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DOE OSTI2022

Machine learning pipeline to predict defect behavior in metallic alloy systems

The interaction between defect and solute atoms is critical to the thermodynamic and kinetic behavior of metallic alloys under exposure to high-energy radiation, causing irradiation damage in materials. Radiation can generate non-equilibrium concentrations of point defects such as vacancies and interstitials. The excess point defects not only accelerate diffusional processes such as precipitation that cause radiation embrittlement, but also change the pathway of phase transformations, including nucleation processes. Understanding these defect behaviors is complicated by the challenge and complexity of addressing each possible local and discrete distribution of environments and chemical interactions around targeted defects-solute or solute-solute complexes. To resolve the challenge, machine learning regression techniques have emerged as powerful tools that can train and construct an energy model to accurately describe the chemical interactions of solutes and defects. In Fiscal Year 2022, the work focused on the workflow development and demonstration using machine learning regression, density functional theory, cluster expansion, and Monte Carlo simulation to predict the effects of ternary solute elements (e.g., aluminum and molybdenum) and point defects on the Cr-rich $\alpha^{\prime}$ precipitation in multicomponent FeCr model alloys. The computational outcomes include the prediction of the ternary phase diagram, vacancy formation energy for different compositions, and the effect of vacancies on the nucleation of Cr-rich clusters. The simulations predict a pronounced change of Cr solubility in bcc Fe by the addition of Al and the rejection of Al atoms from $\alpha^{\prime}$ precipitates. Additionally, the simulations show the formation of Cr-vacancy clusters as the initial nuclei for stable nucleation and growth of $\alpha^{\prime}$ particles. The results demonstrate important outcomes and applications of using machine learning pipeline to study model or commercial alloys with multicomponent solute species and point defects.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Thermodynamics of Bimetallic Joints between Titanium and Tantalum Produced by Laser Powder Bed Fusion

Laser powder bed fusion (LBPF) is currently the most mature metal additive manufacturing (AM) technology. While it does not have the same flexibility as directed energy deposition techniques to produce compositional gradients, LPBF can still be used to generate bimetallic parts by depositing one metal on a build plate made of another. Here, in this study, we print combinations of Ti-6Al-4V with Ta and characterize defects that occur at the interface. We use thermodynamic modeling to explain the formation of keyhole porosity and solidification cracks when Ta is built on a Ti baseplate, and the lack of defects when the materials are reversed. By understanding the mechanisms that lead to defect formation, the methodology demonstrated here can be applied to other material systems to efficiently design bimetallic LPBF processes.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Ta–Zr carbides: Synthesis advances via carbothermal reduction and defect evolution observed through transmission electron microscopy ion irradiation

The thermodynamic stability of six distinct compositions within the Zr—Ta—C ternary system is investigated in this study, marking the first report of their synthesis through carbothermic reduction in vacuum. A prolonged annealing process at 2200°C enabled high densification and phase equilibrium. Detailed phase identification and microstructural characterization through microscopy and X-ray diffraction techniques revealed clear compositional trends and stable phase formations. Two compositions ((Ta 0.2 Zr 0.8 )C 0.6 and (Ta 0.5 Zr 0.5 )C 1 ) were selected for ion irradiation experiments using 200 keV Kr + at 600°C—representing the first-ever irradiation study on the Zr—Ta—C system. The findings indicated defect accumulation and nanoscale cavity formation without any evidence of amorphization, highlighting the system's structural stability under irradiation. Together, the synthesis and irradiation results provide a basis for further investigation of the system and suggest its relevance for applications under extreme environments.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Thermodynamic stability and contributions to the Gibbs free energy of nanocrystalline Ni 3 Fe

