Function Of Misorientation Angle Research Articles

Correlated subgrain and particle analysis of a recovered Al-Mn alloy by directly combining EBSD and backscatter electron imaging

Correlated analysis of (sub)grains and particles in alloys is important to understand transformation processes and control material properties. A multimodal data fusion workflow directly combining subgrain data from electron backscatter diffraction (EBSD) and particle data from backscatter electron (BSE) images in the scanning electron microscope is presented. The BSE images provide detection of particles smaller than the applied step size of EBSD down to 0.03 μm in diameter. The workflow is demonstrated on a cold-rolled and recovered Al-Mn alloy, where constituent particles formed during casting and dispersoids formed during subsequent heating affect recovery and recrystallization upon annealing. The multimodal dataset enables statistical analysis including subgrains surrounding constituent particles and dispersoids' location with respect to subgrain boundaries. Among the subgrains of recrystallization texture, Cube{001}〈100〉 subgrains experience an increased Smith-Zener drag from dispersoids on their boundaries compared to CubeND{001}〈310〉 and P{011}⟨5¯6¯6⟩ subgrains, with the latter experiencing the lowest drag. Subgrains at constituent particles are observed to have a growth advantage due to a lower dislocation density and higher boundary misorientation angle. The dispersoid size per subgrain boundary length increases as a function of misorientation angle. The workflow should be applicable to other alloy systems where there is a need for analysis correlating grains and grain boundaries with secondary phases smaller than the applied EBSD step size but resolvable by BSE imaging.

Evaluation of the anisotropic grain boundaries and surfaces of α-U via molecular dynamics

Alloys based on uranium-zirconium are gaining renewed interest as fuels for the Versatile Test Reactor and a number of microreactor designs. Implementing metallic fuel in reactors creates the need for robust descriptive and predictive fuel performance modeling. The current state of metallic fuel performance modeling relies on empirical equations derived from historical experiments, which may be unreliable when applied outside of their temperature, power, and composition phase space. One area where such data is lacking is the irradiation behavior of α-U, specifically tearing and porosity formation at the early stages of irradiation. While grain boundaries likely play a key role in this fuel behavior, relatively little is known about grain boundaries in α-U. Thus, we evaluate the grain boundary, surface energy, and work of adhesion of α-U utilizing molecular dynamics. Symmetric tilt grain boundaries (STGBs) are analyzed with the tilt plane oriented along each major crystallographic axis, for a total of eighty unique grain boundaries. The effect of temperature, tilt plane, and misorientation angle on interfacial energies are analyzed. The interfacial energies typically increase with temperature and there is significant variance as a function of misorientation angle, irrespective of the tilt plane. At 500 K, the average surface energy (1.23 J/m2) is approximately 1.5 times the grain boundary energy (0.79 J/m2), and the work of adhesion is approximately twice the grain boundary energy (1.68 J/m2). Orientations for the likely formation of twins and likely failure planes are identified.

Associating GB characteristics with its sink efficiency in absorbing Frank loops in Cu

Molecular dynamics (MD) simulations are performed to investigate the interaction of a migrating grain boundary (GB) with interstitial Frank loops, using a set of GBs along the [100] tilt axis in Cu as model systems. Our results show that the interaction is directly related to the misorientation angle. Specifically, three modes of interaction are observed as a function of misorientation angle. The sink efficiency of a GB, namely, the capability of a GB to absorb the Frank loops, increases with misorientation angle. The above trends are explained based on the differences in the structural units comprising the GB. Additionally, the transition angle between different modes can be altered by varying the local GB structure.

Dynamic drags acting on moving defects in discrete dispersive media: From dislocation to low-angle grain boundary

Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory mainly stems from the discrete nature of the core region, which induces a drag force on the dislocation core during glide. Depending on external conditions, different drag mechanisms are activated that govern the dynamics of dislocations in their own way. This is revealed by the resultant speed of the dislocation. In this work, we develop a theoretical framework that generally describes the dynamic drag on dislocations and, as a result, derive a phenomenological cubic constitutive equation. Furthermore, given that a low-angle grain boundary (LAGB) can be regarded as an array of dislocations, we extend the model to describe the mobility law of LAGBs as a function of misorientation angle. As a result, we prove that both dislocations and LAGBs follow the developed constitutive equation with the same mathematical form despite their different governing drag sources. The suggested model is also supported by molecular dynamics simulations. Therefore, this work has significance for a fundamental understanding of the dynamic drag acting on defects and facilitates a general description of various drag mechanisms.

