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At least 271 records · Page 15

T3tris: AI-Driven Inverse Design of Cellular Materials

Los Alamos National Laboratory has developed T3tris, a generative AI platform that enables real-time inverse design of architected cellular materials. This capability transforms how mechanical metamaterials are designed by generating microstructural topologies that conform to target nonlinear stress-strain curves, even at high compressive strain (up to 50%).

36 MATERIALS SCIENCE↗

Optimizing the Design of Diatom Biosilica-Targeted Fusion Proteins in Biosensor Construction for Bacillus anthracis Detection

In vivo functionalization of diatom biosilica frustules by genetic manipulation requires careful consideration of the overall structure and function of complex fusion proteins. Although we previously had transformed Thalassiosira pseudonana with constructs containing a single domain antibody (sdAb) raised against the Bacillus anthracis Sterne strain, which detected an epitope of the surface layer protein EA1 accessible in lysed spores, we initially were unsuccessful with constructs encoding a similar sdAb that detected an epitope of EA1 accessible in intact spores and vegetative cells. This discrepancy limited the usefulness of the system as an environmental biosensor for B. anthracis. We surmised that to create functional biosilica-localized biosensors with certain constructs, the biosilica targeting and protein trafficking functions of the biosilica-targeting peptide Sil3T8 had to be uncoupled. We found that retaining the ER trafficking sequence at the N-terminus and relocating the Sil3T8 targeting peptide to the C-terminus of the fusion protein resulted in successful detection of EA1 with both sdAbs. Homology modeling of antigen binding by the two sdAbs supported the hypothesis that the rescue of antigen binding in the previously dysfunctional sdAb was due to removal of steric hindrances between the antigen binding loops and the diatom biosilica for that particular sdAb.

59 BASIC BIOLOGICAL SCIENCES↗

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

36 MATERIALS SCIENCE↗

Effects of Strain and Strain Rate on Dynamic Grain Growth and Subgrain Evolution During Plastic Deformation of an Interstitial-Free Steel at 850 ° C

Here, the effects of strain and strain rate on dynamic grain growth (DGG) and subgrain evolution are reported for an interstitial-free steel deformed at 850 ° C. Microstructures produced during tension tests at true-strain rates of 10 -4 and to 10 -3 s -1 true strains ranging from 0.02 to 0.2 were preserved following deformation. These were characterized using electron backscatter diffraction (EBSD), including the application of spherical harmonic transform indexing to produce high-angular-resolution EBSD (HR-EBSD) data. HR-EBSD data resolved the small misorientation angles of subgrain boundaries while imaging much larger data fields than possible with previously available techniques. The resulting data confirmed that steady-state flow stress is inversely proportional to the average subgrain size and that subgrain boundary misorientation angle increases with strain. The following new observations are reported. The rate of DGG increased with respect to time but decreased with respect to strain as strain rate increased. This behavior is rationalized through a simple model using separate rate parameters for the effects of time and strain. Subgrain size was not constant during steady-state deformation, but decreased slowly with increasing strain. Subgrain size distributions and subgrain boundary misorientation angle distributions were measured, and both remained approximately log-normal during steady-state deformation. Subgrain evolution demonstrated no dependence on parent grain size, crystallographic orientation, or Taylor factor. These new data suggest that steady-state flow stress is more likely controlled by the dislocation density internal to subgrains than by the spacing between subgrain boundaries.

dynamic grain growth↗

Resolving crystallographic geometrically necessary dislocations in three dimensions in a hexagonal close packed titanium alloy

Abstract Geometrically necessary dislocation (GND) content is measured from mm 3 -scaled Ti7Al three-dimensional (3D) microstructural data using a theory extended for hexagonal close packed crystals, which accounts for basal, prismatic and pyramidal ⟨ c + a ⟩ type dislocation content. The Ti7Al samples have been mechanically pre-strained to two different strain levels, and will then be strained along the same axis in uniaxial tension during simulation. Both inter- and intragranular GNDs across the microstructures have been characterized, with a large contribution of pyramidal ⟨ c + a ⟩ GNDs, consistent with the relative slip activity involved in pre-straining. The spatially resolved crystallographic GND distributions within the 3D microstructures are used to instantiate a microstructure model for forward modeling deformation simulations by a dislocation density hardening elasto-viscoplastic fast Fourier transform framework. Coarsening the voxel resolution during the initial microstructure construction procedure is shown to strongly impact both the magnitude and spatial distribution of the GNDs and in turn the forward deformation response of the pre-strained material. This study indicates that the voxel resolution desired when transferring from measured to model microstructures need not only be proportionally scaled with the microstructure but also sufficiently fine to capture the subgranular orientation gradients that may already be present in the material.

