Crystal Lattice Orientation Research Articles

Localization models for the plastic response of polycrystalline materials using the material knowledge systems framework

Crystal plasticity finite element simulations provide physics-based predictions of the plastic response in polycrystalline metals subjected to large plastic strains. Despite their demonstrated high fidelity in a number of applications, these approaches have not yet been adopted broadly by the metal working industry because of their extremely high computational cost. This work develops and applies a novel strategy for reduced-order partitioning of the macroscopically applied plastic stretching tensor on a polycrystalline aggregate to regions within individual grains (i.e. localization of the plastic stretching tensor). This new strategy is seen to provide reasonable predictions for the localized plastic stretching tensors at dramatically reduced computational cost. The strategy presented here extends the prior successes of the materials knowledge system (MKS) framework for the localization of the plastic stretching tensor in composites of two isotropic phases to polycrystalline volumes through the use of the generalized spherical harmonics as a Fourier basis for capturing the functional dependence of the localization kernels on the crystal lattice orientation. It is demonstrated that this extension of the MKS framework is capable of providing good predictions for all components of the second-rank local plastic stretching tensor for any given macroscale imposed plastic stretching tensor with about three to four orders of magnitude savings in the computational cost. This work has the potential to open new research avenues for computationally low-cost, fully coupled, multiscale simulations of plastic deformations in polycrystalline metals.

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

This paper presents a two-step Bayesian framework for the estimation of the intrinsic single crystal elastic stiffness parameters from the measurements of spherical indentation stress-strain responses in multiple individual grains of a polycrystalline sample, whose crystal lattice orientations have been measured using electron back-scattered diffraction technique. The first step requires the establishment of the functional dependence of the indentation elastic modulus given the lattice orientation and the intrinsic single crystal elastic stiffness parameters. Previous efforts for this step required a large database of computationally expensive finite element (FE) simulations in order to establish this function with adequate accuracy. In this paper, it is shown that the introduction of a Bayesian framework can greatly reduce the number of simulations necessary to establish this function, while introducing practically useful measures of uncertainty which can guide the selection of specific additional simulations that are expected to best improve the predictive accuracy of the function. The second step involves a Markov Chain Monte-Carlo (MCMC) sampling of the distribution of possible values for the single crystal elastic stiffness parameters based on a given set of experimentally measured elastic indentation moduli in individual grains of different lattice orientations. This second step is accomplished by calibrating the available experimental data to the function established in the first step. This novel framework is presented and demonstrated in this paper for an as-cast cubic polycrystalline Fe-3% Si sample and a hexagonal polycrystalline commercially pure (CP-Ti) titanium sample.

Bayesian Sequential Design of Experiments for Extraction of Single-Crystal Material Properties from Spherical Indentation Measurements on Polycrystalline Samples

This paper explores a formal strategy for the extraction of single-crystal elastic constants of cubic polycrystalline metals based on the optimal design of spherical indentation experiments. Recent work has formulated the extraction of elastic constants using a two-step protocol. The first step established a surrogate model to capture the dependence of the indentation elastic modulus on the grain (i.e., crystal lattice) orientation and values of single-crystal elastic constants. The second step involved the use of Markov chain Monte Carlo to establish distributions on the elastic constants consistent with experimentally measured indentation moduli in grains of different orientations. The present study refines the second step in order to sequentially identify specific grains that should be indented to provide the most utility in improving the estimated distributions on the elastic constants. The proposed workflow is demonstrated for the extraction of elastic constants for an as-cast cubic polycrystalline Fe-3%-Si sample.

Reconstruction of Grains in Polycrystalline Materials From Incomplete Data Using Laguerre Tessellations.

Far-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries-and, therefore, individual grain shapes-are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.

Structure and Charge Carrier Dynamics in Colloidal PbS Quantum Dot Solids.

