scholarly journals Rietveld refinement round robin. I. Analysis of standard X-ray and neutron data for PbSO4

1992 ◽  
Vol 25 (5) ◽  
pp. 589-610 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Single Crystal ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Analysis ◽  
Data Sets ◽  
X Rays ◽  
Neutron Data ◽  
X Ray ◽  
Atomic Coordinates

The Commission on Powder Diffraction of the International Union of Crystallography has undertaken an intercomparison of Rietveld refinements performed with two `standard' PbSO4 powder diffraction patterns: a conventional (two-wavelength) X-ray pattern collected on a Bragg–Brentano diffractometer with Cu Kα radiation and a constant-wavelength neutron pattern collected on the D1A diffractometer at the Institut Laue–Langevin. The aims of this project were: (i) to evaluate a cross section of currently used Rietveld refinement software; (ii) to examine the range and effect of various strategies of Rietveld refinement; (iii) to assess the precision and accuracy (spread) of the parameters derived by Rietveld analysis. 23 participants provided 18 refinements with the X-ray data and 20 refinements with the neutron data, using 11 different Rietveld-analysis programs. Analysis of the submitted results shows that refinement strategies play a large part in determining the detailed outcome of a Rietveld refinement. The wide variation in the values of the agreement indices obtained in these studies of the same data sets highlights the need for standardization both of the refinement procedures and of the type of data included in the algorithms used for assessing the fit. The major factors limiting the accuracy of the derived PbSO4 crystal structure parameters were: (i) use of insufficiently flexible peak shape and/or background functions; (ii) elimination of the high-angle diffraction data from the refinement; (iii) inclusion of an insufficiently wide range of diffraction angles on either side of the centroid of each peak during the step intensity calculation; and, additionally for X-rays, (iv) simultaneous release of the O-atom site-occupancy and displacement parameters. Rietveld analysis of the PbSO4 X-ray powder diffraction data provided atomic coordinates and isotropic displacement parameters for the Pb and S atoms that are precise (i.e. have small e.s.d.s) and are in reasonable agreement with the values derived from a single crystal study (viz the spread of coordinates is over the range 0.007–0.042 Å). On the other hand, the `light' O-atom parameters show relatively poor precision and have a disconcertingly wide spread of values about the weighted mean (viz 0.12–0.19 Å for the coordinates). Despite the much lower intrinsic resolution of the neutron data (i.e. peak widths some four times those of the X-ray data), the coordinates and anisotropic displacement parameters obtained for the Pb and O atoms are very precise and have a relatively narrow distribution about the single-crystal results, namely 0.004–0.020 Å for the coordinates. The range of coordinates determined from the neutron data for the relatively `light' S atom is correspondingly larger, namely 0.024–0.043 Å, about equivalent to that obtained from the X-ray data. In general, and as expected, the e.s.d.s from the Rietveld analyses are substantially smaller than the observed inter-refinement variation of the unit-cell dimensions, atomic coordinates and isotropic displacement parameters by factors of up to, respectively, 17, 5 and 22 for X-rays, and 25, 3 and 5 for neutrons. This investigation indicates that results of possibly high precision but low accuracy are not uncommon in Rietveld analysis. The disparity between individual refinements can be expected to increase further when, unlike here, the analyses are undertaken using data sets collected under diverse experimental conditions.

scholarly journals Lower resolution Laue neutron data yield correct nanocluster formulations

2014 ◽  
Vol 70 (a1) ◽  
pp. C187-C187
Author(s):  
Alison Edwards
Keyword(s):  
Neutron Diffraction ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Precise Determination ◽  
Data Sets ◽  
X Rays ◽  
Low Resolution ◽  
Neutron Data ◽  
X Ray ◽  
Product Formulation

