Volume 222, Issue 2

The charge-flipping structure-solution algorithm introduced by Oszlányi and Süto in 2004 has been adapted to accommodate powder diffraction data. In particular, a routine for repartitioning the intensities of overlapping reflections has been implemented within the iterative procedure. This is done by modifiying the electron density map with a histogram-matching algorithm, and then using the Fourier coefficients obtained from this map to repartition the structure factor amplitudes within each overlap group. The effectiveness of the algorithm has been demonstrated with five test examples covering different classes of materials of varying complexity (ZSM-5 ([Si 96 O 192 ]), cimetidine (C 10 H 16 N 6 S), a polysalicylide ((C 7 O 2 H) 6 ), the low-temperature modification of 4-methylpyridine-N-oxide (C 6 H 7 NO) with 8 molecules in the asymmetric unit, and a zirconium phosphate phase (|(C 5 H 6 N) 4 (H 2 O) 2 | [Zr 12 P 16 O 60 (OH) 4 F 8 ])). It was also used to solve the structure of a layer silicate (|(CH 3 ) 4 N) 8 (H 2 O) 20 | [Si 24 O 56 ]), whose space group was unclear. These structures, with 17–64 non-H atoms in the asymmetric unit (68–288 in the unit cell), could all be solved in a straightforward manner. Histogram matching proved to be an essential component of the algorithm for the more complex structures. The clear advantages of the charge-flipping algorithm are that (1) all calculations are performed in P 1, so space group ambiguities, which are common with powder diffraction data, are irrelevant, (2) no chemical information such as bond distances, bond angles, or connectivity are required, so there is no danger of making incorrect assumptions about the structure, (3) it is equally effective for both organic and inorganic structures, and (4) it is fast, requiring only seconds to minutes per run.

Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set Λ within a given cut and project scheme is a Delone set that is defined through a window W in internal space. The autocorrelation measure of Λ is a pure point measure whose coefficients can be calculated via the so-called covariogram of W . Two windows with the same covariogram thus result in homometric model sets. On the other hand, the inverse problem of determining Λ from its diffraction image ultimately amounts to reconstructing W from its covariogram. This is also known as Matheron’s covariogram problem. It is well studied in convex geometry, where certain uniqueness results have been obtained in recent years. However, for non-convex windows, uniqueness fails in a relevant way, so that interesting applications to the homometry problem emerge. We discuss this in a simple setting and show a planar example of distinct homometric model sets.

A series of microcrystalline products containing the γ -Bi 2 O 3 phase doped with Co, Fe, Mn, Pb, Sb, Si, Ti, V and Zn has been prepared by solid state reaction. Based on the heating temperature and heating time, the following order of increasing relative stability of the doped γ -Bi 2 O 3 phases was established: Sb 5+ < Co 2+ ≈ Mn 4+ < Fe 3+ ≈ Si 4+ < Ti 4+ < V 5+ < Zn 2+ < Pb 2+ . The unit cell parameters of the prepared samples were compared with available structural data, which were also further analyzed concerning the geometrical parameters and overall reliability. The analysis confirmed the so-called Radaev’s model for the doped γ -Bi 2 O 3 structure, which assumes the presence of Bi2 3+ ions slightly displaced from the tetrahedral M site and corresponding vacancies (resulting from a lone pair on Bi2 3+ ) in the coordinating oxygen positions. In addition, the analysis suggested that this model can be further improved. The existence of an approximate linear relationship between the unit cell parameters of the doped γ -Bi 2 O 3 phases and the ionic radii of the M cations was found.

Kinetic ordering of cations in solid solutions of alums showing anomalous birefringence was studied by means of single crystal X-ray diffraction. The crystal structures of two samples of K(Al 0.6 Cr 0.4 )(SO 4 ) 2 · 12 H 2 O and (K 0.45 (NH 4 ) 0.55 )Al(SO 4 ) 2 · 12 H 2 O, respectively, taken from {111} growth sectors were refined in the ideal space group Pa -3 and in two of its subgroups – trigonal R -3 and triclinic P -1 with R 1 = 0.028 – 0.032. The final choice of trigonal symmetry is based on the analysis of the diffraction patterns and of the cation distributions over the crystallographic sites. The correctness of the crystal structure refinements is supported by the disappearance of both ordering and birefringence upon crystal annealing. Also, an optically isotropic sample of (Rb 0.3 (NH 4 ) 0.7 )Al(SO 4 ) 2 · 12 H 2 O (growth sector {111}) exhibiting random cation distribution is found to have cubic symmetry (space group Pa -3, R 1 = 0.027).

