Lattice Misorientation Research Articles

An EBSD Study of the Deformation of Service-Aged 316 Austenitic Steel

Electron backscatter diffraction (EBSD) has been used to examine the plastic deformation of an ex-service 316 austenitic stainless steel at 297 K and 823 K (24 °C and 550 °C) at strain rates from 3.5 × 10−3 to 4 × 10−7 s−1. The distribution of local misorientations was found to depend on the imposed plastic strain following a lognormal distribution at true strains <0.1 and a gamma distribution at strains >0.1. At 823 K (550 °C), the distribution of misorientations depended on the applied strain rate. The evolution of lattice misorientations with increasing plastic strain of up to 0.23 was quantified using the metrics kernel average misorientation, average intragrain misorientation, and low angle misorientation fraction. For strain rate down to 10−5 s−1, all metrics were insensitive to deformation temperature, mode (tension vs compression), and orientation of the measurement plane. The strain sensitivity of the different metrics was found to depend on the misorientation ranges considered in their calculation. A simple new metric, proportion of undeformed grains, is proposed for assessing strain in both the aged and unaged materials. Lattice misorientations develop with strain faster in aged steel than in unaged material, and most of the metrics were sensitive to the effects of thermal aging. Ignoring aging effects leads to significant overestimation of the strains around welds. The EBSD results were compared with nanohardness measurements, and good agreement was established between the two techniques of assessing plastic strain in aged 316 steel.

3D diffraction imaging and orientation mapping in deformed ice crystals

A method to acquire three dimensional diffraction data and orientation mapping with the 2D imaging setup of Hasylab beamline G3 is presented. The method has been successfully applied to undeformed large grains extracted from ice samples and extended to the 2D determination of lattice misorientation and lattice orientation distribution within deformed grains.

A neutron diffraction study of lattice distortion, mismatch and misorientation in a single-crystal superalloy after different heat treatments

Two-dimensional neutron diffraction measurements of superlattice and fundamental lattice reflections from a single-crystal superalloy confirm the existence of angular distortion and shear stress in the γ′ phase, and reveal its correlation with the morphology and deformation of the γ′ phase during heat treatment. The tetragonal distortions with c/a>1 are developed and retained during subsequent heat treatments, whereas the angular distortions are enhanced for the γ′ phase during the aging treatments. The evolution of the lattice mismatch and anisotropy during the subsequent heat treatments are consistent with the transformation of certain macroscopic anisotropic compositional and stress distributions in the as-cast sample to the microscopic level at the γ/γ′-interface upon reprecipitation and the growth of the γ′ from the supersaturated γ-matrix. The high negative γ/γ′ lattice mismatch of the alloy is consistent with the high levels of refractory elements, in particular Cr, in the alloy. Comparison between superlattice and fundamental lattice reflections is revealing. Firstly, the existence of lattice misorientation at the γ/γ′-interface and the discrete misorientations from the splitting of coherently aligned aggregates of γ′-precipitates on the smoothly distributed γ -matrix is shown. Secondly, the measured lattice misorientation correlates with the spacing of dislocations at the γ/γ′-interface and evidenced by the transmission electron microscopy observation. Furthermore, it indicates the anisotropic distribution of dendrites along crystal growth axis and the presence of small misoriented higher-order dendrite arms in variously heat-treated samples.

Crystal splitting and enhanced photocatalytic behavior of TiO2rutile nano-belts induced by dislocations

Crystal splitting and enhanced photocatalytic activities caused by implied dislocations were observed in hierarchical TiO(2) nano-architectures prepared by one-pot hydrothermal synthesis in concentrated HCl. Microstructural observation revealed that the nanowires formed by continuous splitting of TiO(2) nano-belts, which is caused by a lattice misorientation of about 6°, were generated by an array of dislocations. In addition, the larger amount of dislocations implied in TiO(2) nano-architectures induces higher photocatalytic activities under ultra-violet illumination.

The relative grain boundary area and energy distributions in a ferritic steel determined from three-dimensional electron backscatter diffraction maps

The relative grain boundary area and energy distributions of a ferritic steel were characterized as a function of lattice misorientation and boundary plane orientation using focused ion beam serial sectioning combined with electron backscatter diffraction. The grain boundary energy and population depended on both the grain boundary plane orientation and lattice misorientation. When misorientation was ignored grain boundary planes with the (111) orientation had the minimum energy and the largest relative areas. The most commonly observed boundaries were {112} symmetric tilt boundaries with the Σ3 misorientation; this boundary also had a low energy. On average there was a strong inverse correlation between the relative areas of different types of grain boundaries and the relative grain boundary energies.

