Search NASA⌕ Search

SEARCH · Search NASA

Results for “first principles simulations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Ion Solvation and Transport in Narrow Carbon Nanotubes: Effects of Polarizability, Cation-π Interaction, and Confinement

Understanding ion solvation and transport under confinement is critical for a wide range of emerging technologies, including water desalination and energy storage. While molecular dynamics (MD) simulations have been widely used to study the behavior of confined ions, considerable deviations between simulation results depending on the specific treatment of intermolecular interactions remain. In the following, we present a systematic investigation of the structure and dynamics of two representative solutions, that is, KCl and LiCl, confined in narrow carbon nanotubes (CNTs) with a diameter of 1.1 and 1.5 nm, using a combination of first-principles and classical MD simulations. Our simulations show that the inclusion of both polarization and cation-π interactions is essential for the description of ion solvation under confinement, particularly for large ions with weak hydration energies. Beyond the variation in ion solvation, we find that cation-π interactions can significantly influence the transport properties of ions in CNTs, particularly for KCl, where our simulations point to a strong correlation between ion dehydration and diffusion. Finally, our study highlights the complex interplay between nanoconfinement and specific intermolecular interactions that strongly control the solvation and transport properties of ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

First-principles-integrated Study of Blazar Synchrotron Radiation and Polarization Signatures from Magnetic Turbulence

Blazar emission is dominated by nonthermal radiation processes that are highly variable across the entire electromagnetic spectrum. Turbulence, which can be a major source of nonthermal particle acceleration, can widely exist in the blazar emission region. The Turbulent Extreme Multi-Zone (TEMZ) model has been used to describe turbulent radiation signatures. Recent particle-in-cell (PIC) simulations have also revealed the stochastic nature of the turbulent emission region and particle acceleration therein. However, radiation signatures have not been systematically studied via first-principles-integrated simulations. In this paper, we perform combined PIC and polarized radiative transfer simulations to study synchrotron emission from magnetic turbulence in the blazar emission region. We find that the multiwavelength flux and polarization are generally characterized by stochastic patterns. Specifically, the variability timescale and average polarization degree (PD) are governed by the correlation length of the turbulence. Interestingly, magnetic turbulence can result in polarization angle swings with arbitrary amplitudes and duration, in either direction, that are not associated with changes in flux or PD. Surprisingly, these swings, which are stochastic in nature, can appear either bumpy or smooth, although large-amplitude swings (>180°) are very rare, as expected. Our radiation and polarization signatures from first-principles-integrated simulations are consistent with the TEMZ model, except that in the latter, there is a weak correlation, with zero lag, between flux and degree of polarization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high-quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree—quantities which are otherwise not directly accessible from the physical model—from first-principles path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and nonequilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high-density and high-temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from first-principles quantum Monte Carlo simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Understanding dynamic properties of materials using neutron spectroscopy and atomistic simulation

Recent developments in first-principles lattice dynamics and classical force field based molecular dynamics are revolutionising the field of neutron spectroscopy. Herein we present a short review of these methods, their critical role in the supporting of cutting-edge experiments, and how they are improved by matching experimental data. We begin with a brief overview of how lattice dynamics calculations can be compared to inelastic neutron scattering (INS) and molecular dynamics simulations to both INS and quasi-elastic neutron scattering (QENS). We then provide a series of exemplar applications where lattice dynamics and molecular dynamics have been used in conjunction with neutron spectroscopy to bring significant understanding to topical areas of materials science namely: (i) lattice dynamics and INS for the study of hybrid organic-inorganic perovskites (ii) lattice dynamics and INS for the study of flexible porous solids and (iii) molecular dynamics and QENS for probing molecular behaviour in zeolite catalysis. In all three cases, the understanding gained through the synergy of experiment and computation would have been significantly reduced using either in isolation. Finally, we consider the current state of the art, describing outstanding challenges and suggesting future directions in this exciting and fertile area of physical science.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ab initio ultrafast spin dynamics in solids

Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and are capable of nanosecond to millisecond simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe, and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent electronic spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over nanoseconds at any temperatures and doping levels. We first apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We found that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes dominant at low temperatures for spin relaxation in n-type GaAs. We further examine ultrafast dynamics in novel spin-valleytronic materials: monolayer and bilayer WSe 2 with realistic defects. We find that spin relaxation is highly sensitive to local symmetry and chemical bonds around defects. For the bilayer WSe 2 , we identify the scattering pathways in ultrafast dynamics and determine relevant dynamical properties, essential to its utilization of unique spin-valley-layer locking effects. In conclusion, our work provides a predictive computational platform for spin dynamics in solids, which has potential for designing new materials ideal for spintronics and quantum information technology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Towards Ab-Initio Simulations of Crystalline Defects at the Exascale Using Spectral Quadrature Density Functional Theory

