Marzouki Mohamed Amine, Souvignier Bernd, Nespolo Massimo
Radboud University Nijmegen, Faculty of Science, Mathematics and Computing Science, Institute for Mathematics, Astrophysics and Particle Physics, Postbus 9010, 6500 GL Nijmegen, The Netherlands.
Université de Lorraine, Faculté des Sciences et Technologies, Institut Jean Barriol FR 2843, CRM2 UMR CNRS 7036, BP 70239, Boulevard des Aiguillettes, F-54506 Vandoeuvre-lès-Nancy Cedex, France.
Acta Crystallogr A Found Adv. 2014 Jul;70(Pt 4):348-53. doi: 10.1107/S2053273314007335. Epub 2014 May 17.
Staurolite has been long considered an enigma because of its remarkable pseudosymmetry and the frequent twinning. Staurolite gives two twins whose occurrence frequency seems to contradict the condition of lattice restoration requested by the reticular theory of twinning, in that the more frequent one (Saint Andrews cross twin) has a twin index of 12, whereas the less frequent one (Greek cross twin) has a twin index of 6. The hybrid theory of twinning shows that the former is actually a hybrid twin with two concurrent sublattices and an effective twin index of 6.0. However, this is still not sufficient to explain the observed higher occurrence frequency of the Saint Andrews twin. The (pseudo)-eigensymmetry of the crystallographic orbits of staurolite has been analysed and it was found that the whole substructure built on anions is restored (with small deviations) by both twin laws, which explains why twinning is frequent in staurolite. On the other hand, 45% of the cation sites are quasi-restored in the Saint Andrews cross twin, against only 19% for the Greek cross twin: this difference finally explains the different occurrence frequencies of the two twins.
由于其显著的假对称性和频繁的孪晶现象，十字石长期以来一直被视为一个谜。十字石有两种孪晶，其出现频率似乎与孪晶的网状理论所要求的晶格恢复条件相矛盾，因为较常见的一种（圣安德鲁十字孪晶）的孪晶指数为12，而较不常见的一种（希腊十字孪晶）的孪晶指数为6。孪晶的混合理论表明，前者实际上是一种具有两个并发子晶格且有效孪晶指数为6.0的混合孪晶。然而，这仍然不足以解释观察到的圣安德鲁孪晶较高的出现频率。对十字石晶体轨道的（假）本征对称性进行了分析，发现基于阴离子构建的整个子结构通过两种孪晶法则都能恢复（有小的偏差），这解释了十字石中孪晶频繁出现的原因。另一方面，在圣安德鲁十字孪晶中45%的阳离子位置近似恢复，而希腊十字孪晶中只有19%：这种差异最终解释了两种孪晶不同的出现频率。
