Volume 214, Issue 2

In two preceding papers by Jagodzinski (Phys. Stat. Sol.(a) 146 (1994) 477; Acta Crystallogr. A 52 (1996) 675), a new method of phase determination has been described. Using latent lattices of point scatterers for a single kind of atoms, the structure is generated by shift vectors, displacing the atoms from the origins of the latent lattice into their correct positions. The mathematical treatment of this procedure resulted in very complex formulae for structure factors E ′( h ), normalised such that E ′( 0 ) = 1. The three components of the displacement vectors define a new real and reciprocal shift space. The method is briefly described in the first three sections of this paper. There is an important difference between one and higher dimensions: the number of latent lattices with different shift functions is infinite, but only very few of them are optimal. Phases and amplitudes of the Fourier coefficients of the shift function are strongly correlated. This property results from the transformation of diffraction data and the prohibition of trespassing of points, caused by large Fourier coefficients of the shift function. In addition to the well known influence of strong reflections, the approximate [unk]-symmetries of the diffraction data and the areas of minimum intensity play an outstanding role for the selection of the optimal latent lattice. Its corresponding shift function has small displacements and small amplitudes of the Fourier coefficients. In the case of complicated structures, these properties demand a careful computer evaluation of the intensity distribution in reciprocal space, in order to determine the optimal latent lattice of a given structure. – The unit cell of the structure contains M (= number of atoms) cells of the latent lattice. As long as M is a product of three integers M x M y M z , there is no difficulty in finding the optimal latent lattice in diffraction. Each set of directions has to be tested in reciprocal space. In all other cases difficulties arise which may only be overcome with the aid of latent sublattices (smaller cell, more atoms in the structure), or latent superlattices (larger cell, less atoms in the structure). Both cases are discussed, and it is shown that the existence of the various types of latent lattices may be found in the normal diffraction pattern, applying the criteria derived in this paper. The meaning of latent sub- and superlattices is discussed from the structural point of view, and phase relations, caused by the prohibition of trespassing of points, are derived. The great power of the new method will be discussed in a later paper, where differences of shift functions are introduced. Their important consequences for phase determination will be demonstrated with the aid of certain systems of linear equations.

Single crystals of optical quality of citric acid (monoclinic), citric acid monohydrate (orthorhombic), trilithium citrate tetrahydrate (monoclinic), trisodium citrate pentahydrate (orthorhombic) and tripotassium citrate monohydrate (monoclinic) have been grown from aqueous solutions by standard methods. Elastic constants c ij and thermoelastic constants T ij = d log c ij /d T have been determined from ultrasonic resonance frequencies of plane-parallel plates and their shift with temperature T , respectively. Further, the tensors of thermal expansion have been measured with the aid of an optical Fizeau interferometer. Citric acid and its monohydrate exhibit a distinct depression of their mean elastic stiffness and also stronger thermal volume expansion and mean thermoelastic effect compared to the three citrates. The rules governing the mean elastic stiffness via the S values are also obeyed by the citrates, despite their different structures. The contribution of the Coulomb interaction of a single monovalent cation with the trivalent citric anion to the mean elastic stiffness is somewhat comparable to that with a monovalent anion.

The title compounds are already known in the literature, however, they have only been characterized by their subcells on the basis of X-ray powder data. Well crystallized samples of ZrIrSn, HfCoSn, and HfRhSn were prepared from the elements by arc-melting and subsequent annealing at 970 K. ZrIrSn, HfCoSn, and HfRhSn crystallize with a pronounced subcell of space group P [unk]2 m (ZrNiAl type). Additional very weak reflections required a doubling of the c axis. The three structures (all space group P ([unk]2 c ) were refined from single-crystal X-ray data: a = 732.1(2) pm, c = 732.2(2) pm, wR 2 = 0.0367, 539 F 2 values, 18 variables for ZrIrSn, a = 713.1(3) pm, c = 705.4(3) pm, wR 2 = 0.0930, 342 F 2 values, 16 variables for HfCoSn, and a = 732.0(3) pm, c = 714.8(2) pm, wR 2 = 0.0259. 528 F 2 values, 18 variables for HfRhSn. The three stannides crystallize with a substitution derivative of the Mg 2 Ga structure. The Zr(Hf) and tin atoms are ordered on the magnesium positions and the Co(Rh,Ir) atoms on the gallium positions of the Mg 2 Ga type. The distortions in the structures of ZrIrSn, HfCoSn, and HfRhSn are most likely due to packing reasons (size of the zirconium and hafnium atoms). The structures of ZrIrSn, HfCoSn, and HfRhSn are described considering a group-subgroup scheme, also including the FePdP, Lu 3 Co 2 In 4 , Mg 9 Sn 5 , Ti 4 Ni 2 Ga 3 , and TiFeSi type structures.