Materials Science↗

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗

Strain-driven surface reconstruction and cation segregation in layered Li(Ni 1– x – y Mn x Co y )O 2 (NMC) cathode materials

The composition, structure and phase transformations occurring on cathode surfaces greatly affect the performance of Li-ion batteries. Li-Ion diffusion and surface–electrolyte interaction are two major phenomena that impact the capacity and cell impedance. The effects of surface reconstruction (SR) of cathode materials on the performance of Li-ion batteries are of current interest. However, the origin and evolution of the SR are still not well understood. In this work, density functional theory (DFT) calculations are used to investigate the processes taking place during surface segregation and reconstruction. Facet dependent segregation was found in Li(Ni 1– x – y Mn x Co y )O 2 (NMC) cathodes. Specifically, Co tends to segregate to the (104) surface of the primary particles within the transition metal layer, while Ni ions tend to segregate to the (012) surface in the Li layer, forming a SR. Experimental evidence shows the SR to be epitaxial with the bulk of the as-synthesized material, and the new SR phase is pinned to the NMC unit cell leading to a strained SR. Here, we demonstrate that strain can stabilize a spinel structure of the SR layers. Understanding the effects of surface strain opens a new avenue for the design of cathode materials with enhanced surface properties.

25 ENERGY STORAGE↗

Laser Powder Directed Energy Deposition of Steels for Nuclear Applications

This comprehensive investigation examines the structure–property relationships in two nuclear alloy systems—Alloy 709 (A709) austenitic stainless steel and Grade 92 (G-92) ferritic/martensitic (F/M) steel—manufactured via directed energy deposition (DED) for sodium-cooled fast reactor applications. This study establishes the fundamental mechanisms for controlling microstructures for optimizing the mechanical performance of additively manufactured nuclear materials through systematic heat treatment optimization and multiscale characterization. As-deposited A709 steel develops a complex multiscale strengthening architecture consisting of a fine cellular solidification structure with diameter of 2-3 µm within10–50 µm grains, elevated dislocation densities from rapid thermal cycling, and grain boundary precipitates that activate concurrent Hall–Petch, dislocation, and precipitation hardening mechanisms to achieve exceptional properties [yield strength (YS): 603 MPa, ultimate tensile strength (UTS): 844 MPa, Vickers hardness: 220 HV] that achieve a 44% superior strength compared to that of the wrought material. Heat treatments produce different results. Solution annealing (SA) dissolves the cellular structure and reduces the hardness to 190 HV. Precipitation treatment (PT) keeps the cellular structure but adds carbides, allowing the hardness to reach 205 HV. The best approach combines both treatments (SA+PT) and creates uniform precipitate distributions with M 23 C 6 carbides at the grain boundaries and MX carbonitrides in the matrix, achieving a hardness of 195 HV. However, directional differences persist, with a 12%–15% strength variation between orientations due to the inherited layered microstructural architecture that survives aggressive heat treatment. While tensile testing at 550°C demonstrates 40%–50% thermal softening with dynamic strain aging, DED A709 steel still maintains a 71% higher YS than that of the wrought material. Ion irradiation studies (100–400 dpa) of DED A709 steel reveal progressive radiation damage with increasing void density and radiation-induced segregation causing nickel enrichment and chromium depletion, which will ultimately compromise mechanical properties. As-deposited G-92 exhibits exceptional strength (UTS: 1650–1700 MPa, 430 HV) through a complex microstructure containing both ferrite and martensite phases, a high geometrically necessary dislocation (GND) density (17.04×10 14 /m 2 ), and fine carbides. Heat treatments create distinct changes. Normalizing produces fresh martensite with the highest hardness (460 HV) and an increased GND density (20.23×10 14 /m 2 ). Tempering develops dual precipitation systems and reduces the hardness to 290 HV. The optimal approach uses sequential normalizing plus tempering, achieving balanced properties with the lowest hardness (250 HV) and a reduced GND density (11.01×10 14 /m 2 ). A processing-dependent anisotropy is observed: horizontal specimens achieve superior ductile behavior, while vertical specimens exhibit brittle failure. A tempering heat treatment successfully mitigates this anisotropic behavior by transforming the hard martensitic as-deposited structure into tempered martensite enabling both horizontal and vertical specimens to exhibit similar stress–strain characteristics with visible necking behavior. Remarkably, testing at 550°C reveals a reversal in the anisotropy, where as-deposited specimens achieve near isotropy with superior thermal stability (a 15%–20% strength reduction), while tempered specimens develop an orientation dependence with a 25%–30% strength reduction. Both alloy systems demonstrate that DED processing creates specimens with a superior strength through refined microstructural features, though with distinct strengthening mechanisms—austenitic through cellular structures and precipitates versus F/M through phase transformations and precipitates. Heat treatment optimization requires alloy-specific approaches, with A709 benefiting from controlled precipitation while G-92 requires careful phase transformation control. The results show that DED manufacturing can produce nuclear materials with exceptional performance, but directional effects and temperature-dependent behavior must be carefully considered for reactor component design and qualification.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Enhanced negative thermal expansion of boron-doped Fe 43 Mn 28 Ga 28.97 B 0.03 alloy