Associating damage nucleation and distribution with grain boundary characteristics in Ta

The effect of grain boundary (GB) characteristics (as represented by misorientation angle) on its dynamic response is investigated by sampling a large set of 185 GBs in Ta bi-crystals. These GBs encompass both ordered and disordered structures – typically referred to as metastable structures, in order to reflect the diversity in the local atomic structure observed in realistic GBs. The results reveal four distinct regimes in damage distribution and failure modes as a function of misorientation angle. The above trends also correlate with the variation in the corresponding void nucleation stress.

Role of Random and Coincidence Site Lattice Grain Boundaries in Liquid Metal Embrittlement of Iron (FCC)-Zn Couple

Liquid metal embrittlement (LME) has frequently been reported in various systems: Cu-Bi, Ni-Bi, Al-Ga, and Fe-Zn for more than 60 years. Although advances have been made in understanding the phenomenon, the role of grain boundary (GB) type and characteristics in LME has remained unclear. The present work shows that liquid metal penetration only occurs in random GBs, where its propagation path is a function of misorientation angle (θ) and stress component perpendicular to GB plane. In contrast, low-Σ coincidence site lattice (CSL) boundaries: Σ3 (θ = 60 deg) and Σ5 to 9 (~ θ = 40 deg) resist LME, even at the maximum stress component. Triple junctions of CSL and random GB block liquid metal penetration by modifying of the random GB misorientation angle. These findings provide insights to employ grain boundary engineering techniques to increase population of CSLs over random GBs and, hence, mitigate LME.

A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model

The Kobayashi–Warren–Carter (KWC) phase-field model was originally conceived for two-dimensional systems to model grain boundary migration and grain rotation, which play a crucial role in nanocrystalline materials, and in phenomena such as superplasticity and recrystallization. Existing generalizations of the KWC model to three-dimensions construct the grain boundary energy as a function of misorientation angle between the grains, described as a scalar, and the inclination of the grain boundary. It is well-known that grain boundary energy is described on a five-dimensional space, where three dimensions describe misorientations and two describe inclinations. In this work, we generalize the KWC model by constructing a frame-invariant energy density that is sensitive to all the five-dimensions of misorientations and inclinations. In addition, we derive representations for energy density that result in different forms of anisotropies in inclination and misorientation. The developed framework enables us to introduce the effect of material symmetry on the inclination-dependence. We demonstrate the richness of the model using various three-dimensional numerical examples that simulate anisotropic grain coarsening and grain rotation.

Low angle boundary migration of shot-peened pure nickel investigated by electron channeling contrast imaging and electron backscatter diffraction.

Study on recrystallization of deformed metal is important for practical industrial applications. Most of studies about recrystallization behavior focused on the migration of the high-angle grain boundaries, resulting in lack of information of the kinetics of the low angle grain boundary migration. In this study, we focused on the migration of the low angle grain boundaries during recrystallization process. Pure nickel deformed by shot peening which induced plastic deformation at the surface was investigated. The surface of the specimen was prepared by mechanical polishing using diamond slurry and colloidal silica down to 0.02 μm. Sequential heat treatment under a moderate annealing temperature facilitates to observe the migration of low angle grain boundaries. The threshold energy for low angle boundary migration during recrystallization as a function of misorientation angle was evaluated using scanning electron microscopy techniques. A combination of electron channeling contrast imaging and electron backscatter diffraction was used to measure the average dislocation density and a quantitative estimation of the stored energy near the boundary. It was observed that the migration of the low angle grain boundaries during recrystallization was strongly affected by both the stored energy of the deformed matrix and the misorientation angle of the boundary. Through the combination of electron channeling contrast imaging and electron backscatter diffraction, the threshold stored energy for the migration of the low angle grain boundaries was estimated as a function of the boundary misorientation.

