Subgrain Boundary Misorientation Research Articles

Study on subgrain boundaries in cast monocrystalline silicon

Cast monocrystalline silicon (mono-Si), also known as quasi-mono-Si, has been recognized for its potential as a high-performance crystalline silicon material due to its low manufacturing costs and high crystal quality. This study investigated the occurrence of high-density dislocation loops in cast mono-Si, which exhibited grid-like propagation caused mostly by subgrain boundaries. The study looked at the fundamental properties of these subgrain boundaries as well as the mechanisms that allow them to propagate in a grid-like pattern within cast mono-Si. Observations revealed differences in the crystallographic misorientation of subgrain boundaries across the ingot, ranging from 1 to 3°. Electron Beam Induced Current (EBIC) tests revealed strong recombination activity at these boundaries under typical conditions. As the temperature gradually decreases from 300 K to 80 K during EBIC testing, subgrain boundaries with shallower energy states emerge, which become more apparent in photoluminescence (PL) tests conducted on Si wafers cut from different heights of the ingot.

A Petrological and Microstructural Study of Ten Brachinites: A Cumulate Texture?

AbstractBrachinites are igneous, ultramafic and unbrecciated primitive achondrites mainly composed of olivine and pyroxene, with a partial melt residue or cumulate origin that is still debated. This study presents a petrological and microstructural study of 10 brachinite meteorites to identify igneous and deformation processes responsible for their formation. Detailed microstructural analyses were performed using secondary electron microscopy, electron probe microanalysis, and electron backscatter diffraction. The olivine‐spinel and two‐pyroxene closure temperatures of these brachinites ranged from 814 ± 27 to 909 ± 20°C. Olivine [001] axes coincide with the elongation of olivine grains and the crystallographic preferred orientations (CPO) of clinopyroxene [001] axes, which led us to infer lineation as olivine [001] axes parallel to X for all samples. Olivine CPO displays a strong or medium concentration of [001] axes parallel to X and [010] axes parallel to Z pointing to a B‐type fabric. Limited internal deformation of olivine grains and slip systems identified from low‐angle boundary misorientation analyses are inconsistent with the CPO and grain misorientation distributions are close to those found in untextured rocks. Olivine B‐type fabrics may therefore result not from plastic deformation but rather from rigid crystal rotation or preferential crystal growth during compaction. Olivine subgrain boundary misorientation axes imply limited activation of [001](100) and [100](001) slip systems, which could be due to primary plastic deformation during or after crystal settling. These new results reveal that brachinites developed a cumulate texture and accommodated only weak plastic deformation during early differentiation processes in the parent body.

Improved Predictability of Microstructure Evolution during Hot Deformation of Titanium Alloys.

Two different mesoscale models based on dislocation reactions are developed and applied to predict both the flow stress and the microstructure evolution during the hot deformation of titanium alloys. Three distinct populations of dislocations, named mobile, immobile, and wall dislocations, describe the microstructure, together with the crystal misorientation and the densities of boundaries. A simple model consisting of production and recovery terms for the evolution of dislocations is compared with a comprehensive model that describes the reactions between different type of dislocations. Constitutive equations connect the microstructure evolution with the flow stresses. Both models consider the formation of a high angle grain boundary by continuous dynamic recrystallization due to progressive lattice rotation. The wall dislocation density evolution is calculated as a result of the subgrain size and boundary misorientation distribution evolutions. The developed models are applied to two near-β titanium alloys, Ti-5553 and Ti-17, and validated for use in hot compression experiments. The differences in the predictability between the developed models are discussed for the flow stress, dislocation densities and microstructure evolutions. Only the comprehensive model can predict the different reactions and their contributions to the evolution of mobile and immobile dislocation densities. The comprehensive model also allows for correlating the elastic strain rate with the softening and hardening kinetics. Despite those differences, the selection of the model used has a small influence on the overall prediction of the subgrain size and the fraction of high angle grain boundaries.

