Distribution Of Grain Orientations Research Articles

Recognition of ancient carbonate wind deposits: lessons from a modern analogue, Chrissi Island, Crete

AbstractCarbonate aeolian deposits are common along arid to semiarid, wind‐exposed, present‐day coastlines bordered by productive carbonate ramps. Lithified carbonate dunes (aeolianites) have been described around the world in marine terraces of Quaternary age, but these deposits have seldom been identified in the Pre‐Quaternary record. Several authors have suggested that this scarcity reflects that these deposits form and are preserved only during icehouse periods characterized by high‐amplitude sea‐level changes. Others [e.g. McKee and Ward Carbonate Depositional Environments (1983), AAPG Memoirs, Vol. 33, pp. 131–170] suggest that the scarcity of aeolianites in the Pre‐Quaternary record could reflect the ‘great difficulty in recognising wind blown carbonate deposits and in differentiating between them [aeolianites] and other carbonate sands of nearshore environments’. It has been considered that carbonate shoreface/foreshore deposits are very difficult to discriminate petrographically from backshore deposits. This petrographic study of recent sediments from the shoreface to backshore along the northern coast of Chrissi Island, Crete, confirms that carbonate aeolian sands can be very easily misinterpreted as shoreface deposits. Textural examination of thin sections by image analysis techniques indicates, however, that grain orientation patterns differ between facies. Shoreface deposits exhibit a unimodal distribution of grain orientation (flat rose diagram), whereas backshore deposits show a tendency towards a bimodal distribution with a significant proportion of vertical grains. This observation has been confirmed in Pleistocene aeolianites from Tunisia and Western Australia. Grain verticality thus seems to be a reliable criterion for discriminating wind‐lain carbonate bodies from shoreface deposits. Vertical grains in aeolian carbonate deposits could reflect gravity effects (e.g. reorientation of grains because of meteoric water percolation and air pull‐up). Laboratory experiments conducted on carbonate sands under the action of percolating waters confirm this hypothesis. This reorganization process is preferentially developed in recently deposited and loosely packed sands resulting from grainfall and/or grainflow. In addition, this suggests that the presence of vertical grain orientation might be an indicator of the frequency and intensity of rainfalls during deposition.

Numerical homogenization of nonlinear viscoplastic two-dimensional polycrystals

In this article, we numerically determine the effective stress-strain relation of some two-dimensional polycrystals. These are aggregates of a few tens of perfectly bonded single-crystal (hexagonal atomic lattice) grains, with varying orientations. Each grain obeys a given nonlinear viscoplastic stress-strain relation, which depends on the orientation of the grain. Precise calculations performed with this microscopic model are compared with calculations done with a macroscopic approximate model (in which matter has no microstructure) in order to determine the macroscopic constitutive law. We find an effective behaviour for the stationary response which appears to be also consistent for the transient response. The influence of the number of grains as well as that of the distribution of grain orientations are investigated.

Evolution of matt surface topography in aluminium pack rolling. Part I: model development

Roughening of the matt surface of pack rolled aluminium foil has been modelled. The model is based on the finite element method using isotropic plasticity. A distribution in material properties has been used to simulate the distribution of grain orientations through the material. It is found that the formation of shear bands causes roughening of the matt surface. The length of these shear bands allows individual grains or the hard roll to influence the roughness a significant distance away. Results show the effect of the ratio of the grain size to the strip thickness on the predicted roughness generated. The predictions show good qualitative agreement with the reported experiments. It is concluded that the model is able to simulate efficiently the effect of the granular behaviour of polycrystals on the matt surface roughness.

