for macroscale diffusivity. This combination of machine learning with diffusion theory promises insight into other complex materials.

cond-mat.mtrl-sci↗

arXiv2024

Discovering Melting Temperature Prediction Models of Inorganic Solids by Combining Supervised and Unsupervised Learning

The melting temperature is important for materials design because of its relationship with thermal stability, synthesis, and processing conditions. Current empirical and computational melting point estimation techniques are limited in scope, computational feasibility, or interpretability. We report the development of a machine learning methodology for predicting melting temperatures of binary ionic solid materials. We evaluated different machine-learning models trained on a data set of the melting points of 476 non-metallic crystalline binary compounds, using materials embeddings constructed from elemental properties and density-functional theory calculations as model inputs. A direct supervised-learning approach yields a mean absolute error of around 180~K but suffers from low interpretability. We find that the fidelity of predictions can further be improved by introducing an additional unsupervised-learning step that first classifies the materials before the melting-point regression. Not only does this two-step model exhibit improved accuracy, but the approach also provides a level of interpretability with insights into feature importance and different types of melting that depend on the specific atomic bonding inside a material. Motivated by this finding, we used a symbolic learning approach to find interpretable physical models for the melting temperature, which recovered the best-performing features from both prior models and provided additional interpretability.

cond-mat.mtrl-sci↗

arXiv2023

Explainable Machine Learning for Hydrogen Diffusion in Metals and Random Binary Alloys

Hydrogen diffusion in metals and alloys plays an important role in the discovery of new materials for fuel cell and energy storage technology. While analytic models use hand-selected features that have clear physical ties to hydrogen diffusion, they often lack accuracy when making quantitative predictions. Machine learning models are capable of making accurate predictions, but their inner workings are obscured, rendering it unclear which physical features are truly important. To develop interpretable machine learning models to predict the activation energies of hydrogen diffusion in metals and random binary alloys, we create a database for physical and chemical properties of the species and use it to fit six machine learning models. Our models achieve root-mean-squared-errors between 98-119 meV on the testing data and accurately predict that elemental Ru has a large activation energy, while elemental Cr and Fe have small activation energies. By analyzing the feature importances of these fitted models, we identify relevant physical properties for predicting hydrogen diffusivity. While metrics for measuring the individual feature importances for machine learning models exist, correlations between the features lead to disagreement between models and limit the conclusions that can be drawn. Instead grouped feature importances, formed by combining the features via their correlations, agree across the six models and reveal that the two groups containing the packing factor and electronic specific heat are particularly significant for predicting hydrogen diffusion in metals and random binary alloys. This framework allows us to interpret machine learning models and enables rapid screening of new materials with the desired rates of hydrogen diffusion.

cond-mat.mtrl-sci↗

arXiv2023

Spline-based neural network interatomic potentials: blending classical and machine learning models

While machine learning (ML) interatomic potentials (IPs) are able to achieve accuracies nearing the level of noise inherent in the first-principles data to which they are trained, it remains to be shown if their increased complexities are strictly necessary for constructing high-quality IPs. In this work, we introduce a new MLIP framework which blends the simplicity of spline-based MEAM (s-MEAM) potentials with the flexibility of a neural network (NN) architecture. The proposed framework, which we call the spline-based neural network potential (s-NNP), is a simplified version of the traditional NNP that can be used to describe complex datasets in a computationally efficient manner. We demonstrate how this framework can be used to probe the boundary between classical and ML IPs, highlighting the benefits of key architectural changes. Furthermore, we show that using spline filters for encoding atomic environments results in a readily interpreted embedding layer which can be coupled with modifications to the NN to incorporate expected physical behaviors and improve overall interpretability. Finally, we test the flexibility of the spline filters, observing that they can be shared across multiple chemical systems in order to provide a convenient reference point from which to begin performing cross-system analyses.

cond-mat.mtrl-sci↗

arXiv2018

Geometries of edge and mixed dislocations in bcc Fe from first principles calculations

