Layer group

Abstract: The [LiAl2(OH)6]+ layer obtained from gibbsite–Al(OH)3 belongs to the layer group symmetry P-312/m. This layer satisfies the defining characteristics of a synthon in that it predicts all the polymorphic modifications of the layered double hydroxides of Li and Al. The various possible ways of stacking these layers can be derived by the systematic elimination of the principal symmetry elements comprising the layer group. This approach yields the complete universe of possible structures. When the 3 axis of the layer is conserved in the stacking, the resultant crystal adopts the structure of the 1H, 2H, or 3R polytypes (H, hexagonal; R, rhombohedral). When the 3 axis is destroyed and the 2/m axis is retained, the crystal adopts monoclinic symmetry and crystallizes in the structures of the 1M1 or 1M2 (M, monoclinic) polytypes; the two polytypes differ only in their translational component. Experimentally, gibbsite-based precursors yield the 2H polytype, and bayerite-based precursors yield the 1M polytype. Faul...

Abstract: Using evolutionary algorithm and first-principles calculations, we predict a family group of two-dimensional node-line semimetals MX (M=Pd, Pt; X=S, Se, Te), which has zig-zag type mono-layer structure in Pmm2 layer group. Band structure analysis reveals that node-line features are caused by band inversion and the inversion exists even in the absence of spin-orbital-coupling. Tests are carried out to confirm that the node-line loop is protected by crystal symmetry. This work extends our knowledge of node-line materials to two-dimensional cases, i.e., a group of metal-group VI compounds sharing the same lattice structure which has time reversion and crystal-mirror inversion symmetries.

Abstract: A method of printing a three-dimensional object is provided. The method comprises providing a plurality of stationary printhead layer groups, each layer group comprising at least one printhead for printing a respective layer of the object; conveying a partially-formed object past the layer groups; and simultaneously printing material from at least one printhead in each layer group, such that a plurality of different layers are printed simultaneously by the layer groups.

Abstract: In a molecular crystal, intermolecular interactions will correspond to specific symmetry elements. If one chooses molecules carefully, one can reliably predict specific intermolecular interactions and the corresponding symmetry operations. The symmetry operations of one and two dimensional networks of molecules can be combined to form rod and layer groups respectively. In many cases of chemical interest the sequence of moving from a molecule to a one dimensional array, then on to two and three dimensions corresponds directly to the symmetry combinations leading from the point group to rod group, to layer group and on to the space group. The structures of a number of disubstituted urea derivatives were determined and are used to illustrate these ideas of molecular design.