Predictive Crystal Plasticity Modeling of Single Crystal Nickel Based on First-Principles Calculations
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Materials Science↗
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A sensitivity analysis of twinning crystal plasticity finite element model using single crystal and poly crystal Zircaloy
The popularity of crystal plasticity finite element method (CPFEM) models is increasing due to their ability to predict the mechanical response of crystalline materials such as metals and metal alloys more accurately than traditional continuum mechanics models. This is since the crystal plasticity models consider the effect of atomic structure, microstructural morphology, and properties of individual grains. These CPFEM models use a large number of material parameters in order to capture the mesoscale physics which comes with the downside of the tedious calibration process. In this paper, a CPFEM code was developed to include the twinning induced grain reorientation and subsequent crystallographic slip for HPC material. The developed code is incorporated in a large-scale, parallelized nonlinear solver WARP3D. Further, a sensitivity analysis with respect to 22 material parameters was then conducted using single crystal and polycrystal representative volume element (RVE) of Zircaloy material. Loading was applied along five different crystallographic orientations for single crystal RVE and along three directions namely, rolling (RD), transverse (TD), and normal (ND) direction for polycrystal RVE. Results obtained from the sensitivity analysis were used for the calibration of material parameters for Zircaloy. Finally, developed code along with calibrated material parameters was used to investigate the effect of the hydride phase formation in Zircaloy which is a typical case observed for nuclear applications. It was found that the volume fraction of the hydride phase has a significant impact on the mechanical properties of Zircaloy.
36 MATERIALS SCIENCE↗
Electro-chemo-mechanical finite-element model of single-crystal and polycrystalline NMC cathode particles embedded in an argyrodite solid electrolyte
Not Available
Taghikhani, Kasra (ORCID:0000000277638315)↗
Modeling Single-Crystal Battery Materials: From Fundamental Understanding to Performance Evaluation
The performance of rechargeable batteries is fundamentally influenced by the physicochemical properties and microstructural features of their key material components. Recent experimental advancements have highlighted the potential of single-crystal (SC) morphologies to address inherent limitations of polycrystalline (PC) electrodes and solid-state electrolytes, offering tunable charge transport kinetics and improved cell cycling performance. Here, this review examines how state-of-the-art computational modeling, from atomistic and mesoscale to continuum-level approaches, including machine learning methodologies, has been utilized to investigate the critical factors governing the electrochemical behavior of SC battery materials. We explore how predictive modeling can elucidate the processing–structure–property–performance relationships of SC cathodes, anodes, and solid-state electrolytes, with a focus on unique SC characteristics such as crystallographic anisotropy, size effects, and facet-dependent properties. Additionally, we identify limitations in commonly used modeling techniques and discuss strategies to address these challenges. By integrating high-fidelity simulations with experimental insights, this review aims to outline a clear path for the rational design and optimization of SC battery components, paving the way for accelerated advancements in energy storage technologies.
Materials science↗
Single Crystal Plasticity Model with Deformation Twinning for the High Rate Deformation of β-HMX
Deformation twinning is an active deformation mechanism during loading along certain crystallographic directions of β-cyclotetramethylene tetranitramine (β-HMX). In this work, a finite strain thermomechanical model is extended to include twinning as a deformation mechanism in addition to plastic slip. The stress is derived from the free energy expression including a term representing the equation of state. The crystal plasticity framework is used to divide the total strain into inelastic and elastic component, where the elastic part is used in the expression for the free energy. The twin systems are treated as pseudo slip systems and the shear rate on the twin systems is evaluated in terms of the twin resistance and the projection of the stress tensor. The model parameters were calibrated against a set of plate impact experiments performed on β-HMX by Dick et al. The remaining plate impact experiments are used to evaluate the predictive capability of the model. The quality of the model fits and predictions is discussed from a physical and modeling perspective. Particularly, the role of twin modeling on results is highlighted. Finally, the model is used to explore the relationship between the propensity for twinning and crystal orientation.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters
Here, this work describes a crystal plasticity formulation combining several mathematical, numerical, and implementation choices to produce a highly efficient model. Specifically, the key choices in the implementation are (1) representing orientations with modified Rodrigues parameters, (2) implementing a fully coupled implicit time integration for the elastic stretch, the crystal orientations, and the model internal variables, (3) implementing the model in the NEML2 constitutive modeling framework, based on PyTorch, to vectorize the calculations and port the computation to GPUs and other hardware accelerators, and (4) an exact implementation of the consistent tangent matrix, even for arbitrary coupling to other field variables beyond the displacements, like temperature, neutron fluence, etc. The first two features of the model are, to our knowledge, novel. The paper considers each of these choices individually as well as the final model as a whole. This includes a full description of modified Rodrigues parameters, their advantages over other representations of orientations, the mathematical formulae and tools required to implement a model with modified Rodrigues parameters, and a detailed description of the geometry of the space of modified Rodrigues parameters (in an appendix). It also includes a description of a fully implicit time integration scheme for the orientations and the advantages in representing orientations with modified Rodrigues parameters in implementing such a model. The work then assess, via numerical examples, the advantages of fully coupled implicit time integration versus more common decoupled and explicit time integration schemes. These studies demonstrate the computational advantages of fully coupled integration versus other time integration algorithms, though the performance of the competing models depends on the complexity of the underlying single crystal model. The study concludes by demonstrating that the choice of time integration method affects the sharpness of the predicted texture, with explicit methods for integrating the orientations overestimating texture sharpness and implicit methods underestimating texture sharpness.