In-situ EBSD study on the cube texture evolution in 3 wt% Si steel complemented by ex-situ EBSD experiment — From nucleation to grain growth

Cube ({100}〈001〉) texture in steel sheet is preferable for magnetic applications since the easy magnetization axis 〈001〉 is parallel to the rolling and transverse directions which are common magnetic flux directions. Several advanced processes have been proposed to obtain the cube texture, such as severe cold rolling or vacuum annealing all requiring unconventional processing techniques. Here, we report a much simpler processing route leading to a strong cube texture in 3 wt% Si steel, which is based on conventional processing techniques. The cube orientation is developed by means of increasing the grain size before cold rolling. In this manuscript, the mechanism of the creation of the cube oriented grain is described with regards to nucleation and grain growth. Knowledge of the nucleation site of the cube oriented grains, determined by conventional ex-situ electron back-scatter diffraction (EBSD), allowed to define the observation area for in-situ heating EBSD measurements to observe where cube oriented grains were formed. The following sequence of cube texture evolution is proposed: (i) grains with cube and near cube orientations are nucleated from fragments of deformed {411}〈148〉 grains; (ii) these grains grow inside prior grain boundaries and their coarsening speed is higher than that of other grains with different orientations due to a higher relative grain boundary mobility; (iii) the cube oriented grains start to grow beyond the prior grain boundaries and become dominant due to the size effect. Nuclei for cube orientations were experimentally observed and an equation is derived to predict the relative grain bounday mobility as a function of misorientation angle and temperature.

Orientation Dependence of Columnar Dendritic Growth with Sidebranching Behaviors in Directional Solidification: Insights from Phase-Field Simulations

In this study, a thin-interface phase-field model was employed to study the orientation dependence of the columnar dendritic growth with sidebranching behaviors in directional solidification. It was found that the dimensionless tip undercooling increases with the increase of misorientation angle for three pulling velocities. The primary spacing is found to be a function of misorientation angle, and the dimensionless primary spacing with respect to the misorientation angle follows the orientation correction given by Gandin and Rappaz (Acta. Metall. 42:2233–2246, 1994). For the analysis of the dendritic tip, the two-dimensional (2-D) form of the nonaxisymmetric needle crystal was used to determine the radius of the tilted columnar dendrite. Based on the definitions of open side and constrained side of the dendrite, the analysis of the width active sidebranches and the dendritic area in 2-D with respect to the distance from the dendritic tip was carried out to investigate the asymmetrical dendrite envelop and sidebranching behaviors on the two sides in directional solidification. The obtained prefactor and exponent with respect to misorientation angle are discussed, showing that the sidebranching behaviors of a tilted columnar dendritic array obey a similar power-law relationship with that of a free dendritic growth.

Grain Boundary Plane Orientation Fundamental Zones and Structure-Property Relationships.

Grain boundary plane orientation is a profoundly important determinant of character in polycrystalline materials that is not well understood. This work demonstrates how boundary plane orientation fundamental zones, which capture the natural crystallographic symmetries of a grain boundary, can be used to establish structure-property relationships. Using the fundamental zone representation, trends in computed energy, excess volume at the grain boundary, and temperature-dependent mobility naturally emerge and show a strong dependence on the boundary plane orientation. Analysis of common misorientation axes even suggests broader trends of grain boundary energy as a function of misorientation angle and plane orientation. Due to the strong structure-property relationships that naturally emerge from this work, boundary plane fundamental zones are expected to simplify analysis of both computational and experimental data. This standardized representation has the potential to significantly accelerate research in the topologically complex and vast five-dimensional phase space of grain boundaries.