"The renaissance in Laue studies - at neutron sources - provides us with access to single crystal neutron diffraction data for synthetic compounds without requiring synthesis of prohibitively large amounts of compound or improbably large crystals. Such neutron diffraction studies provide vital data where proof of the presence or absence of hydrogen in particular locations is required and which cannot validly be proved by X-ray studies. Since the commissioning of KOALA at OPAL in 2009[1] we have obtained numerous data sets which demonstrate the vital importance of measuring data even where the extent of the diffraction pattern is at relatively low resolution - especially when compared to that obtainable for the same compound with X-rays. In the Laue experiment performed with a fixed radius detector, data reduction is only feasible for crystals in the ""goldilocks"" zone – where the unit cell is relatively large for the detector, a correspondingly low resolution diffraction pattern in which adjacent spots are less affected by overlap will yield more data against which a structure can be refined than a pattern of higher resolution – one where neighbouring spots overlap rendering both unusable (in our current methodology). Analogous application of powder neutron diffraction in such determinations is also considered. Single crystal neutron diffraction studies of several important compounds (up to 5KDa see figure below)[2] in which precise determination of hydride content by neutron diffraction was pivotal to the final formulation will be presented. The neutron data sets typically possess 20% or fewer unique data at substantially "lower resolution" than the corresponding X-ray data sets. Careful refinement clearly reveals chemical detail which is typically unexplored in related X-ray diffraction studies reporting high profile chemistry despite the synthetic route being one which hydride ought to be considered/excluded in product formulation."

Rietveld refinement of the crystal structure of γ-Mo4O11

1999 ◽  
Vol 14 (4) ◽  
pp. 284-288 ◽  
Author(s):  
Hoong-Kun Fun ◽  
Ping Yang ◽  
Minoru Sasaki ◽  
Masasi Inoue ◽  
Hideoki Kadomatsu
Keyword(s):  
Crystal Structure ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Room Temperature ◽  
Rietveld Analysis ◽  
Powder Diffraction Data ◽  
Orthorhombic System ◽  
Space Group ◽  
X Ray

The crystal structure of γ-Mo4O11 was obtained at room temperature (296 K) by Rietveld analysis with X-ray powder diffraction data. The crystal belongs to orthorhombic system, space group: Pna21, Z=4, Mr=559.753 (Atomic weights 1977), Dx=4.1228 g/cm3, F(000)=1024.0, μ=451.293 cm−1 (Int. Tab. Vol. C, Table 4.2.4.2, p. 193, λ=1.540 60 Å), a=24.4756(5) Å, b=6.7516(1) Å, c=5.4572(1) Å, and V=901.80(3) Å3. The structure was refined to Rwp=5.60%, Rp=4.27%, Rb=3.36%, and Rf=2.74% for 65 parameters with 3541 step intensities and 3055 peaks. Goodness of the fit S=3.35.

Rietveld Structure Refinement of the Apophyllite Crystals from Deccan Basalt Plateau Using X-ray Powder Diffraction Data

2020 ◽  
Vol 70 (12) ◽  
pp. 4248-4254
Keyword(s):  
Crystal Structure ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Method ◽  
X Rays ◽  
Powder Diffraction Data ◽  
Deccan Basalt ◽  
X Ray ◽  
Basalt Plateau

The crystal structure of a rare sample of natroapophyllite from Pune district (western India) located in the Deccan Basalt Plateau has been refined using X-Ray powder diffraction data and the Rietveld method. The Rietveld refinement was carried out using the computer program Diffracplus TOPAS 4.1. The pseudo-Voigt (pV) profile function was used for the fit of the peaks. The Rietveld refinement of the analyzed sample in space group Pnnm (No.58): a=8.94771 Å, b=8.98013 Å, c=15.78878 Å, Z=2, confirm the basic natroapophyllite structure. The chemical composition of the apophyllite crystals from Pune region (India) was determined by EDX analysis. The paper presents a new set of the unit cell parameters and fractional coordinates that define the natroapophyllite crystal structure. The quality of the sample analyzed was pristine, the sample being collected from an association of apophyllite-stilbite crystals of centimetric dimensions. Keywords: natroapophyllite, crystal structure, X-rays diffraction, EDX, Rietveld method