A dislocation-based model for the microstructure evolution and the flow stress of a Ti5553 alloy

The plastic deformation at high temperatures of two-phase titanium alloys is modelled using a mesoscale approach to describe the complex interactions between different populations of dislocation densities. The static and dynamic recovery, as well as of continuous dynamic recrystallization, is modelled. The flow stresses of both α and β phases are calculated using constitutive equations combined with a load partitioning model between the α and β phases. The dislocation populations are separated into three categories, named mobile, immobile and walls, and separated rate equations are developed for each reaction between them. Several microstructure features are calculated, such as mean subgrain size, grain size, dislocation densities and boundary misorientation. Additionally, glide velocity is also estimated. Hot compression experiments of a Ti-5553 alloy at temperatures between 1073 K and 1193 K and strain rates between 0.001 s−1 and 10 s−1 are used for validation. The flow softening observed in the α+β domain is attributed to the change in load partitioning. Moreover, the decrease in grain and subgrain size with the increase in strain rate and decrease in temperature is well predicted by the proposed model as well as the evolution of a fully static recrystallized microstructure into a continuous dynamic recrystallized one.

Stored Energy Evaluation for High Strength Dual-Phase Steels with Different Pre-annealing Conditions

The purpose of this study was to determine the stored energy of dual-phase (DP) steels after hot rolling, coiling, and cold reduction using electron backscattered diffraction analysis. Three methods for stored energy evaluation were examined and compared: the sub-grain boundary, image quality, and kernel average misorientation methods. The results demonstrated that the sub-grain method, in which stored energy was calculated as a function of sub-grain boundary misorientations and total sub-grain boundary length, can provide more accurate stored energy values, since cold work was responsible for forming numerous dislocation structures such as shear bands, cells, and cell walls. As expected, the steels with the combination of a low coiling temperature of 580 °C and 60 pct cold reduction had the highest stored energy values. This information is important in defining how pre-anneal processing conditions might control the response of DP steels to the various transformations occurring during continuous galvanizing line simulations.

Orientation Independent and Dependent Subgrain Growth during Iso-Thermal Annealing of High-Purity and Commercial Purity Aluminium

The orientation dependence on recovery has been studied in cold-rolled and annealed polycrystalline high-purity aluminium (99.99 wt%), binary Al-0.25Mn and commercial purity aluminium. The growth mechanisms were found to be independent of the alloy system and the microchemistry only influences the coarsening kinetics. Orientation-dependent subgrain growth, mainly studied in high-purity aluminium and measured in lamellar bands of uniform orientation, occurs in three distinct ways, depending of the size of the local orientation gradients. Following the evolution in average subgrain size and boundary misorientation by detailed electron backscatter diffraction (EBSD) characterization during annealing, it was found that the rate of subgrain growth in Cube- and Goss-oriented grains were faster than in the typical deformation texture components, particularly after an incubation time when discontinuous subgrain growth occurs. In commercial purity aluminium, general orientation-independent subgrain growth is faster than the orientation-dependent growth because more growth occurs in regions near high-angle grain boundaries separating differently oriented lamellar bands. It appears as if subgrains misoriented by more than 3.5° have a growth advantage over less misoriented subgrains, typically in the interior of lamellar bands. While the average boundary misorientations are decreasing, the individual boundary misorientations are increasing.

Microstructure evolution of the TiB2/Al composites fabricated by powder metallurgy during hot extrusion

The microstructure evolution near the central axis during hot extrusion for the fine-grained TiB2/Al-Zn-Mg-Cu composites fabricated by powder metallurgy is studied by experimental observation at different locations in the remaining die. The significant increase of the fraction of ultrafine grains and texture evolution indicates the extensive dynamic recrystallization at the narrowest position of the die. The deformed grains are distinguished from the undeformed grains with the parameter of grain orientation spread (GOS). And the deformed grains are generally rotated around the extrusion direction. Additionally, the introduced submicron TiB2 particles have the potential to stimulate the dynamic recrystallization associated with progressively increased misorientation of subgrain boundaries, and even change the spatial distribution of the low angle grain boundaries. The preferential activation of {111} 〈1−10〉 system and non-octahedral (NOC) slip system {001} 〈110〉 contributes to the formation of strong deformation fiber texture according to the analysis of the Schmid factor. It is supposed that grain boundary sliding accommodated dislocation slip mechanism controls the microstructure evolution.

