Nespolo Massimo
Université de Lorraine, CNRS, CMR2, Nancy, France.
Acta Crystallogr A Found Adv. 2018 Jul 1;74(Pt 4):332-344. doi: 10.1107/S2053273318005351. Epub 2018 Jul 5.
Plesiotwins and diperiodic twins have in common the fact of being characterized by a low degree of lattice restoration. Plesiotwins differ from twins by the fact that the relative orientation of the individuals is obtained by a non-crystallographic rotation about the normal to the composition plane, whereas for twins this rotation is crystallographic, apart from possible small deviations coming from metric pseudosymmetries. In the case of plesiotwins, the low degree of lattice restoration comes from a large coincidence site lattice (CSL) in the composition plane. Diperiodic twins, instead, have a small CSL in the composition plane but the second plane of the same family contributing to the overall lattice restoration is too far away from the composition plane to be considered significant. It is shown that plesiotwins can occur as reflection twins if the composition plane is not parallel to the twin plane, and as rotation twins in the case of parallel hemitropy. Diperiodic twins can in principle occur in any category, but either the metric conditions to obtain a diperiodic twin are actually in contrast with the metric pseudosymmetry required for twinning or the result is actually a hybrid twin. This justifies why no confirmed examples of diperiodic twins are known to date.
近孪晶和双周期孪晶的共同特点是晶格恢复程度较低。近孪晶与孪晶的不同之处在于，个体的相对取向是通过绕成分平面法线的非晶体学旋转获得的，而对于孪晶，除了可能由于度量伪对称性产生的小偏差外，这种旋转是晶体学的。在近孪晶的情况下，晶格恢复程度较低是由于成分平面中存在大的重合位置点阵（CSL）。相反，双周期孪晶在成分平面中有小的CSL，但对整体晶格恢复有贡献的同一家族的第二个平面离成分平面太远，以至于不被认为是显著的。结果表明，如果成分平面不与孪晶平面平行，近孪晶可以作为反映孪晶出现；在平行半面性的情况下，则作为旋转孪晶出现。双周期孪晶原则上可以出现在任何类别中，但要么获得双周期孪晶的度量条件实际上与孪晶所需的度量伪对称性相矛盾，要么结果实际上是一个混合孪晶。这就解释了为什么迄今为止还没有已知的双周期孪晶的确切例子。
