Search NASA⌕ Search

SEARCH · Search NASA

Results for “Massively Parallel 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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

4.0 MOOSE: Enabling massively parallel Multiphysics simulation

Approaching 18 years of existence, MOOSE—the Multiphysics Object-Oriented Simulation Environment—is being developed at a higher pace than ever before. With significant support from four research institutions across the globe, and dozens of new contributors, the capabilities of the framework are being expanded to meet modeling challenges in a wide variety of fields from nuclear system design, to geomechanics, to material science. This includes new development in equation discretization techniques, solver methods, meshing capabilities, application deployment, and user interface improvements. Applications built on MOOSE benefit from all these improvements.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Dataset of simulated vibrational density of states and X-ray diffraction profiles of mechanically deformed and disordered atomic structures in Gold, Iron, Magnesium, and Silicon

This dataset is comprised of a library of atomistic structure files and corresponding X-ray diffraction (XRD) profiles and vibrational density of states (VDoS) profiles for bulk single crystal silicon (Si), gold (Au), magnesium (Mg), and iron (Fe) with and without disorder introduced into the atomic structure and with and without mechanical loading. Included with the atomistic structure files are descriptor files that measure the stress state, phase fractions, and dislocation content of the microstructures. All data was generated via molecular dynamics or molecular statics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. This dataset can inform the understanding of how local or global changes to a materials microstructure can alter their spectroscopic and diffraction behavior across a variety of initial structure types (cubic diamond, face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) for Si, Au, Mg, and Fe, respectively) and overlapping changes to the microstructure (i.e., both disorder insertion and mechanical loading).

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2025

Intelligently Partitioned Phasor-EMT Hybrid Simulations of Large-Scale, High-IBR Power Systems

As the penetration level of power electronics-interfaced renewables such as photovoltaics (PV) and wind has surged in modern electric grids, new operational risks caused by the dynamics of those inverter-based resources (IBRs) are emerging in parallel. Lessons learned from various grid events include that the impact of IBRs on system-level grid stability will become prominent along with the increase of renewables and that the short-timescale dynamic impacts of IBRs on grid stability are not fully captured by current commercial dynamic simulation tools [1] [2]. For example, IBRs can be controlled to mitigate those destabilizing interactions, but conventional phasor-domain tools (e.g. PSS/E, PSLF) often cannot capture that; likewise, the existing electromagnetic transient (EMT) simulation tools (e.g. PSCAD, EMTP) can simulate detailed IBR controls, but for large power systems with many IBRs, slow simulation speeds severely impede the ability to study dynamic events [3] [4]. Massively paralleling simulations using high-performance computing (HPC) can help address this, especially now that cloud-based HPC capability is widely available, but today s EMT tools are not HPC-compatible, and parallelization of dynamic simulation solvers is not trivial because each region can dynamically affect the others. Thus, dynamic simulation of grids with very large numbers of IBRs potentially poses a barrier to the ongoing energy transition.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Comparison of DeePMD, MTP, GAP, ACE and MACE Machine‐Learned Potentials for Radiation‐Damage Simulations: A User Perspective

Accurate and efficient interatomic potentials are essential for molecular dynamics (MD) simulations of radiation damage, gas diffusion, and phase stability in complex ceramics such as LiAlO 2 , especially under extreme conditions relevant to tritium production. Here, we evaluate the performance of six machine-learned interatomic potentials (MLIPs), moment tensor potential (MTP), Gaussian approximation potential, deep potential (DeePMD), atomic cluster expansion (ACE), message-passing ACE (multilayer atomic cluster expansion (MACE) pretrained) and MACE (trained from-scratch), all trained on the same density functional theory dataset with inclusion of tritium. The MLIPs are benchmarked against traditional Buckingham and ReaxFF potentials in terms of energy accuracy, density predictions, thermal equilibration behavior, threshold displacement energy (E d ), tritium diffusivity, and computational cost. Among the models, MTP shows the best overall balance between efficiency and accuracy, with low force and energy errors and realistic E d values for Li and Al. The ACE and MACE (pretrained and trained from scratch) models exhibit high E d (>200 eV) and unphysical pair interactions. DeePMD underestimates Ed due to overly repulsive behavior even at equilibrium distances. All models over-estimate tritium diffusion but the pretrained MACE model behaves well during tritium-diffusion simulations up to 500 K, maintaining diffusivities in the physically consistent 10 −11 m 2 /s range. Finally, we quantify the computational cost of each potential in large-scale atomic/molecular massively parallel simulator, finding that only MTP is more efficient than traditional empirical potentials, while others are significantly more expensive. These findings explain the trade-offs between accuracy and computational cost in MLIP development and provide essential guidance for use in high-throughput radiation damage and gas diffusion simulations in nuclear ceramics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

