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The interpretation of X-ray diffraction patterns from twinned crystals and the solution of other problems involving twin formation can be assisted by the use of certain formulae. Given the indices of the twin plane ( HKL ) or the twin axis [ UVW ], it is possible to find the indices of a plane in the twinned part of a crystal in terms of those of the corresponding plane in the parent crystal, or to formulate the corresponding transformation for zone axes. A general relationship applicable to any crystal systems has been derived in matrix form. A particular form of the matrix and a new relationship follow for cubic crystals. Examples are given of the use of the matrix and formulae. These refer to twins on {111} planes in face-centred cubic metals and other cubic crystals and to twinning titanium and in uranium.
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Andrews et al. (1955) studied this question.
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