Modeling of continuous dynamic recrystallization of Al-Zn-Cu-Mg alloy during hot deformation based on the internal-state-variable (ISV) method

Al-Zn-Cu-Mg alloys (e.g., AA7075) have been widely used to form structural components in aerospace and other industries. For Al-Zn-Cu-Mg alloys, although dynamic recovery was dominant in hot deformation, dynamic recrystallization also occurred frequently, such as continuous dynamic recrystallization (CDRX), for which various mechanisms were found, e.g. subgrain boundary migration, subgrain coalescence, and subgrain rotation. However for the as-extruded AA7075 alloy subjected to hot compression, the mechanisms of CDRX process and model for it are lacking. In this paper by conducting thermal simulation compression tests combined with electron back scattered diffraction (EBSD) experiments, a continuous dynamic recrystallization (CDRX) process during the hot deformation of the as-extruded Al-Zn-Cu-Mg alloy (AA7075) is revealed based on the analysis on deformation behavior and characteristics of the recrystallized microstructures. It was found that subgrains, which were formed through dynamic recovery (DRV), rotated by absorbing dislocations into its boundaries, and resulted in the formation of the recrystallized grains. Then based on the explored CDRX mechanism, the dislocation density, subgrain boundary area, recrystallized grain boundary area, high angle grain boundary area and subgrain boundary misorientation were determined as internal-state-variables, and a continuous dynamic recrystallization model for AA7075 alloy was developed. In the established model, the process of subgrain rotation was described by introducing subgrain boundary stored energy, which related to dislocation density, subgrain size and misorientation. Finally, the continuous dynamic recrystallization model was combined with a constitutive model for the unified prediction of the flow stress and the microstructure evolution during the hot deformation of AA7075. Predictions of the model are in good agreement with the experimental ones.

Stress evolution and associated microstructure during transient creep of olivine at 1000–1200 °C

We study the mechanical response and correlated microstructure of axial deformed fine-grained olivine aggregates as a function of incremental finite strains. Deformation experiments were conducted in uniaxial compression in an internally heated gas-medium deformation apparatus at temperatures of 1000 and 1200 °C, at strain rates of 10−6 s−1 to 10−5 s−1 and at confining pressure of 300 MPa. Sample volumes are around 1.2 cm3. Finite strains range from 0.1 to 8.6% and corresponding maximal (final) differential stresses range from 80 to 1073 MPa for deformation at 1000 °C and from 71 to 322 MPa for deformation at 1200 °C. At 1200 °C, samples approach steady state deformation after about 8% of strain. At 1000 °C, significant strain hardening leads to stresses exceeding the confining pressure by a factor of 3.5 with brittle deformation after 3% of strain. Deformed samples were characterized by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). EBSD maps with step sizes as low as 50 nm were acquired without introducing analytical artifacts for the first time. The grain size of deformed samples ranges from 2.1 to 2.6 µm. Despite clear strain hardening, texture or microstructure do not change as a function of stress or finite strain. This observation is supported by a constant texture strength (J-index) and symmetry (BA-index), constant grain shape and aspect ratio, constant density of geometrically necessary dislocations, grain orientation spread, and constant subgrain boundary spacing and misorientation in between samples. TEM shows that all samples exhibit unambiguous dislocation activity but with a highly heterogeneous dislocation distribution. Olivine grains display evidence of [1 0 0] and [0 0 1] slip activity, but there is no evidence of interaction between the dislocations from the different slip systems. Several observations of grain boundaries acting as dislocation sources have been found. We find no confirmation of increasing dislocation densities as the cause for strain hardening during transient creep. This suggests other, yet not fully understood mechanisms affecting the strength of deformed olivine. These mechanisms could possibly involve grain boundaries. Such mechanisms are relevant for the deformation of uppermost mantle rocks, where the Si diffusion rate is too slow and dislocation glide must be accommodated in another way to fulfill the von Mises criterion.