Defects in crystalline solids play a crucial role in determining properties of materials at the nano, meso- and macroscales, such as the coalescence of vacancies at the nanoscale to form voids and prismatic dislocation loops or diffusion and segregation of solutes to nucleate precipitates, phase transitions in magnetic materials via disorder and doping. First principles Density Functional Theory (DFT) simulations can provide a detailed understanding of these phenomena. However, the number of atoms needed to correctly simulate these systems is often beyond the reach of many widely used DFT codes. The aim of this article is to discuss recent advances in first principles modeling of crystal defects using the spectral quadrature method. The spectral quadrature method is linear scaling with respect to the number of atoms, permits spatial coarse-graining, and is capable of simulating non-periodic systems embedded in a bulk environment, which allows the application of appropriate boundary conditions for simulations of crystalline defects. In this article, we discuss the state-of-the-art in ab-initio modeling of large metallic systems of the order of several thousand atoms that are suitable for utilizing exascale computing resourses.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Static and dynamic properties of multi-ionic plasma mixtures

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multi-component systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, "Pseudo-Ions in Jellium" (PIJ), based on an iso-electronic assumption (iso-n e ). With a multi-component hypernetted-chain integral equation, we verify the quality of the iso-n e prescription for describing the static structure of the mixtures. This semi-analytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Further, applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Machine-learning interatomic potentials for interfaces in all-solid-state batteries: Perspectives on training data, model selection, and validation

Interfaces play a pivotal role in dictating the performance and reliability of all-solid-state batteries (ASSBs), where complex electro-chemo-mechanical phenomena at grain boundaries (GBs) and interfaces can lead to degradation and failure. Traditional atomistic simulation methods, such as first-principles calculations and classical molecular dynamics, face limitations in modeling these interfaces due to either high computational cost or insufficient transferability to the diverse atomic environments evolving at interfaces. Machine-learning interatomic potentials (MLIPs) have emerged as a transformative approach, enabling large-scale, high-accuracy simulations of disordered and chemically complex systems by leveraging the predictability of machine learning models trained on first-principles data. Recent applications of MLIPs have demonstrated their ability to capture intricate behaviors at ASSB interfaces, including ion transport, interfacial evolution, and degradation mechanisms, with accuracy and efficiency unattainable by conventional methods. This prospective paper presents comprehensive analysis and practical guidance for MLIP development for GBs and interfaces in ASSBs, with a focus on three key pillars: data generation, model selection, and validation. Here, we review the current state of MLIP applications for GBs and interfaces in both general and ASSB-specific materials, highlighting best practices and challenges in constructing diverse and representative datasets, choosing appropriate machine learning architectures, and rigorously validating model performance. We also discuss emerging strategies and opportunities for improved reliability and efficiency of MLIPs to simulate realistic interfaces in ASSBs.

Energy - Storage↗
DOE OSTI2025

Machine learning enabled discovery of superhard and ultrahard carbon polymorphs

The demand for multifunctional materials has motivated the move from near-equilibrium materials to metastable i.e. out-of-equilibrium phases that can meet several desired target properties. The search for such metastable phases with exotic properties is non-trivial and often serendipitous. Inverse design approaches based on evolutionary search have been powerful tools, but such traditional searches have focused on identifying primarily stable and metastable materials with the lowest enthalpy. The inverse design of materials, with a focus on a desired property such as, for example, hardness is a challenging task because of the expensive computational cost involved in sampling multiple structures. The recent advances in machine learning have brought new powerful AI techniques to the forefront which can potentially revolutionize the inverse design and discovery of materials, especially metastable phases capable of meeting multifunctionality. Here, in this work, we develop and apply an automated reinforcement learning workflow for inverse design that integrates first principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the superhard and ultrahard metastable phases of Carbon. We demonstrate an automatic machine learning based inverse design workflow to map new undiscovered metastable states ranging from near equilibrium to those far-from-equilibrium that satisfy multiple property objectives, specifically bulk moduli, shear moduli and hardness. We create a comprehensive library of carbon stable and metastable phases with varying hardness and subsequently shortlist 10 top performing candidate carbon structures, including two newly reported phases, based on their hardness and characterize their temperature dependent mechanical properties. A neural network model is built using featurization of allotropes of carbon to predict the quasi-harmonic Gibbs free energies. The Gibbs free energies of the top performing phases are analyzed to get an estimate of the experimental synthesizability of these superhard and ultrahard carbon phases. In general, we show using machine learning based inverse design approaches how hitherto inaccessible metastable states can be identified and potentially synthesized to meet the demand for multifunctional materials.

