Grain Boundary Plane Distributions Research Articles

Study on deviation distribution of Σ3 and Σ9 boundaries in Hastelloy C-276 superalloy with different hot rolling reductions

In this study, the deviation distributions of Σ3 and Σ9 grain boundaries in a Hastelloy C-276 sheet were measured using electron backscatter diffraction technology (EBSD) and the grain boundary plane orientation was analyzed using a five-parameter technique after hot rolling at 900 °C with different thickness reductions. The results show that the relative areas of Σ3 grain boundary planes reveal a strong peak at the (111) twist position, and the corresponding intensity significantly decreases as the reduction increases. The hot rolling generates dislocations, resulting in significant deviation of Σ3 grain boundary orientations and the loss of special properties. However, the Σ9 grain boundary plane distribution (GBPD) becomes more diffused with increasing deformation, and the multiples of random distribution (MRD) value is ∼2. In addition, the large deviation of the Σ9 grain boundary orientation varies across the different strain samples. In low-strain samples, the deviation of the Σ9 grain boundary orientation may be affected by the Σ3 grain boundary deviation with construction of the Σ3–Σ3–Σ9 triple junction. The deformation microstructures mainly determine the deviation of the Σ9 grain boundary orientation in high-strain samples. Moreover, the distorted grain boundaries act as potent nucleation sites of dynamic recrystallization (DRX) during the hot rolling process.

Formation of intergranular phases in precipitation hardening nickel-based alloy 725

From the two possible intergranular phases in nickel alloy 725 (UNS N07725, Inconel 725), i.e., M23C6 and the σ-related F phase, the abundant formation of F phase was found to critically compromise the hydrogen embrittlement resistance of the alloy. Nevertheless, the processing conditions and microstructural features that favor the formation of one phase over the other are yet to be investigated. Herein, intergranular phases in commercial batches in their as-received condition and after selective thermal treatments were studied to better understand the precipitation behavior. The distribution of grain boundary planes of the nickel matrix was assessed using stereological analysis of electron backscatter diffraction data. Results showed a direct correlation between the extent of F phase precipitation and the population of grain boundaries terminated on (111) planes, which provide low-energy nucleation sites for F phase. Our results suggest that while intergranular precipitates formed during aging, the preceding thermomechanical and thermal treatments defined the relative abundance of nucleation sites for each phase by affecting the grain boundary character distribution. Thus, targeted grain boundary engineering approaches could be developed to avoid susceptible microstructures and improve the hydrogen embrittlement resistance of the alloy. Furthermore, the results may help produce samples with different extents of intergranular M23C6 and F phase to evaluate, in future studies, the individual effect of the phases on the properties of the alloy.

Calculating the grain boundary inclination of voxelated grain structures using a smoothing algorithm

We have developed a flexible method for calculating the grain boundary (GB) inclinations of voxelated grain structure data using smoothing algorithms. We compared the performance of four algorithms: the linear interpolation, Allen–Cahn, level-set, and vertex algorithms. We assessed their accuracy using 2D and 3D cases with known inclinations. The vertex algorithm provided the best balance between accuracy and efficiency for 2D structures while the linear interpolation algorithm provided the best balance for 3D structures. We compared the GB inclinations calculated using our smoothing method on a 3D high energy X-ray diffraction microscopy (HEDM) dataset to those determined by meshing the GBs. The two approaches determined similar GB plane distributions, though they varied significantly at triple junctions. Finally, the smoothing method was demonstrated for two sources of 3D voxelated grain structures: HEDM data and results from Monte Carlo Potts grain growth simulations.

