Groupoid of orientational variants.
Groupoid of orientational variants.
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方向变体的群形。
DOI：
10.1107/s010876730503686x
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
C. Cayron
中科院分区：
文献类型：
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作者：
C. Cayron
与母体晶体具有取向关系的子晶体称为变体。它们可以通过结构相变(朗道或重建)、孪生或沉淀产生。从父相和子相的点群以及从变换矩阵定义的内部和外部变换类允许确定不同变体的取向。它们与左陪集在代数上是一致的，它们的数目由拉格朗日公式给出。一个简单的等式将正向和反向转变的变种数量联系在一起。变量间变换的等价类与双陪集(算子)同构，其个数由Burnside公式给出。取向变种和算符构成了一个广群，它的合成表作为转变的结晶学标志。还描述了确定是否可以从一个以上的母体晶体遗传两个子体变体的一般方法。编制了计算任何结构转变的所有这些性质的计算机程序；给出了钢的Burgers相变和马氏体相变的一些结果。简要讨论了由热循环产生的取向变量构成的分形系统的复杂性、不可逆性和熵。
Daughter 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.