Subgrain Rotation Recrystallization During Shearing: Insights From Full‐Field Numerical Simulations of Halite Polycrystals

AbstractWe present, for the first time, results of full‐field numerical simulations of subgrain rotation recrystallization of halite polycrystals during simple shear deformation. The series of simulations show how microstructures are controlled by the competition between (i) grain size reduction by creep by dislocation glide and (ii) intracrystalline recovery encompassing subgrain coarsening by coalescence through rotation and alignment of the lattices of neighboring subgrains. A strong grain size reduction develops in models without intracrystalline recovery, as a result of the formation of high‐angle grain boundaries when local misorientations exceed 15°. The activation of subgrain coarsening associated with recovery decreases the stored strain energy and results in grains with low intracrystalline heterogeneities. However, this type of recrystallization does not significantly modify crystal preferred orientations. Lattice orientation and grain boundary maps reveal that this full‐field modeling approach is able to successfully reproduce the evolution of dry halite microstructures from laboratory deformation experiments, thus opening new opportunities in this field of research. We demonstrate how the mean subgrain boundary misorientations can be used to estimate the strain accommodated by dislocation glide using a universal scaling exponent of about 2/3, as predicted by theoretical models. In addition, this strain gauge can be potentially applied to estimate the intensity of intracrystalline recovery, associated with temperature, using quantitative crystallographic analyses in areas with strain gradients.

Microstructural and geochemical constraints on the evolution of deep arc lithosphere

AbstractMantle xenoliths from the Sierra Nevada, California, USA, sampled a vertical column (60–120 km) of lithosphere that formed during Mesozoic continental arc magmatism. This lithosphere experienced an anticlockwise P‐T‐t path resulting in rapid cooling that effectively “quenched in” features inherited from earlier high‐temperature conditions. Here we combine new mineral chemistry data (water, trace element, and major element concentrations) with mineral crystallographic preferred orientations (CPOs) to investigate the relationship between melt infiltration and deformation. The peridotites record a refertilization trend with increasing depth, starting from shallow, coarse‐protogranular, less‐melt‐infiltrated spinel peridotite with strong, orthorhombic olivine CPO to deep, fine‐porphyroclastic, highly melt‐infiltrated garnet peridotite with weak, axial‐[010] olivine CPO. In contrast to the observed axial‐[010] CPOs, subgrain boundary orientations and misorientation axes suggest the dominant activation of the (001)[100] slip system, suggesting deformation under moderately hydrous conditions. After accounting for effects of subsolidus cooling, we see coherent trends between mineral trace element abundance and water content, indicating that melt infiltration led to an increase in water content of the peridotites. However, measured olivine and pyroxene water contents in all peridotites (5–10 and 30–500 wt ppm, respectively) are lower than that required to promote dominant (001)[100] slip system observed in both natural and experimental samples. These results suggest that deformation occurred earlier along the P‐T path, probably during or shortly after hydrous melt infiltration. Subsequent rapid cooling at 90 Ma led to water loss from olivine (owing to decreased solubility at low temperature), leaving behind a deep arc lithosphere that remained viscously coupled to the Farallon slab until the opening of the slab window in the late Cenozoic.

Evolution of the substructure of a novel 12% Cr steel under creep conditions

In this work we study the microstruture evolution of a newly developed 12% Cr martensitic/ferritic steel in as-received condition and after creep at 650°C under 130MPa and 80MPa. The microstructure is described as consisting of mobile dislocations, dipole dislocations, boundary dislocations, precipitates, lath boundaries, block boundaries, packet boundaries and prior austenitic grain boundaries. The material is characterized employing light optical microscopy (LOM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD) and electron backscatter diffraction (EBSD). TEM is used to characterize the dislocations (mobile+dipole) inside the subgrains and XRD measurements are used to the characterize mobile dislocations. Based on the subgrain boundary misorientations obtained from EBSD measurements, the boundary dislocation density is estimated. The total dislocation density is estimated for the as-received and crept conditions adding the mobile, boundary and dipole dislocation densities. Additionally, the subgrain size is estimated from the EBSD measurements. In this publication we propose the use of three characterization techniques TEM, XRD and EBSD as necessary to characterize all type of dislocations and quantify the total dislocation densty in martensitic/ferritic steels.

