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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Assessing the Role of Interfacial and Metal Sites in Pt/TiO2-Catalyzed Acetic Acid Hydrodeoxygenation

Thermochemical conversion of biomass to produce drop-in quality biofuels typically involves hydrodeoxygenation (HDO) steps following catalytic fast pyrolysis (CFP) to remove excess oxygen and create a more-stable bio-oil product. HDO reactions are performed by co-feeding the CFP vapor-phase product and H2 gas over a bi-functional catalyst. Noble-metal catalysts supported on reducible metal oxides (e.g., Pt/TiO2) are active and selective toward these HDO reactions. Griffin and co-workers showed that Pt/TiO2 catalysts promote the desired deoxygenation steps for m-cresol HDO while mitigating undesired C-C bond-breaking steps that reduce the overall value/energy density of the biofuel. Such model-compound studies to inform the design of improved catalysts for HDO chemistry are necessary to improve the overall process economics/efficiencies for biofuels production. One important class of bio-derived compounds that has not been studied extensively with respect to HDO chemistry, particularly at the atomic level, is carboxylic acids. Past experimental work indicates that Pt/C and Pt/TiO2 catalysts are selective toward C-C and C-O bond-dissociation products for acetic acid HDO, respectively. To understand the role of Pt/TiO2 active sites in this observed change in selectivity and guide catalyst development, the work in this presentation focuses on modeling the role of Pt-metal and Pt-TiO2-interfacial sites in promoting key C-C bond-breaking, C-O bond-breaking, and (de)hydrogenation steps in acetic acid HDO. Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP). The exchange-correlation functional was approximated by the Perdew-Burke-Ernzerhof functional. Dispersion interactions were captured using the D3 method. Projector augmented-wave potentials described electron-ion interactions, and electron wavefunctions were expanded via a planewave basis with an energy cutoff of 500 eV. Activation barriers were calculated using the climbing image nudged elastic band method. Results and Discussion: To discern the role of Pt-metal and Pt-TiO2 interface sites in promoting acetic acid HDO chemistry, Pt(111) slab and anatase TiO2(101)-supported Pt-nanowire (PtNW/OH-TiO2) surface models were constructed, respectively. Because H2 is co-fed in HDO reactions, the anatase support was terminated with OH groups. Interfacial vacancies have been shown to facilitate Ru/TiO2-catalyzed phenol HDO; thus, an interfacial model with an OH vacancy was also considered (PtNW/OHv-TiO2). Pt-TiO2-interface sites stabilize adsorption of all studied acetic acid HDO surface intermediates relative to terrace Pt-metal sites, particularly when an interfacial-OH vacancy is present. Oxygenated species prefer to bind at the OH vacancy through the O atom, suggesting a preference for C-O over C-C bond cleavage at these sites. This hypothesis is supported by net-negative and net-positive average shifts in the reaction energy and activation energy barriers for C-O and C-C bond-breaking steps, respectively, at Pt-TiO2-interface sites relative to Pt-metal sites. Using the calculated energetics, the predicted minimum-energy pathway was determined for each surface. Pt(111) is predicted to follow decarboxylation, producing undesired methane and carbon dioxide. Conversely, PtNW/OH-TiO2 and PtNW/OHv-TiO2 are both predicted to produce desired acetaldehyde and ethane. The interfacial vacancy may also play a key role in facilitating the first C-O bond-breaking step in acetic acid HDO, lowering the barrier by 0.6 eV relative to the defect-free interface model. These results demonstrate the critical role of the Pt-TiO2 interface in the shift in acetic acid HDO selectivity experimentally observed on Pt/C and Pt/TiO2 catalysts. The results herein demonstrate the important role of the Pt-TiO2 interface and interfacial oxygen vacancies in improving the carbon efficiency for HDO reactions in CFP upgrading.

BIOMASS FUELS,INORGANIC, ORGANIC, PHYSICAL, AND AN↗
DOE OSTI2020

DFT Accurate Interatomic Potential for Molten NaCl from Machine Learning

Molten alkali chloride salts are a critical component in concentrated solar power and nuclear applications. Despite their ubiquity, the extreme chemical reactivity of molten alkali chlorides at high temperatures has presented a significant challenge in characterizing atomic structures and dynamic properties experimentally. In this work, we we investigate molten NaCl by performing high temperature molecular dynamics simulations using a Gaussian Approximation Potential (GAP) trained on Density Functional Theory (DFT) datasets. Our GAP model, trained with a meager 1000 atomic configurations, arrives at near ab initio accuracy with a mean absolute error of 1.5 meV/atom thus enabling fast analysis of high temperature salt properties on large length (5000 ion pairs) and time (> 1ns) scales currently inaccessible to ab initio simulations. Calculated structure factors and diffusion constants from our GAP model simulations show excellent agreement with experiments. Our results indicate that GAP models are able to capture the many-body interactions required to accurately model ionic-systems.

