Band 146, Heft 4-6

In refining a structure by the method of least squares a modified way of computation is suggested with the aid of cycles and subcycles. Usually about five to ten cycles of refinements are needed for the completion of refinement, whereas with the use of subcycles, the same degree of refinement can be reached with the computational work equivalent to that of one or two cycles. This procedure reduces the computation time by a factor of about five. The method is illustrated for the positional parameters.

The crystal and molecular structure of C.I. Pigment Red 2, l′-(2,5-dichlorophenyl)azo-2′-hydroxy-3′-phenylamidonaphthalene has been determined by x-ray diffraction techniques. It crystallizes in the monoclinic system with cell parameters a = 10.309 ± 0.006 Å, b = 9.051 ± 0.003 Å c = 21.991 ± 0.015 Å, β = 104.33 ± 0.10°. The space group is P 2 1 / c and there are four molecules per unit cell. The structure was solved using direct methods and least-squares refinement has been completed on three-dimensional data with θ less than 35° (Cn Kα radiation). The hydrogen atoms have been found and included but not refined. The final residual is 15.3%. The molecule is probably in the form of the hydrazone tautomer. The intramolecular hydrogen bonds keep most of the molecule approximately planar while it appears that the remainder is held in the same plane due to steric hinderence between the molecules. The molecules are packed in columns with alternate molecules antiparallel and are linked by van der Waals forces.

A modification of tridymite with an orthorhombic structure exists between monoclinic low tridymite and orthorhombic high tridymite. The three unit-cell edges of this structure are parallel with the corresponding ones of orthorhombic high tridymite but the a translation is three times as long as that of the latter. The crystal structure was determined by the use of x-ray intensities at about 155°C on a crystal from refractory silica brick. The space group is P 2 1 2 1 2 1 and the unit cell of, dimensions a = 26.171(3), b = 4.986(4) and c = 8.196(4) Å, contains twenty-four formula units. The six-membered rings of the silica tetrahedra are distorted in a way similar to those of monoclinic low tridymite: two thirds have a ditrigonal shape and one third have an oval shape in (001). The same ring types stack on top of one another along the orthorhombic c axis (parallel with the c direction of hexagonal ideal tridymite). This is not the case in monoclinic low tridymite. The mean Si–O distance, uncorrected for thermal motion, is 1.58 Å and the mean values of the Si–O–Si angles are 170.4° for tetrahedra joined nearly parallel to c , and 153.0° for those nearly in (001).

The hydroxyl orientations in Sr(OH) 2 have been determined by electrostatic-energy calculations. In this structure, the hydroxyls lie on a mirror plane so that starting models were obtained by first arbitrarily choosing a reasonable orientation for one of the two hydrogens, OH(1), and then calculating the electrostatic energy for the other, OH(2), as a function of its orientation in the plane. This resulted in two minima each of which was used in turn as an orientation for OH(2) while OH(1) was similarly rotated. This produced a total of seven structure models. For each, the electrostatic energy was minimized as a function of hydroxyl orientation. In the minimum-energy structure, OH(1) lies nearly in the edge of the coordination polyhedron about strontium (CN = 7). The Sr–H(1) distance of 2.388 Å is much less than the average Sr–O distance of 2.598 Å. This and considerations of the ionic radii indicate that the hydrogen is in contact with the strontium. The hydroxyl orientations are more strongly influenced by Sr–H repulsion than by H–H repulsion since the minimum-energy has the least total Sr–H repulsion.

LiH 2 PO 4 crystallizes in space group Pna 2 1 ; a = 6.253(4), b = 7.656(4), c = 6.881(4) Å, Z = 4. With 1268 observed reflections measured on a single-crystal diffractometer (Mo Kα radiation), the structure was solved (Patterson methods) and refined anisotropically (least-squares) to R = 0.022. The hydrogen atoms had been located from difference maps. LiO 4 coordination polyhedra are linked by vertices and form [100] isolated chains. The two independent hydrogen bridges, 2.684 and 2.564 Å long, connect the PO 4 polyhedra building up a three-dimensional framework; [100] channels containing H atoms are observed in the structure. Similarities with the structure of NaH 2 PO 4 · H 2 O are discussed. The effect of increasing the alkali cation size in the series MH 2 PO 4 causes a progressive condensation of the coordination polyhedra by sharing vertices and edges, from single chains (LiH 2 PO 4 ) to very compact frameworks (CsH 2 PO 4 ) of polyhedra. Shorter hydrogen bonds are observed when larger alkali cations are present; this effect is discussed in the light of bond-strength balance concepts.

The crystal structure of diamminesilver dinitroargentate, [Ag(NH 3 ) 2 ]-Ag(NO 2 ) 2 , has been determined by X-ray diffraction methods. Diamminesilver dinitroargentate crystallizes tetragonal with the space group S 4 1 – P [unk]. The lattice constants are a = 9.633 ± 0.005 Å and c = 8.330 ± 0.005 Å. There are 4 formula units within the unit cell. The point positions of the silver atoms were obtained by the heavy-atom method whereas those of the light atoms were found by difference Fourier syntheses. Coordinates and anisotropic temperature factors were refined by block-diagonal least-squares methods with the result R = 0.040 for 1618 independent reflections. The structure is built up from a framework of silver and nitrite ions intercalating pairs of linear diamminesilver ions. There is disorder in the orientation of the nitrite ions with respect to one of the two neighboring silver ions.