The Distribution of Grain Boundary Planes in Interstitial Free Steel

The grain boundary character distribution in a commercial IF steel has been measured as a function of lattice misorientation and boundary plane orientation. The grain boundary plane distribution revealed a relatively low anisotropy with a tendency for grain boundaries to terminate on low index planes having relatively low surface energy and large interplanar spacings. Although the most common grain boundary plane orientation was (111), grain boundaries terminated on higher index planes were sometimes found. For instance, at a misorientation angle of 60 deg about [111], symmetric {112} tilt boundaries were far more populous than [111] twist boundaries. The current observation revealed an inverse relationship between the measured populations and the previously reported grain boundary energies.

Effects of heterogeneous elasticity coupled to plasticity on stresses and lattice rotations in bicrystals: A Field Dislocation Mechanics viewpoint

Abstract In the present paper, the static Field Dislocation Mechanics (FDM) theory is first recalled and next formulated for heterogeneous elasticity and plasticity with respect to a reference homogeneous medium. The issue of an infinite bicrystal with planar boundary undergoing piecewise uniform plastic distortions and elastic properties is then considered. The static FDM theory is accordingly used to derive explicit closed-form solutions of stress and lattice misorientation fields in the general context of heterogeneous anisotropic elasticity. These expressions are validated by Crystal Plasticity Finite Element simulations performed on a bicrystal with periodic boundary conditions. As a result of analytical expressions, it is possible to quantify the contribution of the different incompatibility sources, namely the contribution arising from elastic incompatibilities alone, that due to plastic incompatibilities alone and the one due to couplings between elastic and plastic incompatibilities. Besides, residual stresses and lattice misorientations are accordingly calculated in elastic/plastic bicrystals for different orientations of the elastic crystal. Results are compared with the corresponding homogeneous isotropic elasticity approximation. It is shown that elastic–plastic coupling incompatibilities may have consequent effects on residual stresses and lattice misorientations depending on the degree of elastic anisotropy of the material and the relative orientation of both crystals. As a conclusion, the consideration of coupling incompatibilities in multiscale plasticity models when predicting internal stresses and texture developments is discussed.

Doping-Induced Lattice Mismatch and Misorientation in 4H-SiC Crystals

The c- and a-lattice constants of nitrogen-doped 4H-SiC were measured in the wide temperature range (RT - 1100°C). The samples used in this study were heavily doped substrates and lightly-doped free-standing epilayers. The lattice constants at room temperature are almost identical for all the samples. However, the lattice contraction by heavy nitrogen doping was clearly observed at high temperatures, which indicates that the thermal expansion coefficients are dependent on the nitrogen concentration. The lattice mismatch (Δd/d) between a lightly-doped free-standing epilayer (Nd = 6x1014 cm-3) and a heavily-doped substrate (Nd = 2x1019 cm-3) was calculated as 1.7x10-4 at 1100°C. The authors also investigated lattice constants of high-dose N+, P+, and Al+-implanted 4H-SiC. Reciprocal space mapping (RSM) was utilized to investigate the lattice mismatch and misorientation. The RSM images show the c-lattice expansion and c-axis tilt of the ion-implanted layers, irrespective of ion species. The authors conclude that the lattice expansion is not caused by heavy doping itself, but by secondary defects formed after the ion-implantation and activation-annealing process.

Predictive Theory for the Grain Boundary Character Distribution

Mesoscale experiment and simulation permit harvesting information about both geometric featuresand texture in material microstructures. The grain boundary character distribution (GBCD) is an em-pirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misori-entation and grain boundary normal. During the growth process, an initially random texture distribu-tion reaches a steady state that is strongly correlated to the interfacial energy density [9]. In simulation,it is found that if the given energy depends only on lattice misorientation, then the steady state GBCDand the energy are related by a Boltzmann distribution. This is among the simplest non-random dis-tributions, corresponding to independent trials with respect to the energy. Why does such a simpledistribution arise from such a complex system?.

Synthesizing Annealing Twins in Three-Dimensional Voxel-Based Microstructures

The five-parameter grain boundary character distribution (GBCD) of a material contains both the grain boundary plane orientation and the lattice misorientation information. This work focuses on generating three-dimensional microstructures that match the full five-parameter GBCD obtained from experimentally observed microstructures. In face-centered cubic metals, the density of high symmetry boundaries is often maximized in order to improve grain boundary dependent properties, such as the resistance to intergranular corrosion and fatigue cracking. Twinning events have been found to be very effective in introducing these high symmetry boundaries that are denoted by low sigma values for Coincident Site Lattice relationships. Therefore, in this investigation, microstructures that contain annealing twins are of particular interest. The statistics that are used to quantify the differences between the synthetic and experimentally observed structures are texture or orientation distribution (OD), GBCD, number and area fractions of S3 and coherent S3 boundaries, S3 cluster distribution, and twin density.

