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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy↗
DOE OSTI2020

A pathway to synthesizing single-crystal Fe and FeCr films

Nuclear reactor environments provide a unique scientific and engineering challenge wherein materials must tolerate prolonged exposure to concurrent irradiation, elevated temperatures, and corrosive media. However, uncontrolled variability in material composition and structure often prohibits truly single-variable experiments that can reveal basic aspects of environmental damage. Here, Magnetron sputtering is used to provide a more controlled model system for these fundamental studies, yielding reproducible single-crystal Fe and FeCr thin films containing 8 and 18 at.% Cr. Electron microscopy is used to determine the systematic correlations between growth conditions and the resulting film microstructure and surface morphology. It is found that the substrate temperature and applied radio frequency (RF) bias can be tuned to obtain consistent homogeneous and single crystal films with a minimal amount of Ar impurities from the RF bias process. Epitaxial, single-crystal Fe films are obtained on MgO substrates at 500 °C with 10 Watt (W) RF bias deposition. However, when Cr is alloyed with Fe, higher substrate temperatures (600 °C) and applied RF biases (15 W) are required to achieve a similar epitaxial single-crystal FeCr film. Accelerated molecular dynamics simulations reveal that Cr impedes surface transport, explaining the need for higher temperature and bias during the growth of the Cr-bearing films.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Effect of interfacial structures on phonon transport across atomically precise Si/Al heterojunctions

Phonons are important carriers of energy and information in many cryogenic devices used for quantum information science and in fundamental physics experiments such as dark matter detectors. In these systems phonon behavior can be dominated by interfaces, hence there is increasing demand for a more detailed understanding of interfacial phonon transport in relevant material systems. Previous studies have focused on understanding thermal transport over the entire phonon spectrum at and above room temperature. At ultra-low temperatures, however, knowledge is missing regarding athermal phonon behavior due to the challenge in modeling the extreme conditions in micro-scale, heterogeneous cryogenic systems, as well as extracting single-phonon information from a large ensemble. In this work, we delineate interfacial phonon transport using a combination of classical molecular dynamics (MD) and phonon wave packet simulations, to illustrate the consistency and differences between the ensemble- and single-phonon dynamics. We consider three single-crystal Si surface reconstructions --- (1×1), (v3×v3) and (7×7) --- and model both experimentally observed Si(1×1)/Al interfaces and hypothesized Si(v3×v3)/Al and Si(7×7)/Al interfaces. The overall interfacial thermal conductance calculated from non-equilibrium MD shows that for the Si(1×1)/Al system, the presence of Al twin grain boundaries can hinder phonon transport and reduce thermal conductance by 2--12% relative to single-crystal Al; whereas the Si (v3×v3) and (7×7) reconstructions can enhance it by 6--19%. Normal mode decomposition reveals that both the increase and decrease in conductance are related to inelastic phonon scattering. Single-phonon wave packet simulations show results consistent with NEMD, while further suggesting that phonon polarization conversion is significant even when elastic transmission dominates, and that the interfacial structures have anisotropic impacts on atomic vibrations along different lattice directions. Our findings suggest alternative perspectives in achieving selective phonon transport through controlling interfacial structures of materials with atomically-precise fabrication techniques, and that the phonon wave packet formalism is a potentially powerful method for developing a detailed understanding of non-equilibrium phenomena in the low-temperature limit.

Lu, Zexi↗
DOE OSTI2023

Crystal plasticity modeling for the strengthening effect of multilayered copper–graphene nanocomposites

The paper explores plastic deformation mechanisms in metal–graphene nanocomposites, illustrating their material strengthening effects through a crystal plasticity finite element (CPFE) model. This model is compared with published experimental results, which have previously shown that the two-dimensional shape of graphene effectively controls dislocation motion and significantly enhances the strength of metals. Simulated nanopillar compression tests, using a physics-based CP model that incorporates surface nucleation and single-arm source dislocation mechanisms, help us understand dislocation motions at submicron length scales. The crystal plasticity models are applied to nanolayered composites with copper grain layers and monolayer graphene, featuring repeat layer spacings of 200 nm, 125 nm, and 70 nm, respectively. This study quantifies the accumulation of dislocations at the graphene interfaces, contributing to the ultra-high strength of copper–graphene composites. Furthermore, a Hall–Petch-like correlation is established between yield strength and the number of embedded graphene layers.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Superconductivity in pressurized trilayer La 4 Ni 3 O 10-$δ$ single crystals