FENIX: Towards a Fully Integrated Multiphysics Framework for Plasma Facing Component Modeling

Computational tools have a crucial role to play in accelerating the deployment of fusion as a clean, reliable, abundant, and sustainable energy source. Multiphysics, high-fidelity simulation capabilities can help model, study, and predict intricate interactions between materials performance, plasma exposure, neutron irradiation, and engineering processes. As such, they can assist in the resolution of scientific and engineering challenges underpinning design, construction, and commission of fusion power plants. To address these needs, ongoing efforts are leveraging the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework and delivering new computational tools for the fusion community. These tools inherit crucial attributes from MOOSE. They are open-source, modular, integrated with nuclear industry-standard software quality assurance processes, and enable multiphysics, multi-fidelity, fully integrated, zero- to three-dimensional, and massively parallel simulations. After a short overview of these capabilities, we will present the development of Fusion ENergy Integrated multiphys-X (FENIX), a MOOSE-based application designed to enable plasma facing component design and performance evaluation. Throughout their lifetime, plasma facing components are exposed to extreme thermal loads, repeated thermal shocks, and irradiation by plasma ions, neutral particles, and high-energy neutrons. Consequently, designing a plasma facing component with acceptable lifetime degradation is extremely challenging. FENIX aims to model the multiphysics environment in which plasma facing components evolve to accelerate their design studies. To that end, FENIX couples existing MOOSE capabilities such as heat transfer, thermomechanics, and thermal hydraulics, with tritium transport via the MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8), with neutronics via the MOOSE-based high-fidelity neutron-photon transport and fluid dynamics code Cardinal, and finally with Particle-in-Cell plasma simulation capabilities being developed in this project. In this study, we present the current FENIX capabilities and preliminary results of its application to model the Tritium Plasma Experiment set up at Idaho National Laboratory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations

Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stochastic symplectic reduced-order modeling for model-form uncertainty quantification in molecular dynamics simulations in various statistical ensembles

Here, this work focuses on the representation of model-form uncertainties in molecular dynamics simulations in various statistical ensembles. In prior contributions, the modeling of such uncertainties was formalized and applied to quantify the impact of, and the error generated by, pair-potential selection in the microcanonical ensemble (NVE). In this work, we extend this formulation and present a linear-subspace reduced-order model for the canonical (NVT) and isobaric (NPT) ensembles. The symplectic reduced-order basis is randomized on the tangent space of the Stiefel manifold to provide topological relationships and capture model-form uncertainty. Using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), we assess the relevance of these stochastic reduced-order atomistic models on canonical problems involving a Lennard-Jones fluid and an argon crystal melt.

42 ENGINEERING↗
DOE OSTI2025

Developing reliable machine learning interatomic potential for Fe–Cr–Ni austenitic alloys

Gaining atomistic understanding of mechanical behavior of heat-resistant structural materials such as Fe–Cr–Ni-based alloys requires an approach with an accuracy close to density functional theory (DFT) that considers the intrinsic properties of the bulk lattice and important defects such as stacking faults, grain boundaries, and surfaces. This work aims to develop reliable machine learning interatomic potential (MLIAP) at cross-scale for Fe–Cr–Ni ternary alloys with a focus on the face-centered-cubic (fcc) solid solution structure. Leveraging the advantages of moment tensor potentials, which typically necessitate a relatively small training dataset and enable rapid calculations using the large-scale atomic/molecular massively parallel simulator package, we ensure the stability and accuracy of the trained potentials. Important defects such as stacking faults, grain boundaries, and surfaces for wide-range compositions are investigated. Structural, thermal, elastic, and defect properties are determined from molecular dynamics simulations comprising several thousand atoms, generated via canonical Monte Carlo simulations guided by the trained potential. The trained potential allows efficient atomic simulations of structural, thermal, and mechanical properties of fcc Fe–Cr–Ni solid solution alloys as a function of composition and temperature. Therefore, the MLIAP approach represents a major advancement from DFT calculations that are limited to small simulation sizes and traditional molecular dynamics simulations using relatively low accuracy potentials. Furthermore, this work outlines a practical foundation for further investigating the structural evolution and mechanical behavior of austenitic stainless steel and nickel-based alloys in a wide array of applications in extreme environments.

