12.18. Compute GBPD (Metric-Based Approach)
Group (Subgroup)
Statistics (Crystallography)
Description
This Filter computes the Grain Boundary Plane Distribution (GBPD), which describes the relative frequency of grain boundary plane orientations in a polycrystalline material, regardless of the misorientation across the boundary. While the GBCD (see Compute GBCD) describes boundaries in the full 5D space of misorientation + plane normal, the GBPD considers only the 2D distribution of boundary plane normals.
An example GBPD is shown in Fig. 1.
Metric-Based Approach
This filter uses a metric-based approach adapted from the Compute GBCD (Metric-Based Approach) filter, as described by K. Glowinski and A. Morawiec in Analysis of experimental grain boundary distributions based on boundary-space metrics, Metall. Mater. Trans. A 45, 3189-3194 (2014).
The distribution is sampled at evenly distributed directions. For each sampling direction, the areas of mesh segments whose normals fall within a limiting angle ρp of that direction are summed. Crystal symmetry is applied so that each boundary segment is represented by up to 4 × nS equivalent vectors (where nS is the number of symmetry transformations). Only directions within the standard stereographic triangle need to be sampled; values at other points are obtained from symmetry.
After summing boundary areas, the distribution is normalized to multiples of a random distribution (MRD). A value of 1.0 means that plane orientation is as frequent as in a random polycrystal; values above 1.0 indicate preferred boundary plane orientations.
This Filter also calculates statistical errors of the distributions using the formula
ε = ( f n v )1/2, where ε
is the relative error of the distribution function at a given point, f is the value of the function at that point, and n stands for the number of grain boundaries (not the number of mesh triangles) in the considered network. The errors can be calculated either as their absolute values, i.e., ε × f or as relative errors, i.e., 100% × ε. The latter are computed in a way that if the relative error exceeds 100%, it is rounded down to 100%.
See also the documentation for Compute GBCD (Metric-Based Approach) for additional information.
Format of Output Files
Output files are formatted to be readable by GMT plotting program. The first line is always “0.0 0.0 0.0 0.0”. Each of the remaining lines contains three numbers. The first two columns are angles (in degrees) describing a given sampling direction; let us denote them col1 and col2, respectively. The third column is either the value of the GBCD (in MRD) for that direction or its error (in MRD or %, depending on user’s selection). If you use other software, you can retrive spherical angles θ and φ of the sampling directions in the following way:
θ = 90° - col1
φ = col2
Then, the directions are given as [ sin θ × cos φ , sin θ × sin φ , cos θ ].
Feedback
In the case of any questions, suggestions, bugs, etc., please feel free to email the author of this Filter at kglowinski at ymail.com
Required Input Sources
This filter operates on a grain-boundary surface mesh and requires the following upstream steps:
Triangle Geometry with Face Labels, Face Normals, Face Areas, and Node Types – produced by a surface meshing filter such as Quick Surface Mesh, followed by Compute Triangle Normals and Compute Triangle Areas.
Feature Phases – produced by Compute Feature Phases.
Crystal Structures – ensemble-level array read from EBSD data or created by Create Ensemble Info.
Input Parameter(s)
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Phase of Interest |
Scalar Value |
Int32 |
Index of the Ensemble for which to compute GBPD; boundaries having grains of this phase on both its sides will only be taken into account |
Limiting Distance [deg.] |
Scalar Value |
Float32 |
The max angle from within which mesh segments are selected |
Number of Sampling Points (on a Hemisphere) |
Scalar Value |
Int32 |
The approximate number of sampling directions |
Exclude Triangles Directly Neighboring Triple Lines |
Bool |
If checked, only interiors of Faces are included in GBCD |
|
Save Relative Errors Instead of Their Absolute Values |
Bool |
Whether or not to save the distribution errors as relative (if exceeds 100%, then rounded down) or absolute |
|
Triangle Geometry |
Geometry Selection |
Triangle |
The complete path to the triangle geometry |
Input Triangle Geometry Vertex Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Node Types |
Array Selection |
Allowed Types: int8 Comp. Shape: 1 |
Specifies the type of node in the Geometry |
Input Triangle Geometry Face Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Face Labels |
Array Selection |
Allowed Types: int32 Comp. Shape: 2 |
Specifies which Features are on either side of each Face |
Face Normals |
Array Selection |
Allowed Types: float64 Comp. Shape: 3 |
Specifies the normal of each Face |
Face Areas |
Array Selection |
Allowed Types: float64 Comp. Shape: 1 |
Specifies the area of each Face |
Input Triangle Geometry Face Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Feature Face Labels |
Array Selection |
Allowed Types: int32 Comp. Shape: 2 |
Specifies which original Features are on either side of each boundary Feature |
Input Feature Data
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Average Euler Angles |
Array Selection |
Allowed Types: float32 Comp. Shape: 3 |
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 |
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 Parameters
Parameter Name |
Parameter Type |
Parameter Notes |
Description |
|---|---|---|---|
Output Distribution File |
FileSystemPath |
The output distribution file path (extension .dat, GMT format) |
|
Output Distribution Errors File |
FileSystemPath |
The output distribution errors file path (extension .dat, GMT format) |
References
[1] K. Glowinski and A. Morawiec, Analysis of experimental grain boundary distributions based on boundary-space metrics, Metall. Mater. Trans. A 45, 3189-3194 (2014)
Example Pipelines
License & Copyright
Please see the description file distributed with this Plugin.
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