In this study, the pursuit of discovering new high-temperature superconductors that diverge from the copper-based model has profound implications for explaining mechanisms behind superconductivity and may also enable new applications. Here our investigation shows that the application of pressure effectively suppresses the spin–charge order in trilayer nickelate La 4 Ni 3 O 10-δ single crystals, leading to the emergence of superconductivity with a maximum critical temperature (T c ) of around 30 K at 69.0 GPa. The d.c. susceptibility measurements confirm a substantial diamagnetic response below T c , indicating the presence of bulk superconductivity with a volume fraction exceeding 80%. In the normal state, we observe a strange metal behaviour, characterized by a linear temperature-dependent resistance extending up to 300 K. Furthermore, the layer-dependent superconductivity observed hints at a unique interlayer coupling mechanism specific to nickelates, setting them apart from cuprates in this regard. Our findings provide crucial insights into the fundamental mechanisms underpinning superconductivity, while also introducing a new material platform to explore the intricate interplay between the spin–charge order, flat band structures, interlayer coupling, strange metal behaviour and high-temperature superconductivity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effects of Microstructural Composition, Porosity, and Microcracks on the Elastic Moduli of Nuclear Graphites

The elastic responses of nuclear graphite not only depend on the graphitic content itself but are largely dictated by the microstructural constitution of the material. The types of raw materials combined with the manufacturing processes used to produce the graphite yield the microstructural content that primarily includes graphite filler, graphitized pitch binder, and voids/defects that typically occupy approximately 20% of the volume. Among these microstructural components, porosity and microcracking (considered to be part of voids/defects) heavily influence the overall properties of the material, including the elastic moduli. It is widely accepted that the primary effect of oxidation is to increase porosity, but the related effect on the moduli cannot be explained satisfactorily by simply noting changes to porosity. Models describing the elastic moduli of porous, polycrystalline graphite materials have been developed to interpret experimental determinations of Young's modulus and shear modulus in oxidized graphites. Beyond porosity, the moduli are heavily influenced by microcracks, and their effects can be assessed using physical property models based on orientation distribution coefficients and microcrack-modified, single-crystal moduli to represent the combined effects of crystallite orientation and microcracking. This work demonstrates how most modulus measurements in nuclear graphites can be understood using relatively simple models that describe the effects of porosity and microcracking. We also present directions to be pursued to account for microstructure-related effects that occur as a result of neutron irradiation.

Spicer, James B.↗
DOE OSTI2022

Elucidating size effects on the yield strength of single-crystal Cu via the Richtmyer–Meshkov instability

Capturing the dynamic response of a material under high strain-rate deformation often demands challenging and time consuming experimental effort. While shock hydrodynamic simulation methods can aid in this area, a priori characterizations of the material strength under shock loading and spall failure are needed in order to parameterize constitutive models needed for these computational tools. Moreover, parameterizations of strain-rate-dependent strength models are needed to capture the full suite of Richtmyer–Meshkov instability (RMI) behavior of shock compressed metals, creating an unrealistic demand for these training data solely on experiments. Herein, we sweep a large range of geometric, crystallographic, and shock conditions within molecular dynamics (MD) simulations and demonstrate the breadth of RMI in Cu that can be captured from the atomic scale. In this work, yield strength measurements from jetted and arrested material from a sinusoidal surface perturbation were quantified as Y RMI = 0.787 ± 0.374 GPa, higher than strain-rate-independent models used in experimentally matched hydrodynamic simulations. Defect-free, single-crystal Cu samples used in MD will overestimate Y RMI , but the drastic scale difference between experiment and MD is highlighted by high confidence neighborhood clustering predictions of RMI characterizations, yielding incorrect classifications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Polycrystal thermo-elasticity revisited: theory and applications