Crystal structure↗
DOE OSTI2024

Integrating machine learning interatomic potentials with hybrid reverse Monte Carlo structure refinements in RMCProfile

Structure refinement with reverse Monte Carlo (RMC) is a powerful tool for interpreting experimental diffraction data. To ensure that the under-constrained RMC algorithm yields reasonable results, the hybrid RMC approach applies interatomic potentials to obtain solutions that are both physically sensible and in agreement with experiment. To expand the range of materials that can be studied with hybrid RMC, we have implemented a new interatomic potential constraint in RMCProfile that grants flexibility to apply potentials supported by the Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) molecular dynamics code. This includes machine learning interatomic potentials, which provide a pathway to applying hybrid RMC to materials without currently available interatomic potentials. To this end, we present a methodology to use RMC to train machine learning interatomic potentials for hybrid RMC applications.

Cuillier, Paul↗
DOE OSTI2024

Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms

Continuous advancements in scientific and engineering understanding of earthquake phenomena, combined with the associated development of representative physics-based models, is providing a foundation for high-performance, fault-to-structure earthquake simulations. However, regional-scale applications of high-performance models have been challenged by the computational requirements at the resolutions required for engineering risk assessments. The EarthQuake SIMulation (EQSIM) framework, a software application development under the US Department of Energy (DOE) Exascale Computing Project, is focused on overcoming the existing computational barriers and enabling routine regional-scale simulations at resolutions relevant to a breadth of engineered systems. This multidisciplinary software development—drawing upon expertise in geophysics, engineering, applied math and computer science—is preparing the advanced computational workflow necessary to fully exploit the DOE’s exaflop computer platforms coming online in the 2023 to 2024 timeframe. Achievement of the computational performance required for high-resolution regional models containing upward of hundreds of billions to trillions of model grid points requires numerical efficiency in every phase of a regional simulation. This includes run time start-up and regional model generation, effective distribution of the computational workload across thousands of computer nodes, efficient coupling of regional geophysics and local engineering models, and application-tailored highly efficient transfer, storage, and interrogation of very large volumes of simulation data. This article summarizes the most recent advancements and refinements incorporated in the workflow design for the EQSIM integrated fault-to-structure framework, which are based on extensive numerical testing across multiple graphics processing unit (GPU)-accelerated platforms, and demonstrates the computational performance achieved on the world’s first exaflop computer platform through representative regional-scale earthquake simulations for the San Francisco Bay Area in California, USA.

58 GEOSCIENCES↗
DOE OSTI2025

Optimizing Grain Boundary Structures with LAMMPS Using Evolutionary Algorithms

Grain boundary structure optimization is an important part of materials modeling. Current methods for grain boundary structure optimization involve inefficient, time-consuming processes that do not fully explore the interface parameter space. Evolutionary algorithms have recently been demonstrated to be effective at determining both stable and metastable grain boundary interface structures. In this work, we demonstrate the use of GBOpt, a grain boundary structure optimization software designed to use the Large-scale Atomic/Molecular Massively Parallel Simulation (LAMMPS) software to efficiently determine grain boundary structures. We demonstrate that a only a few manipulations, namely atom insertion, atom removal, and relative grain displacement, are sufficient to explore much of the grain boundary structure parameter space. The efficacy of this approach is demonstrated on an FCC Ni system, and a BCC Fe system. The computational cost is compared against the gamma-surface sampling approach to demonstrate performance improvement.