Enhanced negative thermal expansion (NTE) properties are achieved by introducing a little amount of boron in the Fe 43 Mn 28 Ga 28.97 B 0.03 alloy. As a result, this alloy shows a giant NTE coefficient of alpha(1) = -79.7 x 10 -6 K -1 in a wide temperature range from 277 K to 136 K. Compared to the NTE characteristics in Fe 43 Mn 28 Ga 29 , the NTE operation temperature window has expanded by 74% with the corresponding coefficient of thermal expansion increased by 57% within the NTE temperature window for the boron-doped Fe 43 Mn 28 Ga28.97B0.03. Additionally, in-situ synchrotron high-energy X-ray diffraction results suggest that by boron substitution, the large unit cell volume change across martensitic transformation and the wide phase transition temperature interval are responsible for the pronounced NTE behavior in Fe 43 Mn 28 Ga 28.97 B 0.03 . Moreover, for the Fe 43 Mn 28 Ga 28.97 B 0.03 NTE material, the compressive strength and strain are significantly improved compared with that of Fe 43 Mn 28 Ga 29 . The present study indicates that Fe 43 Mn 28 Ga 28.97 B 0.03 with enhanced NTE across martensitic transformation may be used for practical application as thermal-expansion compensators.

36 MATERIALS SCIENCE↗

Ultrafast x-ray diffraction of high-pressure phases in dynamically compressed TiO 2

Here, we investigate the high-pressure polymorphism of Ti⁢O 2 under laser-shock compression from 54(5) to 137(7) GPa using in situ femtosecond x-ray diffraction. Our results provide experimental evidence of the 𝑃⁢𝑐⁢𝑎⁢2 1 -type distorted fluorite structure formed from polycrystalline Ti⁢O 2 dynamically compressed to 54(5) GPa. Upon higher compression, we observe the direct formation of the ninefold coordinated F⁡e 2 ⁢P-type phase at 68(4) and 78(3) GPa in polycrystalline and [001]-oriented Ti⁢O 2 , respectively. This represents an unprecedented 100 GPa reduction in the shock synthesis pressure of the F⁡e 2⁢ P-type structure relative to quasihydrostatic loading conditions. On pressure release, the F⁡e 2⁢ P-type phase transforms to the α-Pb⁢O 2 structure and, at later times, reverts to rutile. Thus, the rutile →F⁡e 2⁢ P and α-Pb⁢O 2 →rutile transformations are both observed to occur on nanosecond timescales. Our results highlight the unique ability of high-strain-rate uniaxial compression to synthesize novel high-pressure phases and also indicate the importance of in situ atomic-level probes in developing pressure-temperature phase diagrams.