The self-consistent (SC) theory is the most commonly used mean-field homogenization method to estimate the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The original elastic SC method can be extended to thermo-elasticity by adding a stress-free strain to an elastic constitutive relation that expresses stress as a linear function of strain. With the addition of this independent term, the problem remains linear. Although the thermo-elastic self-consistent (TESC) model has important theoretical implications for the development of self-consistent homogenization of non-linear polycrystals, in this paper, we focus on TESC applications to actual thermo-elastic problems involving non-cubic (i.e. thermally anisotropic) materials. To achieve this aim, here we provide a thorough description of the TESC theory, which is followed by illustrative examples involving cooling of polycrystalline non-cubic metals. The TESC model allows studying the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on the effective thermo-elastic response of the aggregate and on the internal stresses that develop at the local level.

36 MATERIALS SCIENCE↗
DOE OSTI2025

X-ray Diffraction Studies of Single-Crystal Materials for Broad Battery Applications

Single-crystal materials have attracted growing interest in battery research due to their well-defined crystallographic orientation, absence of grain boundaries, and enhanced mechanical and electrochemical stability. This Review provides a comprehensive overview of recent advances in the synthesis, structural evolution, and performance optimization of single-crystal electrodes and solid electrolytes. Particular focus is placed on the application of advanced X-ray diffraction (XRD) techniques, including operando synchrotron diffraction, reciprocal space mapping, and Bragg coherent diffraction imaging, which have enabled in-depth investigations of lattice strain, cation disorder, phase transitions, and defect formation. Representative case studies across Ni-rich layered oxides, spinel-type cathodes, and garnet-based electrolytes are examined to highlight the structural features unique to single crystals. Additionally, the synergistic integration of XRD with machine learning, tomography, and spectroscopy is discussed as a powerful direction for real-time analysis and predictive modeling. Furthermore, these insights provide critical guidance for the rational design of high-performance single-crystal materials in lithium, sodium, and solid-state battery systems.

25 ENERGY STORAGE↗
DOE OSTI2023

Pertechnetate/perrhenate–capped Zr/Hf–Dihydroxide Dimers: Elucidating Zr–TcO 4 Co–Mobility in the Nuclear Fuel Cycle

Spent nuclear fuel contains heavy element fission products that must be separated for effective reprocessing for a safe and sustainable nuclear fuel cycle. 93 Zr and 99 Tc are high-yield fission products that co-transport in liquid-liquid extraction processes. Here we seek atomic-level information of this co-extraction process, as well as fundamental knowledge about Zr IV (and Hf IV ) aqueous speciation in the presence of topology-directing ligands such as pertechnetate (TcO 4 – ) and non-radioactive surrogate perrhenate (ReO 4 – ). In this context, we show that the flat tetrameric oxyhydroxyl-cluster [M IV 4 (OH) 8 (H 2 O) 16 ] 8+ (and related polymers) is dissociated by perrhenate/pertechnetate to yield isostructural dimers, M 2 (OH) 2 (XO 4 – ) 6 (H 2 O) 6 • 3H 2 O (M=Zr/Hf IV ; X=Re/Tc VII ), elucidated by single-crystal X-ray diffraction. We used these model compounds to understand the pervasive 93 Zr- 99 Tc coextraction with further speciation studies in water, nitric acid, and tetrabutylphosphate (TBP) -kerosene; where the latter two media are relevant to nuclear fuel reprocessing. SAXS (small angle X-ray scattering), compositional evaluation, and where experimentally feasible, ESI-MS (electrospray ionization mass spectrometry) showed that perrhenate/pertechnetate influence Zr/Hf IV -speciation in water. Here, in Zr-XO 4 solvent extraction studies to simulate fuel reprocessing, we provide evidence that TcO 4 – enhances extraction of Zr IV , and compositional analysis of the extracted metal-complexes (Zr-ReO 4 study) is consistent with the crystallized Zr IV 2 (OH) 2 (Re VII O 4 – ) 6 (H 2 O) 6 •dimer.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Magnetic Properties Tuning via Broad Range Site Deficiency in Square Net Material UCu x Bi 2