Statistically representative three-dimensional microstructures based on orthogonal observation sections

Techniques are described that have been used to create a statistically representative three-dimensional model microstructure for input into computer simulations using the geometric and crystallographic observations from two orthogonal sections through an aluminum polycrystal. Orientation maps collected on the observation planes are used to characterize the sizes, shapes, and orientations of grains. Using a voxel-based tessellation technique, a microstructure is generated with grains whose size and shape are constructed to conform to those measured experimentally. Orientations are then overlaid on the grain structure such that distribution of grain orientations and the nearest-neighbor relationships, specified by the distribution of relative misorientations across grain boundaries, match the experimentally measured distributions. The techniques are applicable to polycrystalline materials with sufficiently compact grain shapes and can also be used to controllably generate a wide variety of hypothetical microstructures for initial states in computer simulations.

Birefringence and Depolarized Light Scattering from Ordered Block Copolymers with Anisotropic Distributions of Grain Orientations Produced by Shear Flow

We have observed birefringence and depolarized light scattering patterns with 2-fold symmetry from a cylindrical diblock copolymer solution that was ordered under shear flow. We have developed a theory to account for such 2-fold symmetric scattering patterns, based on a model that assumes an anisotropic orientation distribution of ellipsoidal grains in the sample. We also show how scattering patterns can be approximately reduced to the sum of three terms of the form Cn(θ) cos(nφ), where θ and φ are polar angles in the detection plane and n = 0, 2, and 4. By comparing the experimentally determined Cn(θ) functions with theoretical calculations, we estimated the fraction of the sample that is composed of misaligned grains, their size and eccentricity, and the angular range over which their optic axes were distributed (Δϑ). The analysis of the optical properties of these kinds of systems is complicated by the fact that the signal from misaligned grains diminishes extremely rapidly as Δϑ decreases.

Optical propagation loss of ZnO films grown on sapphire

Optical propagation losses from ZnO thin films grown on c-cut sapphire were measured for 632.8 nm light using prism coupling and a charge coupled device detection method. Propagation losses varied according to growth temperature and growth rate. No relationship between the distribution of crystallographic orientation and propagation losses was observed. However, propagation losses were found to be insensitive to changes in the distribution of grain orientations. Neither the depth of surface roughness nor the mean interval of the surface undulations was found to be a dominant factor contributing to the losses. A mean angle of surface roughness, α, is proposed as a parameter to comprehensively characterize both effects. Loss is found to depend on α for propagation of both TE0 and TE1 modes. This demonstrates that the parameter α effectively characterizes surface morphology for optical device applications.

Analysis of surface roughening in AA6111 automotive sheet

The finite element method is used to numerically simulate the topographic development in an aluminium sheet, AA6111, under stretching. The measured electron backscatter diffraction (EBSD) data are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. The effect on surface roughening of sample geometry, strain rate sensitivity, work hardening, imposed deformation path, as well as the EBSD step size, spatial orientation distribution and inhomogeneous deformation within individual grains are discussed. It is concluded that surface roughening is controlled by the spatial distribution of grain orientations through the thickness of the specimen.

Effect of Annealing on Structural Properties of Co Thin Films and Co/Cu Multilayers

The subject of the present investigation is the influence of annealing on the microstructure of Co thin films. In particular, the evolution of the texture during annealing is studied and compared with that of Co/Cu multilayers of different individual layer thicknesses. 400nm thick Co films show a h.c.p. structure with a weak preference of the <001> texture component and a broad distribution of grain orientations. Annealing at about 350°C results in a strong increase of the h.c.p. <001> component, nearly complete disappearance of the statistical distribution and grain growth of a minor f.c.c. fraction in the films. In-situ XRD measurements on single Co films during annealing confirm that the texture change is irreversible. Multilayer stacks of Co/Cu layers show various texture changes depending on the individual layer thickness (ranging between 100nm and 1nm). Generally, with decreasing individual layer thickness and increasing annealing temperature the f.c.c. content in the multilayers increases at the expense of the h.c.p. fraction.

