Orientation can be only described by rotations in order to transform one grain into another. If a twin is described by a mirror operation the "left variety" will be then transformed into the "right variety", e.g. left- and right-handed quartz. These both varieties are not identical (for quartz). Is this a general feature? In other words, if for an enantiomorphic structure (not centrosymmetric) a structure description exists and twins of mirror-operation occur...does this mean that the same structure needs to be described as "inverse" structure as well?
Dear Dr Nolze,
Maybe some insight can come from enatiomeric molecular compounds (e.g. Lactic acid, RR/SS tatrates) which crystallize not as a racemate but separately as enatiomorphic crystals. In that case these enatiomorphic crystals are to be regarded as two different phases which have, however, identical properties. The melt then typically forms a totally symmetric eutectic (or there is some recemic compound) and two eutectics. A mirror operation than transforms the two phases into each other. In non-molecular compounds like Quartz it is interesting: there is no configurational entropy from mixing the two molecule and therefore no eutectic, and there you can regard it as a single-(pseudo)component system. Interesting to think about application of Gibbs phase rule in such different cases....
Best regards
Andreas Leineweber
Dear Prof. Leineweber,
for enantiomorphic crystals the probelem appears more or less clear although I wonder whether - as in case of quartz - enantiomorphic crystals are always described by different space-group types? A more general question is: Do twins of centrosymmetric phases represent only a special case and are actually rotations as well? And what is with phases which are not enantiomorphic but also not centrosymmetric (like polar crystal structures), e.g. like AIIIBV semiconductor compounds? There, twins can be described by a 4-fold rotation around [001] or a 180° rotation around [10-10].
Best greetings
G. Nolze
... at least as it regards the space groups: P3(1)12 and P3(2)12 are the two enantionmorphs. Its works similar with space group pairs containing 64/62 or 41/43. In other cases the two space group types of the enantiomorphs have the same space group type (e.g. P2(1)2(1)2(1))...