Misorientation dependence of Al2O3 grain boundary thermal resistance

The room-temperature thermal resistance of model low-angle (0001) twist bicrystal Al2O3 grain boundaries was measured as a function of misorientation angle using the 3ω thermal conductivity testing technique. The work yields interfacial thermal resistances of 0.44 × 10−8, 1.2 × 10−8, and 1.54 × 10−8 Km2 W−1 for the ∼1.3°, ∼8.0°, and ∼13° twist grain boundaries, respectively. The interfacial thermal resistance correlates with the grain boundary energy calculated from the Read-Shockley model. The results indicate significant anisotropy in the Kapitza resistance whose magnitude is dominated by local structural defects at the grain boundary rather than spectral mismatch between grains.

Investigation of Local Texture Correlations in Bi-2223 High Temperature Superconductor Tapes

In this paper we report a study using fully automated EBSP orientation measurements on the texture and microstructure of fully processed Bi-2223 tapes produced by the powder-in-tube method. For the automated analysis a new unit cell describing the quasi-tetragonal Bi-2223 phase has been developed. The texture data confirm that a strong fibre texture is produced during processing, with the c-axis of the Bi2223 plates parallel to the tape normal direction. Quantitative analysis suggests that the orientation density along the fibre texture is close to random. In contrast the distribution of misorientations shows significant correlations between the orientations, and is skewed towards low misorientation angles. A more detailed investigation reveals that the structure consists of colonies of plates, with low angle misorientations within each colony. Analysis of the rotation axes shows some differences as a function of misorientation angle.

Optical Grain Size Measurements: What is Being Measured? Comparative Study of Optical and EBSD Grain Sizes Determination in 2D Al Foil

Reflected light optical analysis and Electron Backscatter Diffraction (EBSD) analysis have been used to m easure grain sizes in 2D Al foil samples, annealed for different times. There are significant differences in the results of the two techniques. It is shown that in Al it is possible to detect boundaries in optical images down to a misorientation angle of 7-8º. Nevertheless, in most samples the critical angle of easy etching lies above 10º. The observed differences in grain size measurements between optical analysis and EBSD analysis can be largely attributed to three phenomena: (1) individual samples may behave slighty differently due to differences in the effectiveness of etching (2) the grain size is heterogeneous over large areas and (3) the effect of etching is not only a function of misorientation angle but also grain boundary plane. Despite these uncertainties, optical analysis seems to be reliable for analysis of processes in which mainly grain boundaries with misorientation angle of > 10º are involved i.e. grain growth.

Grain Boundary Energy and Grain Growth in Highly-Textured Al Films and Foils: Experiment and Simulation

Relative grain boundary energy as a function of misorientation angle was measured in a cube-oriented, 120 µm-thick Al foil and in a <111> fiber-textured, 1.7 µm-thick Al film using a multiscale analysis of the grain boundary dihedral angles. For the Al foil, the energies of low-angle boundaries increased with misorientation angle, in good agreement with the Read-Shockley model. For the Al film, two energy minima were observed for high-angle boundaries. Grain growth was studied in 25 and 100 nm-thick films that were annealed at 400 °C for a series of times in the range of 0.5 to 10 h. For the 100 nm-thick film, grains approximately doubled their size (equivalent circular diameter) before grain growth stagnated. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo Potts and partial differential equation based simulations showed excellent agreement with each other, even when anisotropic boundary energies were used. However, the simulated distributions had fewer small grains than the experimental distributions.

Electrical resistance of low-angle tilt grain boundaries in acceptor-doped SrTiO3 as a function of misorientation angle

The transport of charge across symmetrical low-angle [001] tilt grain boundaries in Fe-doped SrTiO3 was examined. Grain boundary resistances were obtained from impedance spectroscopy measurements on bicrystals with misorientation angles θ=2.3°, 5.4°, and 7.8° as a function of temperature and oxygen partial pressure. By comparing these data with values predicted from a double Schottky-barrier model, we show that the resistance of a low-angle tilt grain boundary in acceptor-doped SrTiO3 is correlated with its dislocation content, but in a nontrivial manner.