The effective pyroelectric and thermal expansion coefficients of ferroelectric ceramics

We present a micromechanical analysis on the effective pyroelectric and thermal expansion coefficients of ferroelectric ceramics in terms of their microstructural information. The overall behaviors of ferroelectric ceramics are profoundly influenced by the microstructural phenomena, where the macroscopic pyroelectric effect can be induced in an originally isotropic, thus non-pyroelectric ceramic composed of randomly oriented ferroelectric grains through poling, during which the polar axes of grains are switched by the applied electric field or mechanical stress. To analyze these complicated phenomena, we will first establish an exact connection between the effective thermal moduli and the effective electroelastic moduli of ferroelectric ceramics, and then combine the exact connection with the effective medium approximation to provide an estimate on the effective pyroelectric and thermal expansion coefficients of ferroelectric ceramics in terms of the orientation distribution of grains and poling conditions, where the texture evolution as a result of domain switching during poling has been taken into account. Numerical results are presented and good agreements with known theoretical results and some experimental data are observed.

An off-normal fibre-like texture in thin films on single-crystal substrates.

In the context of materials science, texture describes the statistical distribution of grain orientations. It is an important characteristic of the microstructure of polycrystalline films, determining various electrical, magnetic and mechanical properties. Three types of texture component are usually distinguished in thin films: random texture, when grains have no preferred orientation; fibre texture, for which one crystallographic axis of the film is parallel to the substrate normal, while there is a rotational degree of freedom around the fibre axis; and epitaxial alignment (or in-plane texture) on single-crystal substrates, where an in-plane alignment fixes all three axes of the grain with respect to the substrate. Here we report a fourth type of texture--which we call axiotaxy--identified from complex but symmetrical patterns of lines on diffraction pole figures for thin films formed by solid-state reactions. The texture is characterized by the alignment of planes in the film and substrate that share the same d-spacing. This preferred alignment of planes across the interface manifests itself as a fibre texture lying off-normal to the sample surface, with the fibre axis perpendicular to certain planes in the substrate. This texture forms because it results in an interface, which is periodic in one dimension, preserved independently of interfacial curvature. This new type of preferred orientation may be the dominant type of texture for a wide class of materials and crystal structures.

On the development of the <111> fiber texture in nanocrystalline gold during growth and annealing

ABSTRACTThe evolution during growth and subsequent annealing of the <111> fiber texture in magnetron-sputtered nanocrystalline Au films has been studied experimentally using X-ray diffraction with synchrotron radiation. To quantitatively investigate this fiber texture, grain orientation distributions were recorded in situ during growth and during subsequent annealing using Bragg-Brentano geometry. The (111) diffraction intensity was measured as a function of the sample tilt χ, the tilt axis lying at the intersection of the film surface and the scattering plane. As a quantitative measure of the texture, we used the width of the orientation distributions. The grain-orientation distributions narrowed during annealing. The activation energy for the process behind this texture change was found to be 0.64 ± 0.05 eV, close to the activation energy for grain boundary self-diffusion in nanocrystalline Au. This and the narrowing of the grain orientation distributions led us to suggest that the observed changes in texture originated from grain rotations and not from grain growth. Grain growth did not take place at the lower temperatures, where changes in orientation distributions were observed.

Planar Double-Slip Model for Polycrystal Plasticity and Micro Tension Tests of Pure Nickel and Copper

Many natural minerals and manmade materials are aggregates of crystals or polycrystalline solids with a nonrandom distribution of grain orientations. Macroscopic behavior in such textured polycrystals depends on directions and is thus anisotropic. In this paper we develop experimental and theoretical procedures for investigating grain orientation evolution and its effect on the tensile stress-strain curve. The micro-tensile experiments were executed in a self-developed micro-forcing-heating device together with a micro-recorder-image analyzer system. In the experiments the 0.1 mm thin foil specimens of pure nickel and copper were gradually loaded toward final failure and the evolution of grain boundaries and slip bands inside grains was observed and recorded digitally via microscope and CCD camera throughout the whole time history. The texture image data were then used in a theoretical micro-macro transformation procedure to simulate the orientation evolutions and the stress-strain curves. The procedure was based on a double-slip model of polycrystal plasticity and on averaging of polycrystalline behavior over all grain orientations weighted by an orientation distribution function. The comparisons made between the simulated and experimental data of orientation evolutions and between the simulated curves and the macro-curves concurrently obtained in the experiments confirm the proposed procedures capable of simulating the considered micro-macro relations.