Evolutionary algorithms↗
DOE OSTI2025

Massively parallel phase-field simulations targeting exascale

The interface thickness in the phase-field (PF) method limits its simulation scales. Consequently, large-scale PF simulations become prohibitively expensive for resolving the extremely fine microstructures that typically form during rapid solidification processing. This challenge is significant in predicting microstructure evolution in metal additive manufacturing and has been identified by the United States Department of Energy’s Exascale Computing Project. Here, to address this, we develop a multi-GPU and MPI-based massively parallel simulation code, utilizing state-of-the-art algorithms, software, and libraries, for large-scale three-dimensional (3D) PF simulations. We report the first GPU-parallel PF simulations on Frontier (currently the second TOP500 exascale cluster) and Summit machines, taking dendritic growth as an example problem. We evaluate the parallel performance of our implementation using scaling studies with more than 24 000 GPUs (among the largest known computations to date) and the acceleration performance using large-scale simulations of dendritic growth in 3D. Finally, massively parallel GPUs in these supercomputers enabled the first coupled multiscale simulations of laser melting and subsequent dendritic solidification on the scale of a full melt-pool, demonstrating the feasibility of performing PF simulations with a point total over 2 billion grid points within an acceptable time.

Exascale↗
DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Accelerating Thermochemical Equilibrium Calculations for Nuclear Reactor Applications

Thermochemical properties play a key role in modeling and simulation of several key phenomena in nuclear reactors. There has been an increasing interest in incorporating CALPHAD-based formulations in multiphysics simulations including for Molten Salt Reactors where knowledge of phase evolution of the salt and the chemical potentials of various elements are of utmost importance in source term analyses and redox control. However, the size of such simulations is often limited by the high computational cost of full thermodynamic equilibrium calculations. This work discusses the current efforts aimed at accelerating thermochemical equilibrium calculations for multiphysics simulations performed using the open-source finite element / finite volume code Multiphysics Object Oriented Simulation Environment (MOOSE) [1]. While several methods have been proposed for accelerating phase equilibrium calculations [2], most focus on relatively small systems and often rely on a- priori knowledge of the state-space of the system. Nuclear materials, however, are often multi-component systems owing to the evolution of composition under irradiation and an approach based on a-priori mapping of phase diagram is often not enough. This work is aimed at demonstrating an on-the-fly surrogate modeling framework that uses active learning to reduce the number of full equilibrium calculations that must be performed. By combining with efficient coupling approaches, the surrogate framework helps in reducing the computational cost of thermodynamic equilibrium informed multiphysics simulations of nuclear materials. The performance is benchmarked against full coupling with the thermochemistry library Thermochimica [3]. This work uses a machine learning based approach for constructing surrogate models to predict the stable phases in a multicomponent system. The surrogates were constructed using neural networks and Gaussian process classification. In this work, we compare the relative performance of the two methods. We also demonstrate the use of caching previous calculations by interpolating the values from nearest neighbors. References [1] Lindsay, A.D., et al. "2.0 – MOOSE: Enabling massively parallel multiphysics simulation", SoftwareX, 20 (2022): 101202. [2] Roos, W.A. and Zietsman J.H. "Accelerating complex chemical equilibrium calculations – A Review", Calphad, 77 (2022): 102380. [3] Piro, M.H.A., et al. "The thermochemistry library Thermochimica", Computational Materials Science, 67 (2013): 266-272.

36 MATERIALS SCIENCE↗
DOE OSTI2026

KRAS4a and KRAS4b show distinct lipid-dependent regulation of RAS-RAF membrane dynamics

KRAS4a and KRAS4b are important regulators of signaling, and their interactions with the plasma membrane are dynamic and influenced by lipid composition. KRAS 4a and 4b have nearly identical globular domains but differ in their membrane-associated hyper variable region (HVR). The functional distinctions between these isoforms remain unclear, particularly with regards to their dependence on specific lipids and the membrane environment. Previous work showed that the membrane orientation of KRAS4b affects its ability to bind to RAF kinase RBDCRD and that the KRAS–RBDCRD complex adopts different poses on the membrane as well as influences the size and composition of the lipid environment. To model differences between KRAS 4a and 4b protein–lipid interactions, we extended the Multiscale Machine-Learned Modeling Infrastructure (MuMMI) to incorporate continuum simulations in the grand canonical ensemble, enabling sampling across macroscopic, coarse-grained, and all-atom resolutions. Using this framework, we systematically altered PIP2 concentrations, KRAS 4a versus 4b, and RAF RBDCRD complexation to assess impacts on membrane–protein interactions and dynamics. Our results reveal that reducing PIP2 shifts and broadens the membrane orientational preference of both KRAS 4b and 4a, with stronger effects on 4b HVR localization versus 4a. We demonstrate that with depletion of the strong negatively charged PIP2 lipid, the less charged phosphatidylserine replaces PIP2. Our findings highlight similarities and distinctions in the dynamics and lipid dependency of KRAS isoforms and suggest that ordering of the local lipid composition by HVRs is a shared property and key modulator of RAS-mediated signaling at the plasma membrane.

