Volume 210, Issue 3

A new method is described which allows to determine half-automatically and with high precision changes in optical path differences of single crystals. It uses a special interferometric arrangement which yields an extremely stable interference pattern resulting in a high resolution intensity distribution. Applications for the analysis of the linear electrooptic and electrostrictive effects of quartz and KH 2 PO 4 are demonstrated.

A simple procedure for twinning mode prediction has been worked out and a new classification of the modes is presented. Criteria have been laid down for the selection of twinning modes out of all those geometrically admissible. Numerical examples are given and the calculated twinning modes and the magnitudes of shear for various crystal systems are summarized.

From three-dimensional regular polyhedra, all non-isomorphic edge-bicolorings are derived. The notion of edge-bicoloring is generalized to edge ( k + 1)-colorings.

In order to evaluate the precision and/or accuracy of the refined parameters, the interatomic distances d (Si–O) and d (Al–O) calculated from the data reported in ten powder refinements of both well ordered and partially disordered kaolinite and dickite specimens were compared. The main tool used in our considerations were median-based box-and-whisker plots. It was found that the d (Si–O) lie within the interval 〈1.43, 1.87〉 Å, while d (Al–O) vary from 〈1.64, 2.12〉 Å; the expected values being 1.617 Å and 1.91 Å, respectively. The comparison of powder refinements with two reliable single crystal analyses of dickite has shown that the spread of distances in only one case is comparable with single-crystal refinements. The authors have reported rather precise but inaccurate distances or vice versa. All powder refinements have provided very close median distances, but the sizes of the boxes vary significantly from one refinement to another. The accuracy of the interatomic distances obtained from powder refinements is almost independent on the presence or absence of disorder in the structure.

Single crystals of nearly stoichiometric CuMnO 2 were grown using a LiBO 2 flux. They crystallize in the monoclinic space group C 2/ m with cell parameters a = 557.8(6) pm, b = 288.1(2) pm, c = 588.6(7) pm, β = 104.00(5)° and Z = 2. The structure can be described as a close packing of linear [O–Cu–O] 3− groups parallel to the c -axis where Mn III -ions occupy edge sharing MnO 6 octahedra forming layers perpendicular to the c -axis. It is closely related to that of delafossite, CuFeO 2 , but the Jahn-Teller effect of Mn III -ions breaks the three-fold symmetry.

The crystal structure of the synthetic compound Pb 11 Ge 3 O 17 , M r = 2769.0, has been determined based on 16134 intensity data; R = 0.065, R w = 0.072. Monochromatized synchrotron radiation of wavelength 1.198 Å was used for data collection. The compound crystallizes triclinic in the space group P [unk] with lattice parameters a = 22.259(4) Å, b = 19.910(4) Å, c = 7.361(1) Å, α = 97.59(1)°, β = 95.15(1)°, γ = 92.35(2)°; V = 3215.8 Å 3 , Z = 6, D x = 8.579 Mg m −3 . As in PbO and other examples of lead germanate oxides with nongermanate O atoms, the Pb and Ge atoms are arranged like a cubic close packing of spheres. The fcc -like sequence of layers parallel to (100) is, however, interrupted after every fifth layer by two layers of hcp -like sequence: ccccchhccccchh … Taking the crystal structure into account, the chemical formula should be written as Pb 11 [GeO 4 ][Ge 2 O 7 ]O 6 .

C 6 H 14 N 3 O 7 P, M r = 271.16, orthorhombic, P 2 1 2 1 2 1 , a = 8.354(1) Å, b = 8.919(1) Å, c = 14.381(1) Å, V = 1071.5(1) Å 3 , Z = 4, D x = 1.68 g cm −3 , λ(Mo K α ) = 0.71069 Å, μ = 2.8 cm −1 , F (000) = 568, T = 293(2) K, R = 0.031 for 1770 observed reflections ( I > 3 σ ( I )). The L-histidinium phosphate monohydrate (LHP) crystals present very strong hydrogen bonds. The most important intermolecular interactions involve the phosphate group, as the P–O–H … O–C, P–O–H … O–P and N–H … O–P contacts.

