The precise crystal symmetry, and hence the emergence of electric polarization, still remains an open question in multiferroic $R$Mn${}_{2}$O${}_{5}$ ($R$=rare earth, Bi, Y). While previous diffraction studies have indicated centrosymmetric space group $P\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m$, atomic displacement allowing for polarization would require a nonce...

This paper focuses on the symmetries of space lattice crystal cells. All 32 point groups of three dimensional crystal cells are exclusively described by vectors (three for one particular cell) taken from the physical cell. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. The set...

In the crystal structure, the title Schiff base compound, C(23)H(30)N(2)O(4), exhibits crystallographic twofold rotation symmetry. The imino group is coplanar with the aromatic ring with an N-C-C-C torsion angle of -179.72 (9)°. An intra-molecular O-H⋯N hydrogen bond forms a six-membered ring, producing an S(6) ring motif. The dihedral angle between symmetry related benzene rings is 28.05 (5)°....

The vibration-rotation states of a tetrahedral molecule in a field of D3h symmetry are studied by an extended group theory. Symmetry adapted rotational wave functions for the ground and the triply degenerate excited vibrational states are constructed. The crystal field potential is derived explicitly for a tetrahedral molecule in a hexagonal close-packed crystal. As an example, the rovibrationa...

We report the complete macroscopic average strain tensor for a cold-rolled uranium plate. The strain tensor was determined by the least-squares refinement of interplanar spacings for 19 Bragg reflections, as determined from the neutron TOF measurements at LANSCE. An annealed uranium plate was used as a reference sample, thus providing reference interplanar spacings for all 19 reflections. We al...

The highly explosive molecules As(N(3))(3) and Sb(N(3))(3) were obtained in pure form by the reactions of the corresponding fluorides with (CH(3))(3)SiN(3) in SO(2) and purification by sublimation. The crystal structures and (14)N NMR, infrared, and Raman spectra were determined, and the results compared to ab initio second-order perturbation theory calculations. Whereas Sb(N(3))(3) possesses a...

The crystal structure of human muscle creatine kinase has been determined by the molecular-replacement method and refined at 3.5A resolution. The structures of both the monomer and the dimer closely resemble those of the other known structures in the creatine kinase family. Two types of dimers, one with a non-crystallographic twofold symmetry axis and the other with a crystallographic twofold s...

A macroscopic symmetry group describing the superconducting state of an orthorhombically twinned crystal of YBCO is introduced. This macroscopic symmetry group is different for different symmetries of twin boundaries. Josephson tunneling experiments performed on twinned crystals of YBCO determine this macroscopic symmetry group and hence determine the twin boundary symmetry (but do not experime...

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal sur...

The title mol-ecule, C(12)H(14)N(8)S(2), has point symmetry [Formula: see text] since it is situated on a crystallographic centre of symmetry. The 1-meth-yl/5-thio groups are in an anti-periplanar conformation. The dihedral angle between the benzene and tetra-zole rings is 84.33 (2)°. In the crystal, C-H⋯N hydrogen bonds link mol-ecules into ladder-like chains running along the b axis. There ar...