Biological and medical sciences↗
DOE OSTI2025

Effects of Galactic Irradiation on Thermal and Electronic Transport in Tungsten

The impact of irradiation on the thermal and electronic properties of materials is a persistent puzzle, particularly defect formation at the atomic and nanoscales. This work examines the nanoscale effects of low-energy irradiation on tungsten (W), focusing on defect-induced modifications to thermal and electronic transport. Using the site-projected thermal conductivity (SPTC) method [A. Gautam et al. PSS-RRL, 2400306, 2024], bulk and twin-grain boundary W with vacancy defects based on the Norgett–Robinson–Torrens displacements per atom model is analyzed. SPTC provides a detailed prediction of postcascade spatial thermal conductivity distribution. Electronic conductivity activity is estimated using the “N 2 method” [K. Nepal et al. Carbon, 119711, 2025] to explore the consequences of vacancies and grain boundaries, highlighting the defect-dependent nature of charge transport behavior. These findings offer high-resolution insights into irradiation-driven transport phenomena, with implications for space-exposed materials and nanoscale thermal/electronic management.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

HPC for Optimizing Process Parameters to Control Material Evolution in Seamless Induction Hardening of Wind Turbine Main Shaft Bearings

Work proposed in this project focused on understanding the effect of martensitic transformation in the steel on the potential for cracking during seamless induction hardening (SIH) as a function of process conditions to allow the process to optimally scale up. Large-scale, three-dimensional phase-field simulations of martensitic transformation were performed using MEUMAPPS-SS (Microstructure Evolution Using Massively Parallel Phase-field Simulations – Solid State) code developed at Oak Ridge National Laboratory. The simulations were guided by location-specific thermal history generated by experimental measurements of time-temperature history generated at The Timken Company. The simulations were able to capture the morphological evolution of the martensite variants in an Fe-1.0C-1.5Cr steel based on the Nishiyama-Wasserman (NW) orientation relationship. The simulations were also able to quantify the stress-state at the interface between impinging martensite variants. The simulations indicated that the magnitude of the various stress and strain components were dependent on the sizes of the impinging plates with a reduction in these quantities with reduced plate size in agreement with experimental findings. The results obtained from the simulations will be used to guide the optimization of the alloy thermal conditions to eliminate quench cracking during SIH of bearing steels.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Additive Manufactured Composite Phase-Change Material for Thermal Energy Storage Applications

Phase-change materials play a critical role in industrial energy storage applications to drive efficiency improvements, thermal energy management, and carbon emissions reductions. Recently, it has been shown that rapid solidification of alloys with metastable immiscibility in the liquid phase has the potential to form unique microstructures in which a low-melting phase is uniformly distributed in a high-melting matrix. This feature can be exploited using additive manufacturing to produce components with complex geometries containing such unique phase-change microstructures. Phase-field simulations utilizing high-performance computing were used to provide a detailed description of the evolution of the active phase during service in terms of their morphology and composition in different polycrystalline matrix grain morphologies that are typically produced during additive manufacturing. Phase field simulations were performed using, MEUMAPPS-SL (Microstructure Evolution Using Massively Parallel Phase-field Simulations – Solid Liquid) code that was developed in-house by the Oak Ridge National Laboratory. The simulations utilized the capabilities of the Kestrel supercomputer at the National Renewable Energy Laboratory. The simulation results were compared with experimental results generated at Siemens Energy, Inc. The results indicate that the kinetics of liquid spreading along grain boundaries is largely determined by the mobility of the triple line along the intersection of the grain boundary liquid and the grain boundary plane.

25 ENERGY STORAGE↗