Orientation relationship of texture development in hot-rolled W during annealing

Severe through-thickness texture inhomogeneity is apt to occur during hot-rolling of tungsten. This raises the intriguing notion of how is the inhomogeneity affected by stress-involved or heat-involved factors of the thermo-mechanical process. The texture development in the bulk and at the surface were investigated, and the main focus was on the role of grain boundaries on texture development. The deformed texture at the surface and in the bulk seems similar, but the recrystallized texture of them evolves in entirely different manner, hence, the through-thickness effect is considered to be unilaterally triggered by heat-involved factor, i.e., “annealing” rather than “straining”. In the bulk, the recrystallized orientation basically retains the starting deformed γ-texture and θ-texture even if grain growth occurs. Meanwhile some subtle alternations (nucleation behaviors) show statistically a strong correlation with CSL relationships. At the surface, the deformed γ-texture is completely replaced by a prominent Goss texture ({110}〈001〉) at 1100 °C. The grain boundary plane distribution (GBPD) analysis demonstrates that the formation of Goss texture at the surface is controlled by low angle grain boundaries (LAGBs) and {112}〈111〉 or {100}〈110〉 oriented nucleation is controlled by Σ3 CSL boundary.

Equilibrium and kinetic shapes of grains in polycrystals

The equilibrium crystal shape is a convex shape bound by the lowest energy interfaces. In many polycrystalline microstructures created by grain growth, the observed distribution of grain boundary planes appears to be dominated at low driving forces (after long grain growth times) by the planes present in the equilibrium crystal shape. However, at earlier stages of grain growth, it is expected that kinetic effects will play an important role in grain boundary motion and morphology. Analogous to the equilibrium crystal shape, the kinetic crystal shape of seed crystals growing from a liquid at higher supersaturations is bound by the slowest growing orientations. This study presents an equivalent construction for grain boundaries in polycrystals and uses it to determine the kinetic crystal shape for strontium titanate as a function of temperature. Relative grain boundary mobilities for strontium titanate for the low energy crystallographic orientations from seeded polycrystal experiments are used to calculate the kinetic crystal shapes as a function of temperature and annealing atmosphere. The kinetic crystal shapes are then compared to the morphologies and orientations of the interfaces of the growing seed crystals, and to the equilibrium crystal shapes, as well.The conclusions are that (1) the kinetic crystal shape is extremely anisotropic and displays significant transitions as a function of temperature that do not mirror changes in equilibrium crystal shape, (2) the kinetic shapes observed in the microstructures are dominated by the growing side of the interface (single crystal) and not by the dissolving side (polycrystalline matrix), and (3) faster growing orientations break up into macroscopic facets composed of slower growing orientations. The implications for grain growth underscore the applicability of crystal growth models to grain growth in polycrystals. In particular, in strontium titanate, the anisotropy of the grain boundary mobility as represented in the kinetic crystal shape is expected to be reduced from five macroscopic parameters to two (interface normal) allowing for incorporation of growth rate anisotropy in simulations of microstructure evolution at the earliest stages of grain growth, i.e. at the highest driving forces.

Role of inclination dependence of grain boundary energy on the microstructure evolution during grain growth

The role of inclination dependence of grain boundary energy on the microstructure evolution and the orientation distribution of grain boundary planes during grain growth in polycrystalline materials is investigated by three-dimensional phase-field simulations. The anisotropic grain boundary energy model uses the description of the faceted surface structure of the individual crystals and constructs an anisotropic energy of solid-solid interface. The energy minimization occurs by the faceting of the grain boundary due to inclination dependence of the grain boundary energy. The simulation results for a single grain show the development of equilibrium shapes (faceted grain morphologies) with different families of facets which agrees well with the theoretical predictions. The results of grain growth simulations with isotropic and anisotropic grain boundary energy for cubic symmetry show that inclination dependence of grain boundary energy has a significant influence on the grain boundary migration, grain growth kinetics and the grain boundary plane distribution. It has been shown that the model essentially reproduces the experimental studies reported for NaCl and MgO polycrystalline systems where the anisotropic distribution of grain boundary planes has a peak for the low-index {100} type boundaries.

Determination of the five parameter grain boundary character distribution of nanocrystalline alpha-zirconium thin films using transmission electron microscopy

Grain boundary engineering and other fundamental materials science problems (e.g., phase transformations and physical properties) require an improvement in the understanding of the type and population of grain boundaries in a given system – yet, databases are limited in number and spare in detail, including for hcp crystals such as zirconium. One way to rapidly obtain databases to analyze is to use small-grained materials and high spatial resolution orientation microscopy techniques, such as ASTAR™/precession electron diffraction. To demonstrate this, a study of grain boundary character distributions was conducted for α-zirconium deposited at room temperature on fused silica substrates using physical vapor deposition. The orientation maps of the nanocrystalline thin films were acquired by the ASTAR™/precession electron diffraction technique, a new transmission electron microscope based orientation microscopy method. The reconstructed grain boundaries were classified as pure tilt, pure twist, 180°-twist and 180°-tilt grain boundaries based on the distribution of grain boundary planes with respect to the angle/axis of misorientation associated with grain boundaries. The results of the current study were compared to the results of a similar study on α-titanium and the molecular dynamics results of grain boundary energy for α-titanium.