Crystal plasticity↗
High dopant activation in arsenic doped single-crystal CdTe thin films: Insights from MBE growth and rapid thermal processing
Single-crystal model systems are valuable tools to investigate fundamental material properties. In this work, we use molecular beam epitaxy to deposit in situ arsenic (As) doped single-crystal CdTe films on large area Si substrates to better understand As doping for photovoltaic applications. We found that As incorporation is highly temperature dependent: a substrate temperature difference of 50 °C can lead to several orders of magnitude difference in As concentration. Cd overpressure during in situ doping may limit out-diffusion of As but decrease As incorporation, especially at lower growth temperatures. Carrier concentrations greater than 10 16 cm −3 can be achieved with or without Cd overpressure when annealed at temperatures above 500 °C. However, unlike the low (∼1% to 5%) dopant activation commonly observed in polycrystalline CdTe, our films achieve significantly higher activation ratios—exceeding 50%, and in some cases approaching 80%. These values are consistent with or exceed prior reports in single-crystal CdTe systems. In addition to as-deposited arsenic concentrations, we also consider arsenic distribution after different rapid thermal processing temperatures. We propose a detailed definition and description of how arsenic incorporation is considered and calculated. Due to carrier concentration saturation, As incorporation also needs to be controlled to average levels of 10 17 cm −3 to achieve high activation. These findings suggest that higher annealing temperature regimes may be beneficial to polycrystalline CdTe based PV devices.
36 MATERIALS SCIENCE↗
Elucidating CO Oxidation Pathways on Rh Atoms and Clusters on the “29” Cu 2 O/Cu(111) Surface
We report single-atom catalysts have attracted a great deal of attention due to their distinct reactivity and potential for cost savings. However, despite the wealth of literature in recent years, identifying the exact nature of the active sites and associated reaction mechanisms remains challenging in many cases. Herein, we take a surface science approach to understand how Rh single atoms and small clusters behave on the thin film “29” Cu 2 O grown on Cu(111). We find that in contrast to Pt, which is present solely as single atoms on the “29” Cu 2 O surface, Rh atoms and clusters coexist and each enable low-temperature CO oxidation, but via different pathways. Specifically, the single Rh atoms produce CO 2 at 444 K via a Mars van Krevelen mechanism whereas the Rh clusters can also dissociate CO, as demonstrated via isotope labeling, and liberate CO 2 at 313 K. Density functional theory (DFT) calculations quantify the energetics of these different pathways and demonstrate that only extended Rh is capable of CO dissociation. Low-temperature scanning tunneling microscopy (STM) reveals that unlike Pt atoms on the same surface, which stay atomically dispersed, the distribution of Rh structures is dependent on pretreatment conditions. DFT calculations reveal the greater tendency of Rh atoms to cluster than Pt, and STM image simulations confirm the active sites. Ambient pressure X-ray photoelectron spectroscopy studies on the same single crystal model systems demonstrate that 1% of a monolayer of Rh on the “29” Cu 2 O thin film significantly accelerates its reduction by CO at 400 K, thus confirming the ultrahigh vacuum surface science findings. Together, these results illustrate how well-defined single crystal experiments are useful in building structure–function relationships that elucidate the reactivity of different ensemble sizes with a level of detail beyond what is possible with high surface area catalysis.
