![]() Weyl semimetals from noncentrosymmetric topological insulators. Weyl points and line nodes in gyroid photonic crystals. Multi-Weyl topological semimetals stabilized by point group symmetry. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4. Weyl semimetal in a topological insulator multilayer. Chiral gauge field and axial anomaly in a Weyl semimetal. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Classification of topological quantum matter with symmetries. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. There was an interessing discussion on this on the fmf forum (but with more focus on cyclic rutile twins.Murakami, S. On the other hand reticulated twins exist and I wonder how they actually grow. Actually I don't rember having seen a zig-zag type twin (or other reticulated twins) with 'extra' outer symmetries as in your rutile example either. I have never seen such a twin in real life. Also for the gypsum twin with the transation symmetry, I don't know of an underlying crystal structure element that would cause such a translation. I believe that if you would accurately measure twins like these you would find no proof for a existing glide-reflection symmetry (as you would for a wheat spike). I can't imagine a crystal growth mechanism or a property of twinned crystal structures that would 'encode' for an outer form with glide-reflection symmetry twin like the zig-zag rultile twin from you first example. The outer form is a consequence of the internal structure. Just as the outer shape of the classic gypsum twin is directly related to the crystal structure of the twin. The wheat spike is a good example, the symmetry of the spike is there because it is encoded in the genetic makeup of the wheat plant. The point is that is that I don't believe this symmetry really exist. If I am correct you use the glide-reflection to describe the symmetry of the (macroscopic) crystal, wich indeed is a different concept. The picture of a wheat spike shows a botanical example of glide reflection: what about minerals?Ģnd Sep 2013 10:40 UTC Mark Holtkamp Hi Pablo, Look at this example in te picture: on the left we have a symple drawing of a classical gypsum contact twinning according to a plane symmetry law on the right we have the same diagram but a translation τ, of course it is an ideal case. Maybe they are different concepts? The plane π for the glide refection τσ doesn't need to be a glide plane, and doesn't need to be a symmetry element for the untwinned crystal. > because symmetry elements of the untwinned structure cannot act as twin elements. Also you can't check the spacegroup to see if the twin plane is a glide plane Anyway, it was only a wrong example, I wrote it here to introduce the glide reflection. ![]() Well, there would be an advantage, because you describe the whole set using only two geometrical elements: one plane π and one vector τ if you use a sequence of twins, you need a different plane (for symmetry) or a different axe (for rotation) each time. > twinning but isn't it simpler to see them as a > twins as in your drawing as glide-reflection > I can see it is tempting to describe repeated Currier Digital LibraryOpen discussion area. Techniques for CollectorsOpen discussion area. Minerals and MuseumsOpen discussion area. Mineralogical ClassificationOpen discussion area. Lost and Stolen SpecimensOpen discussion area. ╳Discussions □ Home □ Search □ Latest Groups EducationOpen discussion area.
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