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Probabilities of Random Disorientation Axes in Cubic Polycrystals
Author(s) -
Basson F.
Publication year - 1997
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188989601045x
Subject(s) - cubic crystal system , materials science , crystallography , geometry , mathematics , chemistry
The theoretical function describing the probability density of disorientation axes is obtained for cubic polycrystals (recalling that the disorientation axis is the rotation axis associated with the smallest angle of rotation required to rotate a cube into a standard orientation). An analytical expression for this density function is determined in spherical coordinates and then in stereographic projection coordinates to facilitate graphical representation. The results provide a basis for a rigorous interpretation of experimental disorientation data. In particular, they demonstrate a high probability of finding 45° (111) disorientations in randomly oriented cubic polycrystals.