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.