Estimate of halo ellipticity as a function of radius with flexions

The cold dark matter theory predicts triaxial dark matter haloes. The radial distribution of halo ellipticity depends on baryonic processes and the nature of dark matter particles (collisionless or collisional). Here we show that we can use lensing flexion ratios to measure the halo ellipticity as a function of radius. We introduce a weight function and study the relationship between the first and second order statistics of flexion ratios, both of which can be used to reduce the bias in the estimate of ellipticity. we perform numerical tests for our method, and demonstrate that it can reduce the bias and determine the halo ellipticity as a function of radius. We also point out that the minimum mean flexion ratio can be used to trace the centres of galaxy clusters.Comment: 9 pages,9 figures, MNRAS accepte

High-pressure phases and transitions of the layered alkaline earth nitridosilicates SrSiN2 and BaSiN2

We investigate the high-pressure phase diagram of SrSiN2 and BaSiN2 with density-functional calculation. Searching a manifold of possible candidate structures, we propose new structural modifications of SrSiN2 and BaSiN2 attainable in high-pressure experiments. The monoclinic ground state of SrSiN2 transforms at 3 GPa into an orthorhombic BaSiN2 type. At 14 GPa a CaSiN2-type structure becomes the most stable configuration of SrSiN2. A hitherto unknown Pbcm modification is adopted at 85 GPa and, finally, at 131 GPa a LiFeO2-type structure. The higher homologue BaSiN2 transforms to a CaSiN2 type at 41 GPa and further to a Pbcm modification at 105 GPa. Both systems follow the pressure-coordination rule: the coordination environment of Si increases from tetrahedral through trigonal bipyramidal to octahedral. Some high-pressure phases are related in structure through simple group–subgroup mechanisms, indicating displacive phase transformations with low activation barriers

9-Ethyl-N-(3-nitro­benzyl­idene)-9H-carbazol-3-amine

The title compound, C21H17N3O2, crystallizes with two mol­ecules in the asymmetric unit. The carbazole groups show relatively small deviations from planarity [maximum displacements from the mean carbazole plane are 0.077 (7) and 0.101 (7) Å]. The dihedral angles between the 3-nitro­benzyl­idene­amine and carbazole groups are 37.9 (1) and 37.0 (1)° in the two mol­ecules

5-Methyl-7,8,9,10-tetra­hydro­cyclo­hepta­[b]indol-6(5H)-one

In the title mol­ecule, C14H15NO, the dihedral angle between the benzene and pyrrole rings is 1.99 (12)°. The cyclo­heptene ring adopts a slightly distorted boat conformation

1-Diphenyl­methyl­ene-2-(9H-fluoren-9-yl­idene)hydrazine

In the title mol­ecule, C26H18N2, the 9H-fluorene unit is almost planar, as the cyclo­penta­diene ring makes dihedral angles of 1.12 (6) and 1.46 (6)° with the fused benzene rings. The dihedral angle between the two phenyl rings of the diphenyl­methyl­ene residue is 61.78 (6)°

{5-Methyl-1-[8-(trifluoro­meth­yl)quinolin-4-yl]-1H-1,2,3-triazol-4-yl}(morpholino)methanone

In the title mol­ecule, C18H16F3N5O2, the dihedral angle between the pyridine ring and the fused benzene ring is 4.50 (10)°. The triazole ring makes dihedral angles of 54.48 (12) and 57.91 (11)° with the pyridine and benzene rings, respectively. The morpholine ring atoms are disordered over two positions; the site-occupancy factors are ca 0.53 and 0.47. Inter­molecular C—H⋯F hydrogen bonding is found in the crystal structure. Furthermore, C—H⋯O and C—H⋯N intra­molecular contacts are also present

4,5-Dimethyl-1,2-diphenyl-1H-imidazole monohydrate

In the title compound, C17H16N2·H2O, the imidazole ring is essentially planar [maximum deviation = 0.0037 (7) Å]. The imidazole ring makes dihedral angles of 80.74 (7) and 41.62 (7)° with the phenyl rings attached to the N and C atoms, respectively. The dihedral angle between the two phenyl rings is 75.83 (8)°. Inter­molecular O—H⋯N and O—H⋯O hydrogen bonds are found in the crystal structure

High-pressure phase and transition phenomena in ammonia borane NH3BH3 from X-ray diffraction, Landau theory, and ab initio calculations

Structural evolution of a prospective hydrogen storage material, ammonia borane NH3BH3, has been studied at high pressures up to 12 GPa and at low temperatures by synchrotron powder diffraction. At 293 K and above 1.1 GPa a disordered I4mm structure reversibly transforms into a new ordered phase. Its Cmc21 structure was solved from the diffraction data, the positions of N and B atoms and the orientation of NH3 and BH3 groups were finally assigned with the help of density functional theory calculations. Group-theoretical analysis identifies a single two-component order parameter, combining ordering and atomic displacement mechanisms, which link an orientationally disordered parent phase I4mm with ordered distorted Cmc21, Pmn21 and P21 structures. We propose a generic phase diagram for NH3BH3, mapping three experimentally found and one predicted (P21) phases as a function of temperature and pressure, along with the evolution of the corresponding structural distortions. Ammonia borane belongs to the class of improper ferroelastics and we show that both temperature- and pressure-induced phase transitions can be driven to be of the second order. The role of N-H...H-B dihydrogen bonds and other intermolecular interactions in the stability of NH3BH3 polymorphs is examined.Comment: 23 pages, 7 figure

(E)-6-Chloro-2-(furan-2-yl­methyl­idene)-2,3,4,9-tetra­hydro-1H-carbazol-1-one

In the title compound, C17H12ClNO2, the carbazole unit is nearly planar [maximum deviation = 0.052 (1) Å]. The pyrrole ring makes dihedral angles of 1.92 (8) and 4.71 (11)° with the benzene and furan rings, respectively. Inter­molecular N—H⋯O hydrogen bonds form R 2 2(10) rings in the crystal structure