In this work, the heat capacities of nanocrystalline Ni 3 Fe and control materials with larger crystallites were measured from 0.4–300 K. The heat capacities were integrated to obtain the enthalpy, entropy, and Gibbs free energy and to quantify how these thermodynamic functions are altered by nanocrystallinity. From the phonon density of states (DOS) measured by inelastic neutron scattering, we find that the Gibbs free energy is dominated by phonons and that the larger heat capacity of the nanomaterial below 100 K is attributable to its enhanced phonon DOS at low energies. Besides electronic and magnetic contributions, the nanocrystalline material has an additional contribution at higher temperatures, consistent with phonon anharmonicity. The nanocrystalline material shows a stronger increase with temperature of both the enthalpy and entropy compared to the bulk sample. Its entropy exceeds that of the bulk material by 0.4 $k_B$/atom at 300 K. This is insufficient to overcome the enthalpy of grain boundaries and defects in the nanocrystalline material, making it thermodynamically unstable with respect to the bulk control material.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Distinctive features of structural evolution and thermodynamic response in wide-bandgap semiconductors driven by intense electronic excitation

Radiation-tolerant material selection requires balancing lattice rigidity, defect dynamics, and electronic stability, as shown by covalent SiC outperforming ionic Ga 2 O 3 and GaN under extreme environments. Responding to intense electronic excitation, irradiation-driven phase segregation (β → δ/κ in Ga 2 O 3 ) and core–shell track (disordered structure in GaN), accompanied by elemental redistribution, contrastingly, exceptional radiation tolerance manifested by comparatively minimal lattice distortion (0.17 % strain variation) was demonstrated in SiC. These differential responses are primarily attributed to two fundamental mechanisms: (i) thermodynamic driving forces governing defect migration and phase separation, and (ii) the synergistic effects of robust covalent bonding composition coupled with efficient defect recombination processes. Here, the stronger electron–phonon (e-ph) coupling in Ga 2 O 3 (4.34 × 1018 W m −3 K −1 ) and GaN (3.55 × 10 18 W m −3 K −1 ) enhances lattice energy deposition, triggering thermal spikes (ΔT ≫ T m ) and structural transition behaviors, whereas weaker e-ph coupling in SiC (3.69 × 10 18 W m −3 K −1 ), relatively high thermodynamic parameters and efficient energy dissipation suppress thermal spikes to maintaining lattice integrity. The photoresponse degradation driven by enhanced radiative recombination is dominant in N-doped SiC, while V-doped systems achieve defect-mediated photoconduction optimization characterized by abrupt current transitions, matching fluorescence yield evolutions, and directly connecting defect engineering to optoelectronic performance.

Intense electronic excitation↗

DOE OSTI2024

Defect Engineering of Bi 2 SeO 2 Thermoelectrics

Abstract Bi 2 SeO 2 is a promising n ‐type semiconductor to pair with p ‐type BiCuSeO in a thermoelectric (TE) device. The TE figure of merit zT and, therefore, the device efficiency must be optimized by tuning the carrier concentration. However, electron concentrations in self‐doped n ‐type Bi 2 SeO 2 span several orders of magnitude, even in samples with the same nominal compositions. Such unsystematic variations in the electron concentration have a thermodynamic origin related to the variations in native defect concentrations. In this study, first‐principles calculations are used to show that the selenium vacancy, which is the source of n ‐type conductivity in Bi 2 SeO 2 , varies by 1–2 orders of magnitude depending on the thermodynamic conditions. It is predicted that the electron concentration can be enhanced by synthesizing under more Se‐poor conditions and/or at higher solid‐state reaction temperatures ( T SSR ), which promote the formation of selenium vacancies without introducing extrinsic dopants. The computational predictions are validated through solid‐state synthesis of Bi 2 SeO 2 . More than two orders of magnitude increase are observed in the electron concentration simply by adjusting the synthesis conditions. Additionally, a significant effect of grain boundary scattering on the electron mobility in Bi 2 SeO 2 is revealed, which can also be controlled by adjusting T SSR . By simultaneously optimizing the electron concentration and mobility, a zT of ≈0.2 is achieved at 773 K for self‐doped n ‐type Bi 2 SeO 2 . The study highlights the need for careful control of thermodynamic growth conditions and demonstrates TE performance improvement by varying synthesis parameters according to thermodynamic guidelines.