Crystal structures↗

Effect of laser scanning speed on the microstructure, phase transformation and mechanical property of NiTi alloys fabricated by $\mathrm{LPBF}$

This study investigated the effects of laser scanning speed on the microstructure, phase transformation and properties of NiTi alloys fabricated by laser powder bed fusion (LPBF). In this study, the contributions of metallurgical factors under different scanning speeds, such as Ni evaporation, Ni4Ti3 precipitation, dislocations and internal stress, to the transformation temperature and transformation latent heat were clarified through specially designed experiments. Ni evaporation is found to have the most profound effect, followed by precipitation. Increasing scanning speed is found to reduce Ni loss, thus cause less increase in the transformation temperature and transformation heat of the LPBF-NiTi alloys. Increasing scanning speed also increases the microstructure non-uniformity and thus widens the transformation temperature interval. The orientations of residual stress exhibit strong crystallographic stiffness dependence. The LPBF-NiTi alloys with different scanning speeds all exhibited high strains (>13.4%) and excellent shape memory effect. A LPBF-NiTi honeycomb structure exhibited 96% shape recovery rate after a 60% pre-compressive deformation. Besides, there is an optimum scanning speed for minimum porosity and smallest average pore size. However, the pore structure is found to have weak influence on the tensile behaviour of the LPBF-NiTi alloys, possibly due to the high defect tolerance of the martensitic transformation.

36 MATERIALS SCIENCE↗

Sulfur assimilation using gaseous carbonyl sulfide by the soil fungus Trichoderma harzianum

Fungi have the capacity to assimilate a diverse range of both inorganic and organic sulfur compounds. It has been recognized that all sulfur sources taken up by fungi are in soluble forms. In this study, we present evidence that fungi can utilize gaseous carbonyl sulfide (COS) for the assimilation of a sulfur compound. We found that the filamentous fungus Trichoderma harzianum strain THIF08, which has constitutively high COS-degrading activity, was able to grow with COS as the sole sulfur source. Cultivation with 34 S-labeled COS revealed that sulfur atom from COS was incorporated into intracellular metabolites such as glutathione and ergothioneine. COS degradation by strain THIF08, in which as much of the moisture derived from the agar medium as possible was removed, indicated that gaseous COS was taken up directly into the cell. Escherichia coli transformed with a COS hydrolase (COSase) gene, which is clade D of the β-class carbonic anhydrase subfamily enzyme with high specificity for COS but low activity for CO 2 hydration, showed that the COSase is involved in COS assimilation. Comparison of sulfur metabolites of strain THIF08 revealed a higher relative abundance of reduced sulfur compounds under the COS-supplemented condition than the sulfate-supplemented condition, suggesting that sulfur assimilation is more energetically efficient with COS than with sulfate because there is no redox change of sulfur. Phylogenetic analysis of the genes encoding COSase, which are distributed in a wide range of fungal taxa, suggests that the common ancestor of Ascomycota, Basidiomycota, and Mucoromycota acquired COSase at about 790–670 Ma.

59 BASIC BIOLOGICAL SCIENCES↗

Strain-relaxed tetragonal MAPbI 3 results in efficient mesoporous solar cells

In mesoporous organo-halide perovskite solar cells, the coexistence of tetragonal phase and cubic phase in the perovskite layer is found to result in strained crystal structure at the mesoporous TiO 2 (mp-TiO 2 )/perovskite heterointerface. This results in structural defects pinholes, grain boundaries, and interfacial porosity which is detrimental towards photovoltaic performance and device stability. The strain at the interface originates from the lattice mismatch between the mp-TiO 2 nanoparticles (NPs) and perovskite. Here, a transformative approach is demonstrated to realize relaxed and high purity tetragonal phase MAPbI 3 (RP) near the mp-TiO 2 interface region. This approach involves inserting a ~2 nm lattice matched buffer layer of cubic CsPbBr 3 between mp-TiO 2 NPs and MAPbI 3 , which serves as a template for epitaxial growth for top MAPbI 3 . As a result, the solar cell with relaxed MAPbI3 shows a power conversion efficiency (PCE) of 22.12% with significantly enhanced environmental, light, and thermal stability.

