I have one question about the lattice rotation symmetry. For example, Sr3Ru2O7 exhibits orthorhombic space group Bbcb but a=b. If a is not equal to b, it has 2-fold lattice rotation symmetry for sure. But Sr3Ru2O7, a is equal to b. Does it have 4-fold or 2-fold lattice rotation symmetry? Thank all of you for your attention to my question and any advice is very welcome!
Dear Qiang,
Bbcb does not correspond to any space group in standard settings, hence, I presume that the space group you ask for is #68 (Ccca) with alternative axis and origin.
Anyway, if the symmetry is orthorhombic, only 2-fold axis and/or planes are permitted (the 3 orthorhombic point-groups from which all the orthorhombic space groups come from are: 222, mm2, mmm), if there is any 4-fold axis the crystal system must be tetragonal.
Best,
Pedro
This question is a bit tricky and actually nearly philosophical. In principle Pedro answered correctly taking the symmetry description into account. However, he perhaps did not carefully read your question. De facto you are also right. Your lattice reflects a lattice of tetragonal metric. It looks like tetragonal but the distribution of your atoms does not. Therefore, any description of triklinic like all lattice parameter are different and all angles between the basis vectors are not 90 degrees is wrong. If you look into the international tables for Crystallography triclinic is described by "no conditions" which means, also for triclinic phases a cubic metric is not excluded. The translation symmmetry needs to fullfill the symmetry, i.e. it can have a higher symmetry.In databases you can find triclinik phases with a=b=c and all angles 90 degrees. You will not rarely find monclinic phases with all angles 90 degrees, etc. However, this does not mean that there is a fourfold axis. This is definitely missing, anyway how your lattice parameters (translation lattice) is defined. This is one form of pseudosymmetry.
Dear Pedro,
Thank you very much for your advice! I totally agree with you.
Dar Giang,
your crystal belongs to the symmetry class "mmm" and hence it is orthorhombic, even if the two parameters normal to the c axis are equal. This may be due to a pseudo-symmetry , according to the Gert opinion. There are many cases of pseudosymmetry, in literature: Hydroxyapatite, for instance, looks like hexagonal, even if it is monoclinic, as it follows from the resultys obtained in our research group...
Anyway, a crystal is something more complex than its bulk structure (obtained from X-ray diffractometry. ) Looking at the surfaces of the (001) faces , if any, of your crystal, by means of an AFM (or with an optical microscope), you will find the real structure of the surface and, consequently, the true symmetry of the growing layers. Also the SEM investigations can help you to solve this exciting problem.
All the best !
Dino
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