The crystal structure of calcium glutarate monohydrate, Ca(C 5 H 6 O 4 ) · H 2 O, has been determined by single crystal X-ray diffraction. The crystals 1 are orthorhombic with a = 6.805(1) Å, b = 18.486(2) Å, c = 5.884(1) Å, space group P 2 1 2 1 2 1 , Z = 4, V = 740.1 (2) Å 3 , d m = 1.69, and d c = 1.688 Mg m −3 . The structure was refined by full-matrix least-squares techniques to R = 0.019, R w = 0.026, for 1198 reflections with I ≥ 3 σ ( I ). The absolute configuration was determined. Ca is coordinated to seven oxygen atoms and the coordination polyhedron is best described as pentagonal bipyramid. One carboxylate group of the glutarate ion is bonded to three different Ca ions, forming a four-membered chelate ring with one Ca ion and unidentate bridge bonds to two other Ca ions. The other carboxylate group links to two Ca ions through unidentate bonds. The Ca-glutarate chains are packed approximately parallel to the b -axis, with the hydrocarbon chains sandwiched between the polar regions consisting of the Ca and carboxylate ions and water molecules.

Reaction of 2,4-dibromo-1-methyl-5-nitroimidazole 1 with sodium methoxide in methanol or with potassium cyanide in DMSO implies univocal nucleophilic substitution of 2-bromine atom by methoxy or cyano group as revealed by the crystalline structures of 4-bromo-2-methoxy-1-methyl-5-nitroimidazole 2 and 4-bromo-2-cyano-1-methyl-5-nitroimidazole 3 . Compound 2 (C 5 H 6 BrN 3 O 3 ) crystallizes in the monoclinic system, space group P 2 1 / c , a = 13.433(5) Å, b = 9.065(2) Å, c = 14.027(5) Å, β = 103.99(2)°, Z = 8. The 4-bromo-2-cyano-1-methyl-5-nitroimidazole 3 (C 5 H 3 BrN 4 O 2 ) crystallizes in the monoclinic system, space group P 2 1 , a = 9.705(9) Å, b = 6.328(2) Å, c = 25.809(9) Å, β = 95.44(4)°, Z = 8. Structures found by molecular mechanics are in good agreement with the solid state geometries.

2-[Bis(triphenylphosphine)silver(I)]benzisothiazol-3(2 H )-one 1,1-dioxide crystallizes in the triclinic P [unk] space group ( a = 13.1200(8) Å, b = 17.124(2) Å, c = 19.450(1) Å, α = 65.396(6)°, β = 83.249(5)°, γ = 72.925(6)°). The unit cell contains two independent molecules that show trigonal coordination at silver (molecule a : Ag–P = 2.452(3) Å, 2.454(3) Å, Ag–N = 2.285(8) Å, Σ angle Ag = 358.4(5)°; molecule b : Ag–P = 2.440(3) Å, 2.432(3) Å, Ag–N = 2.270(8) Å, Σ angle Ag = 359.3(5)°). The structure has been refined to R = 0.055 for 5656 I ≥ 3 σ ( I ) reflections. 2-[Bis(triphenylphosphine)silver(I)]-4,5-dimethylisothiazol-3(2 H )-one 1,1-dioxide crystallizes as an ethanol solvate in the triclinic P [unk] space group ( a = 12.0154(6) Å, b = 13.333(1) Å, c = 14.511(2) Å, α = 90.907(9)°, β = 102.789(9)°, γ = 115.332(5)°). The molecule also shows trigonal coordination at silver (Ag–P1 = 2.468(2) Å, Ag–P2 = 2.434(2) Å, Ag–N = 2.259(7) Å; Σ angle Ag = 362.0(5)°). The structure has been refined to R = 0.070 for 4732 I ≥ 3 σ ( I ) reflections.

The title compound was obtained as an unexpected by-product in the attempted biaryl coupling of phenyl 1-methoxy-2-naphthoate with 2-methoxy-1-naphthyl magnesium bromide. From ether/petroleum ether it crystallizes from the purified reaction mixture as colorless plates of the space group P 2 1 / a ; a = 1258.7(5) pm, b = 1791.1(8) pm, c = 583.8(2) pm, and β = 93.68(3)°. The most characteristic feature of the structure is an intramolecular hydrogen bond quasi forming a fourth 6-membered nearly planar ring system.

Pure single crystals of lead iodide have been grown from vapor and characterised by X-ray diffraction for their polytypism and related phenomena. The theoretical estimation of the Jackson's α -factor and the surface micrographs of the crystals, coupled with the results of X-ray diffraction, indicate crystal growth by two-dimensional nucleation. Comparison of the experimental results with the earlier ones on gel-grown and melt-grown crystals reveals an obvious influence of the impurities on polytype formation, besides confirming the high purity of the vapor-grown crystals.

The efficiency of routine data collection using conventional diffractometers can easily be increased with little loss of precision. The largest single improvement arises from the avoidance of pre-scans. Crystallographers are encouraged to consider a more felicitous allocation of measuring time to structural problems.