Novitskii, Andrei [MANA, National Institute for Ma↗

DOE OSTI2025

First-Principles Thermodynamic Assessments of Sr-Containing Secondary Phase Formation in La1-xSrxMnO3±δ Perovskites for Solid Oxide Cell Applications

Sr-secondary phase formation is a potentially significant degradation mode threatening solid-oxide cell (SOC) commercial viability. A first-principles thermodynamic study was performed for rhombohedral perovskite (La1-xSrx) MnO3±δ (LSM) to assess its stability against Sr secondary phase formation in SOC applications. In this work, the Sr secondary phase formation reaction free energies were determined by combining ab initio lattice dynamics calculations for the solid phases and an ab initio thermodynamics approach for the gas phases. Furthermore, this approach goes beyond previous thermodynamic modeling studies by integrating first-principles based point-defect equilibria into the analyses. The modeling results indicate an increased tendency to form SrO oxide from LSM upon decreasing the oxygen partial pressure. Additionally, enhancing factors to form the Sr-related secondary phase from the associated SrO activity in LSM are further quantified by considering the equilibrium of SrO reacting with contaminant gas species as a function of temperature and gas pressure.

Defect and phase stability↗

DOE OSTI2025

Resolving Lonsdaleite's decade-long controversy: Atomistic insights into a metastable diamond polymorph

Lonsdaleite, a theoretically proposed hexagonal diamond polymorph, has remained at the center of a five-decade scientific controversy since its 1967 identification. While some studies claim it exhibits superior hardness through compression-induced structural changes, others contend it is merely a stacking-faulted cubic diamond. Meteoritic samples and synthetic preparations have yielded conflicting evidence, with even advanced characterisation techniques like XRD and TEM failing to provide definitive proof. In this work, we employ first-principles density functional theory (DFT) and molecular dynamics (MD) simulations to generate unambiguous theoretical fingerprints through XRD, Raman, and SAED patterns that distinguish true Lonsdaleite from cubic diamond and its defective variants. Our atomistic approach quantifies the thermodynamic metastability of Lonsdaleite under realistic pressure-temperature conditions, reveals distinct spectral signatures through simulated Raman and resolves the structural ambiguity through generalised stacking fault energy analysis. By establishing clear criteria for definitive identification, this study provides long-awaited clarity to the Lonsdaleite debate while offering a robust computational framework for characterising metastable carbon phases in meteoritic, synthetic and industrial materials.

DFT↗

DOE OSTI2025

Microstructure and mechanical behavior of a TiC nanoprecipitate strengthened V Alloy

The V-4Cr-4Ti (V44) alloys have been proposed as the prime candidate structural material for self-cooled liquid Li blanket and other designs for fusion energy applications. However, the applications of the V44 alloy are limited to a narrow operation temperature window, due to reduction in creep strength at or above 700 °C and susceptibility to irradiation hardening and embrittlement when irradiated below 400 °C. Here, in this work, we explore the feasibility of designing a novel V alloy to form a high number density of TiC nanoprecipitates, in order to simultaneously improve creep strength and provide defect sinks to mitigate irradiation hardening. Computational thermodynamics was used to design a new alloy (V44C) to achieve our goal of high TiC nanoprecipitates density within the alloy V44 matrix. To ensure scalability, the new alloy was made through arc-melting and ingot-casting followed by hot forging, cold rolling and heat treatments of homogenization and precipitation aging. The microstructure was characterized by SEM, TEM, XRD and APT, confirming the existence of nanoprecipitates predicted in the thermodynamic calculations. In addition to microstructural evaluation tensile properties at room temperature and 700 °C, and Charpy impact energy at room temperature were measured. The microstructure and mechanical properties were then compared with those from a historic reference V44 alloy. The tensile strength improvement in V44C was rationalized based on particle and solid solution strengthening mechanism. The fracture behavior was discussed based on the fractography results and necking deformation behavior.