A Rietveld refinement investigation of a Mg-stabilized triclinic tricalcium silicate using synchrotron X-ray powder diffraction data

2004 ◽  
Vol 19 (4) ◽  
pp. 356-358 ◽  
Author(s):  
Vanessa Kate Peterson
Keyword(s):  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Analysis ◽  
Tricalcium Silicate ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Triclinic Form

A Mg-stabilized triclinic tricalcium silicate form of type Ca3−xMgxSiO5, T3, was synthesized. Rietveld analysis using synchrotron X-ray powder diffraction data suggested that unlike the T1 form, the T3 structure was unmodulated. This refinement illustrated that the only existing model for a triclinic form of tricalcium silicate (T1) can be used to describe the nonmodulated T3 form.

X-ray powder diffraction data for calcium galactarate tetrahydrate CaC6H8O8·4H2O and Rietveld refinement of the crystal structure

2000 ◽  
Vol 15 (3) ◽  
pp. 175-179
Author(s):  
B. Barbier ◽  
H. Euler
Keyword(s):  
Crystal Structure ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
White Wine ◽  
Crystal Data ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Single Crystal Study ◽  
Atomic Coordinates

The powder pattern of calcium galactarate tetrahydrate (CaC6H8O8·4H2O) is presented. The compound was found in white wine stored for 4 years. A Rietveld refinement using the atomic coordinates from a single crystal study as starting values was refined with 55 parameters and without preferred orientation to RB=5.97%, RF=4.44%, Rp=10.39%, and Rwp=13.43% for 84 reflections. Crystal data: Mr=320.14, orthorhombic, Pcan, a=7.3359(1) Å, b=11.6296(3) Å, c=15.0978(6) Å, V=1288.05(6) Å3, Z=4, Dx=1.651 g/cm3, λ(CuKα1)=1.54060 Å, μ=46.76 cm−1.

Rietveld Refinement of the BaTiO3 from X-Ray Powder Diffraction

2009 ◽  
Vol 79-82 ◽  
pp. 593-596
Author(s):  
Feng Sun ◽  
Yan Sheng Yin
Keyword(s):  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Method ◽  
Structural Parameters ◽  
Ferroelectric Ceramic ◽  
Powder Diffraction Data ◽  
Ceramic Powders ◽  
Space Group ◽  
X Ray

The ferroelectric ceramic BaTiO3 was synthesized at 1000 °C for 5 h. The structure of the system under study was refined on the basis of X-ray powder diffraction data using the Rietveld method. The system crystallizes in the space group P4mm（99）. The refinement of instrumental and structural parameters led to reliable values for the Rp, Rwp and Rexp.We use the TOPAS software of Bruker AXS to refine this ceramic powders and show its conformation

scholarly journals Rubidium tetrafluoridobromate(III): redetermination of the crystal structure from single-crystal X-ray diffraction data

IUCrData ◽  
2019 ◽  
Vol 4 (11) ◽  
Author(s):  
Artem V. Malin ◽  
Sergei I. Ivlev ◽  
Roman V. Ostvald ◽  
Florian Kraus
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Single Crystals ◽  
Diffraction Data ◽  
Structure Type ◽  
X Ray Diffraction ◽  
X Ray ◽  
Square Planar ◽  
Atomic Coordinates

Single crystals of rubidium tetrafluoridobromate(III), RbBrF4, were grown by melting and recrystallizing RbBrF4 from its melt. This is the first determination of the crystal structure of RbBrF4 using single-crystal X-ray diffraction data. We confirmed that the structure contains square-planar [BrF4]− anions and rubidium cations that are coordinated by F atoms in a square-antiprismatic manner. The compound crystallizes in the KBrF4 structure type. Atomic coordinates and bond lengths and angles were determined with higher precision than in a previous report based on powder X-ray diffraction data [Ivlev et al. (2015). Z. Anorg. Allg. Chem. 641, 2593–2598].

Sign in / Sign up

Export Citation Format

Share Document