36 MATERIALS SCIENCE↗
An Eulerian crystal plasticity framework for modeling large anisotropic deformations in energetic materials under shocks
Here, this paper demonstrates a novel Eulerian computational framework for modeling anisotropic elastoplastic deformations of organic crystalline energetic materials (EM) under shocks. While Eulerian formulations are advantageous for handling large deformations, constitutive laws in such formulations have been limited to isotropic elastoplastic models, which may not fully capture the shock response of crystalline EM. The present Eulerian framework for high-strain rates, large deformation material dynamics of EM incorporates anisotropic isochoric elasticity via a hypo-elastic constitutive law and visco-plastic single-crystal models. The calculations are validated against atomistic calculations and experimental data and benchmarked against Lagrangian (finite element) crystal plasticity computations for shock-propagation in a monoclinic organic crystal, octahydro-1,3,5,7-tetranitro-1,3,5,7 tetrazocine (β-HMX). The Cauchy stress components and the resolved shear stresses calculated using the present Eulerian approach are shown to be in good agreement with the Lagrangian computations for different crystal orientations. The Eulerian framework is then used for computations of shock-induced inert void collapse in β-HMX to study the effects of crystal orientations on hotspot formation under different loading intensities. The computations show that the hotspot temperature distributions and the collapse profiles are sensitive to the crystal orientations at lower impact velocities (viz., 500 m/s); when the impact velocity is increased to 1000 m/s, the collapse is predominantly hydrodynamic and the role of anisotropy is modest. The present methodology will be useful to simulate energy localization in shocked porous energetic material microstructures and other situations where large deformations of single and polycrystals govern the thermomechanical response.
42 ENGINEERING↗
Revisiting Néel 60 years on: The magnetic anisotropy of L1 0 FeNi (tetrataenite)
The magnetocrystalline anisotropy energy of atomically ordered L1 0 FeNi (the meteoritic mineral tetrataenite) is studied within a first-principles electronic structure framework. Two compositions are examined: equiatomic Fe 0.5 Ni 0.5 and an Fe-rich composition, Fe 0.56 Ni 0.44 . It is confirmed that, for the single crystals modeled in this work, the leading-order anisotropy coefficient K 1 dominates the higher-order coefficients K 2 and K 3 . To enable comparison with experiment, the effects of both imperfect atomic long-range order and finite temperature are included. While our computational results initially appear to undershoot the measured experimental values for this system, careful scrutiny of the original analysis due to Néel et al. [J. Appl. Phys. 35, 873 (1964)] suggests that our computed value of K 1 is, in fact, consistent with experimental values, and that the noted discrepancy has its origins in the nanoscale polycrystalline, multivariant nature of experimental samples, that yields much larger values of K 2 and K 3 than expected a priori. These results provide fresh insight into the existing discrepancies in the literature regarding the value of tetrataenite’s uniaxial magnetocrystalline anisotropy in both natural and synthetic samples.
36 MATERIALS SCIENCE↗
Three-dimensional modeling and simulations of single-crystal and bi-crystal titanium for high-strain-rate loading conditions
High purity single crystal titanium (Ti) under shock wave loading is modeled under both one-dimensional and three-dimensional cylindrical conditions. Cylinder sizes of 10 μm and 20 μm radius are both considered in order to assess influence of boundary conditions. A thermodynamically consistent single crystal model for application to shock conditions is presented. The model accounts for the coupled non-linear elastic, dislocation slip, deformation twinning, and structural phase transformation response of the titanium material. Plate impact experiment results using a copper flyer are used to compare against the simulations for crystals oriented in [0001] and [10$\overline1$1] crystallographic directions. The one-dimensional and threedimensional simulations of the two differently oriented single crystals indicate differences between the one-dimensional and three-dimensional representation, especially for the [10$\overline1$1] oriented single crystal. This orientation breaks the relative orientation symmetry between the crystal and cylinder which otherwise exists for the [0001] oriented single crystal. A significant amount of heterogeneity in the field response of the[10$\overline1$1] oriented simulation was demonstrated due to the highly coupled nature of the deformation. A bi-crystal model composed of both the [0001] and [10$\overline1$1] orientations with the boundary between the two along the axis of the cylinder is also considered for a cylinder model size of 10 μm. The results indicate a strong interaction between the two grains that affects the ω phase volume fraction achieved relative to the single crystal calculations.
36 MATERIALS SCIENCE↗
A crystal-plasticity-informed Gaussian Process Regression model to capture anisotropy in single crystal shape memory alloys
This work presents a machine learning (ML) framework that model the anisotropic actuation responses in a shape memory alloy. A Gaussian Process Regression (GPR) based ML model is trained on a set of different crystal orientations subjected to different actuation conditions. The training employed thermo-mechanical responses from a crystal-plasticity model that captures phase-transformation, stress-induced plasticity, and transformation-induced plasticity. Further, on training the GPR-ML model at fixed stress level for different orientations, it captured the thermo-mechanical responses accounting for the anisotropy, and predicted responses for new orientations with good accuracy. The GPR-ML model is able to capture the transformation temperature variations even when trained using multiple stress levels, and the transformation strain showed significant deviations. The developed GPR-ML model gave reasonable predictions for an unexplored sample set of orientations and loading conditions.