High-energy transmission Laue micro-beam X-ray diffraction: a probe for intra-granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern-matching approach. The results highlight the inability of a simple Schmid-factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.

Correlation between SEM and X-Ray Diffraction Imaging of Defect Structure in Single-Crystal Ni-Based Superalloy

In the work the single-crystalline alloy CMSX-4 was studied. The main aim of the study was an attempt to find correlations between images of X-Ray topography, X-ray diffraction maps of lattice parameter and misorientation angle and Scanning Electron Microscopy (SEM) images obtained by back-scattered electron (BSE) technique. Topography images were obtained by Auleytner method with wide beam. Diffractometer provided by EFG company was used for obtaining orientation and lattice parameter maps. Material for research was produced in Research and Development Laboratory for Aerospace Materials of Rzeszów University of Technology. Casts were obtained in ALD furnace by the Bridgman technique. It was found that X-ray topograms were correlated with SEM images of microstructures as well as with orientation and lattice parameter maps. X-Ray topograms showed high contrast bands which corresponded to dendrite arms. There was a correlation between low angle boundary and lattice parameter map.

Grain Boundary Analysis of Crept Alloy 617

ABSTRACTAlloy 617, a high-temperature creep-resistant, nickel-based alloy, is being considered for the primary heat exchanger for the next generation nuclear plant, which is highly influenced by thermal creep. The main objective of this study is to inspect the crept grain boundaries under its imitated working condition, and to determine which boundaries are susceptible to damage and which are more resistant, in order to help improve its creep resistance in future manufacturing. Electron backscatter diffraction was used to measure the proportions of each boundary by observing and analyzing these crept microstructures. The grain-boundary distribution can be expressed in terms of five parameters including three parameters of lattice misorientation and two parameters of the grain-boundary plane normal. Three conditions were analyzed: the original material, metal that was annealed without stress, and ones that were crept at 1000ºC at 19 MPa and 25 MPa for various times. Though observation, it is found that the voids seldom occur at low angle grain boundaries, and coherent twin boundaries are also resist to creep damage.

Three‐dimensional distortion measurements by section rocking curve imaging: Application to ice crystals

AbstractWe present a new method to measure distortions in the entire crystal volume, down to a scale of 50 × 50 × 50 µm3 elementary volume. The method combines rocking curve imaging (RCI), section‐ and pinhole diffraction topography. As results we obtain three‐dimensional (3D) maps providing the integrated diffracted beam intensity and the fields of angular lattice misorientation. Angular misorientations down to 10−5–10−6 have been measured. In this paper the method is applied to one of the grains of a three‐grained ice polycrystal (tri‐crystal).

Mapping of femtosecond laser-induced collateral damage by electron backscatter diffraction

The distribution of the collateral damage beneath craters produced by ultrafast (femtosecond) laser single pulses in a nickel base superalloy single crystal has been analyzed using electron backscatter diffraction. The procedure is based on measurements of the localized crystal rotations caused by the dislocations generated by the shock wave that is produced as an effect of laser pulse interaction with a material. Damage in the form of lattice misorientation created by excess dislocations was negligible at laser fluences up to 2 J/cm2. At higher fluences (5.1-41 J/cm2), the depth of the damage zone beneath the crater increased linearly with laser fluence. Based on lattice misorientation, excess dislocation densities as high as 3 × 1010/cm2 are calculated to be present below the ablated surface in the high fluence regime.

Watching a metal collapse: Examining cerium’s γ ↔ α transformation using X-ray diffraction of compressed single and polycrystals

