Iván da Silva

Space-group determination from powder diffraction data: a probabilistic approach

Experimental powder diffraction diagrams, once indexed and decomposed into single diffraction intensities, can be submitted to statistical analysis for the determination of space-group symmetry. A new algorithm is illustrated, which is able to provide, on a quantitative basis, a probability value for each extinction symbol compatible with the previously established lattice symmetry. The algorithm has been implemented in EXPO2004 [Altomare, Caliandro, Camalli, Cuocci, Giacovazzo, Moliterni & Rizzi (2004). J. Appl. Cryst. 37, 1025–1028] and has been successfully tested using a large set of experimental data.

Space group determination: improvements in EXPO2004

In the ideal process for crystal structure solution, the determination of the space group usually follows the indexation step. When powder data are used, peak overlap, background definition and possible impurity peaks may hinder the identification of the correct extinction group. The recent automatic procedure implemented in EXPO2004 has been further developed; the modifications are based on additional statistical criteria, with new algorithms for a better definition of the background and for the removal of impurity peaks. The new version also offers a more powerful graphical interface. Failures occur rarely, as shown by examples.

New hybrid diphosphates Ln2(NH2(CH2)2NH2)(HP2O7)2 · 4 H2O(Ln = Eu, Tb, Er): synthesis, single crystal and powder X-ray crystal structure

Crystals of lanthanide ethylenediamine diphos phates Ln2(NH2(CH2)2NH2)(HP2O7)2 · 4 H2O (Ln = Eu (1), Tb (2), Er (2)) have been synthesized and investigated by single crystal X-ray diffractometry (Eu and Tb phases) and by powder X-ray diffractometry (Er phase). The three structures resulted to be isostructural within triclinic space group P-1, with unit cell parameters of a = 6.5050(6) Å; b = 6.9990(2) Å; c = 9.8450(9) Å; α = 81.548(5)°; β = 80.631(19)°; γ = 88.369(9)°; V = 437.44(6) Å3(1), a = 6.4360(7) Å; b = 6.9480(12) Å; c = 9.816(4) Å; α = 81.987(19)°; β = 80.595(16)°; γ = 88.591(13)°; V = 428.82(19) Å3(2), a = 6.39658(2) Å; b = 6.86682(2) Å; c = 9.78849(3) Å; α = 81.6811(4)°; β = 80.2304(3)°; γ = 88.3812(3)°; V = 419.255(3) Å3(3).The three-dimensional network is built up by the repetition of ab-parallel layers of LnO8 polyhedra corner-sharing with (HP2O7) groups; ethylenediamine molecules lie between such layers, acting both as receptors and donors in strong hydrogen bonds which assure the stabilizing of the entire framework.

The use of error-correcting codes for the decomposition of a powder diffraction pattern

The decomposition of a powder diffraction pattern consists of the extraction of the intensities of the individual reflections from the experimental profile. The process is crucial for structure determination from powder diffraction data, but its accuracy is limited by the intrinsic peak overlap. A substantial improvement is achieved by considering clusters of reflections in strong overlap and partitioning in a systematic way the total intensity of each cluster among the constituent reflections. In this paper, error-correcting codes are used to explore the set of decomposition trials obtained by combining the partitions of various clusters of overlapping reflections. Linear ternary codes resulting from modifications of the Hamming codes [13, 10] and [40, 36] have been considered as the most suited for the present problem. They have been included in the EXPO program via their generator matrices. Tests on a set of experimental powder patterns show that an efficient decomposition procedure consists of performing only 27 decomposition trials, determined as the codewords of an [ndoub, 3] code, where ndoub is the number of doublets of strong overlapping reflections found in the experimental profile. This allows a reduction in the number of trials, thus processing about 2% of the number used in a previous design of the same procedure, leading to a reduction of the total execution time by nearly the same amount.

New thallium diphosphates Tl2Me(H2P2O7)2 · 2 H2O, Me = Mg, Mn, Co, Ni and Zn. Synthesis, single crystal X-ray structures and powder X-ray structure of the Mg phase

