Heidrun Sowa

Effect of hydrostatic pressure on the γ-polymorph of glycine 1. A polymorphic transition into a new δ-form

Abstract The results of a high-resolution powder diffraction study of the effect of high hydrostatic pressure up to 8 GPa on the pure γ-polymorph of glycine (P31) are discussed. A phase transition with a jumpwise change of cell volume and cell parameters was observed. The transition starts at about 2.73 GPa and is still not complete even at 7.85 GPa. The crystal structure of the previously unknown high-pressure polymorph of glycine (δ-polymorph) could be solved and refined in the space group Pn. In this structure, glycine zwitter-ions are linked via NH…O hydrogen bonds into layers, which form double-layered bands via additional NH…O hydrogen bonds. The structure of the individual layers in the high-pressure polymorph is similar to that in the previously known α- (P21/n) and β- (P21) forms, but the packing of the layers is essentially different. The pressure-induced polymorphic transformation in the γ-glycine can be compared with a change in the secondary structure of a peptide, when a helix is transformed into a sheet.

High-pressure X-ray investigation of zincite ZnO single crystals using diamond anvils with an improved shape

A high-pressure cell for single-crystal investigations requires large opening angles. If it does not contain any beryllium but only two diamonds mounted on steel backing plates, normally only lower pressures can be attained without risk of disruption of the diamond anvils [Ahsbahs (2004). Z. Kristallogr. 219, 305–308]. In order to enable pressures up to at least 10 GPa, specially shaped anvils were designed. In a first study with such anvils, the high-pressure behaviour of zincite ZnO was investigated up to the transition pressure of about 9.5 GPa. A slight decrease of the axial ratio c/a with increasing pressure was observed. The fit of the Birch–Murnaghan equation of state gave a bulk modulus K = 146.5 (8) GPa with a fixed pressure derivative K′ = 4. During the phase transformation, the single crystals were destroyed. The pronounced preferred orientation of the obtained material, however, enabled the determination of the orientation relations between the low-pressure wurtzite-type and the high-pressure NaCl-type phase. The orientation relations are similar to those in CdS and CdSe.

A comparative study of the anisotropy of lattice strain induced in the crystals of DL-serine by cooling down to 100 K, or by increasing pressure up to 8.6 GPa. A comparison with L-serine

Summary The anisotropy of lattice strain in the crystals of DL-serine (P21/n) on cooling down to 100 K and with increasing hydrostatic pressure up to 8.6 GPa was studied by single-crystal X-ray diffraction. In contrast to L-serine undergoing pressure-induced phase transitions at about 5 and 8 GPa, no phase transitions were observed in DL-serine at least up to 8.6 GPa (the highest pressure reached in the experiment). The anisotropy of strain in DL-serine on cooling was shown to be radically different from that with increasing pressure. The response of the crystal structure of DL-serine to cooling and to increasing pressure was considerably different from that of L-serine.

Hexagonal and trigonal sphere packings. I. Invariant and univariant lattice complexes

All homogeneous sphere packings and all interpenetrating sphere packings have been derived that refer to the seven invariant and the 23 univariant lattice complexes belonging to the hexagonal crystal family. The respective sphere packings may be assigned to 66 types. In addition, one case of interpenetrating sphere packings was found. For five types, the inherent symmetry of some sphere packings with specialized metrical and coordinate parameters may become cubic. For two further types, namely 8/4/c1 (body-centered cubic lattice) and 12/3/c1 (face-centered cubic lattice), the inherent symmetry is cubic for all corresponding sphere packings. By means of a large number of examples, the applicability of sphere packings for the comparison and description of simple crystal structures is demonstrated.

Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres.

All systems of interpenetrating sphere packings that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family are tabulated. Homogeneous sphere packings belonging to 49 different types may be intertwined to systems of interpenetrating sphere packings belonging to 74 types. For all compatible lattice complexes, the coordinate and lattice parameters are given. The corresponding patterns of interpenetration are analysed. For the interpenetration of two, three, four, five and eight sphere packings, eleven, three, five, one and two different patterns, respectively, are distinguished. In addition, four types of interpenetrating layers of spheres were found. Each such sphere configuration splits into two or three subsets of parallel sphere layers with an angle of 90 degrees or of 120 degrees , respectively, between the directions of the normals of the layers. A single sphere layer corresponds either to a honeycomb net or to a net built up from quadrangles and octagons.

Hexagonal and trigonal sphere packings. II. Bivariant lattice complexes.

All homogeneous sphere packings were derived which correspond to point configurations of the 26 bivariant lattice complexes belonging to the hexagonal crystal family. They may be assigned to 109 sphere-packing types. Among these, there is a type of sphere packing with contact number 10 that was not described before. For seven of the 109 types, the inherent symmetry of the sphere packings with minimal density is cubic. In addition, three types of interpenetrating sphere packings were found and one type of interpenetrating 6(3) sphere layers. Such an arrangement was unknown so far. Some frequently occurring structure types that can be related to sphere packings are described as examples.

A transition path for the pressure-induced wurtzite- to NaCl-type transformation described in Pna21

Quite recently, two further mechanisms for the pressure-induced transition from the wurtzite to the NaCl type were proposed [Shimojo et al. (2004). Phys. Rev. B, 70, 184111-1-6] but no symmetry information was given. It will be shown that a slight modification of one of the assumed transition pathways allows a crystallographic description on the basis of a deformation of a heterogeneous 4-connected sphere packing in Pna2(1). All investigations were done with the help of the corresponding homogeneous packing in Pnma where the transition may be described as a deformation of a lonsdaleite configuration into a cubic primitive lattice cP. During the transformation, all sphere contacts are maintained. The new transition model is compared with the well known Cmc2(1) mechanism. Further related mechanisms can also be derived.

A transition path from the zinc-blende to the NaCl type

In order to find a transition path from the zinc-blende to the NaCl type both structures are described with the aid of heterogeneous sphere packings. If all atoms in such crystal structures are replaced by like ones, atomic arrangements result that correspond to homogeneous sphere packings belonging to the diamond type or forming a cubic primitive lattice, respectively. It is shown, that a diamond configuration may be deformed into a cubic primitive lattice within the Wyckoff position Imma 4(e) mm2 0,¼,z. The corresponding phase transition in binary compounds from the zinc-blende to the NaCl type can be described as a deformation of a heterogeneous sphere packing in the subgroup Imm2 of Imma. Since no bonds have to be broken this type of transition is displacive. In addition, structural relations between high-pressure phases of semiconductors like silicon and germanium and related AB compounds are shown.

Orthorhombic sphere packings. I. Invariant and univariant lattice complexes

All homogeneous sphere packings and all interpenetrating sphere packings were derived that refer to the 6 invariant and the 11 univariant lattice complexes belonging to the orthorhombic crystal system. In total, sphere packings of 38 types have been found. Only for 17 types is the maximal inherent symmetry of their sphere packings orthorhombic. By means of a number of examples, the applicability of sphere packings for the comparison and description of simple crystal structures is demonstrated.

On the density of homogeneous sphere packings

For some types of sphere packing with typical one- and two-dimensional parameter regions, the sphere-packing density as a function of the free parameters is discussed. In addition, some sphere-packing types with extraordinary density properties are presented. Until now, it was generally assumed that sphere packings with minimal density are also those of highest inherent symmetry. An example to prove the opposite is given.