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

Mechanisms of Ethylene Epoxidation over Silver from Machine Learning-Accelerated First-Principles Modeling and Microkinetic Simulations

In this work we employed machine learning-augmented density functional theory (DFT) thermodynamic calculations to assess the stability of different AgO x structures under catalytic ethylene epoxidation reaction conditions. We found that there are multiple AgO x surface motifs that could co-exist under the relevant conditions. These included Ag surface oxides (e.g., AgO_p(4 × 4) and Ag 1.83 O) and atomic oxygen-covered Ag(111) surfaces. Furthermore, we employed DFT calculations to evaluate the energetics of different reaction mechanisms by which ethylene and oxygen can react on these surfaces. These studies revealed several energetically viable reaction pathways for ethylene epoxidation. Microkinetic modeling analyses, based on the DFT-calculated reaction pathways, showed that ethylene epoxidation can proceed on all surfaces and that multiple pathways, including those involving Langmuir–Hinshelwood and Eley–Rideal mechanisms, could be involved in selective and unselective reactions. The diversity of mechanisms that we discovered in the context of the relatively simple ethylene epoxidation reaction on Ag suggests that the richness and complexity of surface chemistry are most likely a rule rather than an exception in heterogeneous catalytic chemical transformations on metal surfaces and that the concept of a single or even a dominant mechanism and reaction intermediates might need to be revisited for many reactions.

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

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

Two-dimensional materials (2DMs) continue to attract a lot of attention, particularly for their extreme flexibility and superior thermal properties. Molecular dynamics simulations are among the most powerful methods for computing these properties, but their reliability depends on the accuracy of interatomic interactions. While first principles approaches provide the most accurate description of interatomic forces, they are computationally expensive. In contrast, classical force fields are computationally efficient, but have limited accuracy in interatomic force description. Machine learning interatomic potentials, such as Gaussian Approximation Potentials, trained on density functional theory (DFT) calculations offer a compromise by providing both accurate estimation and computational efficiency. Here, in this work, we present a systematic procedure to develop Gaussian approximation potentials for selected 2DMs, graphene, buckled silicene, and h-XN (X = B, Al, and Ga, as binary compounds) structures. We validate our approach through calculations that require various levels of accuracy in interatomic interactions. The calculated phonon dispersion curves and lattice thermal conductivity, obtained through harmonic and anharmonic force constants (including fourth order) are in excellent agreement with DFT results. HIPHIVE calculations, in which the generated GAP potentials were used to compute higher-order force constants instead of DFT, demonstrated the first-principles level accuracy of the potentials for interatomic force description. Molecular dynamics simulations based on phonon density of states calculations, which agree closely with DFT-based calculations, also show the success of the generated potentials in high-temperature simulations.

2D Materials↗
DOE OSTI2025

Development of interatomic potential and effect of ordering on defect properties in CrMnV

Developing materials that can withstand extreme environments, such as high radiation doses and elevated temperatures, is crucial for next-generation particle accelerators, including the 2.4 MW Long-Baseline Neutrino Facility. High-Entropy Alloys have emerged as promising candidates for beam window materials due to their superior mechanical strength, corrosion resistance, and radiation tolerance. In this study, we focus on the Cr–Mn–V alloy system, developing and employing machine-learning interatomic potentials (MLIPs) to investigate the formation of an ordered phase and its influence on defect properties. Using hybrid Monte Carlo-Molecular Dynamics simulations, we observe the formation of a B2-ordered phase at lower temperatures, consistent with Density Functional Theory (DFT) predictions. Ordered structures display a bimodal distribution of migration energies and reduced mean square displacement values, indicating suppressed vacancy diffusion. Our results also show that the migration energy barrier varies based on the atomic species, with Mn and V exhibiting the highest and lowest average barriers, respectively. These findings suggest that atomic ordering inhibits defect mobility, potentially enhancing the radiation resistance of CrMnV alloys. The validated MLIP provides a reliable framework for simulations that are faster than traditional DFT while maintaining the accuracy required to study defect and ordering properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Spin-informed universal graph neural networks for simulating magnetic ordering

