Dislocations in solids
Dislocations in solids
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DOI：
10.1107/s0108767388014606
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发表时间：
1989-07
期刊：
影响因子：
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通讯作者：
A. Parasnis
中科院分区：
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作者：
A. Parasnis
*如果旋转角度不是180，那么旋转的感觉也必须是守恒的。例如，这个归一化器缺少通过b的镜像平面。然而，这不会改变它的不变子空间。例如，平面上的反射，归一化器包含所有平行平移，所有垂直平面上的反射等。然而，表3第二列中简短而明显的描述足以产生第三列中列出的不变子空间。后一列与表1的第二列一致。因此，随后的定义变成：对称操作W的几何元素由属于W的欧几里得归一化器的所有操作的子空间(s)不变量组成。以下注释适用于表3:(i)旋转反演出现三个项目（而不是表1中的两个）不是一个差异：如果点是不变量，则直线的不变量遵循平面的不变量，反之亦然。因此，后两者中有一个是多余的。（ii）“子空间”应该在适当的意义上取，因为在不适当的意义上（“所有空间”），它对任何同余都是不变的。它必须添加到所有几何元素中，但不会增加它们的信息内容。（iii）只需要获得整个子空间的不变性，而不一定像SCIPRO定义所要求的那样是逐点的。（iv）需要注意的是，上面提到的同余运算是点空间中的运算（见ITA83，§8.1）。5)，而不是向量空间。因此，几何元素的定义只适用于点空间中的对称操作，而不适用于向量空间中的对称操作。
* If the rotation angle is not 180, then the sense of rotation must also be conserved. The normalizer then lacks mirror planes through b, for instance. However this does not change its invariant subspaces. reflection in a plane, for example, the normalizer contains all parallel translations, reflections in all perpendicular planes, etc. The short and rather obvious description in the second column of Table 3 is, however, sufficient to yield the invariant subspaces listed in the third column. This latter column is in accordance with the second column of Table 1. The ensuing definition hence becomes: the geometric element of a symmetry operation W consists of the subspace (s) invariant for all operations belonging to the Euclidean normalizer of W.The following remarks apply to Table 3:(i) The occurrence of three items for the rotoinversion (instead of two in Table 1) is not a discrepancy: if the point is invariant, invariance of the line follows from that of the plane, and vice versa. Hence, one of the latter two is redundant.(ii)'Subspace'should be taken in the proper sense, because in the improper sense ('all space') it is invariant for any congruence. It would have to be added to all geometric elements but would not increase their information content.(iii) The invariance need only obtain for the subspace as a whole, not necessarily pointwise as required in the SCIPRO definition.(iv) It should be noted that the congruence operations referred to above are operations in point space (see ITA83, § 8.1. 5), not vector space. The given definition of geometric elements hence applies to symmetry operations in point space only, not to those in vector space.