12.15. Compute GBCD
Group (Subgroup)
Statistics (Crystallography)
Description
This Filter computes the Grain Boundary Character Distribution (GBCD) for a Triangle Geometry. The GBCD is a statistical description of the types of grain boundaries present in a polycrystalline material. It answers the question: “What fraction of the total grain boundary area has a given misorientation and boundary plane orientation?”
What is the GBCD?
In a polycrystalline material, grains meet at boundaries. Each boundary can be described by five parameters:
3 parameters for the misorientation – the rotational difference between the crystal orientations of the two grains on either side of the boundary
2 parameters for the boundary plane normal – the direction the boundary surface faces, expressed in the crystal reference frame
The GBCD is a histogram over this 5-dimensional space. It records how much grain boundary area exists for each combination of misorientation and boundary plane orientation, normalized so that a random distribution would give a value of 1.0. Results are reported in multiples of a random distribution (MRD), so a value of 2.0 means there is twice as much boundary of that type as would be expected in a random polycrystal.
How This Filter Works
For each triangular face on the grain boundary mesh, the filter identifies the two grains on either side.
It computes the misorientation between the two grains and determines the boundary plane normal in the crystal reference frame.
Crystal symmetry is applied to map each boundary into a unique representation.
The boundary is placed into the appropriate bin of the 5D histogram, weighted by its area.
The result is normalized by the total boundary area.
The GBCD Resolution parameter controls the bin size of the histogram. Smaller values give finer resolution but require more boundary data for statistical reliability.
Note
Only boundaries between grains of the same phase are included in the calculation. The GBCD can be visualized by using the Write GBCD Pole Figure (GMT) or Compute GBCD Pole Figure filters.
For an alternative approach to computing the GBCD using continuous metrics instead of binning, see the Compute GBCD (Metric-Based Approach) filter.
Required Input Sources
This filter operates on a grain-boundary surface mesh and requires the following upstream steps:
Triangle Geometry – produced by a surface meshing filter such as Quick Surface Mesh, optionally followed by Laplacian Smoothing.
Face Labels – produced alongside the mesh by Quick Surface Mesh.
Face Normals – produced by Compute Triangle Normals.
Face Areas – produced by Compute Triangle Areas.
Feature Euler Angles / Feature Phases – the feature-level average Euler angles and phases. Averages are produced by Compute Average Orientations; phases by Compute Feature Phases.
Crystal Structures – ensemble-level array read from EBSD data or created by Create Ensemble Info.
References
[1] G. S. Rohrer, “Grain boundary energy anisotropy: a review,” Journal of Materials Science, vol. 46, pp. 5881-5895, 2011. DOI: 10.1007/s10853-011-5677-3
[2] G. S. Rohrer, “Measuring and Interpreting the Structure of Grain-Boundary Networks,” Journal of the American Ceramic Society, vol. 94, no. 3, pp. 633-646, 2011. DOI: 10.1111/j.1551-2916.2011.04384.x
Input Parameter(s)
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
GBCD Spacing (Degrees) |
Scalar Value |
Float32 |
The resolution in degrees for the GBCD calculation |
Input Triangle Geometry
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Triangle Geometry |
Geometry Selection |
Triangle |
Path to the triangle geometry for which to calculate the GBCD |
Face Labels |
Array Selection |
Allowed Types: int32 Comp. Shape: 2 |
Array specifying which Features are on either side of each Face |
Face Normals |
Array Selection |
Allowed Types: float64 Comp. Shape: 3 |
Array specifying the normal of each Face |
Face Areas |
Array Selection |
Allowed Types: float64 Comp. Shape: 1 |
Array specifying the area of each Face |
Input Ensemble Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Crystal Structures |
Array Selection |
Allowed Types: uint32 Comp. Shape: 1 |
Enumeration representing the crystal structure for each Ensemble |
Output Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Average Euler Angles |
Array Selection |
Allowed Types: float32 Comp. Shape: 3 |
Array specifying three angles defining the orientation of the Feature in Bunge convention (Z-X-Z) |
Phases |
Array Selection |
Allowed Types: int32 Comp. Shape: 1 |
Specifies to which phase each Feature belongs |
Output Face Ensemble Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Face Ensemble Attribute Matrix |
DataObjectName |
The name of the created face ensemble attribute matrix |
|
GBCD |
DataObjectName |
5 parameter GBCD data. The 6th component is used internally to track the northern vs. southern hemisphere of the Lambert sphere |
Example Pipelines
(08) Small IN100 GBCD
License & Copyright
Please see the description file distributed with this Plugin
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