Polycrystalline CsBSi 5 O 12 was prepared from a stoichiometric mixture by solid-state reaction above 1000 °C. The solid solutions Cs 1–x Rb x BSi 5 O 12 were obtained at 1000 °C during a long heat treatment of polycrystalline Cs 1–x Rb x BSi 2 O 6 boropollucites ( x Rb = 0, 0.05, 0.2, 0.4). A new borosilicate compound and its solid solutions were studied using X-ray powder diffraction (XRD), annealing, differential scanning calorimetry (DSC), and thermogravimetry (TG). For Cs,Rb-boropollucites the new phase formation is accompanied by significant mass losses detected by DSC and TG. The following mechanism of phase transformations is assumed: (Cs,Rb)BSi 2 O 6 → (Cs,Rb)BSi 5 O 12 + (Cs,Rb)BO 2 ↑. The zeolite phase forms as a result of the boropollucite decomposition over 1000 °C. Zeolite decomposes also on further heating and the SiO 2 reflections are observed in the XRD pattern only. Thus above 1000 °C both boropollucite and zeolite phases are unstable presumably due to the ability of the alkali cations to leave the structure. Using XRD the unit cell parameters of CsBSi 5 O 12 have been determined in the orthorhombic crystal system: a = 16.242(4) Å, b = 13.360(4) Å, c = 4.874(1) Å. The compound is isostructural with the zeolite compound CsAlSi 5 O 12 . In the crystal structure of Cs 1–x Rb x BSi 5 O 12 solid solutions the changes of cell parameters are insignificant under the substitution of Cs by Rb atoms that indicates a very limited substitution range.

Starting with wurtzite-type single crystals, AgI was investigated at room temperature and pressures up to 0.5 GPa by means of a polarizing light microscope and with the precession technique. Distinct orientation relations were observed between four different AgI phases that occur suc cessively under increasing pressure. At 0.35 GPa a reverse-obverse (111) twin of zincblende-type AgI is formed with twin plane parallel to the (001) plane of the wurtzite-type structure. The antilitharge type of AgI occurs at 0.39 GPa. Its tetragonal [001] direction runs parallel to one of the (100) directions of the zincblende type. At almost the same pres sure the transformation to the NaCl-type form takes place. This AgI modification shows also twinning on (111) and the basis vectors are oriented parallel to those of the zincblende type. The transition between the zincblende- and the anti litharge-type phase shows a hysteresis: The back transfor mation occurs at 0.35 GPa. NaCl-type AgI transforms di rectly to the zincblende-type form at approximately 0.2 GPa when pressure is released. The observed orientation relations between zincblende-, antilitharge- and NaCl-type AgI support transition mecha nisms that have been proposed earlier [Keen & Hull, J. Phys.: Condens. Matter 5 (1993) 23–32].

Powder diffraction measurements are fast, and sample preparation does not require time consuming manipulations what is very important for toxic, unstable or explosive samples. In addition, very good results can be also obtained at structure solution level by nowadays methods. Unfortunately, structure solution results can sometimes be biased towards assumed structure models in most popular nowadays ‘direct space search procedures’. However, in typical applications crystal structure studies can be performed using ‘ab initio’ methods. Using this approach the crystal structures of two very unstable tetraperoxovanadates (V) — (NH 4 ) 3 [V(O 2 ) 4 ] and K 3 [V(O 2 ) 4 ] — have been ab initio solved from powder diffraction data by direct methods. The two ammonium and potassium salts are isotypic with lattice parameters: a = 6.9769(5), c = 8.211(1) and a = 6.6861(4), c = 7.708(2) Å, V = 399.68(7) Å 3 and 344.6(6) Å 3 , respectively. The space group is I -4 2m (No. 121) with Z = 2 for both compounds.

Two N-substituted phenylene diamines, C 30 H 28 N 2 S 2 O 4 (I) and C 30 H 28 N 2 S 2 O 5 (II), have been synthesized, and characterized by spectroscopic and single crystal X-ray analyses. Intermolecular N—H···O and C—H···O hydrogen bonds link the molecules of (I) into centrosymmetric dimers, which are further joined by C—H···O hydrogen bonds to form one-dimensional polymeric chain propagating along the [100] direction. The two molecules, A and B, in the asymmetric unit of (II) are connected by a pair of N—H···O hydrogen bonds forming a characteristic R 2 2 (14) dimeric ring centered at (0.245, 0.510, 0.252). The interlinking of adjacent dimers in (II) via C—H···O hydrogen bonds generates infinite one-dimensional ABBAAB… polymeric chain along the [101] direction.