The screening and discovery of magnetic materials are hindered by the computational cost of first-principles density-functional theory (DFT) calculations required to find the ground state magnetic ordering. Although universal machine-learning interatomic potentials (uMLIPs), also known as atomistic foundation models, offer high-fidelity models of many atomistic systems with significant speedup, they currently lack the inputs required for predicting magnetic ordering. In this work, we present a data-efficient, spin-informed graph neural network framework that incorporates spin degrees of freedom as inputs and preserves physical symmetries, extending the functionality of uMLIPs to simulate magnetic orderings. This framework speeds up DFT calculations through better initial guesses for magnetic moments, determines the ground-state ordering of bulk materials and even generalizes to magnetic ordering in surfaces. Furthermore, we implement a closed-loop anomaly detection approach that effectively addresses the classic "chicken-and-egg" problem of creating a high-quality dataset while developing a uMLIP, unearthing anomalies in large benchmark datasets and boosting model accuracy.

Xu, Wenbin↗
DOE OSTI2021

Machine-learning accelerated geometry optimization in molecular simulation

Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of thermodynamic and kinetic properties of molecular and crystal structures. This process is slow at the quantum level of theory because it involves an iterative calculation of forces using quantum chemical codes such as density functional theory (DFT), which are computationally expensive and which limit the speed of the optimization algorithms. It would be highly advantageous to accelerate this process because then one could do either the same amount of work in less time or more work in the same time. Here, we provide a neural network (NN) ensemble based active learning method to accelerate the local geometry optimization for multiple configurations simultaneously. We illustrate the acceleration on several case studies including bare metal surfaces, surfaces with adsorbates, and nudged elastic band for two reactions. In all cases, the accelerated method requires fewer DFT calculations than the standard method. In addition, we provide an Atomic Simulation Environment (ASE)-optimizer Python package to make the usage of the NN ensemble active learning for geometry optimization easier.

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

Enhancing high-fidelity neural network potentials through low-fidelity sampling

The efficacy of neural network potentials (NNPs) critically depends on the quality of the configurational datasets used for training. Prior research using empirical potentials has shown that well-selected liquid–solid transitional configurations of a metallic system can be translated to other metallic systems. This study demonstrates that such validated configurations can be relabeled using density functional theory (DFT) calculations, thereby enhancing the development of high-fidelity NNPs. Training strategies and sampling approaches are efficiently assessed using empirical potentials and subsequently relabeled via DFT in a highly parallelized fashion for high-fidelity NNP training. Our results reveal that relying solely on energy and force for NNP training is inadequate to prevent overfitting, highlighting the necessity of incorporating stress terms into the loss functions. To optimize training involving force and stress terms, we propose employing transfer learning to fine-tune the weights, ensuring that the potential surface is smooth for these quantities composed of energy derivatives. This approach markedly improves the accuracy of elastic constants derived from simulations in both empirical potential-based NNPs and relabeled DFT-based NNPs. Overall, this study offers significant insights into leveraging empirical potentials to expedite the development of reliable and robust NNPs at the DFT level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Davis Computational Spectroscopy Workflow—From Structure to Spectra

Here, we describe an automated workflow that connects a series of atomic simulation tools to investigate the relationship between atomic structure, lattice dynamics, materials properties, and inelastic neutron scattering (INS) spectra. Starting from the atomic simulation environment (ASE) as an interface, we demonstrate the use of a selection of calculators, including density functional theory (DFT) and density functional tight binding (DFTB), to optimize the structures and calculate interatomic force constants. We present the use of our workflow to compute the phonon frequencies and eigenvectors, which are required to accurately simulate the INS spectra in crystalline solids like diamond and graphite as well as molecular solids like rubrene. We have also implemented a machine-learning force field based on Chebyshev polynomials called the Chebyshev interaction model for efficient simulation (ChIMES) to improve the accuracy of the DFTB simulations. We then explore the transferability of our DFTB/ChIMES models by comparing simulations derived from different training sets. We show that DFTB/ChIMES demonstrates ~100× reduction in computational expense while retaining most of the accuracy of DFT as well as yielding high accuracy for different materials outside of our training sets. The DFTB/ChIMES method within the workflow expands the possibilities to use simulations to accurately predict materials properties of increasingly complex structures that would be unfeasible with ab initio methods.

