# Find Distances to Characteristic Grain Boundaries¶

## Group (Subgroup)¶

Statistics (Crystallographic)

## Description¶

This Filter computes 'approximate distances' from a given boundary to the nearest boundaries of characteristic geometries, i.e., tilt, twist, symmetric, and 180°-tilt boundaries.

Five-tuples of macroscopic boundary parameters constitute the five-dimensional boundary space. Crystal and grain-exchange symmetries imply that different 5-tuples may represent the same physical boundary. All these equivalent representations need to be considered. Differences in geometries of boundaries can be quantified by means of a metric defined in the space. With a properly defined metric the distance between two boundaries (minimized over all representations) is small (large) if they are similar (distinct). Boundaries of special geometric features serve as reference points in the boundary space, and general boundaries may be characterized by their distances to the nearest reference boundaries. Since calculation of the distances to the nearest characteristic boundaries is numerically expensive, the accurate distances are replaced by parameters defined in A. Morawiec, K. Glowinski, On "macroscopic" characterization of mixed grain boundaries, Acta Mater. 61, 5756-5767 (2013) and K. Glowinski, On identification of symmetric and improperly quasi-symmetric grain boundaries, J. Appl. Cryst. 47, 726-731 (2014). These parameters are not only fast to calculate, but it was also proved that they are strongly correlated with the true distances.

The parameters approximating the distances to the nearest characteristic boundaries are defined as follows: + To the nearest tilt boundary: αL = min { α } + To the nearest twist boundary: αN = 90° - max { α } + To the nearest symmetric boundary: αS = min { [ α2 + (180° - ω)2 ]1/2 } + To the nearest 180°-tilt boundary: αI = min { [ (90° - α)2 + (180° - ω)2 ]1/2 }

In the above formulas, α = | u * n1 | with u and n1 being unit vectors representing the misorientation axis and boundary normal given in first of the crystallites, respectively; ω stands for the misorientation angle, and minimization is over symmetrically equivalent boundary representations.

### Why are some distances equal to 999.0?¶

If phases of Features separated by a Face are the same, i.e., if the Face is a grain boundary, then the distances are computed as defined above; the number of equivalent boundary representations processed is determined by crystal symmetry of the given phase.

However, if the phases of Features separated by a Face are different, then that Face is not a grain boundary, but an interphase boundary, and all distances are therefore set to 999.0° (a value which is out of the ranges for the distances). 999.0 is also ascribed to triangles lying at the outer surface of the volume.

None

Image + Triangle

## Required Objects¶

Kind Default Name Type Component Dimensions Description
Ensemble Attribute Array CrystalStructures uint32_t (1) Enumeration representing the crystal structure for each Ensemble
Feature Attribute Array AvgEulerAngles float (3) Three angles defining the orientation of the Feature in Bunge convention (Z-X-Z)
Feature Attribute Array Phases int32_t (1) Specifies to which phase each Feature belongs
Face Attribute Array FaceLabels int32_t (2) Specifies which Features are on either side of each Face
Face Attribute Array FaceNormals double (3) Specifies the normal of each Face

## Created Objects¶

Kind Default Name Type Component Dimensions Description
Face Attribute Array DistanceToTilt float (1) αL, given in degrees
Face Attribute Array DistanceToTwist float (1) αN, given in degrees
Face Attribute Array DistanceToSymmetric float (1) αS, given in degrees
Face Attribute Array DistanceTo180tilt float (1) αI, given in degrees

## 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

## References¶

[1] A. Morawiec, K. Glowinski, On "macroscopic" characterization of mixed grain boundaries, Acta Mater. 61, 5756-5767 (2013)

[2] K. Glowinski, On identification of symmetric and improperly quasi-symmetric grain boundaries, J. Appl. Cryst. 47, 726-731 (2014)

[3] J. Li, S.J. Dillon and G.S. Rohrer in 'Relative Grain Boundary Area and Energy Distributions in Nickel', Acta Mater. 57, 4304-4311 (2009)

## Example Pipelines¶

Please see the description file distributed with this Plugin.