Grain Boundary Energy Distribution Research Articles

Engineering grain boundary energy with thermal profiles to control grain growth in SrTiO3

AbstractThis study investigates the influence of thermal history on grain boundary (GB) energy and the grain growth behavior of SrTiO3 at 1425°C. Two thermal profiles were explored: (1) a single‐step sintering at 1425°C for 1 h and (2) a two‐step profile with sintering completed at 1425°C for 1 h with an additional 10 h at 1350°C. Electron backscattered diffraction and atomic force microscopy were utilized to measure the grain size and GB energy distributions, respectively, for the samples before and after grain growth at 1425°C for 10 h. The two‐step profile exhibits fewer abnormal grains and a slower growth rate at 1425°C than the single‐step profile. Additionally, the two‐step sample comprises few high‐energy GBs and a narrow GB energy distribution, which suggests that it had a lower driving force for subsequent grain growth. The thermal profile was able to sufficiently change the growth rate such that the two‐step sample results in a finer grain size than observed for the single‐step sample after 10 h at 1425°C despite being exposed to elevated temperatures for almost twice as long. These results suggest that GB energy engineering through thermal profile modification can be used to control the grain growth rate and abnormal grain growth likelihood.

Relative grain boundary energies from triple junction geometry: Limitations to assuming the Herring condition in nanocrystalline thin films

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning, and this data can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 min annealing at 400 °C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum Σ3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials.

Relative Grain Boundary Energies from Triple Junction Geometry: Limitations to Assuming the Herring Condition in Nanocrystalline Thin Films

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 minutes annealing at 400{\deg}C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum {\Sigma}3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials.

Determining grain boundary energies from triple junction geometries without discretizing the five-parameter space

Grain boundary energy anisotropy plays an important role in many science and engineering problems. This paper presents a new numerical method for determining the grain boundary energy distribution (GBED) from the microstructures of polycrystalline materials. The method assumes that triple junctions are in local equilibrium, that this equilibrium is described by the Herring equation, and can be expressed using the Hoffman-Cahn formalism of the capillarity vector. The conventional method discretizes the five-parameter space and then fits the energy for each discrete bin. The new method minimizes the difference between similar boundaries in the dataset while obeying the equilibrium equation at triple junctions. This non-parametric approach shows smaller error than the conventional method, and it can also determine the grain boundary energies from datasets that have small numbers of triple junctions if their configurations are clustered in the five-parameter space, which is not possible using the conventional method. In addition, the proposed non-parametric approach performs better when the number of triple junctions increases, which is not always true for the conventional method.

Grain growth prediction with inclination dependence of 〈1 1 0〉 tilt grain boundary using multi-phase-field model with penalty for multiple junctions

Multi-phase-field (MPF) model with a higher-order term representing energetic penalty for multiple junctions was proposed to predict the grain growth accompanying the inclination dependence of grain boundary (GB) energy and mobility. The inclination effect was introduced on the basis of GB energy obtained from molecular dynamics (MD) simulations. The preliminary grain growth simulation of an isolated grain surrounded by Σ3 GB certified that the analytical equilibrium shape was well reproduced. The augmented higher-order term added to conventional MPF model could improve convergence and stability of numerical calculations around triple junction (TJ) region even if there exists the large GB energy gap at the TJ. Moreover, the present MPF model can realize well the Young’s relation with no GB inclination effect and further extend to the case with that effect. For the polycrystalline grain growth simulations with the GB energy distribution according to the misorientation angle of Al 〈1 1 0〉 tilt GB, Σ3 GB inclination lead the weak anisotropy characterized by Σ3{111} twin boundary. Besides, the inclination dependence can effectively drive the GBs with low GB energy like the low-angle GB during grain growth.

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.

Deriving grain boundary character distributions and relative grain boundary energies from three-dimensional EBSD data

Three-dimensional electron backscatter diffraction data, obtained by serial sectioning a nickel–base superalloy, has been analysed to measure the geometric arrangement of grain boundary planes at triple junctions. This information has been used to calculate the grain boundary character distribution (GBCD) and the grain boundary energy distribution (GBED). The twin content from the three-dimensional GBCD calculation compares favourably with the twin content estimated by stereology. Important factors in the analysis are the alignment of the parallel layers, the ratio of the out-of-plane to in-plane spacing of the discrete orientation data and the discretisation of the domain of grain boundary types. The results show that grain boundaries comprised of (111) planes occur most frequently and that these grain boundaries have a relatively low energy. The GBCD and GBED are inversely correlated.

Characterization of the Grain‐Boundary Character and Energy Distributions of Yttria Using Automated Serial Sectioning and EBSD in the FIB

A dual‐beam focused ion beam scanning electron microscope was used to collect a series of parallel electron backscatter diffraction maps of polycrystalline yttria. Using characteristics of the triple junctions, the individual layers were aligned and the geometries of the grain‐boundary planes between the layers were determined. This information was used to calculate the five‐parameter grain‐boundary character distribution (GBCD) and grain‐boundary energy distribution (GBED). The GBCD derived from the three‐dimensional data was qualitatively the same as that derived from a stereological analysis of the same data. The anisotropy in the GBCD of yttria is relatively weak compared with other ceramics and is inversely correlated to the GBED.

On the relationship between grain boundary character distribution and intergranular corrosion

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning, and this data can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 min annealing at 400 °C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum Σ3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials.

Energy distribution of grain boundary traps in semi-insulating polycrystalline silicon films doped with oxygen

The energy distribution of the grain boundary traps in semi-insulating polycrystalline silicon (SIPOS) films prepared by low pressure chemical vapor deposition (LPCVD) is determined for various oxygen contents taking account of the segregation effect of phosphorus. The energy distribution of the grain boundary traps is expressed as a Gaussian distribution. The surface trap density of the grain boundary and the energy band gap of the films increase with increasing oxygen content. Both peaks of the energy distribution of the donor- and acceptor-type traps are located at 0.49 eV over the valence band in case of poly-Si films, but moves toward the midgap as oxygen content increases in case of SIPOS films.

Influence of Carbon Addition on the Electrical and Structural Properties of Phosphorus and Boron Doped Silicon Layers

Phosphorus and boron doped polycrystalline silicon layers grown by chemical vapor deposition were additionally doped with carbon via the introduction of in the gas phase. Addition of carbon to n‐type and p‐type polycrystalline silicon gives rise to characteristic differences in resistivity vs. input pressures, at least at small input pressures of . The difference in resistivity can be explained by a donor activity of carbon or silicon‐carbon complexes or by an asymmetrical energy distribution of grain boundary traps, both at the grain boundaries. It is also shown that the addition of carbon has a strong influence on the morphology of the growing silicon layer. With increasing values of , the size of the grains in the layer decreases, under certain circumstances even amorphous silicon is formed, and this effect is stronger at the lowest temperatures. The decomposition kinetics of has also been discussed. It is concluded that at high input pressures of the deposition rate of carbon is gas phase diffusion controlled. At lower values and temperatures above 850°C, the formation of Si‐C nuclei is rate‐limiting as far as the introduction of carbon is concerned.