Dynamic magnetization observations and reversal mechanisms of sintered and die-upset Nd–Fe–B magnets

In situ TEM magnetizing experiments combined with Lorentz microscopy in Fresnel and Foucault mode were used to study local features of magnetization reversal in polycrystalline sintered and die-upset Nd–Fe–B magnets. The die-upset (DU) magnets featured well-aligned grain texture along the c-axis, while the sintered (SI) magnets have a much wider distribution of grain orientations. Despite the similarity of the hysteresis curves, we found their nanoscale behavior of the magnetization reversal was quite different. The predominant mechanism controlling reversal in DU-magnets was nucleation of reversed domains, preferentially at misaligned grain interfaces, followed by domain wall pinning at grain boundaries. In contrast, magnetization reversal in SI-magnet progressed first by nucleation and expansion of reversed domain dipoles predominantly in misaligned grains at a high magnetic field, and then by the major irreversible process via nucleation and splitting of magnetic domains near the grain boundaries of well-aligned grains at more negative fields. This process is completed with lateral expansion of newly created domain walls. A simple model for the strong pinning–trapping centers observed in DU-magnets is discussed.

Effect of precipitates on plastic anisotropy for polycrystalline aluminum alloys

The effects of crystallographic texture and precipitate distribution on macroscopic anisotropy in aluminum alloys were investigated. In order to simultaneously consider the effects of crystallographic texture and precipitate distribution on macroscopic anisotropy, predictions of plastic properties were carried out using an anisotropic yield function based on the material texture and a combined isotropic-kinematic hardening rule. The input to the model was a single stress-strain curve, the crystallographic texture, and the precipitate volume fraction, shape, and habit planes. It was shown that the kinematic hardening rule, which expresses a translation of the yield surface in stress space, was a function of all the parameters describing the precipitate distribution. The model was applied to the case of an extruded and recrystallized binary Al-3 wt pct Cu alloy deformed in uniaxial compression in different directions. Excellent agreement was observed between the experimental and predicted yield stress anisotropy and the specimen cross section shape anisotropy. Gaussian distributions of grain orientations around ideal texture components typical of aluminum alloys were generated using computer simulations. These textures were combined with the isotropic-kinematic hardening rule determined for the Al-3 wt pct Cu binary alloy to theoretically assess the influence of precipitates on the r-value (the width-to-thickness plastic strain ratio in uniaxial tension) and yield stress anisotropy for aluminum sheets. It was shown that, for these textures, the precipitate distribution had the effect of reducing plastic anisotropy, in agreement with the trends generally observed in practice.

Orientation Distribution of Grain Planes in Polycrystal Ag/Bi-2223 Tape

For polycrystalline Ag/Bi-2223 tapes, the preferential orientation of grains is a very important issue. The platelike grains in the tapes are generally believed in a high-order alignment. However, microstructural observation by SEM shows that the grain alignment is far from perfect. Theoretically, upper critical field, Hc2, for H parallel to ab plane and c axis was calculated form the relation of M(H). However, the ratio of Hc2 (H//ab) to Hc2(H//c) depends on the angle (θ) between the ab plane of grains and the broad surface of the tapes. Based on the ratio, the orientation distribution of grains is obtained. The results show that grains in Ag/Bi-2223 tapes can grow with ab plans at any angle between 75° > θ > −75°, but no grain can grow with its ab plane perpendicular to the tape broad surface. The overall distribution is that: >90% grains orient in the angle range of |θ| ±85°.