36 MATERIALS SCIENCE↗
Cluster dynamics modeling of irradiation growth in single crystal Zr
Irradiation growth of single-crystal Zr is modeled with a reduced set of cluster dynamics equations. Nucleation and growth of basal and prismatic dislocation loops are both accounted for in the model. Equations are developed for the time evolution of single point defects, a limited number of point defect clusters, interstitial and vacancy loop nucleation rates, as well as for the growth of vacancy loops on basal planes and interstitial loops on prismatic planes. Reduction of the usual infinite hierarchy of cluster dynamics equations to the simple set studied here is justified on the physical basis of the stability of small loops once nucleated. This simplified cluster dynamics model with a small number of adjustable parameters avoids the complexity of explicit representation of higher order point defect clusters. The model shows consistency with experimental observations of the following aspects: (1) the growth rates of Zr crystals along the a- and c-axes; (2) the onset dose for breakaway irradiation growth; (3) the saturation dislocation loop densities of vacancy and interstitial loops; (4) the effects of cold work and temperature on irradiation growth.
36 MATERIALS SCIENCE↗
Effect of Laser Beam Profile on Rotating Lattice Single Crystal Growth in Sb2S3 Model Glass
Laser heating of chalcogenide glasses has successfully produced rotating lattice single crystals through a solid-solid transformation. To better understand the nature of complex, orientation-dependent lattice rotation, we designed heat profiles of the continuous wave laser by beam shaping, fabricated larger Sb2S3 crystal dots in Sb2S3 glass, and investigated the lattice rotation where the crystal could grow in all radial directions under a circular thermal gradient. The results show that the rate of lattice rotation is highly anisotropic and depends on crystallographic direction. The nature of this rotation is the same in crystals of different orientation relative to the surface. The growth directions that align with the slip planes show the highest rate of rotation and the rotation rate gradually decreases away from this direction. Additionally, the presence of multiple growth directions results in a complicated rotation system. We suggest that the growth front influences the density of dislocations introduced during growth under confinement and thus affects the lattice rotation rate in these crystals.
36 MATERIALS SCIENCE↗
Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue
Abstract Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J 2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J 2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J -integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.
36 MATERIALS SCIENCE↗
Acidities of MgO surface sites: implications for the formation mechanism of Mg(OH) 2
The hydroxylation of periclase (MgO) to brucite (Mg(OH) 2 ) is thought to be an important intermediate step when using MgO to capture CO 2 from the atmosphere. However, the mechanism of hydroxylation of MgO to form Mg(OH) 2 is poorly understood. In this work, we used atomic-scale density functional tight binding simulations coupled with the metadynamics rare event method to analyze the surface chemistry of MgO and the acid dissociation equilibrium constants (pK a ) of its surface sites. The method and parameters were validated by calculating the pK a for hydroxylation of the first shell water bound to aqueous Mg 2+ ion. The pK a value derived using a probabilistic method was 12.3, which is in fair agreement with the accepted value of 11.4, with the difference between them equal to a ∼5 kJ mol −1 error in the calculations. We then extended these pK a calculations to probe the hydroxylation reactions of the surface sites of the MgO(100)–water interface, arriving at pK a s of 5.4 to deprotonate terminal water molecules bound to the surface magnesium sites (η-OH 2 or 〉MgOH 2 ), and 13.9 to deprotonate hydroxylated bridging oxygen sites (μ 5 -oxo or 〉O). Hydroxide (OH − ) adsorption on the surface was also probed and found to be less thermodynamically favorable than deprotonation of the terminal water molecule. The plausibility of the computed pK a s was verified using an activity-based speciation model and compared to pH measurements of water equilibrated with MgO nanoparticles and single crystals. The model predicted a solution pH of 7.1 when surface sites buffered and the pH of 12.0 when MgO dissolution dominated. These are close to the experimental initial solution pHs of 7–7.5 and the long term pHs of ∼10.5. The similarity suggests that the calculated pK a values from the DFTB+/metadynamics simulations are plausible and that these methods can be a useful tool to probe reaction mechanisms involving covalent bonds.
Adapa, Sai Krishna Reddy [Oak Ridge National Labor↗