We use DFT to compute core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in bcc Fe. The calculations use flexible boundary conditions (FBC), which allow dislocations to relax as isolated defects by coupling the core to an infinite harmonic lattice through the lattice Green function (LGF). We use LGFs of dislocated geometries in contrast to previous FBC-based dislocation calculations that use the bulk crystal LGF. Dislocation LGFs account for changes in topology in the core as well as strain throughout the lattice. A bulk-like approximation for the force constants in a dislocated geometry leads to LGFs that optimize the cores of the $a_0[100](010)$ edge, $a_0[100](011)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations. This approximation fails for the $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ dislocation, so here we derive the LGF using accurate force constants from a Gaussian approximation potential. The standard deviations of dislocation Nye tensor distributions quantify the widths of the cores. The relaxed cores are compact, and the magnetic moments on the Fe atoms closely follow the volumetric strain distributions in the cores. We also compute the core structures of these dislocations using eight different classical interatomic potentials, and quantify symmetry differences between the cores using the Fourier coefficients of their Nye tensor distributions. Most of the core structures computed using the classical potentials agree well with DFT results. The DFT geometries provide benchmarking for classical potential studies of work-hardening, as well as substitutional and interstitial sites for computing solute-dislocation interactions that serve as inputs for mesoscale models of solute strengthening and solute diffusion near dislocations.

cond-mat.mtrl-sci↗

arXiv2018

A variational principle for mass transport

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and crystalline systems. This unifies different computational approaches for diffusion, and provides a framework for the creation of new approximation methods with error estimation. It gives a different physical interpretation of the Green function. Finally, the variational principle quantifies the accuracy of competing approaches for a nontrivial diffusion problem.

cond-mat.stat-mech↗

arXiv2017

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

cond-mat.stat-mech↗

arXiv2016

Light element diffusion in Mg using first principles calculations: Anisotropy and elastodiffusion

The light elemental solutes B, C, N, and O can penetrate the surface of Mg alloys and diffuse during heat treatment or high temperature application, forming undesirable compounds. We investigate the diffusion of these solutes by determining their stable interstitial sites and the inter-penetrating network formed by these sites. We use density functional theory (DFT) to calculate the site energies, migration barriers, and attempt frequencies for these networks to inform our analytical model for bulk diffusion. Due to the nature of the networks, O diffuses isotropically, while B, C, and N diffuse anisotropically. We compute the elastodiffusion tensor which quantifies changes in diffusivity due to small strains that perturb the diffusion network geometry and the migration barriers. The DFT-computed elastic dipole tensor which quantifies the change in site energies and migration barriers due to small strains is used as an input to determine the elastodiffusion tensor. We employ the elastodiffusion tensor to determine the effect of thermal strains on interstitial diffusion and find that B, C, and N diffusivity increases on crystal expansion, while O diffusivity decreases. From the elastodiffusion and compliance tensors we calculate the activation volume of diffusion and find that it is positive and anisotropic for B, C and N diffusion, whereas it is negative and isotropic for O diffusion.

cond-mat.mtrl-sci↗

arXiv2016

Diffusivity and derivatives for interstitial solutes: Activation energy, volume, and elastodiffusion tensors

Computational atomic-scale methods continue to provide new information about geometry, energetics, and transition states for interstitial elements in crystalline lattices. This data can be used to determine the diffusivity of interstitials by finding steady-state solutions to the master equation. In addition, atomic-scale computations can provide not just the site energy, but also the stress in the cell due to the introduction of the defect to compute the elastic dipole. We derive a general expression for the fully anistropic diffusivity tensor from site and transition state energies, and three derivatives of the diffusivity: the elastodiffusion tensor (derivative of diffusivity with respect to strain), the activation barrier tensor (logarithmic derivative of diffusivity with respect to inverse temperature) and activation volume tensor (logarithmic derivative of diffusivity with respect to pressure). Computation of these quantities takes advantage of crystalline symmetry, and we provide an open-source implementation of the algorithm. We provide analytic results for octahedral-tetrahedral networks in face-centered cubic, body-centered cubic, and hexagonal closed-packed lattices, and conclude with numerical results for C in Fe.

cond-mat.mtrl-sci↗