Abstract Crystals of thallium dihydrogendiphosphate Tl2Me(H2P2O7)2 · 2 H2O (Me = Mg (1), Mn (2), Co (3), Ni (4) and Zn (5)), have been synthesized and analyzed by powder X-ray diffractometry (Mg phase) and single crystal X-ray diffractometry (other phases). They resulted to be isostructural within triclinic group P-1, with the following unit-cell parameters: a = 6.9620(1), b = 7.3635(1), c = 7.7713(1) Å, α = 81.8014(5), β = 70.8597(6), γ = 86.1373(7)°, V = 372.44(8) Å3(1); a = 6.9577(6), b = 7.4745(6), c = 7.8248(7) Å, α = 80.723(2), β = 71.912(1), γ = 85.661(1)°, V = 381.62(6) Å3(2); a = 6.9767(7), b = 7.3634(7), c = 7.7690(7) Å, α = 81.421(2), β = 71.114(2), γ = 86.424(2)°, V = 373.36(6) Å3(3); a = 6.9658(7), b = 7.3079(7), c = 7.7016(7) Å, α = 81.801(2), β = 71.185(2), γ = 86.528(2)°, V = 367.27(6) Å3(4) and a = 6.9628(7), b = 7.3625(7), c = 7.7401(8) Å, α = 81.590(2), β = 71.441(2), γ = 86.323(2)°, V = 372.04(6) Å3(5). Me is octahedrally coordinated by two water molecules and four oxygen atoms belonging to two different diphos phate groups. Thallium cations make up interactions with oxygen atoms within Van der Waals coordination sphere, making up irregular coordination polyhedra. The framework of the present compounds can be described as a three-dimensional framework made from vertex-sharing polyhedra. The basic unit is the [Me(H2P2O7)2 · 2 H2O] moiety, which displays a crystallographic Ci symmetry, with the Me cation on the inversion centre. Such units are held together by an intricate scheme of Tl…O interactions; hydrogen bonds complete the network.

Powder neutron diffraction of Tl2BeF4 at six temperatures from room temperature to 1.5 K.

The structure of thallium fluoroberyllate, Tl2BeF4, has been analysed by the Rietveld method on neutron diffraction patterns collected at 1.5, 50, 100, 150, 200 and 300 K, with the aim of detecting low-temperature instabilities. Atomic parameters based on the isomorphic beta-K2SO4 crystal in the paraelectric phase were used as the starting model at room temperature; no evidence for any phase transition has been detected at lower temperature. The structure was determined in the orthorhombic space group Pnma. All the atoms (except one F atom) occupy sites with m symmetry. We have compared the structure with those of other compounds of the beta-K2SO4 family, at room temperature, in order to gain insight into their observed instabilities. The irregular coordination of the cations may indicate stereochemical activity of the TlI lone pair but does not indicate a possible structural instability.

About the variable-counting-time techniques in powder diffraction data: their use in EXPO2004

High quality data are essential for crystal structure solution, particularly when Direct Methods instead of Global Optimization Techniques are used. In this work we study the performances of the variable-counting-time techniques in the two crucial steps of the phasing process: decomposition of the full diffraction pattern and direct phasing. The experimental data were collected by a conventional X-ray laboratory diffractometer: they were then submitted to the program EXPO2004 for assessing their usefulness in the phasing process. The results are compared with those obtained by using experimental diffraction data collected via the traditional fixed-counting-time technique under the same experimental conditions.

Ab initio crystal structure determination of two chain functionalized pyrroles from synchrotron X-ray powder diffraction data

The financial support from the Spanish Ministerio de Ciencia e Innovacion (PI201060E013) is also acknowledged.

Expo2006: A Tool for Powder Crystallography

In spite of the big progress in diffraction data collection and management (due to a larger use of the synchrotron radiation, of more efficient detectors and of more powerful computer programs) the crystal structure solution from powder diffraction data is still a challenge. Many programs are today available for such purpose, each covering one or more of the five steps in which the crystal structure solution process may be traditionally divided. EXPO2004 (Altomare et al., 2004a) covers all such steps. In particular it is able to: 1) identify the unit cell via the module N-TREOR (Altomare et al., 2000) [see ITO (Visser, 1969), TREOR90 (Werner et al., 1985), DICVOL91(Boultif & Louer, 1991) for alternative programs]; 2) extract the structure factor amplitudes from the experimental diffraction pattern via the Le Bail approach (Le Bail et al., 1988) (see Pawley, 1981, for a different technique); 3) identify the extinction group, and then the space group, via a statistical analysis of the extracted intensities [Altomare et al., 2004b ; see also Markvardsen et al. (2000)]; 4) solve the crystal structures via Direct Methods (DM); 5) refine the crystal structure via Rietveld (1969) techniques (see also McCusker, 1999). EXPO2006 is the heir of EXPO2004. We have implemented in it some new routines, the purpose and the effects of which are below summarised, which make the structure solution process more straightforward.