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Statistical treatment of measured orientation relationships in orientation space
Author(s) -
Werner E.,
Prantl W.
Publication year - 1988
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/s0021889888002316
Subject(s) - orientation (vector space) , distribution (mathematics) , geometry , euler angles , mathematics , space (punctuation) , symmetry (geometry) , distribution function , phase (matter) , mathematical analysis , boundary (topology) , physics , computer science , thermodynamics , quantum mechanics , operating system
Measured orientation relationships between neighbouring grains in single‐phase α ‐ and β ‐ and dual‐phase α + β ‐brasses are analysed by means of the χ 2 ‐test. The orientation relationships are characterized by the three Euler angles and hence can be represented as points in orientation space. A description of the symmetry relations of equivalent points in this space is given and then the distribution function for random orientation relationships is derived. This distribution is compared with the distribution of the measured orientation relationships using only a single χ 2 ‐test for each boundary type. The results of the tests are the same as obtained from the analysis of axis‐angle pairs, in which case two χ 2 ‐tests are necessary. None of the measured distributions is random.