We present results of X-ray structure refinement of γ -Mo 4– x Re x O 11 for 0 ≤ x ≤ 1 at room temperature. Single crystals of γ -Mo 4– x Re x O 11 have been grown by chemical transport reaction. Space group Pna 2 1 has been confirmed. The volume of the unit cell is decreasing with increasing Re content. Re substitutes preferably one out of four Mo sites. We propose that this is accomplished by a mixture of Re 4+ and Re 5+ .

A one-dimensional disorder model has been proposed for the structure of the so-called ϱ -K 0.5 V 2 O 5 studied by Savariault and Galy [J. Solid State Chem. 101 (1992) 110–1271. Computer simulations showed, that the structure published by these authors can be explained by a model in which the layer sequences of the orthorhombic and the monoclinic structures randomly appear in a volume ratio of about 7 to 3. The trigonal-prismatically six-fold coordinated K position has been revealed to be a false maximum in the electron-density difference map. The orthorhombic ( ϱ -K 0.5 V 2 O 5 characterized by this K position does not really exist.

The YbAu 2– x Si x and CaAu 2– x Si x systems were studied by X-ray techniques in the range 0.7 ≤ x ≤ 1.3. The YbAuSi compound forms peritectically at 1478 K and is stable till 1168 K in its high-temperature form (EuAuGe type); below 1168 K the SrAgGe type occurs. No equiatomic compound exists in the Ca–Au–Si system. In the gold- and silicon-rich regions the two systems show similar structural behaviour: the gold-rich phases belong to the CeCu 2 or the EuAuGe type, while the silicon-rich phases crystallize in the A1B 2 type. The magnetic susceptibility at room temperature indicates the divalency of ytterbium in YbAuSi.

The changes in the molecular and crystal structures of the four-coordinate ZnX 2 L 2 complexes through the chloride, bromide, iodide series and with L = acetophenone (acp), pyridine-N-oxide (pyo), dimethylformamide (dmf), dimethylsulfoxide (dmso) and trimethylamine-oxide (tmno) are reviewed. Tmno, as the strongest of these monodentate oxo-ligands, gives the shortest Zn–O and longest Zn–X bonds. As to molecular packing, the chlorides and bromides of the pyo, dmso and tmno series are not isotypic while the bromides and iodides – apart from the pyo complexes – are similar. Evidence from inter-molecular approach distances in the pyo and dmso series indicates a field strength sequence CH––Cl > CH––O > CH––Br and this dominates the molecular packing. It enhances Cl/Br differences, but would not reduce Br/I similarities. The structures of the acp complexes, including the chain-polymeric [{ZnCl 2 (acp)} n ] are dominated by an approach to parallel packing of the large planar ligands. In the pyo series parallel orientation of the planar rings provides efficient packing, but each set of rings is oriented to meet CH––X attraction requirements. The ring orientation is particularly sensitive to halogen size. With the complexes from the non-planar ligands dmso and tmno, structural variations arise from the influence of the methyl substituents as well as from differences in the halogen sizes; but CH––O approaches again become relatively more important in the bromides and iodides. In the dmf series because there is a strong preference for a particular molecular orientation, there is no change in space group, though with the iodide packing instability does lead to a phase change at low temperature.

The molecular and crystal structures of N- para -toluenesulphonyl- α -aminoisobutyric acid fluoride ( 1 ), N- para -toluenesulphonyl-N-methyl- α -aminoisobutyric acid fluoride ( 2 ), N- para -toluenesulphonyl- α -aminoisobutyric acid ( 3 ), and N- para -toluenesulphonyl-N-methyl- α -amino-isobutyric acid ( 4 ) have been determined by X-ray diffraction. Crystal parameters: ( 1 ) monoclinic, space group P 2 1 / a , a = 24.264(3) Å, b = 8.386(2) Å, c = 6.245(1) Å, β = 96.5(2)°, and Z = 4; ( 2 ) monoclinic, space group P 2 1 / n , a = 7.606(1) Å, b = 14.954(2) Å, c = 11.969(2) Å, β = 92.3(2)°, and Z = 4; ( 3 ) monoclinic, space group P 2 1 / n , a = 11.151(2) Å, b = 6.168(1) Å, c = 18.669(2) Å, β = 91.3(2)°, and Z = 4; ( 4 ) monoclinic, space group P 2 1 / c , a = 11.993(2) Å, b = 10.322(2) Å, c = 12.123(2) Å, β = 115.9(2)°, and Z = 4. The structures were solved by direct methods. The least-squares refinements led to conventional R factors of 0.044, 0.059, 0.045, and 0.056 for ( 1 )–( 4 ), respectively. This is the first geometrical and conformational characterization at atomic resolution of two N α -protected α -aminoacids containing the elusive acyl fluoride C-activating group.[unk]