Controlling the surface texture of nickel for hightemperature oxidation inhibition

The possibility of controlling the crystallographic texture of a Ni surface to increasethe resistance against high-temperature oxidation is studied. Polycrystalline Ni coatings and foilswith the <, <110> and <211> textures were manufactured using an electrodepositiontechnique. The initial textures and microstructures of Ni were modified using annealing in an inertatmosphere of argon. Textures of a variety of NiO scales grown on the electrodeposits at 1073 Kin air were measured and compared to the textures of the corresponding Ni substrates. It wasfound that NiO grown on as-deposited Ni has a random distribution of grain orientations for alltypes of the substrate textures. When Ni electrodeposits were annealed prior to oxidation, therewas a strong influence of substrate texture on the texture of NiO. In particular, a surfacetreatment composed of the electrodeposition of Ni primer with a strong < texture followed byannealing leads to an Ni layer with a <111> texture and a low density of structural defects.Such a substrate of Ni promotes the formation of epitaxially oriented, slow growing and highlyprotective NiO scales with the <111> texture.

Crystallography and Microstructure of Thin Films Studied by X-Ray and Electron Diffraction

For the characterization of thin films conventional x-ray and electron diffraction techniques have been modified and dedicated new techniques have been developed recently with special emphasis being laid on unattended operation. They enable the accurate measurement of lattice parameters, crystallographic orientations of individual grains, crystal texture, lattice strain and residual stress. The analysis of local crystal texture in particular is required for the understanding, for example, of anisotropic material properties, nucleation, recrystallization, plastic deformation and failure mechanisms. X-ray diffraction is still the standard technique for averaging over macroscopic specimen areas. On a grain-specific scale crystal texture analysis and phase discrimination are mainly performed by electron diffraction involving the SEM or TEM by interpreting backscatter or transmission Kikuchi patterns. Pole figures of small areas are obtained from thin foils in SAD or from bulk surfaces in RHEED mode of the TEM. A graphical representation of spatial distribution of grain orientations, texture, and lattice strain in the specimen surface is obtained with pseudo-color maps.

Crystal plasticity forming limit diagram analysis of rolled aluminum sheets

Numerical simulations of forming limit diagrams (FLDs) are performed based on a rate-sensitive polycrystal plasticity model together with the Marciniak-Kuczynski (M-K) approach. Sheet necking is initiated from an initial imperfection in terms of a narrow band. The deformations inside and outside the band are assumed to be homogeneous, and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the polycrystal model needs only to be applied to two polycrystalline aggregates, one inside and one outside the band. Each grain is modeled as an fcc crystal with 12 distinct slip systems. The response of an aggregate comprised of many grains is based on an elastic-viscoplastic Taylor-type polycrystal model. With this formulation, the effects of initial imperfection intensity and orientation, initial distribution of grain orientations, crystal elasticity, strain-rate sensitivity, single slip hardening, and latent hardening on the FLD can be assessed. The predicted FLDs are compared with experimental data for the following rolled aluminum alloy sheets: AA5754-0-A, AA5754-0-B, AA6111-T4-A, AA6111-T4-C, and AA6111-T4-D.

Micro-Raman Study of Pb(Zr,Ti)O3 Thin Films in Feram

AbstractWe examined the Raman spectra of the tetragonal Pb(Zr, Ti)O3 (PZT) films between FeRAM cells with a micro-Raman apparatus. We found that a Raman light peaked at 600cm−1 polarized linearly perpendicular to the polarization of the exciting light had a different intensity for each of the film.We showed that the difference in the intensities can be explained by the differing distributions of grain orientations in the films. Based on this knowledge, we estimated the volume fraction of 90° domains as well as the average spontaneous polarization of the grains.

Grain Growth in Polycrystalline Thin Films of Semiconductors

Grain growth in thin films is usually abnormal, leading not only to an increase in the average grain size, but also to an evolution in the shape of the grain size distribution and to an evolution in the distribution of grain orientations. The latter can be driven by surface, interface or strain energy minimization, depending on film and substrate properties and on deposition conditions, and can lead to different final textures depending on which energy dominates.