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

Direct Ab Initio Simulation of the Synthesis of BaZrO 3 and the Microstructure Impacts on Proton Transport

Controlling and predicting the processing-structure-performance relationship in functional materials is a grand challenge in materials science, with important implications for a wide range of emerging applications; a high fidelity understanding of the performance impact of microstructures formed under synthesis conditions is required to develop advanced materials, such as solid-state fuel cells and electrolyzers. Using the ceramic BaZrO 3 as a case study, we directly simulate the synthesis and investigate how proton transport is dictated by microstructures. We develop a framework that couples density functional theory (DFT), machine-learning interatomic potential (MLIP) driven molecular dynamics, and grand canonical Monte Carlo to perform large-scale, microstructure-resolved, atomistic simulations of proton transport in experimentally representative polycrystalline structures. Our fully ab initio approach, using a MLIP as a proxy for DFT, allows us to quantify the competition between two distinct diffusion mechanisms: one associated with grain-boundary regions and another within grains. When the impacts of grain boundaries are taken into account, proton transport exhibits substantial deviation from the bulk oxide limit. This addresses long-standing discrepancies between theory and experiments. Our integrated approach provides atomistic insight into microstructure-dependent proton pathways in BaZrO 3 and establishes a general protocol for predicting processing-structure-performance relationships.

organic↗
DOE OSTI2024

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Computational Exploration of High Entropy Alloys as Promising Materials for Future Beam Windows

With the ever-increasing demand for high beam power, the currently used beam-intercepting devices (BIDs) such as targets, and beam windows may not be able to handle the high power required for future accelerator complexes or the lifetime may be reduced drastically. As beam power increases, the damage incurred by BIDs, including thermal shock, fatigue, and irradiation damage, also rises. Therefore, it is imperative to design materials that can withstand high beam power for longer lifetimes. High entropy alloys (HEAs) have emerged as potential alternative materials for designing next-generation BIDs. In this study, we primarily focus on materials for developing beam windows for next-generation accelerator complexes. We propose an integrated approach that combines various computational techniques to study and design new materials. Specifically, we use CALPHAD, density functional theory (DFT), and molecular dynamics (MD) to comprehensively investigate the defect properties of suitable HEAs, offering potential alternatives for future beam windows. We begin by scanning the extensive phase space provided by Cr-Mn-V-Ti-Al-Co HEAs, selecting 8 compositions after evaluating approximately 120,000 unique compositions using CALPHAD. We, then employ DFT-informed machine learning techniques to develop force-field parameters. Finally, MD simulations using these developed force-field parameters will be used to study the effects of radiation damage on the defect and mechanical properties of the selected alloys. This research explains the use of the CALPHAD approach and shows how critical modeling (DFT and MD) is in developing novel material such as HEAs. It also highlights the promising role of machine learning in this field. The results from this study will greatly improve the novel materials development to be used in next-generation accelerator components, leading to higher beam power and longer operational times of BIDs.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Spin Decoherence in VOPc@graphene Nanoribbon Complexes

Carbon nanoribbons or nanographene qubit arrays can facilitate quantum-to-quantum transduction between light, charge, and spin, making them an excellent testbed for fundamental science in quantum coherent systems and for the construction of higher-level qubit circuits. Here, in this work, we study spin decoherence due to coupling with a surrounding nuclear spin bath of an electronic molecular spin of a vanadyl phthalocyanine (VOPc) molecule integrated onto an armchair-edged graphene nanoribbon (GNR). Density functional theory (DFT) is used to obtain ground-state atomic configurations. Decay of spin coherence in Hahn echo experiments is then simulated using the cluster correlation expansion method with a spin Hamiltonian involving hyperfine and electric field gradient tensors calculated from DFT. We find that the decoherence time T 2 is anisotropic with respect to magnetic field orientation and determined only by the hydrogen nuclear spins on both VOPc and GNR. Large electron spin echo envelope modulation (ESEEM) due to nitrogen and vanadium nuclear spins is present at specific field ranges and can be completely suppressed by tuning the magnetic field. The relation between these field ranges and the hyperfine interactions is analyzed. The effects of interactions with the nuclear quadrupole moments are also studied, validating the applicability and limitations of the spin Hamiltonian when they are disregarded.