The ligand exchange process is a key step in fabrications of quantum dot (QD) optoelectronic devices. In this work, on the basis of grazing incidence X-ray scattering techniques, we find that the ligand exchange process with halide ions changes the PbS QD superlattice from face-centered-cubic to body-centered-cubic stacking, while the QD crystal lattice orientation also changes from preferentially "edge-up" to "corner-up". Thus, the QDs' shape is supposed to be the main factor for the alignment of QDs in close packed solids. Moreover, we tailor the alignment of the close packed solids by thermal treatments and further investigate their inner charge carrier dynamics by pump-probe transient absorption experiments. An overall better structure alignment optimizes the charge carrier hopping rate, as confirmed by the time dependence of the photon bleaching peak shift. The QD solid treated at 100 °C shows the best inner structure alignment with the best charge carrier hopping rate.

Grain‐scale dependency of metamorphic reaction on crystal plastic strain

AbstractThe Breaksea Orthogneiss in Fiordland, New Zealand preserves water‐poor intermediate and mafic igneous rocks that were partially recrystallized to omphacite granulite and eclogite, respectively, at P ≈ 1.8 GPa and T ≈ 850°C. Metamorphic reaction consumed plagioclase and produced grossular‐rich garnet, jadeite‐rich omphacite, clinozoisite and kyanite. The extent of metamorphic reaction, identified by major and trace element composition and microstructural features, is patchy on the grain and outcrop scale. Domains of re‐equilibration coincide with areas that exhibit higher strain suggesting a causal link between crystal plastic strain and metamorphic reaction. Quantitative orientation analysis (EBSD) identifies gradual and stepped changes in crystal lattice orientations of igneous phenocrysts that are surrounded by homophase areas of neoblasts, characterized by high grain boundary to volume ratios and little to no internal lattice distortion. The narrow, peripheral compositional modification of less deformed garnet and omphacite phenocrysts reflects limited lattice diffusion in areas that lacked three‐dimensional networks of interconnected low‐angle boundaries. Low‐angle boundaries acted as elemental pathways (pipe diffusion) that enhanced in‐grain element diffusion. The scale of pipe diffusion is pronounced in garnet relatively to clinopyroxene. Strain‐induced mineral transformation largely controlled the extent of high‐T metamorphic reaction under relatively fluid‐poor conditions.

Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields

Since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.

Investigation of crystallographic textures in multi-level models for polycrystalline deformation using clustering techniques

The feasibility of applying clustering techniques to describe and investigate crystallographic textures by using numerical results simulated for crystallite (grain, subgrain) lattice orientations with the help of multi-level crystal elasto-visco-plasticity models is considered. The texture clustering problem is stated as partitioning a given sample of crystal lattice orientations into disjoint subsets of elements which are close to each other in a certain sense. To formalize this concept of closeness, a special pseudo-metric distance taking into account rotational lattice symmetry is introduced in the space of orientations. This distance being induced by the natural Riemann metrics determines the minimal rotation angle between the symmetrically equivalent orientations of the arguments. A heuristic algorithm based on alternating well-known clustering methods is formulated to solve the stated problem. The proposed approach allows identifying, for a polycrystalline aggregate, the regions in the space of orientations with the higher density of elements, as well as evaluating some of their effective characteristics for such regions. The developed procedure includes the following stages: dividing a sample of orientations into layers; clustering by reachability (in the sense of the transitive closure of the closeness criterion being adopted for orientations); the so-called medoid-based clustering; splitting weakly localized clusters. The application of the presented clustering technique is demonstrated by considering simple shear and axial compression textures obtained through modeling the inelastic deformation of a representative volume element for polycrystalline copper. In the examined cases, local one-parameter approximations of a given form are found for the density of distribution of the angles between orientations and medoids (conditional centers) of the related clusters. Also, the statistical significance of these approximations is tested using equiprobable intervals.

Bending and branching of calcite laths in the foliated microstructure of pectinoidean bivalves occurs at coherent crystal lattice orientation

Foliated calcite is widely employed by some important pteriomorph bivalve groups as a construction material. It is made from calcite laths, which are inclined at a low angle to the internal shell surface, although their arrangement is different among the different groups. They are strictly ordered into folia in the anomiids, fully independent in scallops, and display an intermediate arrangement in oysters. Pectinids have particularly narrow laths characterized by their ability to change their growth direction by bending or winding, as well as to bifurcate and polyfurcate. Electron backscatter analysis indicates that the c-axes of laths are at a high, though variable, angle to the growth direction, and that the laths grow preferentially along the projection of an intermediate axis between two a-axes, although they can grow in any intermediate direction. Their main surfaces are not particular crystallographic faces. Analyses done directly on the lath surfaces demonstrate that, during the bending/branching events, all crystallographic axes remain invariant. The growth flexibility of pectinid laths makes them an excellent space-filling material, well suited to level off small irregularities of the shell growth surface. We hypothesize that the exceptional ability of laths to change their direction may be promoted by the mode of growth of biogenic calcite, from a precursor liquid phase induced by organic molecules.