Correct Interpretation of Creep Rates: A Case Study of Cu

Traditionally the deformation resistance in creep is characterized by the minimum creep rate ε˙min and its sensitivity to stress (stress exponent n) and temperature (activation energy Q). Various values of constant n have been reported in the literature and interpreted in terms of specific mechanisms. The present case study of coarse-grained Cu at 573 K yields a stress exponent n = 9 for ε˙min in tension and a relatively low activation energy. The evolution of the deformation resistance with strain at constant tensile creep load and comparison with creep in compression without fracture indicates that the tensile ε˙min result from transition from uniform deformation to strain localization during fracture. This is confirmed by the results of creep in compression where fracture is suppressed. Both the tensile ε˙min and the compressive creep rate at strains around 0.3 can be described using existing equations for quasi-stationary deformation containing the subgrain boundary misorientation θ as structure parameter. While in the latter case constant θ leads to monotonic increase of n with stress, the tensile nine-power-law results from variable θ, and has no simple meaning. The result of this case study means that uncritical interpretation of minimum tensile creep rates as stationary ones bears a high risk of systematic errors in the determination of creep parameters and identification of creep mechanisms.

Symmetry Aspects of Dislocation-Effected Crystal Properties: Material Strength Levels and X-ray Topographic Imaging

Several materials science type research topics are described in which advantageous use of crystal symmetry considerations has been helpful in ferreting the essential elements of dislocation behavior in determining material properties or for characterizing crystal/polycrystalline structural relationships; for example: (1) the mechanical strengthening produced by a symmetrical bicrystal grain boundary; (2) cleavage crack formation at the intersection within a crystal of symmetrical dislocation pile-ups; (3) symmetry aspects of anisotropic crystal indentation hardness measurements; (4) X-ray diffraction topography imaging of dislocation strains and subgrain boundary misorientations; and (5) point and space group aspects of twinning. Several applications are described in relation to the strengthening of grain boundaries in nanopolycrystals and of multiply-oriented crystal grains in polysilicon photovoltaic solar cell materials. A number of crystallographic aspects of the different topics are illustrated with a stereographic method of presentation.

What happens to deformed rocks after deformation? A refined model for recovery based on numerical simulations

AbstractDeformation, in large parts of the middle crust, results in strained rocks consisting of grains with variable dislocation densities and microstructures which are characterized by gradual distortion and subgrain structures. Post-deformation residence of these rocks at elevated temperatures results in microstructural adjustments through static recovery and recrystallization. Here, we employ a numerical technique to simulate intragrain recovery at temperatures at or below the deformation temperature. The simulation is based on minimization of the stored energy, related to misorientation through local rotation of physical material points relative to their immediate environment. Three temperature- and/or deformation-geometry-dependent parameters were systematically varied: (1) deformation-induced dislocation types, (2) dislocation mobility and (3) size of dislocation interaction volume. Comparison with previously published in situ experiments shows consistency of numerical and experimental results. They show temperature- and dislocation-type-dependent small-scale fluctuations in subgrain-boundary misorientations and orientation variation within subgrains. These can be explained by the combined effect of increase in dislocation interaction volume and activation of climb. Our work shows microstructure can be significantly modified even if the post-deformational temperature is at or below the deformation temperature: a scenario relevant for most deformed rocks.

Deformation Characteristics and Recrystallization Response of a 9310 Steel Alloy

The flow behavior and recrystallization response of a 9310 steel alloy deformed in the ferrite temperature range were studied in this work. Samples were compressed under various conditions of strain (0.6, 0.8 and multi-axial), strain rate (10−4 seconds−1 to 10−1 seconds−1) and temperature [811 K to 1033 K (538 °C to 760 °C)] using a Gleeble thermo-mechanical simulator. Deformation was characterized by both qualitative and quantitative means, using standard microscopy, electron backscatter diffraction (EBSD) analysis and flow stress modeling. The results indicate that deformation is primarily accommodated through dynamic recovery in sub-grain formation. EBSD analysis shows a continuous increase in sub-grain boundary misorientation with increasing strain, ultimately producing recrystallized grains from the sub-grains at high strains. This suggests that a sub-grain rotation recrystallization mechanism predominates in this temperature range. Analyses of the results reveal a decreasing mean dynamically recrystallized grain size with increasing Zener-Hollomon parameter, and an increasing recrystallized fraction with increasing strain.

