Using the parallel-tempering algorithm to overcome complex problems in structure determination of inorganic materials with laboratory X-rays

 

T. Bataille1, N. Mahé1, E. Le Fur2, J.-Y. Pivan2, D. Louër1

 

Laboratoire de Chimie du Solide et Inorganique Moléculaire (UMR 6511 CNRS), Institut de Chimie,

1Université de Rennes, Avenue du Général Leclerc, 35042 Rennes, France,

2Ecole Nationale Supérieure de Chimie, Campus de Beaulieu, Rennes, France.

 

Ab initio structure solution of inorganic compounds from powder X-ray diffraction data still does not succeed in many cases. The major problem arises from the loss of information in terms of accurate integrated intensities, due to the projection of the three-dimensional reciprocal lattice onto the one-dimensional diffraction pattern. This feature is even enlarged with the use of conventional X-ray sources and with diffraction line broadening observed, for example, for nanocrystalline compounds obtained from solid state transformations. While the recent use of direct-space methods in organic chemistry is often successful, their application in inorganic chemistry remains difficult, due to the great number of degrees of freedom generated when starting from single atoms instead of large molecules. In the present study, we discuss the advantages of using a global optimisation procedure rather than the direct-methods and difference-Fourier syntheses for solving crystal structures of two inorganic powder compounds. In both cases, high quality powder data were collected with a Siemens D500 diffractometer using the Bragg-Brentano geometry and monochromatic CuKa1 radiation.

Na2[VO(PO4)]2(C2O4).2H2O was hydrothermally prepared in powder form in the course of the investigation of open-framework mixed vanado-phosphato-oxalate materials. Pattern indexing with DICVOL04 [1] led to a monoclinic solution with the unit cell dimensions a = 6.349(1) Å, b = 17.144(3) Å, c = 6.557(1) Å, b = 106.59(2)°, V = 684.0 Å3 [refined zero-shift 0.011° (2q), M20 = 48, F32 = 79(0.007,56)]. The conditions for non-extinction were consistent with space group P21/m. The direct methods revealed only the heaviest electron density peaks, but no O atoms were found in order to differentiate V and P atoms. The absence of preferred orientation effect allowed starting the structure solution using the parallel tempering algorithm available in FOX [2]. The initial model consisted in one VO6 octahedron, one PO4 tetrahedron, one rigid C2O4 group, two Na atoms and two water O atoms. A reasonable model was found after 4.4 million trials (110 minutes with a PC equipped with a AMD Athlon 1.7GHz processor), except that one sodium atom needed to be replaced by the water molecule. The final Rietveld refinement converged to the satisfactory R factors Rwp = 0.067, RF = 0.071.

YK(C4O4)2 was prepared from thermal treatment at 240 °C of the inorganic precursor [Y(H2O)6]K(C4O4)2(H2C4O4). As for a majority of decomposition products, its powder pattern exhibits significant diffraction line broadening, i.e. five times larger than the instrumental resolution function of the diffractometer. The first 20 lines were indexed with DICVOL04 on the basis of a tetragonal symmetry, with unit cell dimensions a = 6.2011(5) Å, c = 11.639(1) Å, V = 447.6 Å3 [refined zero-shift 0.007° (2q), M20 = 57, F20 = 71(0.006,44)]. The small number of Bragg peak positions available in the whole pattern, aggravated with the broadening of diffraction lines, was not sufficient for a thorough examination of the conditions for non-extinction. Thus, eleven space groups were retained in this symmetry. Structure determinations with the direct methods were attempted for each selected space group, leading to non reliable models. Consequently, a structure solution was carried out in the triclinic space group P1 by means of the program FOX, starting from two Y and two K atoms and four squarate groups. The solution was found after 6.3 million trials (10 hours). From the atomic positions displayed by the program, symmetry-equivalent positions were deduced, which allowed to find out the correct space group P4/mcc. The final Rietveld refinement led to the R factors Rwp = 0.098, RF = 0.035.

It is shown from these two examples that global optimisation procedures may succeed when the direct methods fail. Finally, considering the crystal structure of the thermal decomposition product g-Zn2P2O7 as starting model (determined ab initio from powder diffraction data [3]), we also discuss the influence of a few profile parameters affecting the quality of powder data on structure solution using the direct methods and a global optimisation algorithm.

 

1. A. Boultif, D. Louër (2004), submitted for publication.

2. V. Favre-Nicolin, R. Cerny, J. Appl. Crystallogr. 35 (2002) 734-743.

3. T. Bataille, P. Bénard-Rocherullé, D. Louër, J. Solid State Chem. 140 (1998) 62-70.