Correlation between heat treatment process parameters, phase composition, texture, and mechanical properties of 12H18N10T stainless steel processed by selective laser melting

The phase composition, texturing degree, oriented stresses and strains of the crystal lattice, the physical and mechanical properties of austenitic steel 12H18N10T (AISI 321) manufactured by selective laser melting (SLM) before and after heat treatment with various temperatures and protective gas composition have been investigated. SLM stainless steel has better mechanical properties, given that the phase volume content is as follows: γ-Fe ∼ 65%, α-Fe ∼20%, NiTi ∼ 5%; the texturing degree equals to T111∼0.70 and the dominant crystal-lattice orientation is (111). Such a phase composition is formed in the steel after annealing at 620 °C in argon. As the temperature rises during the stabilizing annealing process up to 825 °C, the phase transformation γ→α takes place in SLM steel with a change in the phase concentration γ-Fe and α-Fe in the range from 40 to 50%. In the high-temperature intermetallic phase NiTi, dissolution at 825 °C and a multiple rise of the FeO concentration lead to a change in the crystal lattice parameter of the γ-Fe and α-Fe phases and a decrease in the mechanical properties of SLM steel. This study showed that the improvement of mechanical properties was due to the separation of high-temperature intermetallic phase from austenite and an increase in the concentration of iron carbide Fe3C in SLM steel.

A Study of Strain-Driven Nucleation and Extension of Deformed Grain: Phase Field Crystal and Continuum Modeling.

The phase-field-crystal (PFC) method is used to investigate migration of grain boundary dislocation and dynamic of strain-driven nucleation and growth of deformed grain in two dimensions. The simulated results show that the deformed grain nucleates through forming a gap with higher strain energy between the two sub-grain boundaries (SGB) which is split from grain boundary (GB) under applied biaxial strain, and results in the formation of high-density ensembles of cooperative dislocation movement (CDM) that is capable of plastic flow localization (deformed band), which is related to the change of the crystal lattice orientation due to instability of the orientation. The deformed grain stores the strain energy through collective climbing of the dislocation, as well as changing the orientation of the original grain. The deformed grain growth (DGG) is such that the higher strain energy region extends to the lower strain energy region, and its area increase is proportional to the time square. The rule of the time square of the DGG can also be deduced by establishing the dynamic equation of the dislocation of the strain-driven SGB. The copper metal is taken as an example of the calculation, and the obtained result is a good agreement with that of the experiment.

Modeling twinning-induced lattice reorientation and slip-in-twin deformation

The deformation behavior of hexagonal close packed (hcp) materials involves dislocation slip as well as deformation twinning, including a competition between those two. This is due to the limited number of easy to activate slip modes. We present a model that captures dislocation slip, dislocation interaction, size-dependent hardening and deformation twinning. It also accounts for the sudden change of the crystal lattice orientation at the very final stage of the twinning shear process which allows to describe dislocation glide deformation within a twinned region. Along with this, the model further considers the change in the elastic properties associated with the new lattice orientation. Finite element results are presented for the specific example of magnesium (Mg) and for different characteristic loading conditions in order to mimic local stress distributions as they occur in different regions within a single crystal or grain, e.g., close to a boundary and far off. In addition, the impact of twinning on the mechanical response of Mg single crystal during microcompression is investigated. We show that the suggested model is well capable of predicting the complex microstructural deformation behavior in Mg and compare our numerical results to experimental data.

