Volume 134, Issue 1-2

Similar x-ray diffraction patterns of high quartz and compounds of the chemical composition MgO · Al 2 O 3 · x SiO 2 with x = 2–10 show, that these silicates may crystallize in a high-quartz-like structure. A single crystal with x = 3 was used to determine the commonness and differences between high quartz and these high-quartz phases. Only the main reflections of the high-quartz-like subcell have been considered for the investigation, but not additional weak super-structure reflections in form of satellites. Therefore only an average structure could be determined. All atoms take part in the formation of the superstructure by small displacements from the ideal high-quartz positions. The Mg atoms occupy places surrounded by six oxygen atoms.

Probability distributions of two and three structure factors and of their magnitudes are derived which are more accurate over the whole range of values of parameters and variables than those obtained heretofore.

Selected-area electron-diffraction patterns and x-ray diffraction powder patterns were taken of crushed single crystals of Pb 3 MgNb 2 O 9 . Although the x-ray patterns did not indicate any deviation from the cubic perovskite structure, the single-crystal electron-diffraction patterns showed additional spots which were attributed to a superlattice. Those superlattices which are compatible with the experimental data were derived. The diffuse phase transition of Pb 3 MgNb 2 O 9 and the direction in which the spontaneous polarization occurs may be explained by the proposed B -site ordering.

The crystal and molecular structure of [Ni(C 5 H 8 O 2 ] 2 (H 2 O) 2 ](ClO 4 ) 2 has been determined by single-crystal x-ray diffractometry. The unit cell contains two different centrosymmetric structure units, in each of which nickel is octahedrally coordinated. In one, nickel is coordinated by two planar 2,4-pentadione (acaH) ligands and two water molecules, in the other by two non-planar (acaH) ligands and two water molecules. The structural parameters of the non-planar form are entirely consistent with the keto tautomer of acaH whereas those of the planar form are by no means conclusive as regard to which tautomer is present. The Perchlorate ions are linked to the Ni(C 5 H 8 O 2 ) 2 (H 2 O) 2 ions by hydrogen bridge bonds to the oxygen atoms of the water molecules.

Diaboleite, Pb 2 Cu(OH) 4 Cl 2 , is tetragonal, P 4 mm , with a = 5.870 Å and c = 5.494 Å. The structure has been refined by the method of least squares to a conventional R value of 5.0%. Diaboleite is a derivative of the cubic perovskite structure, ABO 3 , with Cu and possibly Cl vacancies. The perovskite-like subcell has dimensions A = a /√2 = 4.151 Å and C = c = 5.494 Å and the formula PbCu 1/2 (OH) 2 Cl or AB 1/2 O 3 . Cu(II) is coordinated by a square pyramid of 4 OH + 1 Cl and Pb(II) by a distorted square antiprism of 4 OH + 4 Cl. Structural distortions are interpreted in terms of Pb–Cu repulsions and the second-order Jahn-Teller effect.

This paper deals with a possible method of determining molecular structure directly, using x-ray data. The peaks chosen from the electron-density map calculated using the signs obtained from the contribution of the heavy atom are assigned site-occupancy values which depend upon the peak heights. The occupancy parameter is refined by the least-squares method and the peaks for which the value of the occupancy parameters increases are taken as real atoms in the subsequent calculation of structure factors and electron-density maps. The method has been tested in two hypothetical cases and in a real case.

The crystal structure of an eighteen-layered polytype of CdI 2 has been worked out. The structure is 1222322211 in Zhdanov symbols and the space group is P 3 m 1. The formation of the polytype is discussed in terms of the stacking faults created during crystal growth.

In an attempt to treat independently the contribution of the inner and outer electrons of the different atoms to the total x-ray scattering the selected-electron shell (SES) method was developped, representing the atomic scattering factor by a three- or four-term Gaussian polynomial and associating the Gaussian constants with the electron shells of the atom. For most atoms however and contrary to the hypothesis no simple relation can be made. Therefore, the atom is considered as a non-rigid body, built up from two distinguishable terms: the core and the outer electrons. The core is assumed to form a closed, spherically symmetric shell, making an overall description of its scattering power by a one-term Gaussian function, within some limits in reciprocal space, quite possible. The G c constant has a value corresponding to fully occupied electron shells and the calculated Gaussian scattering values fit very well with the summation of the individual orbital transforms.

The electrical and optical constant of potassium iodate have been determined. The crystals are found to be ferroelectric in the whole temperature range from −163°C to 214°C. Phase transitions of first order occur at −163°C, −15°C, 72.5°C and 214°C respectively. They can be related to the abrupt changes in the optical and electrical properties. The piezoelectric as well as the reciprocal piezoelectric effects have been measured in the range 20°C to 200°C. The crystals show at room temperature a very strong electro-optical effect.

A new tin mineral, magnesium hexahydroxostannate, MgSn(OH) 6 , occurs as a late-stage hydrothermal alteration product in a contact-metamorphic zone on Brooks Mountain, Seward Peninsula, Alaska. The chemical formula was derived from analysis of a mixture, and electron-microprobe study confirms the assigned composition. The mineral is soluble in HCl and slowly soluble in NaOH. The symmetry is cubic, space group T h 2 – Pn 3, a = 7.759 ± 0.006 Å, Z = 4, density (calc.) 3.483 g/cm 3 . The four strongest lines in the x-ray diffraction powder pattern are 3.88 Å (100), 4.48 Å (50), 2.74 Å (25), and 1.733 Å (25). Differential thermal analyses of natural and synthetic material are in agreement. The name is given in honor of the mathematical crystallographer, A rtur M oritz S choenflies . Some crystallographic data and the densities of magnesium orthostannate and magnesium metastannate are also presented.

The α -type CS 3 Sb 2 Cl 9 crystal is trigonal, with unit-coll dimensions a = 7.633, c = 9.345 Å, Z = 1, and space group P 321. The atomic arrangement is essentially based on closest packing of cesium and chlorine; embedded in this environment are SbCl 3 molecules with bond angle 94°58′ and distances Sb–Cl = 2.42 Å, Cl–Cl = 3.56 Å. This arrangement is similar to that of CS 3 AS 2 Cl 9 .

Patterson maps contain N ( N –1) nonorigin peaks corresponding to N atomic peaks in the unit cell in Fourier map. Patterson peaks are also more broad than the atomic peaks. Both these factors result in tremendous amount of overlapping in Patterson maps which make their interpretation difficult. Usually a few peaks due to heavy atoms show themselves clearly and rest of the peaks are merged in the background. It is suggested that, by considering the weak structure amplitudes as well as the accidentally absent reflections, the resolution in the map would markedly improve. The same ideas can be extended with advantage to difference Fourier maps.

CS 3 Sb 2 Cl 9 crystallizes with two structure types. One is trigonal, the unit-cell dimensions being a = 7.633 Å, c = 9.345 Å and the space group P 321; the other is orthorhombic, with a = 7.63 Å, b = 13.22 Å, c = 18.69 Å and the space group Pcmn .