Balasubramanian, Karthik [Univ. of Illinois, Chica↗
DOE OSTI2020

In Situ Oxidation Studies of High-Entropy Alloy Nanoparticles

Although high-entropy alloys (HEAs) have shown tremendous potential for elevated temperature, anticorrosion, and catalysis applications, little is known on how HEA materials behave under complex service environments. Herein, we studied the high-temperature oxidation behavior of Fe 0.28 Co 0.21 Ni 0.20 Cu 0.08 Pt 0.23 HEA nanoparticles (NPs) in an atmospheric pressure dry air environment by in situ gas-cell transmission electron microscopy. It is found that the oxidation of HEA NPs is governed by Kirkendall effects with logarithmic oxidation rates rather than parabolic as predicted by Wagner's theory. Further, the HEA NPs are found to oxidize at a significantly slower rate compared to monometallic NPs. The outward diffusion of transition metals and formation of disordered oxide layer are observed in real time and confirmed through analytical energy dispersive spectroscopy, and electron energy loss spectroscopy characterizations. Localized ordered lattices are identified in the oxide, suggesting the formation of Fe 2 O 3 , CoO, NiO, and CuO crystallites in an overall disordered matrix. Hybrid Monte Carlo and molecular dynamics simulations based on first-principles energies and forces support these findings and show that the oxidation drives surface segregation of Fe, Co, Ni, and Cu, while Pt stays in the core region. The present work offers key insights into how HEA NPs behave under high-temperature oxidizing environment and sheds light on future design of highly stable alloys under complex service conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Machine learning the metastable phase diagram of covalently bonded carbon

Abstract Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct “metastable” phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n -diamond as a cubic-analog of diaphite-like lonsdaelite phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Cavity-altered superconductivity

Is it feasible to alter the ground-state properties of a material by engineering its electromagnetic environment? Inspired by theoretical predictions, experimental realizations of such cavity-controlled properties without optical excitation are beginning to emerge. Here we devised and implemented a new platform to realize cavity-altered materials. Single crystals of hyperbolic van der Waals (vdW) compounds provide a resonant electromagnetic environment with enhanced density of photonic states and prominent mode confinement. We interfaced hexagonal boron nitride (hBN) with the molecular superconductor κ-(BEDT-TTF) 2 Cu[N(CN) 2 ]Br (κ-ET). The frequencies of infrared hyperbolic modes (HMs) of hBN match the infrared-active carbon–carbon (C=C) stretching molecular resonance of κ-ET implicated in superconductivity. Nano-optical data supported by first-principles molecular Langevin dynamics simulations confirm the presence of resonant coupling between the hBN hyperbolic cavity modes and the C=C stretching mode in κ-ET. Meissner-effect measurements using magnetic force microscopy (MFM) demonstrate a strong suppression of superfluid density near the hBN/κ-ET interface. Non-resonant control heterostructures, including RuCl 3 /κ-ET and hBN/Bi 2 Sr 2 CaCu 2 O 8+x (BSCCO), do not show the pronounced superfluid suppression. These observations suggest that hBN/κ-ET realizes a cavity-altered superconducting ground state. Our work highlights the potential of dark cavities devoid of external photons for engineering electronic ground-state properties of complex quantum materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Na ion dynamics in P2-Na x [Ni 1/3 Ti 2/3 ]O 2 : a combination of quasi-elastic neutron scattering and first-principles molecular dynamics study

In this work, the P2-type layered material Na 2/3 [Ni 1/3 Ti 2/3 ]O 2 was studied as a promising bi-functional electrode material for sodium-ion batteries. To assess the electrochemical performance of this material, we investigated the diffusion mechanism as well as ionic and electronic conductivity with a combination of experimental and computational techniques. The quasi-elastic neutron scattering (QENS) experiments and first-principles molecular dynamics (FPMD) simulations were performed to identify the diffusion mechanism. The QENS data showed that Na ion diffusion can be well described by the Singwi–Sjölander jump diffusion model, where the obtained mean jump length matched the distances between the neighboring edge-share and face-share Na sites. FPMD predicted diffusivity values similar to those from QENS. The computed composition dependence of ionic and electronic conductivity of Na x [Ni 1/3 Ti 2/3 ]O 2 suggested that electronic conductivity changes significantly when x deviates from 2/3 as the redox couple of Ni and Ti is activated, while the change of ionic conductivity with x is relatively small.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Using molten salts to probe outer-coordination sphere effects on lanthanide( III )/( II ) electron-transfer reactions