Grain Boundary Properties and Grain Growth: Al Foils, Al Films

AbstractRelative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 [.proportional]m-thick Al foil using orientation imaging microscopy and a statistical multiscale method. The energies of low-angle boundaries increase with misorientation angle, in good agreement with the Read-Shockley model. The relative energies of high-angle boundaries exhibit little variation with misorientation. Examination of the grain structure of <111> fiber-textured, 100 nm-thick Al films annealed at 400°C for 0.5-10 h shows 5 and 6 sided grains to be the most frequent, and the fraction of four-sided grains to be significant. The mean number of sides is slightly lower than the expected value of 6 for two- dimensional structures. Of lognormal, gamma and Rayleigh distributions, gamma gives the best fit to the grain size data in the films; however, the difference between gamma and lognormal is small. Grain growth is not self-similar and stagnates after one hour of annealing. The evolution of the grain size distribution with time indicates that the growth stagnation in the films is neither consistent with boundary pinning by grooving nor with conventional treatments of solute drag. Surface, elastic-strain and plastic-strain energy driving forces do not play a significant role in the grain growth and the subsequent stagnation since the films are strongly textured even in the as- deposited state. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo and partial differential equation based simulations show excellent agreement with each other, even when anisotropic boundary energies are used. However, comparison with experimental distributions reveals a significantly higher population of small grains in the experiments.

Influence of Mis-Orientation of C-plane Sapphire Substrate on the Early Stages of MOCVD Growth of GaN Thin Films

ABSTRACTWe have studied the early stages of GaN growth to realize the growth mechanism of GaN thin films on mis-oriented sapphire substrates which affects the surface and crystal quality of GaN thin films. As the result, it was found that the larger mis-orientation angle helps the growth of the larger grain of GaN and leads to the earlier shift of growth mode from 3D to 2D. The AFM observation of closed-coalesced GaN thin films revealed the difference in the micro-step structures by the mis-orientation angle of sapphire substrate. The result of x-ray rocking curve as a function of mis-orientation angle well matched with the microstructure of GaN surface, indicating that the larger mis-orientation angle helps the column ordering of GaN crystals.

Grain Boundary Migration in Fe-Si Alloy Bicrystals

Migrations of tilt boundaries in Fe - Si alloy bicrystals have been investigated by Sun and Bauer technique as a function of misorientation angle, driving force, temperature and Si content. Two distinct regions with different migration behaviour are observed on temperature -dependence of mobility: a drastic change in mobility occurs at a critical temperature. The critical temperature depends on the driving force and also the grain boundary (GB) character. The activation energy for grain boundary migration (GBM) is ca. 2/3 of that for Fe bulk self - diffusion in the higher temperature region, suggesting that the boundary motion is governed by GB diffusion. On the other hand, the activation energy increases up to ca. 220 kJ/mol in the lower temperature region, being in agreement with that for Si intrinsic - diffusion in α-Fe. This agreement shows that GB is most likely to move dragging Si atmosphere. Also, it is of great interest that the mobility for coincidence boundary, particularly Σ9 GB, is higher than that for a random boundary in the lower temperature region, but reverse is the case in the higher temperature region. In addition, the mobility depends on Si content in the lower temperature region; it increases with decreasing Si content, whereas such dependence is scarcely observed in the higher temperature region. These results obtained here will be discussed from the viewpoint of the interaction between GB and solute atoms.

Molecular dynamics simulation on low angle grain boundaries

Molecular dynamics simulation has been performed to investigate the microstructure and properties of low angle grain boundaries, employing the embedded atom method(EAM) type interatomic potential for Ni-Al alloy. The energies of the low angle grain boundaries with different dislocation densities were calculated, and the results indicate that the low angle grain boundary energy varies as a function of misorientation angle. The simulation was found in good agreement with the calculation on the basis of the dislocation theories in the low angle scale. The low angle grain boundary energy goes up with the increase of misorientation angle and tends to go down after reaching a maximum. An energy cusp exists when the misorientation angle increases further, but in this scale the dislocation theories are invalid for energy calculation due to the strong interaction of the dislocations at the boundaries. The simulation results also indicate that the microstructure of low angle grain boundaries can still be described as dislocations when the misorientation angle is larger than 10 degrees.