The equilibrium crystal shape of strontium titanate and its relationship to the grain boundary plane distribution

In this study, the equilibrium crystal shape (ECS) of a model system, strontium titanate, is compared with the grain boundary plane distribution (GBPD) as a function of temperature. Strontium titanate has a pronounced surface energy anisotropy and a grain growth anomaly, with the grain growth rate decreasing by orders of magnitude with increasing temperature. The ECS was determined from the shape of small intragranular pores and the GBPD was determined from orientation measurements on surfaces, with the relative areas of grain boundary planes in a polycrystal correlated to the surface energy of both adjacent crystal planes. The grain boundary energy has been previously proposed to be the sum of the surface energy of the adjacent grains less a binding energy that is assumed to be constant. While much experimental evidence exists for this assumption at a fixed temperature, the influence of temperature is not known. While the anisotropy of the ECS was found to decrease with temperature, the anisotropy of the GBPD increased with temperature. These findings indicate that changes in the binding energy with temperature must be considered, as the binding energy links the surface energy to the grain boundary energy. The results are discussed with respect to the grain growth anomaly of strontium titanate, in which the grain growth decreases with increasing temperature.

Crystallography of Interfaces and Grain Size Distributions in Sr‐Doped LaMnO3

Grain‐boundary plane distributions (GBPDs), grain size distribution (GSDs), and upper tail departure from log‐normal GSDs were quantified in dense and porous La0.8Sr0.2MnO3 samples to understand expected microstructures in solid oxide fuel cells. Samples were sintered at 1450°C for 4 h and then annealed between 800°C and 1450°C. The GBPDs and normalized GSDs reached steady state during sintering and little variation occurred during annealing. The GBPDs were nearly isotropic, with the relative areas of {001} planes being slightly higher than random (and the relative areas of {111} planes being less than random). The porous sample had an almost identical GBPD, whereas the almost isotropic pore boundary plane distribution was essentially opposite to the GBPD. The upper tails of the experimental GSDs, and several theoretical distributions, were characterized using peaks‐over‐threshold analysis. Dense samples, and all normal grain growth models, exhibit lower frequencies of large grains in the upper tail than would a log‐normal distribution, and the experimental distributions are similar to the Mullins distribution. Porous samples, however, have an anomalous increased frequency of large grains in the upper tail, as compared to all the model distributions, even though other metrics of the microstructure indicate the dense and porous systems are similar.

Grain Boundary Plane Distributions in a Hot Rolled 5A06 Aluminum Alloy

To investigate the preferential distribution of grain boundary planes in a hot rolled aluminum alloy, the electron backscattered diffraction approach and five‐parameter analysis method are used to characterize the grain boundary plane distributions in a hot rolled 5A06 aluminum alloy, and the results show that the orientations of grain boundary planes are textured. Grain boundary planes favor the {111} orientation at the center of the specimen, and their population is 56% higher than that in a random distribution, whereas grain boundary planes favor the {110} orientation on the surface of the specimen, and their population is 69% higher than that in a random distribution. Moreover, this anisotropic distribution of grain boundary planes occurs at all misorientation angles. The study suggests a new understanding of the pathway to evaluate the crystallographic orientation dependent performances.

The five-parameter grain boundary character distribution of nanocrystalline tungsten

Transmission electron microscopy has been used to collect high-resolution orientation maps from a tungsten thin film with a 100 nm average grain size. The orientation distribution of grain boundary planes at specific lattice misorientations is non-uniform and has characteristics similar to materials with larger grain sizes. A comparison of the populations of grain boundaries in tungsten with the same boundaries in a ferritic steel suggests that polycrystals with a body-centered cubic crystal structure have similar grain boundary character distributions.

