Band 118, Heft 1-2

A substantial improvement in the resolution of the three-dimensional Patterson synthesis, without serious increase of the spurious features due to diffraction ripple, may be effected by modifying the coefficients so that their mean value increases steadily with the Bragg angle. The same technique cannot, however, be used as successfully in one- or two-dimensional Patterson syntheses. The one-, two- and three-dimensional vector-peak shapes corresponding to a number of these terminated “diverging” series have been evaluated. For any given series the resolution is greatest in one, and least in three dimensions so that more strongly divergent series must be used in the latter case to achieve the same resolution. However the diffraction ripple decreases with number of dimensions and the resolution which may be achieved for any given amount of diffraction ripple is almost identical in all three cases. Considerable success has been achieved in a number of difficult problems by the use of these terminated “diverging” series.

The following physical properties of the formates of calcium and cadmium were measured: morphology, structure details (for cadmium formate), elastic, thermoelastic, dielectric and optical constants, coefficients of thermal expansion and thermal conductivity, hardness. The simple relations which exist between physical properties in isotypic cubic crystal groups are also valid in crystals of lower symmetry. The elastic behaviour and the strong effects of anisotropy are explained by a simplified structure model.

Crystals of N-( n -propyl)-dihydro-nicotinamide are monoclinic, with four molecules in a unit cell of dimensions a = 11.00 5 , b = 16.73 4 , c = 5.07 7 , Å, β = 101.8 5 °; space group P 2 1 / a . The structure has been determined from projections along the a , b and c axes, and refined by means of the least-squares method. Within the limits of error the dihydronicotin ring is planar with C = C equal to 1.30 and 1.39 Å, C–C equal to 1.49 and 1.45 Å, and C–N equal to 1.45 and 1.45 Å. The amide group makes angles of 22° with the dihydronicotin ring. The molecules are connected by hydrogen bonds (N–H…O = 3.04 Å) forming a dimer-type structure. The dimers are linked in the c -direction by other hydrogen bonds (N–H…O = 2.99 Å) forming infinite bands.

The orientation of the albite component relative to the K feldspar host was determined by x-ray methods in macro-, micro- and cryptoperthites from 27 different localities. Two main types (with intermediate orientations) were found: Type I , The orientation of the albite indicates separation from a “monoclinic” K feldspar (macro-, micro- and partly cryptoperthite). This orientation was observed when the K feldspar appeared optically “monoclinic” or when the microcline twin structure appeared diffuse and without sharp boundaries. Type II , The orientation shows no relation to an original monoclinic state; on the contrary the albite shows such relations to the microcline that it must be considered to have separated from triclinic microcline (cryptoperthite in larger microcline lamellae which show sharp boundaries and cryptoperthite in large microcline areas which may already be viewed as single crystals). On the basis of the x-ray results the following processes are mainly responsible for the formation of the perthites examined (mostly of pegmatitic character): 1. Formation of relatively coarse “vein perthite” (A ndersen ) through unmixing from a sanidine state; 2. Formation of “film perthite” (A ndersen ) and “monoclinically oriented” cryptoperthite through unmixing from an “orthoclase” state; 3. Formation of “triclinically oriented” cryptoperthite through unmixing from a microcline state; 4. Recrystallization of twinned microcline and of perthitic albite to “single crystal” microcline with albite inclusions, the orientation of which is such that the Al/Si distribution in the microcline and in the albite inclusions is “topologically coherent” (“plate perthite”). The cleavelandites with random orientation to the K feldspar are considered as a relatively late albitization coming from outside.

The crystal and molecular structure analysis of (±)-cadinene dihydrochloride was carried out by two-dimensional Fourier methods. The unit cell has the dimensions a = 6.021 Å, b = 27.509 Å and c = 9.850 Å with β = 102°40′ and contains four formula units. The crystal belongs to the monoclinic space group C 2 h 5 – P 2 1 / n . The heavy-atom method was mainly used for the determination of the phases and the structure was solved by interpreting two electrondensity projections ϱ (0 yz ) and ϱ ( xy 0). Difference Fourier and least-square methods were employed for the refinement of positional and thermal vibration parameters. The analysis showed that the two rings are transfused. The disposition of the chlorines, and of the methyl and isopropyl groups on the basic skeleton is in agreement with the previous x-ray and chemical analyses. The two C–Cl bonds are directed toward the same side of the molecule with distances of 1.788 Å and 1.791 Å. The two chlorines of the same molecule are separated by 4.76 Å. Clear evidence is presented for the existence of a nonrotating isopropyl group in this molecule at room temperature in complete disagreement with the conclusions drawn by H anic from the x-ray work on l -cadinene dihydrobromide.

A refinement for phases in crystal structures after the method of least squares is developed, and the formal analogy with the refinement of atomic coordinates is emphasized.

The crystal structure of sillimanite, Al 2 SiO 5 , has been refined as part of a detailed structural study of the aluminum-silicate minerals. Three-dimensional least-squares refinement reduced the disagreement factor, R , for 347 hkl reflections to 5.6%. The previously determined sillimanite structure was found to be fundamentally correct. Chains of aluminum octahedra, similar to those in andalusite, lie parallel to the c axis. These are supported by double chains of tetrahedra containing aluminum and silicon cations alternating in an ordered sequence. The three independent octahedral Al–O distances are 1.957 Å, 1.919 Å, and 1.861 Å, all ± 0.003 Å. The Si–O distances are 1.629 ± 0.007 Å, 1.633 ± 0.004 Å, 1.633 ± 0.004 Å, and 1.564 ± 0.006 Å. The tetrahedral Al–O distances are 1.758 ± 0.005 Å, 1.800 ± 0.004 Å, 1.800 ± 0.004 Å, and 1.721 ± 0.006 Å. The shortest Si–O and tetrahedral Al–O distances represent bonding to a common oxygen atom through a Si–O–Al angle of 171.6°. The indicated thermal motion of this oxygen atom is nearly twice as great as that of the other three oxygen atoms in the asymmetric unit and, in addition, is strongly anisotropic.

The neutron-scattering cross sections σ 3 , of heavy ice at 4° and 77°K have been measured by transmission experiments as a function of neutron-wave length in the range 5 < λ <50 Å. Above the Bragg cutoff λ Bragg = 2 d max ≈ 8 Å ( d max is the maximum possible distance between the lattice planes) σ s contains two parts: σ spin from the deuteron spin, and a small contribution, σ un , from an eventual deuteron-orientation disorder in the lattice. σ un has been approximately calculated according to the statistical ice model of P auling in an approximation better than that described in an earlier paper. It was found that σ un is smaller than 10 −2 barns for λ > 10 Å. The experimental accuracy is not sufficient to determine this contribution of disorder. Under these circumstances the spin incoherent-scattering cross section, σ spin , could be determined with an accuracy better than that of present values. One finds for deuterium: σ spin = 2,25 ± 0,04 barns. A lcock and H urst have found: σ spin = 2,0 ± 0,13 barns, S hull and W ollan : σ spin = 2,5 ± 0,5 barns (as difference between total and coherent cross section). Measuring the inelastic-scattering cross section at 77°K the effective Debye-Temperature of D 2 O ice was determined as: Θ eff = 228° ± 5°K. This can be compared with Θ = 237°K from Z ajak and Θ eff = 220° ± 10°K from deuteron amplitudes in D 2 O ice measured by P eterson and L evy .

X-ray data of two new compounds with rutile structure, InSbO 4 and ScSbO 4 , are listed. The lattice constants of these compounds are very close to those of SnO 2 .