Solving Crystal Structures from Powder Diffraction Data

Abstract

High resolution powder data from both neutron and X-ray (synchrotron) sources have been used to estimate the possibility of direct structure determination from powder data. Two known structures were resolved by direct methods with neutron and X-ray data. With synchrotron X-ray data, the measured range of data was insufficient for a structure analysis, but the R-factor calculations showed the intensities extracted from the profile data to be of acceptable quality. The results were used to estimate the largest structure that might be solved using routine techniques. It was found that the limit would be near twenty atoms in the asymmetric part of a centro-symmetric structure.

Structure determination by use of pattern decomposition and the Rietveld method on synchrotron X-ray and neutron powder data; the structures of Al2Y4O9and T2O4

“…Pawley (1981) has developed such a method, where the structure factors are variables in calculating the pattern, and where the differences in intensity of neighbouring overlapping reflections are controlled by the inclusion of slack constraints. This approach was first used by Hewat (1982) to solve the structure of ]/-oxalic acid from high-resolution neu-tron data, and its limits of application have more recently been discussed by Christensen, Lehmann & Nielsen (1985). In the present paper we continue this analysis and report on structure solutions of two compounds, A12Y40 9 and I204, from both neutron and synchrotron X-ray data.…”

“…In an earlier paper (Christensen, Lehmann & Nielsen, 1985) the plausible limit for the method was estimated to be a structure with about 20 independent atoms. In that analysis it was assumed that for sin 0/2 around 0.45 ,~,-1 peaks could be separated if they were 0.02 ° or more apart.…”

The Genetic Algorithm: Foundations and Apllications in Structure Solution from Powder Diffraction Data

“…The traditional approach (Christensen et al, 1985;McCusker, 1991;Cheetham & Wilkinson, 1991Rudolf, 1993;Langford & Loue È r, 1996;Poojary & Clear®eld, 1997) for solving crystal structures directly (ab initio) from powder diffraction data has been to extract the intensities I(hkl) of individual re¯ections directly from the powder diffraction pattern and then to solve the structure by using these intensities I(hkl) in the types of calculation (e.g. direct methods and the Patterson method) adopted for single-crystal diffraction data.…”

“…However, many crystalline solids cannot be prepared in the form of appropriate single crystals and are therefore not amenable to structural characterization by conventional single-crystal X-ray diffraction techniques. In such cases, progress relies on the availability of techniques for crystal-structure determination using powder diffraction data (Christensen et al, 1985;Cheetham & Wilkinson, 1991McCusker, 1991;Rudolf, 1993;Langford & Loue È r, 1996;Poojary & Clear®eld, 1997) or microcrystal diffraction data (recorded using synchrotron X-radiation) (Harding, 1996;Harding et al, 1994;Gray et al, 1997;Noble et al, 1997).…”

Optimization of monochromator and ToF powder diffractometers at a long-pulse spallation source using Monte Carlo simulations

“…The value of n varies from 3 for a cubic symmetry [6] to 4 for a triclinic symmetry [3]. Arguments based on the density of lattice nodes in reciprocal space show that the quantity to be minimized instead of the peak width should be d −n Δd, where Δd and d are the peak width and position, respectively, on the lattice spacing scale.…”