14 SOLAR ENERGY↗

Protoplast fusion as a strategy to increase ploidy in Rhodotorula toruloides for strain development

Rhodotorula toruloides is a red oleaginous yeast with growing commercial interest because of its hardiness and exceptional lipid production capacity. Because it is a basidiomycete yeast with a complex life cycle, many of the classical breeding methods used with ascomycetes are unavailable for strain improvement. However, we have been able to construct polyploid yeast by fusing protoplasts of parents with the same mating type. Fusing of Y-6985 (A2) and Y-48190 (A2), which had been transformed with complementary antibiotic markers, led to the recovery of two diploids and one triploid. The stability of the fusion yeasts was tested by plating them on non-selective medium after several growth cycles under antibiotics and then testing five colonies per strain for nuclear DNA contents using flow cytometry and standard cell cycle analysis: the triploid and one diploid were stable. Fusants inherited their mitochondria from a single parent, which was demonstrated using restriction fragment length polymorphism (RFLP) of mitochondrial DNA. The phenotypic properties of the parents and fusants were compared in glucose fed-batch bioreactor studies and cellulosic sugar batch cultures. The final lipid titers for the fed-batch cultures were 24.9–39.7 g/L with Y-6985 and the diploid and triploid performing the best and worst, respectively. The fusants demonstrated intermediate hardiness for growth on hydrolysate prepared with dilute-acid pretreated switchgrass and were outperformed by Y-48190. Unlike one of the haploid parents, the fusants grew in 70% v/v concentrated hydrolysate. Furthermore, they did not grow as fast as the other haploid. In this study, a modernized protoplast fusion method is resurrected a useful tool for strain development in this yeast, which is complementary with other available methods.

Lignocellulose↗

Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.

42 ENGINEERING↗

Fabricating Single Crystal Quantum Dot Solids

The central goal of this research program was to establish fundamental synthesis and processing principles to enable the fabrication of single crystal quantum dot solids (QDS) with programmable structure (i.e., hexagonal and square) and composition. Our approach towards that goal leveraged access to and experience with unique in-situ, multi-probe characterization techniques to understand and ultimately control the fundamental relationship between processing conditions and nucleation and growth of QDS. The program integrated synthesis and fabrication (Hanrath) with in-situ TEM analysis (Kourkoutis) and computational modeling (Clancy) to gain atomic-level insights into the underlying physical phenomena governing assembly and attachment and to guide the development of optimized processing methods. We have established a foundational understanding of physicochemical interactions of self-assembly at a fluid interface, superlattice structure transformation pathways, the critical role of disorder during the initial dimerization of colloidal quantum dot monomers, and the residual strain distribution within the inter-dot epitaxial bridge which hampers the formation of novel electronics states of the quantum dot solids. Collectively, these insights have contributed towards advancing the mechanistic understanding of the complex choreography of assembly and attachment as well as understanding what currently limits further advances in high-fidelity quantum dot solids and tiles.

36 MATERIALS SCIENCE↗

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene

Here, we introduce a multi-reward reinforcement learning (RL) approach to train a flexible bond-order potential (BOP) for 2D phosphorene based on ab initio training data sets. Our approach is based on a continuous action space Monte Carlo tree search algorithm that is general and scalable and presents an efficient multiobjective optimization scheme for high-dimensional materials design problems. As a proof-of-concept, we deploy this scheme to parametrize multiple structural and dynamical properties of 2D phosphorene polymorphs. Our RL-trained BOP model adequately captures the structure, energetics, transformation barriers, equation of state, elastic constants, and phonon dispersions of various 2D P polymorphs. We use this model to probe the impact of temperature and strain rate on the phase transition from black (α-P) to blue phosphorene (β-P) through molecular dynamics simulations. A decrease in critical strain for this phase transition with increase in temperature is observed, and the underlying atomistic mechanisms are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