Controlling structure and reactivity by manipulating the outer-coordination sphere around a given reagent represents a longstanding challenge in chemistry. Despite advances toward solving this problem, it remains difficult to experimentally interrogate and characterize outer-coordination sphere impact. Here, this work describes an alternative approach that quantifies outer-coordination sphere effects. It shows how molten salt metal chlorides (MCl n ; M = K, Na, n = 1; M = Ca, n = 2) provided excellent platforms for experimentally characterizing the influence of the outer-coordination sphere cations (M n+ ) on redox reactions accessible to lanthanide ions; Ln 3+ + e 1– → Ln 2+ (Ln = Eu, Yb, Sm; e 1– = electron). As a representative example, X-ray absorption spectroscopy and cyclic voltammetry results showed that Eu 2+ instantaneously formed when Eu 3+ dissolved in molten chloride salts that had strongly polarizing cations (like Ca 2+ from CaCl 2 ) via the Eu 3+ + Cl 1– → Eu 2+ + ½Cl 2 reaction. Conversely, molten salts with less polarizing outer-sphere M 1+ cations (e.g., K 1+ in KCl) stabilized Ln 3+ . For instance, the Eu 3+ /Eu 2+ reduction potential was >0.5 V more positive in CaCl 2 than in KCl. In accordance with first-principle molecular dynamics (FPMD) simulations, we postulated that hard M n+ cations (high polarization power) inductively removed electron density from Ln n+ across Ln–Cl···M n+ networks and stabilized electron-rich and low oxidation state Ln 2+ ions. Conversely, less polarizing M n+ cations (like K 1+ ) left electron density on Lnn+ and stabilized electron-deficient and high-oxidation state Ln 3+ ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Nanoconfinement matters in humidified CO 2 interaction with metal silicates

With enigmatic observations of enhanced reactivity of wet CO 2 -rich fluids with metal silicates, the mechanistic understanding of molecular processes governing carbonation proves critical in designing secure geological carbon sequestration and economical carbonated concrete technologies. Here, we use the first principle and classical molecular simulations to probe the impact of nanoconfinement on physicochemical processes at the rock–water–CO 2 interface. We choose nanoporous calcium–silicate–hydrate (C–S–H) and forsterite (Mg 2 SiO 4 ) as model metal silicate surfaces that are of significance in cement chemistry and geochemistry communities, respectively. We show that while a nanometer-thick interfacial water film persists at unsaturated conditions consistent with in situ infrared spectroscopy, the phase behavior of the water–CO 2 mixture changes from its bulk counterpart depending on the surface chemistry and nanoconfinement. We also observe enhanced solubility at the interface of water and CO 2 phases, which could amplify the CO 2 speciation rate. Additionally, through free energy calculations, we show that CO 2 could be found in a metastable state near the C–S–H surface, which can potentially react with surface water and hydroxyl groups to form carbonic acid and bicarbonate. These findings support the explicit consideration of nanoconfinement effects in reactive and non-reactive pore-scale processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Pulsed laser deposition of delafossite oxide thin films on YSZ (001) substrates as solar water splitting photocathodes

Development of solar energy converters with earth-abundant and environmentally friendly materials is one of the key routes explored towards a sustainable future. In this work, crystalline delafossite-phase CuAlO 2 and CuFeO 2 thin film solar water splitting photocathodes were fabricated using pulsed laser deposition. It was found that the desired delafossite phase was formed only after high temperature annealing in an oxygen-free atmosphere. Further, the homogeneous delafossite bulk structure of the films was determined by correlating simulation results from first-principles calculations with synchrotron-based X-ray absorption near edge structure (XANES) spectroscopy. Both CuAlO 2 and CuFeO 2 photocathodes are active for solar water splitting, with the latter more efficient due to its narrower band gap and improved light absorption.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Atomate2: modular workflows for materials science

High-throughput density functional theory (DFT) calculations have become a vital element of computational materials science, enabling materials screening, property database generation, and training of “universal” machine learning models. While several software frameworks have emerged to support these computational efforts, new developments such as machine learned force fields have increased demands for more flexible and programmable workflow solutions. This manuscript introduces atomate2, a comprehensive evolution of our original atomate framework, designed to address existing limitations in computational materials research infrastructure. Key features include the support for multiple electronic structure packages and interoperability between them, along with generalizable workflows that can be written in an abstract form irrespective of the DFT package or machine learning force field used within them. Our hope is that atomate2's improved usability and extensibility can reduce technical barriers for high-throughput research workflows and facilitate the rapid adoption of emerging methods in computational material science.

97 MATHEMATICS AND COMPUTING↗