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.

GRAIN BOUNDARY PLANE DISTRIBUTIONS IN 304 STEEL ANNEALED AT HIGH TEMPERATURE AFTER A PARALLEL PROCESSING OF MULTIPLE FORGING AND DIRECT ROLLING

It is well-recognized that low ∑-CSL boundaries are highly populated in the grain boundary character distribution(GBCD) for austenitic stainless steel(SS) processed by low strain and subsequent annealing.However,large-strain plus annealing typically tends to introducing numerous random high angle grain boundaries(RHABs) instead of producing high fraction of∑3,∑9 and∑27 boundaries.In this case,the distribution of grain boundary planes of RHABs must be very relevant to the properties of material.The current study is to explore the evolution of GBCD and grain boundary plane distribution(GBPD) in 304 austenitic SS after large strain and subsequent annealing using electron backscatter diffraction(EBSD) and five-parameter analysis(FPA).After solid solution treatment,304 steel samples were separately processed by multiple forging(MF) and direct rolling (DR) with true straine=2 followed by same annealing at 900℃for 2—120 min.Then the GBCDs and GBPDs of the two groups of samples were examined.The results show that the total∑3~n(n=1, 2,3) special boundaries in any sample as processed take a length fraction of lower than 45%out of the entire boundaries,and with annealing proceeding the incoherent∑3 boundaries tend to be tuned into coherent ones and consequently the summation fractions of∑9 and∑27 boundaries decrease accordingly.In the two samples which were separately processed by MF and DR but followed by the same annealing at 900℃for 120 min,their random boundaries or general high angle boundaries(∑3~n special boundaries filtered) mostly appeare to be the 111 twist and 110 tilt boundaries,indicating there exist grain boundary textures(GBT) in both samples.However,in the condition of some misorientations, the GBPDs of random boundaries are quite different in the two samples.For grain boundaries of 111/30—40°misorientation,more grain boundaries of twist type nearly on the exact {111} plane are found in the specimen processed by DR and annealing for 120 min(DR120) compared to that processed by MF and annealing for 120 min(MF120).For the grain boundaries of 110/50°misorientation,it was found that most of such boundaries in MF120 are tilt type and positioned on {112},{113} and {115} planes,whereas those in DR120 are tilt or mixed type positioned on {001}, {111} and {012}.It was suggested that there are distinct effects of pre-processing on the GBPDs of annealed 304 steel.

Crystallographic Characteristics of Grain Boundaries in Dense Yttria-Stabilized Zirconia

Grain-boundary plane, misorientation angle, grain size, and grain-boundary energy distributions were quantified using electron backscatter diffraction data for dense polycrystalline yttria-stabilized zirconia, to understand interfacial crystallography in solid oxide fuel cells. Tape-cast samples were sintered at 1450°C for 4 h and annealed for at least 100 h between 800°C and 1650°C. Distributions obtained from both three-dimensional (3D) reconstructions and stereological analyses of 2D sections demonstrated that the (100) boundary planes {(111)} have relative areas larger {smaller} than expected in a random distribution, and that the boundary plane distribution is inversely correlated to the boundary energy distribution.

GRAIN BOUNDARY PLANE DISTRIBUTIONS IN THE COLD–ROLLED AND ANNEALED FERRITIC STAINLESS STEEL

The grain boundary plane distribution in the cold-rolled and annealed ferritic stainless steel has been analyzed statistically by a five-parameter method based on the mis-orientations of adjacent grains and the orientations of grain boundary traces determined by electron backscatter diffraction(EBSD) attached to a field emission scanning electron microscope(FE-SEM).The results show that no preferred texture occurrs either in grain orientations or grain boundary mis orientations characterized by axis-angle pairs in the specimens which were cold rolled by 85%reduction in thickness and subsequently annealed at 780℃.However,there are developed textures for the orientations of grain boundary planes.And also,the preferred planes vary with averaged grain size levels.At the level of 9μm,grain boundary planes favor the {100} orientation,with their density distribution 12% higher than a random distribution;Whereas at the level of 15μm,{111} planes are preferred and {100} and {112} planes are sub-preferred,with the density distribution on {111} about 10%higher than a random distribution.Moreover,the anisotropy of grain boundary plane distributions is larger at specific mis-orientations.The discussion points out the preferred grain boundary planes might possess lower energies and tend to being preserved due to their lower growth rates during annealing.