Alloys development↗

DOE OSTI2023

Recent Developments in Revealing the Impact of Complex Metal Oxide Reconstruction on Catalysis

Surface reconstruction of complex metal oxides refers to the alterations of the topmost catalyst surface, relative to the bulk structure, following exposure to pretreatment or reaction conditions during heterogeneous catalysis. (1) This structural and electronic transformation may involve (1) changes of the exposed crystallographic facets, (2) changes in chemical composition, such as the enrichment of specific elements, and, (3) morphological variations, including surface roughness and defects (Scheme 1). Beyond relaxation, surface reconstruction here also encompasses disruptions to the periodicity of the sublayers and changes to its stoichiometry. This change significantly influences the chemical properties of the catalyst surface, such as redox sites, (2) acid/base pairs, hydroxyl groups, (3) and surface defects. Surface reconstruction occurs due to the thermodynamic drive to lower the surface energy of the catalyst under the surrounding environment (e.g., temperature, chemical potential of species present). In addition to the treatment or reaction conditions, the extent of reconstruction also depends on the elements in the metal oxide structure. For instance, annealing ABO 3 perovskites (SrTiO 3 , BaTiO 3 , and BaZrO 3 ) at high temperatures (500 °C) in O 2 has a very different impact on the A/B ratio at the surface (ranging from 0.9 to 2.5), depending on the identity of A and B. (4) Metal oxide surface reconstruction under an electric field and exposure to acidic and alkaline media has recently gained increased attention in electrocatalysis, such as in the oxygen evolution reaction (OER); (5,6) however, in this Viewpoint we focus on the impact of surface reconstruction on thermal catalysis, a critical enduring research theme with ongoing challenges. Here, we start showcasing approaches to characterize surface reconstruction at the topmost surface layer, such as low-energy ion scattering (LEIS), discussing advantages and limitations. Next, we connect characterization of surface reconstruction to site-specific kinetic analysis, enabled via steady-state isotopic transient kinetic analysis (SSITKA), and we express our viewpoint on building structure–performance relationships by deeply understanding reconstructed surfaces. Later, we comment on the potential of tuning surface reconstruction to enhance catalytic performance. Finally, we explore the interplay between surface reconstruction and the “intelligent behavior”.

alcohol conversion↗

NASA NTRS1998

A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

Luo, Li-Shi↗

DOE OSTI2025

Cluster Dynamics Modeling Needs for the Advanced Materials and Manufacturing Technologies Program

This milestone report aims to identify and assess the cluster dynamics (CD) modeling requirements within the Department of Energy's Office of Nuclear Energy (DOE-NE) Advanced Materials and Manufacturing Technologies (AMMT) program and to communicate these needs to the DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The goal is to ensure NEAMS is well-informed about the CD modeling requirements to support AMMT's mission of accelerating the development, qualification, demonstration, and deployment of advanced structural materials and manufacturing for nuclear energy applications. CD modeling is an essential tool for predicting the degradation of structural materials under irradiation, which is a key component of AMMT's accelerated qualification process. The AMMT program focuses on both additively manufactured and wrought structural alloys, such as laser powder-bed fusion 316H austenitic stainless steel, alloy 709, Haynes 244, and alloy 617. These materials require a generalized CD modeling framework to facilitate rapid model development and computational simulation. A flexible, generalized CD software, similar to the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework, would enable modeling of various cluster types, including defect clusters, defect-solute clusters, and multicomponent clusters, incorporating thermodynamics and kinetics parameters. Radiation effects, microstructural feature evolution, and multi-dimensional modeling are critical considerations for the CD model. The usability of the CD code should allow for easy modification and coupling with MOOSE-based simulations. Additionally, the software should adhere to Nuclear Quality Assurance-1 standards, include a testing suite for verification and validation, and be version-controlled within a national laboratory-managed Git repository. Benchmark problems are needed to assess code predictions and performance.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

First-Principles Study of Molecular Hydrogen Activation by Defects in Boron Nitride

