Crystal-structure refinement by profile fitting and least-squares analysis of powder diffractometer data

1983 ◽  
Vol 16 (6) ◽  
pp. 611-622 ◽  
Author(s):  
G. Will ◽  
W. Parrish ◽  
T. C. Huang
Keyword(s):  
Least Squares ◽  
Structure Refinement ◽  
Specimen Preparation ◽  
Crystal Structure Refinement ◽  
Instrument Function ◽  
X Ray ◽  
Profile Fitting ◽  
Fitting Method ◽  
The Individual ◽  
Integrated Intensities

The refinement of crystal structures using X-ray powder data in a two-stage method is described. (1) The integrated intensities of the individual reflections are derived by a profile fitting method in which the profile shapes are accurately defined using an experimentally determined instrument function and the sum of Lorentzian curves. (2) These values are then used in a powder least-squares refinement for structure determination. The results obtained with three simple structures (silicon, quartz and corundum) gave R(Bragg) values of 0.7 to 2.5%. The necessity of correcting for preferred orientation and the importance of proper specimen preparation are also discussed.

scholarly journals Accurate Measurement of Powder Diffraction Intensities Using Synchrotron Radiation

1988 ◽  
Vol 41 (3) ◽  
pp. 403 ◽  
Author(s):  
W Parrish ◽  
M Hart
Keyword(s):  
Synchrotron Radiation ◽  
Structure Refinement ◽  
Specimen Preparation ◽  
Instrument Function ◽  
Beam Geometry ◽  
Profile Fitting ◽  
Powder Samples ◽  
Parallel Beam Geometry ◽  
Integrated Intensities ◽  
Wavelength Selectivity

This paper reviews the advantages of synchrotron radiation for obtaining accurate values of the integrated intensities of powder samples for crystal structure refinement. The higher accuracy than conventional X-ray tube focusing methods results from the parallel beam geometry which has a symmetrical constant instrument function, higher intensity and resolution and easy wavelength selectivity. The importance of specimen preparation and the profile fitting function are discussed.

GENEFP: a full-profile fitting program for X-ray powder patterns using the genetic algorithm

2006 ◽  
Vol 39 (4) ◽  
pp. 615-617 ◽  
Author(s):  
Zhen Jie Feng ◽  
Cheng Dong
Keyword(s):  
Genetic Algorithm ◽  
Grain Size ◽  
Least Squares ◽  
Global Extremum ◽  
X Ray ◽  
Fundamental Parameters ◽  
Profile Fitting ◽  
Full Profile ◽  
Integrated Intensities

GENEFPis a full-profile fitting program, employing a fundamental-parameters method, for Cu-target X-ray powder patterns. In this program, the Le Bail method is used to determine integrated intensities and the genetic algorithm is used to search for the proper fundamental parameters. When some parameters, such as the grain size, have large uncertainties, the genetic algorithm has an advantage over conventional least-squares methods in finding the global extremum.

A Minicomputer and Methodology for X-Ray Analysis

1979 ◽  
Vol 23 ◽  
pp. 313-316 ◽  
Author(s):  
W. Parrish ◽  
G. L. Ayers ◽  
T. C. Huang
Keyword(s):  
Thin Film ◽  
Quantitative Analysis ◽  
Data Reduction ◽  
Fluorescence Spectrometry ◽  
Small Computer ◽  
X Ray ◽  
Fundamental Parameters ◽  
Profile Fitting ◽  
Fitting Method ◽  
Integrated Intensities

AbstractThis paper outlines the use of an IBM Series/1 small computer for instrument automation and data reduction for X-ray polycrystalline diffractometry and wavelength dispersive X-ray fluorescence spectrometry. The profile fitting method is used to determine 2θ, d and relative peak and integrated intensities in diffraction, and the fundamental parameters method (LAMA program) is used for quantitative analysis of bulk and thin film samples. The methods are precise and rapid.

X-ray powder diffraction data and structure refinement of CeFeGe3

1998 ◽  
Vol 13 (4) ◽  
pp. 241-243 ◽  
Author(s):  
Jialin Yan ◽  
Shiwei Wu ◽  
Xiangli Ou ◽  
Lingmin Zeng ◽  
Jianmin Hao
Keyword(s):  
Crystal Structure ◽  
Rare Earth ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Figure Of Merit ◽  
Structure Refinement ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Profile Fitting ◽  
Fitting Method

The crystal structure of the rare earth (RE) compound CeFeGe3 has been studied by X-ray powder diffraction and refined by the Rietveld profile fitting method. The compound has the tetragonal BaNiSn3-type structure, space group I4mm (No. 107) a=4.3294(1) Å, c=9.9444(3) Å, V=186.39 Å3, Z=2, and Dx=7.372 g·cm−3. The figure of merit FN for the powder data is F30=184.3(0.0037,44). The structure refinement was performed with 106 reflections and led to Rp=13.2% and Rwp=18.2%. Powder data are given.

Development of Gas Scintillation Proportional Counter

1999 ◽  
Vol 09 (03n04) ◽  
pp. 169-174
Author(s):  
N. Shigeoka ◽  
K. Mutaguchi ◽  
Y. Nakanishi ◽  
Y. Ito ◽  
T. Mukoyama ◽  
...  
Keyword(s):  
Proportional Counter ◽  
Pulse Height ◽  
Acceleration Region ◽  
X Ray ◽  
Gaussian Profile ◽  
Profile Fitting ◽  
Fitting Method

The properties of gas scintillation proportional counter are investigated for Mn K x-ray spectra. The pulse-height spectra are strongly affected by changing of the value of a potential V 2 in the acceleration region and analyzed by the Gaussian profile fitting method.

