10.18. Compute GBPD (Metric-Based Approach)

Group (Subgroup)

Statistics (Crystallographic)

Description

This Filter computes the grain boundary plane distribution (GBPD) like that shown in Fig. 1. It should be noted that most GBPDs presented so far in literature were obtained using a method based on partition of the grain boundary space into bins, similar to that implemented in the Compute GBCD Filter. This Filter calculates the GBPD using an alternative approach adapted from the one included in the Compute GBCD (Metric-based Approach) Filter and 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). Briefly, the GBPD is probed at evenly distributed sampling directions (similarly to Compute GBCD (Metric-based Approach) Filter) and areas of mesh segments with their normal vectors deviated by less than a limiting angle ρ_p from a given direction are summed. If n_S is the number of crystal symmetry transformations, each boundary plane segment is represented by up to 4 × n_S equivalent vectors, and all of them are processed. It is enough to sample the distribution at directions corresponding to the standard stereographic triangle (or, in general, to a fundamental region corresponding to a considered crystallographic point group); values at remaining points are obtained based on crystal symmetries. After summing the boundary areas, the distribution is normalized. First, the values at sampling vectors are divided by the total area of all segments. Then, in order to express the distribution in the conventional units, i.e., multiples of random distribution (MRDs), the obtained fractional values are divided by the volume v = (A n_S) / (4π), where A is the area of a spherical cap determined by ρ_p.

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) Filter 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

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.

DREAM3D-NX Help

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