The hydrogen atoms in hemimorphite, Zn 4 Si 2 O 7 (OH) 2 · H 2 O, have been located and its crystal structure refined using 415 three-dimensional singlecrystal neutron-diffraction data. The mineral is orthorhombic, space group Imm 2, with a = 8.367(5), b = 10.730(6), c = 5.115(3) Å, and Z = 2. The structure consists of three-membered rings of corner-sharing Zn(OH)O 3 ( × 2) and SiO 4 tetrahedra arranged in compact sheets parallel to (010). Three oxygen atoms in each tetrahedron are bonded to two zinc atoms and one silicon atom, while a fourth oxygen atom forms a bridging bond to an equivalent cation in an adjacent sheet. The water molecules are oriented parallel to (010) inside large cavities between the tetrahedral sheets and are held in place by hydrogen bonds to and from the hydroxyl groups of the Zn – OH – Zn bridging linkages. Mulliken population analyses calculated using constant bond lengths and the observed angles within and between the tetrahedra allow a rationalization of the bond-length variations in the SiO 4 group, but are less successful in the case of Zn(OH)O 3 . Detailed analysis of observed bond length and calculated overlappopulation variations in a variety of tetrahedral oxyanions suggests that the poorer agreement in the case of the Zn tetrahedron is more a function of the larger overall size of the group than of the relative ionic character of the bonds.

The crystal structure of K 4 SrGe 3 O 9 has been determined by means of three-dimensional x-ray data resulting a final R value of 0.069. The lattice constant of the cubic unit cell ( Pa 3- T h 6 ) is a = 16.625(1) Å. The structure consists of isolated puckered twelve-membered rings built up by [GeO 4 ] tetrahedra. This type of silicate and germanate ring has been observed in this structure for the first time. According to their powder diagrams the following compounds are isostructural: Na 4 CaSi 3 O 9 , K 4 CaSi 3 O 9 , K 4 SrSi 3 O 9 and K 4 CaGe 3 O 9 .

RbH 3 (C 8 O 4 H 4 ) 2 · 2H 2 O is monoclinic (space group C 2/ c ) with a = 13.561(4), b = 21.185(6), c = 6.873(2) Å; β = 113.82(4)°; Z = 4. The structure was determined by direct methods and was refined to an R value of 2.0%. The Rb ion is coordinated to eight oxygen atoms. The hydrogen phthalate ion has no intramolecular hydrogen bond, but, two different ions are interconnected by a “very short” O–H–O hydrogen bond [2.447(2) Å]. Assuming space group C 2/ c , the connecting hydrogen atom is in a special position on a twofold axis and the hydrogen bond should be designated as symmetrical. The difference Fourier synthesis, however, reveals indications of a disordered asymmetrical location of this hydrogen atom which is confirmed also by refinement. The crystal under investigation is assumed to be identical with a crystal species which was formerly described as RbHC 8 O 4 H 4 · 11H 2 O.

The crystal structure of Mn-bearing pectolite has been refined to R = 2.1% using crystals from Magnet Cove, Arkansas, U.S.A.: HNaCa 1.969 Mn o.045 Fe 0.014 -Si 3 O 9 , a = 7.980(1) Å, b = 7.023(1) Å, c = 7.018(1) Å, α = 90.54(1)°, β = 95.14(1)°, γ = 102.55(1)°, P [unk], Z = 2, D x = 2.906 gem −3 . The result has established that hydrogen bonds occur between pairs of oxygen atoms, O(3) and O(4), in each silicate chain, the distance between the paired oxygen atoms being 2.473(2) Å. The difference Fourier peak showing the hydrogen atom assumes the following random model rather than a symmetrical bond: The hydrogen atom is mainly associated with O(3) giving the O(3)–H bond length of 1.06(5) Å, and an angle of 171(1)° subtended at the hydrogen atom. There is between O(3) and O(4) another position for hydrogen associated with O(4); the occupancy of hydrogen atom at this position is smaller than that of the other position. The manganese atoms, including Fe, are fully concentrated at the M(2) position.

The crystal structure of the compound K 4 BaGe 3 O 9 has been determined by means of three-dimensional x-ray data resulting a final R value of 0.089. The lattice constants of the monoclinic unit cell ( B 2– C 2 3 ) are: a = 8.364(2), b = 11.399(2), c = 12.366(2) Å and γ = 90.61(2)°. The structure consists of six-membered single chains built up by [GeO 4 ] tetrahedra parallel to the b -axis. The corresponding silicate K 4 BaSi 3 O 9 is isostructural according to the calculated intensities of the powder diagram, however it might be orthorhombie ( Bbm 2– C 2 v 16 ).

Even with the aid of high sensitive methods, no piezoelectric, linear electrooptic, and nonlinear optic effects, and also no optical activity could be detected in Sr(NO 3 ) 2 , Ba(NO 3 ) 2 , and Pb(NO 3 ) 2 . These results are only compatible with point symmetry m 3 in contradiction with B irnstock 'k suggestion of point symmetry 23, based on faint neutron diffraction reflections forbidden in m 3 (Z. Kristallogr. 124 (1967) 310–334). The perturbation-free observation of electrogyration and quadratic electrooptic effects confirms the existence of a centre of inversion. These properties are correlated with the molar polarizability of the crystals.

The magnitude and signs of the piezooptic constants of KCN differ considerably from those of comparable alkali halides. In accordance with the anomalous thermoelastic behaviour of KCN the piezooptic constant q 44 increases rapidly as the temperature approaches the phase transition at 168 K. The total quadratic electrooptic effect consists of two components with opposite signs resulting in a small measurable effect which exhibits no pronounced variation with temperature.

Nickel chelate of the 4,4′-dihydroxy-3,3′-dibenzoyl biphenyl has been prepared. The crystals are monoclinic with the space group P 2 1 / c having cell dimensions a = 7.33, b = 27.83, c = 19.18 Å°, β = 90° 58′, ϱ obs = 1.393, ϱ calc = 1.409 g/cm 3 . M = 844.71, Z = 4.