The crystal and molecular structures of five compounds of the general formula R 2 Sn(S 2 CNR′ 2 )Cl have been determined at room temperature. The colorless crystals of [Me 2 Sn(S 2 CNEt 2 )Cl] are monoclinic, space group P 2 1 / c with unit cell dimensions a = 10.896(2) Å, b = 9.869(4) Å, c = 12.722(2) Å, β = 105.08(1)°, Z = 4 and D x = 1.672 Mg m −3 . The colorless crystals of [Me 2 Sn(S 2 CNCy 2 )Cl] are monoclinic, space group P 2 1 / c with unit cell dimensions a = 6.758(6) Å, b = 19.046(3) Å, c = 15.190(5) Å, β = 98.09(4)°, Z = 4 and D x = 1.512 Mg m −3 . Crystals of colorless [ t Bu 2 Sn(S 2 CN(Et)Cy)Cl] are monoclinic, space group P 2 1 / n with unit cell dimensions a = 13.481(5) Å, b = 11.466(5) Å, c = 15.351(8) Å, β = 107.51(4)°, Z = 4 and D x = 1.382 Mg m −3 . The colorless crystals of [Cy 2 Sn(S 2 CNEt 2 )Cl] are monoclinic, space group P 2 1 / c with unit cell dimensions a = 17.107(6) Å, b = 11.134(2) Å, c = 11.953(6) Å, β = 104.00(3)°, Z = 4 and D x = 1.409 Mg m −3 . The colorless crystals of [Cy 2 Sn(S 2 CNCy 2 )Cl] are monoclinic, space group P 2 1 / n with unit cell dimensions a = 11.411(7) Å, b = 16.942(5) Å, c = 14.712(5) Å, β = 100.45(3)°, Z = 4 and D x = 1.370 Mg m −3 . The structures were solved by direct methods and each refined by a full-matrix least-squares procedure to final R = 0.039 using 1367 reflections for [Me 2 Sn(S 2 CNEt 2 )Cl]; to R = 0.038 using 1881 reflections for [Me 2 Sn(S 2 CNCy 2 )Cl]; to R = 0.049 using 2707 reflections for [ t Bu 2 Sn(S 2 CN(Et)Cy)Cl]; to final R = 0.042 for 1914 reflections for [Cy 2 Sn(S 2 CNEt 2 )Cl]; and to final R = 0.045 for 2550 reflections for [Cy 2 Sn(S 2 CNCy 2 )Cl]. The crystallographic study shows that the tin atom in the R 2 Sn(S 2 CNR′ 2 )Cl compounds exists in a distorted trigonal bipyramidal geometry in which the equatorial plane is defined by the two carbon atoms of the tin-bound organic substituents as well as more tightly held sulfur atom derived from an asymmetrically chelating dithiocarbamate ligand; the axial positions are defined by the less tightly held sulfur atom as well as the chloride atom. Attempts to correlate the Sn-ligand parameters with systematic variations in the Lewis acidity of the tin center (i.e. by moderating R) and the Lewis basicity of the dithiocarbamate ligand (i.e. by moderating R′) were unsuccessful across the series. The compounds have been subjected to geometry optimisation calculations which revealed that more symmetric structures exist in the gas phase. Systematic variations in the Sn-ligand parameters for the gas phase structures could be correlated with the Lewis basicity of the dithiocarbamate ligands in contrast to the solid state structures. Also, trends were found as the Lewis acidity of the tin center was varied. These trends could not, however, be correlated with the electronic structures of the tin-bound substituents alone, indicating that the steric profiles of the substituents also play an important role in moderating the Lewis acidity of the tin center. The results of the combined crystallographic/theoretical investigation of the R 2 Sn(S 2 CNR′ 2 )Cl structures indicate that intermolecular forces, i.e. crystal packing effects, do exert a significant influence on the molecular geometry in these systems.