000203384 001__ 203384
000203384 005__ 20181203023706.0
000203384 0247_ $$2doi$$a10.1107/S010876730503686X
000203384 022__ $$a01087673
000203384 037__ $$aARTICLE
000203384 245__ $$aGroupoid of orientational variants
000203384 260__ $$c2006
000203384 269__ $$a2006
000203384 336__ $$aJournal Articles
000203384 520__ $$aDaughter crystals in orientation relationship with a parent crystal are called variants. They can be created by a structural phase transition (Landau or reconstructive), by twinning or by precipitation. Internal and external classes of transformations defined from the point groups of the parent and daughter phases and from a transformation matrix allow the orientations of the distinct variants to be determined. These are algebraically identified with left cosets and their number is given by the Lagrange formula. A simple equation links the numbers of variants of the direct and inverse transitions. The equivalence classes on the transformations between variants are isomorphic to the double cosets (operators) and their number is given by the Burnside formula. The orientational variants and the operators constitute a groupoid whose composition table acts as a crystallographic signature of the transition. A general method that determines if two daughter variants can be inherited from more than one parent crystal is also described. A computer program has been written to calculate all these properties for any structural transition; some results are given for Burgers transitions and for martensitic transitions in steels. The complexity, irreversibility and entropy of fractal systems constituted by orientational variants generated by thermal cycling are briefly discussed. © 2006 International Union of Crystallography - All rights reserved.
000203384 700__ $$0248450$$aCayron, C.$$g112215
000203384 773__ $$j62$$q21-40$$tActa Crystallographica Section A: Foundations of Crystallography
000203384 909C0 $$0252516$$pLMTM$$xU12903
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000203384 937__ $$aEPFL-ARTICLE-203384
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000203384 980__ $$aARTICLE