Hamiltonians↗
DOE OSTI2025

Strain-driven oxygen vacancy ordering in LaNiO 3 thin films revealed by integrated differential phase contrast imaging in scanning transmission electron microscopy

Rare-earth nickelates, such as LaNiO 3 (LNO), exhibit complex electronic properties, with ordered oxygen vacancies (OOV) influencing conductivity and magnetic behavior. We investigate the structural stability of strain-induced OOV phases in LNO thin films grown on SrTiO 3 substrates and the impact of Ruddlesden–Popper (RP) faults. Using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and integrated differential phase contrast (iDPC) STEM imaging, we conducted atomic-scale structural and compositional analyses of OOV. Geometric phase analysis (GPA) was employed to measure the strain in fault-free and RP fault regions, while density functional theory (DFT) calculations explored different OOV arrangements in the LNO phase. Simulated iDPC-STEM imaging of energy-stabilized structures was performed to correlate with experimental results. Here, our findings reveal superstructure modulation in the chemical composition and atomic-scale lattice structure in LNO, primarily due to the formation of the OOV in Ni–O layers of the LaNiO 2.5 phase. The out-of-plane compressive strain of about 2% stabilizes this phase, reducing the strain, diminishing OOV, and transforming them into LNO.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Noise reduction of stochastic density functional theory for metals

Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.

Chemistry↗
DOE OSTI2026

Ion Distribution and Cation Exchange at Mica–Electrolyte Interfaces Probed with Deep Potential Molecular Dynamics

Here, we investigate the Stern layer structure and cation exchange mechanism at muscovite mica-electrolyte interfaces using nanosecond timescale molecular dynamics simulations based on deep neural network interatomic potentials trained on Density Functional Theory (DFT) data. Focusing on mica with exposed surface K + interfaced with aqueous NaCl and mica with surface Na + interfaced with KCl solution, we find that K + remains predominantly in inner-sphere configurations, while Na + exhibits notable populations in outer-sphere states. Most importantly, our simulations show that contact with an electrolyte solution results in the co-adsorption of multiple cation species, making the mica surface locally overcharged and thus reshaping the cation speciation in a manner that enhances the tendency of neighboring surface cations to desorb. These findings are consistent with recent experimental observations that co-adsorption of different cation species induces changes in cation speciation and slow kinetics of cation exchange at the muscovite-water interface, providing a basis for their detailed understanding.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Intricate short-range order in GeSn alloys revealed by atomistic simulations with highly accurate and efficient machine-learning potentials

GeSn alloys hold promise for silicon-compatible integrated applications in electronics, photonics, and topological quantum devices. However, understanding their intricate structures using density functional theory (DFT) calculations is hindered by spatiotemporal constraints. To overcome this limitation, we develop highly accurate and efficient machine-learning interatomic potentials based on a neuroevolution potential approach with farthest point sampling on a comprehensive DFT data set. The application of the developed machine-learning potential in large-scale atomistic simulations bridges the spatiotemporal gap between modeling and advanced characterizations, and facilitates the discovery of structural intricacies in GeSn alloys. Through extensive statistical sampling, we identify a type of short-range order (SRO) that is distinguished by both its structural signature and electronic band gap from the SRO structure previously predicted. Modeling based on a large simulation cell reveals the coexistence of nano SRO domains with various degrees of ordering, demonstrating a complex spatial heterogeneity of SRO structure. Finally, our study not only reinforces the significance of fine-level structural information in alloys, but it also constitutes an effective framework for exploring SRO in a broad range of complex alloys based on highly accurate and effective machine-learning potentials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Monte-Carlo modeling of phonon thermal transport using DFT-based anisotropic dispersion relations over the full Brillouin zone

In this work, we present a Monte Carlo (MC) approach to solve the phonon Boltzmann transport equation (BTE) in which the anisotropic phonon dispersion relations over the full Brillouin zone (BZ) are used. In this approach, the discretization of the BZ used to compute the phonon relaxation time places constraints on the direction of scattered phonons in the real-space simulation domain. The phonon dispersion and phonon relaxation times are calculated using the density functional theory (DFT) approach. The modified MC approach is validated by a close examination of its ability to simulate phonon transport in both the ballistic and diffusive regimes for multiple materials including GaAs, InAs, ThO 2 , and α-U. In doing so, the phonon thermal conductivities from 100 K to 1000 K are calculated and compared with traditional non-transport solution of the phonon BTE. It is found that the phonon thermal conductivities of α-U and ThO 2 obtained from MC simulations using isotropic dispersion are larger than the values obtained using anisotropic phonon dispersion relations over the full BZ. The effect of phonon-defect scattering on the thermal conductivity of ThO 2 is also studied as an application of the current MC approach and found to agree with previously computed values in the literature. The MC solver developed here has been parallelized as a step to demonstrate its potential to solving computationally intensive phonon thermal transport problems at the mesoscale.

36 MATERIALS SCIENCE↗