The Application of <i>In Situ</i> 3D X-Ray Diffraction in Annealing Experiments: First Interpretation of Substructure Development in Deformed NaCl

n-situ 3D X-ray diffraction (3DXRD) annealing experiments were conducted at the ID-11 beamline at the European Synchrotron Radiation Facility in Grenoble. This allowed us to non-destructively document and subsequently analyse the development of substructures during heating, without the influence of surface effects. A sample of deformed single crystal halite was heated to between 260-400 °C. Before and after heating a volume of 500 by 500 by 300 μm was mapped using a planar beam, which was translated over the sample volume at intervals of 5-10 µm in the vertical dimension. In the following we present partially reconstructed orientation maps over one layer before and after heating for 240min at 260 °C. Additional small syn-heating maps over a constrained sample rotation of 12-30º. The purpose of this was to illuminate a few reflections from 1 or 2 subgrains and follow their evolution during heating. Preliminary results show that significant changes occurred within the sample volume, for which, surface effects can be excluded. Results show a number of processes, including: i) change in subgrain boundary misorientation angle and ii) subgrain subdivision into areas of similar lattice orientation with new subgrain boundary formation. These results demonstrate that 3DXRD coupled with in-situ heating is a successful non-destructive technique for examining real-time post-deformational annealing in strongly deformed crystalline materials with complicated microstructures.

Grain boundary sliding in San Carlos olivine: Flow law parameters and crystallographic-preferred orientation

[1] We performed triaxial compressive creep experiments on aggregates of San Carlos olivine to develop a flow law and to examine microstructural development in the dislocation-accommodated grain boundary sliding regime (GBS). Each experiment included load and temperature steps to determine both the stress exponent and the activation energy. Grain boundary maps, created with electron backscatter diffraction data, were used to quantify grain size distributions for each sample. Inversion of the resulting data produced the following flow law for GBS: GBS = 104.8 ± 0.8 (σ2.9 ± 0.3/d0.7 ± 0.1) exp[(−445 ± 20 kJ mol−1)/RT], with σ, d, and GBS in units of MPa, μm, and s−1, respectively. Although relatively weak, crystallographic-preferred orientations (CPOs) have [010] maxima parallel to the compression direction along with [100] and [001] girdles perpendicular to the compression direction. CPOs and subgrain boundary misorientation axes suggest that the (010)[100] slip system contributes significantly to deformation. We propose that these experimental results are best modeled by a deformation mechanism in which strain is accomplished primarily through grain boundary sliding accommodated by the motion of dislocations. Extrapolation of our flow laws to mantle conditions suggests that GBS is likely to be the dominant deformation mechanism in both lithospheric shear zones and asthenospheric flow, and therefore strong upper mantle seismic anisotropy can not be attributed solely to the dominance of dislocation creep.

TEM Characterization of near Sub-Grain Boundary Dislocations in Directionally Solidified Multicrystalline Silicon

A crystal is known to achieve lower energy if lattice dislocations are re-arranged in arrays forming a sub-grain boundary through a recovery process. Interaction of boundary dislocations with glide dislocations is also expected to bring about local equilibrium. In this work, dislocations localised in the vicinity of a sub-grain boundary (mis-orientation ) are studied in detail by transmission electron microscopy in order to determine their source. Contrary to the processes described above, it appears that the sub-grain boundary is the source of these dislocations, which are emitted from some locally stressed parts of the boundary. Several slip systems have been activated along the boundary resulting in high density of dislocations. It appears, further, that dislocation propagation from one or more sources is disrupted by interaction with other dislocations or other defects. The dislocations from various sources will be piled up against the obstacles of the other, resulting in the localization of the dislocations close to the sub-grain boundary

Effect of Zener-Hollomon parameter on deformation microstructure in Fe-3%Si alloy

Hot deformation of Fe-3%Si alloy within the temperature range of 1073-1473 K and strain rate range of 0.01-5 s-1 was carried out by compression test.Optical microscopy (OM),electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM) were used to characterize the deformation microstructure on various scales.Dynamic recovery is the dominant softening mechanism under all experimental conditions.A dynamic recovery region and partial dynamic recrystallization region can be distinguished according to Zener-Hollomon parameter (Z) based on OM observation.Furthermore,the quantitative description of subgrain size and boundary misorientation has been set up as a function of Zener-Hollomon parameter.