Here, we used density functional theory simulations in combination with ab initio thermodynamics to determine the H 2 partial pressure (p H2 )-dependent energetics associated with H 2 activation and recovery at various defect sites in hexagonal boron nitride (h-BN). We found that some defects are very reactive with hydrogen, thereby definitely trapping hydrogen in defective h-BN. However, depending on hydrogen partial pressure, less reactive defect sites can be populated. Because of the lower binding capability of these sites, they would allow hydrogen to be recycled and recovered. For small defect sizes, we found that hydrogen preferentially binds to nitrogen sites by forming N–H bonds, and if no N sites are available then boron sites would be the next to bind hydrogen. Hydrogen dissociation via frustrated Lewis pair is found to be more favorable than forming only N–H bonds but only if the defect size is large enough to accommodate steric effects. For specific conditions such as T = 400 K, p H2 = 1 bar, and only considering one molecular H 2 per defect, three defects, namely, the N monovacancy, 3V(1B2N), and hexagonal 6V(3B3N) could play a role in both the activation and recycling of H 2 as they would be reacting enough to allow a favorable splitting of H 2 while not binding too strongly to allow its recovery. More broadly, a range of p H2 and hydrogen loading conditions were investigated for different types of defects and the finding suggests that p H2 could be used to fine-tune the Gibbs free energy of hydrogenation, thereby allowing several types of defects at different hydrogen loading contents to play a role in the activation/recovery process of H 2 in defective h-BN.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding

The optical spectra of neutral oxygen vacancies (F 0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. Here, to estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet–singlet decay pathway.

embedding↗

NASA NTRS2019

Complex Intergrowths of Non-Stoichiometric Defect-Structured Hibonite and Al-Rich Spinel in an Allende Ca-Al-Rich Inclusion

Hibonite is a primary ultra-refractory mineral occurring in many Ca-Al-rich inclusions (CAIs) and is predicted to condense as the second major phase from a cooling gas of solar composition. Our previous microstructural studies of hibonite in carbonaceous chondrites revealed its unique microstructures consisting of numerous defects that contain Mg-enriched, wider spinel blocks in stoichiometric hibonite. Han, J. et al. [2 items] demonstrated experimentally that defect-structured hibonites can grow easily in the presence of minor Mg and are kinetically more stable than equilibrium assemblages predicted by thermodynamic calculations. However, a thermo-dynamic vs. structural stability of defect-structured hibonite relative to other early-condensed Al-rich phases such as corundum, grossite, and spinel remains poorly constrained. Here, we present the results of atomic resolution TEM (Transmission Electron Microscopy) imaging of hibonite in a compact Type A CAI in the Allende CV3 chondrite in order to better understand the crystal structure and chemistry of defect-structured hibonite and its associated Al-rich phases, especially non-stoichiometric, Al-rich spinel, in the context of the formation of first refractory solids in the early solar nebula.

Han, J.↗

DOE OSTI2024

High-resolution chemical patterns from negative tone resists for the integration of extreme ultraviolet patterns of metal-oxide resists with directed self-assembly of block copolymers

Extreme ultraviolet (EUV) lithography faces significant challenges in designing suitable resist materials that can provide adequate precision, while maintaining economically viable throughput. These challenges in resist materials have led to printing failures and high roughness in EUV patterns, compromising the performance of semiconductor devices. Integrating directed self-assembly (DSA) of block copolymers (BCPs) with EUV lithography offers a promising solution because, while the BCPs register to the EUV-defined chemical guiding pattern, the thermodynamically determined structures of the BCPs automatically rectify defects and roughness in the EUV pattern. Despite the superior resolution of metal-oxide EUV resists (MORs), their application to DSA is limited by the difficulty in converting them into chemical patterns that allow effective transfer of the rectified patterns of DSA films into inorganic materials. To address this challenge, this study introduces a novel strategy for fabricating chemical patterns using hydrogen silsesquioxane (HSQ), a high-resolution negative tone inorganic resist, as a model system for MORs. Initially, a sacrificial Cr pattern is generated from HSQ patterns via reactive ion etching. The sacrificial Cr pattern is converted into a chemical pattern by first grafting a water-soluble polyethylene oxide brush onto the substrate, then wet etching the Cr, and finally grafting nonpolar polystyrene brushes. Assembling polystyrene-block-poly(methyl methacrylate) on these patterns results in structures oriented and registered with the underlying pattern, achieving 24 nm full-pitch resolutions. In conclusion, this approach has the potential to integrate MOR patterns into the DSA process, thereby enabling the generation of high-quality sub-10 nm patterns with high-χ BCPs.