Numerous investigations have been performed on Ce metal since the discovery of the γ → α phase transformation, where a face-centered cubic structure is believed to collapse isostructurally with a volume change of ∼17%. However, two questions have yet to be answered definitively. First, is the transformation truly isostructural or is the face-centered cubic structure lost in α-Ce due to symmetry breaking? Second, if the transformation is isostructural does the face-centered cubic structure stay in crystallographic orientation through the volume collapse? Here, we use high-pressure and high-temperature X-ray diffraction measurements to examine single and polycrystalline samples of Ce in the vicinity of the γ ↔ α transformation. This was achieved by successive continuous compression and decompression in a diamond anvil cell at temperatures under, at and above the critical point. Our results show that the crystal structure remains face-centered cubic for both the γ and α phases. The results also show that the face-centered cubic structure retains its crystallographic orientation, simply reducing in volume during the γ → α phase transformation. Upon transformation to α, polycrystalline samples show increased diffraction peak broadening, while single crystals show increased streaking. These changes in diffraction can be attributed to increased damage and lattice misorientation from the transformation. Using a simple atomic lattice model, we show that a periodic array of misfit edge dislocation is necessary to accommodate the large volume difference at the γ–α interface and this could act as a source of the edge dislocations needed to produced previously observed deformation bands.

Critical events, entropy, and the grain boundary character distribution

Mesoscale experiment and simulation permit harvesting information about both geometric features and texture in polycrystals. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length [in two dimensions (2D)] or area (in 3D) of an interface with a given lattice misorientation and normal. During the growth process, an initially random distribution of boundary types reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, it is found that if the given energy density depends only on lattice misorientation, then the steady-state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest nonrandom distributions, corresponding to independent trials with respect to the energy. In this paper, we derive an entropy-based theory that suggests that the evolution of the GBCD satisfies a Fokker-Planck equation, an equation whose stationary state is a Boltzmann distribution. Cellular structures coarsen according to a local evolution law, curvature-driven growth, and are limited by space-filling constraints. The interaction between the evolution law and the constraints is governed primarily by the force balance at triple junctions, the natural boundary condition associated with curvature-driven growth, and determines a dissipation relation. A simplified coarsening model is introduced that is driven by the boundary conditions and reflects the network level dissipation relation of the grain growth system. It resembles an ensemble of inertia-free spring-mass dashpots. Application is made of the recent characterization of Fokker-Planck kinetics as a gradient flow for a free energy in deriving the theory. The theory predicts the results of large-scale two-dimensional simulations and is consistent with experiment.

Probing mesoscopic lattice misorientation by strain gradient crystal plasticity modelling and micro-beam Laue diffraction experiments

A lengthscale and rate-dependent strain gradient crystal plasticity framework was employed to simulate the inter- and intra-granular deformation at the meso- to microscopic level in a large-grained polycrystalline Ni foil. The sample was characterised by micro-beam Laue diffraction experiments. Post-processing of the model was carried out both to forward predict the Laue diffraction patterns on the detector and to perform inverse analysis of the local lattice misorientation in the crystal. The anisotropic broadening of the Laue spots ('streaking') was correctly captured by the simulation and further analysed to reveal the local lattice arrangement.

On the nature of the direct image of defects in diffraction methods of X-ray topography

The regularities of X-ray scattering in the most distorted region of the crystal, where the local lattice misorientations associated with the deformation field of a defect reach a maximum, have been analyzed. The assumption is made that one of the possible mechanisms of the formation of a direct image is the wave field scattering at the pseudoboundary in the region of local misorientations, where the crystal comes out of the reflecting position near the defect axis, for example, the dislocation core. The formation of a direct image is demonstrated using numerical simulation of section topographs of model defects as an example. The model sample is a perfect single crystal containing a thin tube oriented in a certain crystallographic direction and filled by the same single-crystal material with the orientation different from that of the parent crystal. Therefore, if the model crystal is in a reflecting position, the Bragg conditions inside the tube are not satisfied. Numerical topographs show that the direct image is formed at the boundary of the tube of the model crystal.

On dislocation models of grain boundaries

Dislocation models of grain boundaries was suggested by Bragg (Proc Phys Soc 52:54–55, 1940) and Burgers (Proc Phys Soc 52:23–33, 1940). The first quantitative study of these models was given by Read and Shockley (Phys Rev 78(3):275–289, 1950). They obtained a formula for the dependence of the grain boundary energy on the misorientation of the neighboring grains, which became a cornerstone of the grain boundary theory. The Read–Shockley formula was based on a proposition that the grain boundary energy is the sum of energies of the two sets of dislocations that come from the two neighboring grains. This proposition was proved under an assumption on a quite special geometry of the slip planes. This paper aims to show that the assumption is not necessary and the proposition holds for arbitrary geometry of slip planes. Another goal of this paper is to provide all basic formulas of the theory: though the dislocation model of grain boundaries is considered in all treatises on dislocation theory, a complete analysis, including the relations for lattice rotations and displacements, has not been given. This analysis shows, in particular, that continuum theory does not yield the proper relations for the lattice misorientations, and these relations must be introduced by an independent ansatz.