Centerband-Only Detection of Exchange NMR with Natural-Abundance Correction Reveals an Expanded Unit Cell in Phenylalanine Crystals.

The NMR pulse sequence CODEX (centerband-only detection of exchange) is a widely used method to report on the number of magnetically inequivalent spins that exchange magnetization via spin diffusion. For crystals, this rules out certain symmetries, and the rate of equilibration is sensitive to distances. Here we show that for C CODEX, consideration of natural abundance spins is necessary for crystals of high complexity, demonstrated here with the amino acid phenylalanine.

Monoclinic sphere packings. III. Trivariant lattice complexes of P2/c and P2/c.

All homogeneous sphere packings were derived that refer to the trivariant lattice complexes of monoclinic space-group types P2/c and P2/c. In total, sphere packings of 55 types have been found. The maximal inherent symmetry is monoclinic for 17 types while the other types comprise at least one sphere packing with cubic (four cases), hexagonal (six cases), tetragonal (eight cases) or orthorhombic (20 cases) symmetry.

Monoclinic sphere packings. II. Trivariant lattice complexes with mirror symmetry.

All homogeneous sphere packings were derived that refer to the three trivariant monoclinic lattice complexes with mirror symmetry. In total, 29 types of sphere packings have been found. Only for three types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for 13 types, tetragonal for eight types, hexagonal for four types and cubic for one type.

Sphere packings as a tool for the description of martensitic phase transformations.

Martensitic transformations which play an important role in metallurgical processes are analysed using group-subgroup relations and sphere-packing considerations. This approach is applied to the transformations between body-centred cubic (b.c.

Monoclinic sphere packings. I. Invariant, univariant and bivariant lattice complexes.

All homogeneous sphere packings were derived that refer to the two invariant, the four univariant and the three bivariant lattice complexes belonging to the monoclinic crystal system. In total, sphere packings of 29 types have been found. Only for five types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for nine types, tetragonal for five types, hexagonal for six types and cubic for four types.

Orthorhombic sphere packings. IV. Trivariant lattice complexes of space groups without mirror planes belonging to crystal class mmm.

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that can be realized in the ten orthorhombic trivariant lattice complexes belonging to the space groups of crystal class mmm without mirror symmetry. Altogether, sphere packings of 186 different types have been found; the maximal inherent symmetry is orthorhombic for 124 of these types. In addition, ten types of interpenetrating sphere packings were detected, and in three lattice complexes interpenetrating 6(3) nets occur.

Intermolecular interactions, disorder and twinning in ciprofloxacin-2,2-difluoroethanol (2/3) and ciprofloxacin-water (3/14.5).

The antibiotic ciprofloxacin [systematic name: 1-cyclopropyl-6-fluoro-4-oxo-7-(piperazin-4-ium-1-yl)-1,4-dihydroquinoline-3-carboxylate], has been crystallized as a 2:3 solvate with 2,2-difluoroethanol, 2C(17)H(18)FN(3)O(3)·3C(2)H(4)O(2), (I), and as a 3:14.5 hydrate, 3C(17)H(18)FN(3)O(3)·14.5H(2)O, (II).

Orthorhombic sphere packings. III. Trivariant lattice complexes with mirror symmetry.

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that refer to the 18 orthorhombic trivariant lattice complexes with mirror symmetry. In total, sphere packings of 51 different types have been found. Only for 28 of these types is the maximal inherent symmetry of their sphere packings orthorhombic.

Three new types of interpenetrating sphere packings.

Three new types of homogeneous interpenetrating sphere packings are described. In the general position of space group Ccce, two sphere packings of type 3/10/o1 can be combined to form interpenetrating sphere packings of type o[3/10/o1]2. The other two types of interpenetrating sphere packings show symmetry Fddd: two packings of type 3/10/t4 are intertwined in o[3/10/t4]2 and three packings of type 3/4/t1 in o[3/4/t1]3.

Orthorhombic sphere packings. II. Bivariant lattice complexes.

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that refer to the 22 orthorhombic bivariant lattice complexes. In total, sphere packings of 90 different types have been found. Only for 47 of these types is the maximal inherent symmetry of their sphere packings orthorhombic.

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.

Hexagonal and trigonal sphere packings. IV. Trivariant lattice complexes of trigonal space groups.

The 13 trivariant lattice complexes with trigonal symmetry are compatible with 218 types of homogeneous sphere packings, 7 types of interpenetrating sphere packings and one type of interpenetrating layers of spheres. Altogether, the lattice complexes with trigonal characteristic space group (with 0, 1, 2 or 3 degrees of freedom) give rise to 225 types of sphere packing. 110 of these types are compatible exclusively with one of the 13 trivariant lattice complexes, 31 in addition with some of the invariant, univariant or bivariant lattice complexes, whereas 6 types occur solely in such a lattice complex.

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.