Grain Boundary Texture

Recently the distribution of grain boundary planes in metals and other materials has begun to be studied in addition to the misorientation distribution. It has been found that a ‘grain boundary texture’, i.e. a non-random distribution of grain boundary planes, often exists. The present paper will show examples of grain boundary texture taken from austenitic stainless steel and rocksalt. The characteristics of the grain boundary texture will be described in terms of low-index boundary planes and tilt/twist descriptors. Reasons for the formation of the particular grain boundary texture and possibilities for exploitation via grain boundary engineering will be discussed.

Correlation between Boundary Energy and Grain Boundary Character Distribution in Fe-Based Polycrystals

The grain boundary energy anisotropy in BCC Fe-based polycrystals is considered. The correlation between the energy in BCC random grain boundaries and the distribution of grain boundary planes in the bulk was examined with a special attention on the presence of low index (low surface energy) planes in the internal surfaces. For a BCC structure, {100} and {110} planes are known to be the lowest energy planes dominating the equilibrium crystal shapes. Experimental evidences demonstrated that these planes were predominant in the texture of surfaces controlled by surface energy [2]. Moreover, the relation between the grain boundary character distribution and the crystallographic dependence on the grain boundary energy in the bulk after annealing treatment was studied. The grain character boundary distribution (GCBD) was calculated using the crystallographic information obtained from OIM-EBSD maps from samples showing columnar grains. Preliminary results showed no particular distribution trend within the standard stereographic triangle (001-101-111).

The distribution of grain boundary planes in polycrystals

During the last ten years, techniques have been developed to measure the distribution of grain boundaries in polycrystals as a function of both lattice misorientation and grain boundary plane orientation. This paper presents a brief overview of the techniques used for these measurements and the principle findings of studies implementing these techniques. The most significant findings are that grain boundary plane distributions are anisotropic, that they are scale invariant during normal grain growth, that the most common grain boundary planes are those with low surface energies, that the grain boundary populations are inversely correlated with the grain boundary energy, and that the coincident site lattice number is a poor predictor of the grain boundary energy and population.

Relation between precipitate-free zone width and grain boundary type in 7075-T7 Al alloy

The effect of grain boundary (GB) type on precipitate-free zone (PFZ) width in friction stir-processed 7075-T7 Al alloy is investigated by transmission electron microscopy (TEM) and stereology. The average half width of PFZs at random GBs is 70.4 ± 0.7 nm. For low-angle GBs, an apparent transition of PFZ half width is observed at a misorientation of 11°. For coincidence site lattice ( Σ) GBs, only Σ1, Σ3 and Σ5 have smaller PFZ width than that of random GBs. Crystal-frame stereology is used to recover the GB plane distribution. It is found that the GB plane distribution is relatively isotropic for most Σ GBs. Low/high index plane combinations are observed for most Σ GBs; furthermore, most Σ GBs have both tilt and twist components. The combined results of TEM and stereology suggest that smaller PFZ width is associated only with low Σ GBs since the formation and growth of PFZs at GBs depends closely on the core structure, in addition to the geometric structure of GBs.

Distribution of misorientations and grain boundary planes in grain boundary engineered brass

The present paper reports the application of a five parameter determination of grain boundary types to grain boundary engineered α brass. Approximately 20 000 grains constituted the total sample population, giving rise to more than 77 000 grain boundary line segments. This is the first time that the orientation of a large sample population of grain boundary planes has been measured in a grain boundary engineered material. The most important findings of the investigation were that the distribution of planes showed a prevalence of 〈 110 〉 tilt boundaries, especially asymmetric tilt types, and the presence of 〈 111 〉 twist boundaries. This distribution is a consequence of the low energy of these boundary types. Furthermore, more than three-quarters of boundaries could be considered to be 'potentially special'. The presence of these boundaries greatly fragmented the grain boundary network. This fragmentation is probably a key factor in the development of superior properties in a grain boundary engineered material.