HfCuSi 2 -type pnictogen compounds have recently been shown to be a versatile platform for designing materials with topologically nontrivial band structures. However, these phases require strict control over the electron count to tune the Fermi level, which can only be achieved in compositions with A 2+ M 2+ Pn 2 and A 3+ M + Pn 2 (A = lanthanides, M = transition metals, Pn = pnictogens P–Bi) charge distribution. While such lanthanide compounds have been thoroughly studied as candidate magnetic topological materials, their heavy element analogs with uranium and bismuth remain largely underexplored. In this report, we present the synthesis of UCu x Bi 2 single crystals and study their magnetic properties. Detailed structural analysis revealed that flux-grown crystals always form as a site-deficient UCu x Bi 2 composition, where x varies between 0.20 and 0.64. Magnetic property measurements revealed a dependence of the magnetic coupling on the Cu site deficiency, linearly changing the Néel temperature from 51 K for UCu 0.60 Bi 2 to 118 K for UCu 0.30 Bi 2 . Moreover, higher Cu concentration promotes a metamagnetic transition in highly magnetically anisotropic UCu 0.60 Bi 2 single crystals. We show that DFT calculations can successfully model site deficiency in the UCu x Sb 2 and UCu x Bi 2 systems. This work paves the way toward using the site deficiency to tune the Fermi level in more ubiquitous A 3+ M 2+ x Pn 2 phases, which previously have not been considered topological candidate materials due to unfavorable electron count.

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

Ultrafast heat transfer in single palladium nanocrystals seen with an X-ray free-electron laser

We report transient highly strained structural states in individual palladium (Pd) nanocrystals, electronically heated using an optical laser, which precede their uniform thermal expansion. Using an X-ray free-electron laser probe, the evolution of individual 111 Bragg peaks is measured as a function of delay time at various laser fluences. Above a laser fluence threshold at a sufficient pump-probe delay, the Bragg peak splits into multiple peaks, indicating heterogeneous strain, before returning to a single peak, corresponding to even heat distribution throughout the lattice expanded crystal. Our findings are supported by a lattice displacement and strain model of a single nanocrystal at different delay times, which agrees with the experimental data. Our observations have implications for understanding femtosecond laser interactions with metals and the potential photo-catalytic performance of Pd.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Prediction of nonlinear specific heat during single crystal HMX phase transition

Here, we develop a thermodynamically consistent chemo-thermo-mechanical model for the β → δ phase transition of energetic HMX crystals. In contrast to previous models, which either considered specific heat to be a constant or utilized a calibrated function, this model provides novel expressions for the specific heats at constant volume and constant elastic strains derived directly from continuum mechanics. In addition, the model provides a novel prediction for the critical temperature at which the chemical heating rate achieves its extremum for Arrhenius kinetics. The numerical solution predicts highly nonlinear specific heat behavior including order of magnitude changes.

42 ENGINEERING↗
DOE OSTI2021

The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

Abstract Polycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c 11 /c 33 ) and shear (c 44 /c 66 ) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Defect evolution in Ni and solid-solution alloys of NiFe and NiFeCoCr under ion irradiation at 16 and 300 K

Single-phase concentrated solid-solution alloys (SP-CSAs) have shown unique chemical complexity at the levels of electrons and atoms, and their defect evolution is expected to be different from conventional dilute alloys. Single crystals of Ni, NiFe and NiFeCoCr are chosen as model systems to understand the chemical complexity on defect formation and damage accumulation in SP-CSAs under ion irradiation. The high-quality crystals were irradiated at 16 and 300 K to different ion fluences, to form irradiated region with little to heavy damages. Additionally, the ion-induced damage was determined using Rutherford backscattering spectrometry technique along a channeling direction (RBS/C) and the level of lattice damage in irradiated Ni and SP-CSAs was quantified from Monte Carlo (MC) simulations. The results are interpreted using the Multi Step Damage Accumulation model to reveal material damage accumulation kinetics. Key findings of the study are that in case of room temperature irradiations the damage level measured for complex alloys at the highest irradiation fluence of 2 × 10 15 cm -2 (~3 dpa) is significantly higher than that obtained for pure nickel samples and suggest two-step damage accumulation process with a defect transformation taking place at a fluence of about 1.5 × 10 15 cm -2 . Furthermore, structural and damage kinetic differences clearly imply that, with increasing degree of chemical complexity and high solid-solution strengthening effects from Ni to NiFe and to NiFeCoCr, the enhanced lattice stiffness resists to randomization of atomic configurations and inhibits the growth of extended defects.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Multi-physics modeling of tungsten collector probe samples during the WEST C4 He campaign

