Showing papers on "Rietveld refinement published in 1982"

Rietveld Refinement with Spallation Neutron Powder Diffraction Data

Abstract: The mathematical functions necessary for Rietveld refinement of time-of-flight neutron powder diffraction patterns from spallation sources are developed and a computer program for least-squares analysis is described. The results of Rietveld refinements of nickel and a low-carbon steel are described and discussed. The method fully exploits the high resolution (Δd/d ~ 0.3 ~ 0.5%) available with powder diffractometers currently in operation on these sources and examples are given of precise determination of atom coordinates, thermal parameters, lattice parameters and the detection of small strains.

Neutron diffraction refinement of the structure of gypsum, CaSO4.2H2O

Abstract: The crystal structure of gypsum, CASO4.2H20, has been refined to R w -0.023 and R -0.036 for 610 neutron diffraction intensities collected at room temperature (294 K) for a unit cell with a = 5.679 (5), b = 15.202 (14), c 6.522 (6) A, fl 118.43 (4) °, and space group I2/a, Z = 4, V = 495.2 A a, d c = 2.3 g cm -3. The refinement was based on a model with anisotropic thermal motion for all atoms, and an isotropic secondary-extinction coefficient. The O H bonds of the water molecule are 0.942(3) and 0.959 (3)A and hence significantly different. The difference, 0.017 (4)A,, is in accordance with spectroscopic stretching-frequency differences for the two O H bonds. The water molecule donates two hydrogen bonds of 1.856 (2) and 1.941 (2) A to sulfate O atoms. The shortest hydrogen bond is not linear, the O H . . . O angle being 170.9 (2) °, whereas the other bond has an angle of 177.2 (2) °. H H is 1.533 (3) A and H O H 107.5 (2) °. The sulfate ion is definitely not a regular tetrahedron. The S O distances are equal [1.474 (1) and 1.471 (1)A], but the O S O angles are not [111.1(1), 111.0(1), 111.1(1) and 106.3 (1)°], leading to differences in the O O tetrahedral edges [2.429 (1), 2.432 (2), 2.426 (2) and 2.357 (1)A]. The shortest edge is shared between the sulfate tetrahedron and the square-bipyramidal CaO s group.

The Rietveld method in neutron and X-ray powder diffraction

Abstract: In the Rietveld method of analysing powder diffraction data, the crystal structure is refined by fitting the entire profile of the diffraction pattern to a calculated profile. There is no intermediate step of extracting structure factors. The method was applied first to diffraction patterns recorded with neutrons at a fixed wavelength. It has now been used successfully for the treatment of results from the four categories of experimental technique, with neutrons or X-rays as the primary radiation and with the scattered intensity measured at a fixed wavelength or at a fixed scattering angle. In this article we discuss the application of the Rietveld method to each of these techniques.

High-Resolution Time-of-Flight Powder Diffractometer at the ZING-P' Pulsed Neutron Source

Abstract: A high-resolution time-of-flight powder diffractometer has been operated at Argonne's ZING-P' pulsed neutron source for over 2½ years. The diffractometer achieves Ad/d<3 x 10 -3 over a broad range of plane spacings. Even though the flux at the sample position is comparatively low due to the 18.37 m incident flight path, count rates competitive with typical two-axis diffractometers are achieved because of large detector areas. A Rietveld refinement of data for a standard AI20 3 sample gives results as good as or better than those obtained with the best two-axis diffractometers.

The analysis of powder diffraction data

Abstract: A comparison has been carried out between the results of analyses of several sets of neutron powder diffraction data using three different methods: the Rietveld method [Rietveld (1967). Acta Cryst. 22, 151-152; (1969) J. Appl. Cryst. 2, 65-71], a modification of the Rietveld method to include off-diagonal terms in the weight matrix [Clarke & Rollett (1982). Acta Cryst. Submitted] and the SCRAP method, which involves the estimation of observed Bragg intensities [Cooper, Rouse & Sakata (1981). Z. Kristallogr. 157, 101-117]. Two simulations have also been carried out to demonstrate the way in which the results can differ in more extreme cases. This study has confirmed that the values of the estimated standard deviations given by the Rietveld method are not reliable and that, of the methods considered, only the SCRAP method will in general give reliable values for the estimated standard deviations of the structural parameters.