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6. Five identical crystalline segments are shown, each of which has twofold rotational symmetry in projection. Pairs of crystal segments meet at a coherent interface or twin plane in which the structures on either side of the twin plane are mirror images of each other. The five crystal segments meet at a central point which exhibits fivefold symmetry as a macroscopic element of point symmetry but the individual crystal segments clearly do not exhibit any fivefold symmetry. Schechtman showed conclusively that twinning such as shown in Fig.
It is little used in crystallography. Solid State Chemistry and its Applications, Second Edition, Student Edition 6 rotation axes (d), a complete layer is easily produced; both the individual hexagons and the overall array exhibit sixfold symmetry. This is not to say that molecules which have pentagonal symmetry, n = 5, cannot exist in the crystalline state. They can, of course, but their fivefold symmetry cannot be exhibited by the crystal as a whole. 2 Quasicrystals The discovery of a new state of matter, the quasicrystalline state, by Schechtman and colleagues in 1982 (and which led to the Nobel Prize in Chemistry in 2011) appeared at first sight to violate the rules concerning allowable rotational symmetries in crystal lattices.
19 Coordination number 12 of shaded sphere in (a) hcp and (b) ccp structures. The shaded sphere is in the B layer, the layer underneath is A and the layer above is either (a) A or (b) C. are known as eutactic structures. Some guidelines as to whether it is appropriate to consider a structure in terms of a cp arrangement are given in Appendix D. 11 Relationship between Cubic Close Packed and Face Centred Cubic The unit cell of a ccp arrangement is the familiar face centred cubic (fcc) unit cell, Fig.