Abstract We describe the results of a multi-scale, multi-physics modeling assessment of SOLPS-ITER, hPIC2, RustBCA and Xolotl, in which five single-crystal tungsten (W) samples were placed in a reciprocating collector probe and exposed to helium (He) plasma in the WEST fusion device. In our models, we considered a pure (100 %) He plasma, as well as one with oxygen (O) present (95% He 5% O) corresponding to the impurity concentration estimated during the C4 He campaign in WEST. Our SOLPS simulations approximately match experimental reciprocating Langmuir probe plasma measurements of plasma density and temperature. Using these plasma parameters as input, hPIC2 and RustBCA predict that the presence of oxygen impurities lead to a 15%–20% decrease in ion and heat fluxes to the surface, and an order of magnitude higher sputtering yields (compared with a pure He plasma). Xolotl predictions for the response of tungsten to plasma surface interactions (PSIs) agree with experimental LAMS analysis, and indicate large near-surface He concentrations, which quickly decay with depth. Our model also shows an increasing role of erosion—in removing the near-surface He—with time. Overall, slightly higher retention is predicted for tungsten exposed to a pure He plasma, with the largest differences in the near-surface gas content caused by the large oxygen-induced erosion. This highlights the important role that impurities play in PSI. Therefore, future work will focus on providing a fully self-consistent description of oxygen (and oxides, etc.) in our models, through multi-species implementation in GITR and inclusion of oxygen and tungsten oxide formation in Xolotl.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Atomistic insight into the ferroelastic post-stishovite transition by high-pressure single-crystal X-ray diffraction

Abstract The post-stishovite transition is a classic pseudo-proper typed ferroelastic transition with a symmetry-breaking spontaneous strain. This transition has been studied using high-pressure spontaneous strains, optic modes, and elastic moduli (Cij) based on the Landau modeling, but its atomistic information and structural distortion remain poorly understood. Here we have conducted synchrotron single-crystal X-ray diffraction measurements on stishovite crystals up to 75.3 GPa in a diamond-anvil cell. Analysis of the data reveals atomic positions, bond lengths, bond angles, and variations of SiO6 octahedra across the transition at high pressure. Our results show that the O coordinates split at ~51.4 GPa, where the apical and equatorial Si-O bond lengths cross over, the SiO6 octahedral distortion vanishes, and the SiO6 octahedra start to rotate about the c axis. Moreover, distortion mode analysis shows that an in-plane stretching distortion (GM1+ mode) occurs in the stishovite structure at high pressure while a rotational distortion (GM2+ mode) becomes dominant in the post-stishovite structure. These results are used to correlate with elastic moduli and Landau parameters (symmetry-breaking strain e1–e2 and order parameter Q) to provide atomistic insight into the ferroelastic transition. When the bond lengths of two Si-O bonds are equal due to the contribution from the GM1+ stretching mode, C11 converges with C12, and the shear wave VS1[110] polarizing along [110] and propagating along [110] vanishes. Values of e1–e2 and Q are proportional to the SiO6 rotation angle from the occurrence of the GM1+ rotational mode in the post-stishovite structure. Our results on the pseudo-proper type transition are also compared with that for the proper type in albite and improper type in CaSiO3 perovskite. The symmetry-breaking strain, in all these types of transitions, arises as the primary effect from the structural angle (such as SiO6 rotation or lattice constant angle) and its relevant distortion mode in the low-symmetry ferroelastic phase.

Geochemistry & Geophysics↗