Atomic force microscopy↗

DOE OSTI2023

Physics-Based Model to Represent Membrane-Electrode Assemblies of Solid-Oxide Fuel Cells Based on Gadolinium-Doped Ceria

This paper reports a physics-based model that predicts membrane-electrode assembly (MEA) performance of solid-oxide fuel cells (SOFCs) with Ce 0.9 Gd 0.1 O 2− δ (GDC10) electrolyte membranes. The paper derives self-consistent thermodynamic and transport properties for GDC1o mobile charged defects (oxide vacancies and reduced-ceria small polarons) by fitting published measurements of oxygen non-stoichiometry and conductivity over ranges of temperature and O 2 partial pressures. The button-cell model is applied to evaluate how mixed ionic-electronic conductivity influences the performance of an SOFC MEA with a GDC10 electrolyte sandwiched between a porous, composite Ni-GDC10 anode and a porous, composite cathode of Sm 0.5 Sr 0.5 CoO 3− δ (i.e., SSC) and GDC10. SSC properties are also derived by fitting published conductivity and oxygen non-stoichiometry measurements. Mixed conductivity of GDC10 and competing charge transfer reactions at both electrodes reduce open circuit voltages due to leakage current and buildup of defect concentrations at electrode-electrolyte interfaces. To fit polarization data, the button-cell model includes heterogeneous reaction rates for defect incorporation on the GDC10 surface along with Butler–Volmer expressions derived for competing charge transfer reaction rates from rigorous analyses assuming rate-limiting, elementary charge transfer reactions for each electrode. The calibrated MEA model can support rigorous SOFC modeling with GDC10 electrolytes over the range of conditions within a fully operating cell.

Electrochemistry↗

DOE OSTI2022

The role of pre-existing heterogeneities in materials under shock and spall

There has been a challenge for many decades to understand how heterogeneities influence the behavior of materials under shock loading, eventually leading to spall formation and failure. Experimental, analytical, and computational techniques have matured to the point where systematic studies of materials with complex microstructures under shock loading and the associated failure mechanisms are feasible. This is enabled by more accurate diagnostics as well as characterization methods. As interest in complex materials grows, understanding and predicting the role of heterogeneities in determining the dynamic behavior becomes crucial. Early computational studies, hydrocodes, in particular, historically preclude any irregularities in the form of defects and impurities in the material microstructure for the sake of simplification and to retain the hydrodynamic conservation equations. Contemporary computational methods, notably molecular dynamics simulations, can overcome this limitation by incorporating inhomogeneities albeit at a much lower length and time scale. This review discusses literature that has focused on investigating the role of various imperfections in the shock and spall behavior, emphasizing mainly heterogeneities such as second-phase particles, inclusions, and voids under both shock compression and release. Pre-existing defects are found in most engineering materials, ranging from thermodynamically necessary vacancies, to interstitial and dislocation, to microstructural features such as inclusions, second phase particles, voids, grain boundaries, and triple junctions. This literature review explores the interaction of these heterogeneities under shock loading during compression and release. Systematic characterization of material heterogeneities before and after shock loading, along with direct measurements of Hugoniot elastic limit and spall strength, allows for more generalized theories to be formulated. Further, continuous improvement toward time-resolved, in situ experimental data strengthens the ability to elucidate upon results gathered from simulations and analytical models, thus improving the overall ability to understand and predict how materials behave under dynamic loading.

36 MATERIALS SCIENCE↗