A micromechanical framework and modified self-consistent homogenization scheme for the thermoelasticity of porous bonded-particle assemblies

Thermoelasticity of porous bonded-particle assemblies is modeled within a micromechanical framework that considers damage at the inter-particle interfaces. Connections between void space and interface damage are developed and incorporated into a modified self-consistent homogenization (M-SCH) scheme that includes a contribution to the mean strain field from local displacement discontinuities over interfacial void spaces. The M-SCH scheme is developed for particles of a general ellipsoidal shape with anisotropic elastic and thermal expansion properties. Two types of porosity are distinguished: (1) dispersed inter-particle porosity and (2) isolated porosity. A means of separating out the relative contributions of each type of porosity to the homogenization scheme is provided, and an explicit expression is obtained for an effective damaged interphase thickness as a function of the dispersed porosity and the particle morphology. Numerical examples are provided for quartz bonded-particle assemblies in order to examine the influence of the porosity type on the predicted elastic moduli. The model is also calibrated to the neutron diffraction measurements provided by Yeager et al. (2016) of triclinic TATB crystal lattice orientation (texture) and lattice strain induced under thermal loading. The model simulations of lattice strain are compared with the measurements, and the predicted statistical distributions of inter-particle displacement discontinuities and contact tractions within the assembly are examined.

From capacitance-controlled to diffusion-controlled electrochromism in one-dimensional shape-tailored tungsten oxide nanocrystals

The engineering of electrochemically active films based on structurally and geometrically controlled transition-metal oxide nanocrystals holds promise for the development of a new generation of energy-efficient dynamic windows that may enable a spectrally selective control of sunlight transmission over the near-infrared regime. Herein, the different spectro-electrochemical signatures of two sets of engineered nanotextured electrodes made of distinct anisotropic-shaped tungsten oxide building blocks are comparatively investigated. The electrodes were fabricated starting from corresponding one-dimensional colloidal nanocrystals, namely solid and longitudinally carved nanorods, respectively, which featured identical crystal phase and lattice orientation, but exposed two distinct space-filled volume structures with subtly different lattice parameters and nonequivalent types of accessible surfaces. The shape of nanocrystalline building blocks greatly impacted on the fundamental electrochemical charge-storage mechanisms and, hence on the electrochromic response of these electrodes, due to concomitant bulk and surface-structure effects that could not be entirely traced to mere differences in surface-to-volume ratio. Electrodes made of carved nanorods accommodated more than 80% of the total charge through surface-capacitance mechanisms. This unique prerogative was ultimately demonstrated to enable an outstanding spectral selectivity as well as an extremely efficient dynamic modulation of the optical transmittance at near-infrared frequencies (~ 80% in the range 700–1600nm).

Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals

In this paper, we demonstrate the first application of a recently formulated two-step approach to the estimation of the average slip resistance in a cubic polycrystalline metal sample from a collection of spherical nanoindentation and lattice orientation measurements. In the first step, a crystal plasticity finite element model of the spherical nanoindentation experiment is developed, validated, and employed to capture the functional dependence of the indentation yield strength on the crystal lattice orientation at the indentation site. This functional dependence is captured in a compact representation using surface spherical harmonics (SSH) functions. In the second step, measured values of the indentation yield strength and the crystal lattice orientations at the indentation site from a polycrystalline sample are fit to the function established in the first step to provide a robust estimate for the value of the average slip resistance in the sample. The validity of this approach is demonstrated for cast and annealed Fe-3% Si using measurements published in prior literature.

Tuning the Electronic Bandgap: An Efficient Way To Improve the Electrocatalytic Activity of Carbon-Supported Co3 O4 Nanocrystals for Oxygen Reduction Reactions.

The achievement of crystal-lattice tuning along low Miller index planes to decrease the bandgap of spinel transition-metal oxides may be an effective way to enhance their electrocatalytic activity for the oxygen reduction reaction (ORR). Herein, we have prepared spherical Co3 O4 nanoparticles with a preferred orientation along the (111) plane by direct nucleation and growth of the oxide on graphitized carbon black (GCB). The formation of the preferred (111) oxide is attributed to a unique chemical interaction at the interface between Co3 O4 and carbon, which results in covalent C-O-Co bonds in the hybrid. Electrocatalysis experiments in an alkaline environment revealed that the electrocatalytic activity for ORR on the preferred (111) oxide increased as a function of the degree of crystal-lattice orientation, which implies a closely intrinsic correlation between the predominant (111) plane and the catalytic activity. Because Co2+ cations are enriched in this plane, they possess a narrow bandgap and unfilled conduction bands at low energy with respect to Co3+ ions in the preferred (111) Co3 O4 , which can contribute to the absorption and activation of active oxygen and lead to improved ORR activity.

Correlation of Thermally Induced Pores with Microstructural Features Using High Energy X-rays

Combined application of a near-field High Energy Diffraction Microscopy measurement of crystal lattice orientation fields and a tomographic measurement of pore distributions in a sintered nickel-based superalloy sample allows pore locations to be correlated with microstructural features. Measurements were carried out at the Advanced Photon Source beamline 1-ID using an X-ray energy of 65 keV for each of the measurement modes. The nickel superalloy sample was prepared in such a way as to generate significant thermally induced porosity. A three-dimensionally resolved orientation map is directly overlaid with the tomographically determined pore map through a careful registration procedure. The data are shown to reliably reproduce the expected correlations between specific microstructural features (triple lines and quadruple nodes) and pore positions. With the statistics afforded by the 3D data set, we conclude that within statistical limits, pore formation does not depend on the relative orientations of the grains. The experimental procedures and analysis tools illustrated are being applied to a variety of materials problems in which local heterogeneities can affect materials properties.

Shock induced damage in copper: A before and after, three-dimensional study

We report on the microstructural features associated with the formation of incipient spall and damage in a fully recrystallized, high purity copper sample. Before and after ballistic shock loading, approximately 0.8 mm3 of the sample's crystal lattice orientation field is mapped using non-destructive near-field High Energy Diffraction Microscopy. Absorption contrast tomography is used to image voids after loading. This non-destructive interrogation of damage initiation allows for novel characterization of spall points vis-a-vis microstructural features and a fully 3D examination of microstructural topology and its influence on incipient damage. The spalled region is registered with and mapped back onto the pre-shock orientation field. As expected, the great majority of voids occur at grain boundaries and higher order microstructural features; however, we find no statistical preference for particular grain boundary types. The damaged region contains a large volume of Σ–3 (60°〈111〉) connected domains with a large area fraction of incoherent Σ-3 boundaries.

Influence of titanium and magnesium nanoinclusions on the strength of aluminum at high-rate tension: Molecular dynamics simulations

With the use of the molecular dynamics simulations, by an example of Ti and Mg inclusions in Al matrix, we consider two different mechanisms of reduction of the tensile strength of a material with inclusions in comparison with a pure material of matrix. The first mechanism is connected with a stress concentration in matrix near a stiff and strong inclusion (Ti); in this case, the fracture occurs inside the matrix and does not touch the inclusion. The second mechanism acts in the case of a soft and weak inclusion (Mg); the fracture begins inside the inclusion and thereafter propagates into the matrix. The strength of the considered systems weakly depends on the orientation of crystal lattice of inclusions relative to the tension direction. The tensile strength of Al+Ti and Al+Mg systems is determined at varied strain rates (in the range from 0.1/ns to 30/ns at the temperature 300K) and varied temperatures (in the range from 300K to 900K at the strain rate 1/ns). The rate sensitivity of strength of a material with inclusions is higher than that for a material without inclusions. Temperature dependences of tensile strength are qualitatively different for the systems Al+Ti and Al+Mg; this fact is explained by the difference in the mechanisms of the material weakening.

Orientation-dependent plasma etch rates of single crystal silicon for dry etcher parts

Abstract We have evaluated the orientation dependence of plasma etch rates for single crystal silicon using SF6/Ar and CF4/Ar/O2 chemical gases in an inductively coupled plasma dry etcher. Etch rates for different crystal orientations having various surface conditions were measured. The results indicate that the <111> crystal lattice orientation is etched at a lower rate than the <100> orientation. The dependence of the silicon etch rate on the crystal orientation is derived from differences in the local neighborhood of the exposed surface atoms, such as number of neighbors, dangling bond, and surface bond. Finishing the silicon parts with mirror-finish polishing results in surfaces with a very thin subsurface damage layer that exhibits a lower plasma etch rate. This compares to the much thicker damage layer caused by abrasive machining of the surface during grinding steps, and to the portion of this that remains after polishing.