Crystal structure of potassium tetraperoxomolybdate (VI) K2[Mo(O2)4]

2005 ◽  
Vol 20 (3) ◽  
pp. 203-206 ◽  
Author(s):  
M. Grzywa ◽  
M. Różycka ◽  
W. Łasocha
Keyword(s):  
Crystal Structure ◽  
Low Temperature ◽  
Diffraction Pattern ◽  
Powder Diffraction ◽  
Rietveld Method ◽  
Structure Refinement ◽  
Crystal Structure Refinement ◽  
Unit Cell Parameters ◽  
X Ray ◽  
Cell Parameters

Potassium tetraperoxomolybdate (VI) K2[Mo(O2)4] was prepared, and its X-ray powder diffraction pattern was recorded at low temperature (258 K). The unit cell parameters were refined to a=10.7891(2) Å, α=64.925(3)°, space group R−3c (167), Z=6. The compound is isostructural with potassium tetraperoxotungstate (VI) K2[W(O2)4] (Stomberg, 1988). The sample of K2[Mo(O2)4] was characterized by analytical investigations, and the results of crystal structure refinement by Rietveld method are presented; final RP and RWP are 9.79% and 12.37%, respectively.

Potassic-jeanlouisite from Leucite Hill, Wyoming, USA, ideally K(NaCa)(Mg4Ti)Si8O22O2: the first species of oxo amphibole in the sodium–calcium subgroup

2019 ◽  
Vol 83 (4) ◽  
pp. 587-593
Author(s):  
Roberta Oberti ◽  
Massimo Boiocchi ◽  
Frank C. Hawthorne ◽  
Giancarlo Della Ventura ◽  
Gunnar Färber
Keyword(s):  
Microprobe Analysis ◽  
Electron Microprobe Analysis ◽  
Structure Refinement ◽  
Crystal Structure Refinement ◽  
Unit Cell Parameters ◽  
X Ray ◽  
International Mineralogical Association ◽  
Cell Parameters ◽  
Mineralogical Association ◽  
Sodium Calcium

AbstractPotassic-jeanlouisite, ideally K(NaCa)(Mg4Ti)Si8O22O2, is the first characterised species of oxo amphibole related to the sodium–calcium group, and derives from potassic richterite via the coupled exchange CMg–1W${\rm OH}_{{\rm \ndash 2}}^{\ndash}{} ^{\rm C}{\rm Ti}_1^{{\rm 4 +}} {} ^{\rm W}\!{\rm O}_2^{2\ndash} $. The mineral and the mineral name were approved by the International Mineralogical Association Commission on New Minerals, Nomenclature and Classification, IMA2018-050. Potassic-jeanlouisite was found in a specimen of leucite which is found in the lava layers, collected in the active gravel quarry on Zirkle Mesa, Leucite Hills, Wyoming, USA. It occurs as pale yellow to colourless acicular crystals in small vugs. The empirical formula derived from electron microprobe analysis and single-crystal structure refinement is: A(K0.84Na0.16)Σ1.00B(Ca0.93Na1.02Mg0.04${\rm Mn}_{{\rm 0}{\rm. 01}}^{2 +} $)Σ2.00C(Mg3.85${\rm Fe}_{{\rm 0}{\rm. 16}}^{2 +} $Ni0.01${\rm Fe}_{{\rm 0}{\rm. 33}}^{3 +} {\rm V}_{{\rm 0}{\rm. 01}}^{3 +} $Ti0.65)Σ5.01T(Si7.76Al0.09Ti0.15)Σ8.00O22W[O1.53F0.47]Σ2.00. The holotype crystal is biaxial (–), with α = 1.674(2), β = 1.688(2), γ = 1.698(2), 2Vmeas. = 79(1)° and 2Vcalc. = 79.8°. The unit-cell parameters are a = 9.9372(10), b = 18.010(2), c = 5.2808(5) Å, β = 104.955(2)°, V = 913.1(2) Å3, Z = 2 and space group C2/m. The strongest eight reflections in the powder X-ray pattern [d values (in Å) (I) (hkl)] are: 2.703 (100) (151); 3.380 (87) (131); 2.541 (80) ($\bar 2$02); 3.151 (70) (310); 3.284 (68) (240); 8.472 (59) (110); 2.587 (52) (061); 2.945 (50) (221,$\bar 1$51).

scholarly journals Recommended X-ray single-crystal structure refinement and Rietveld refinement procedure for tremolite

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
Paolo Ballirano ◽  
Beatrice Celata ◽  
Alessandro Pacella ◽  
Ferdinando Bosi
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Rietveld Refinement ◽  
Structure Refinement ◽  
Point Of View ◽  
Single Crystal Structure ◽  
Crystal Structure Refinement ◽  
Statistical Point ◽  
X Ray ◽  
Refinement Procedure

A detailed description of the structure of the amphibole-supergroup minerals is very challenging owing to their complex chemical composition that renders the process of cation partition extremely difficult, particularly because of the occurrence of multivalent elements. Since amphiboles naturally occur under a fibrous morphology and have largely been used to produce asbestos, there is a growing demand for detailed and accurate structural data in order to study the relationships between structure, composition and toxicity. The present study proposes a recommended refinement procedure for both X-ray single-crystal structure refinement (SREF) and Rietveld analysis for tremolite, selected as a test case. The corresponding structural results are compared to estimate the `degree of confidence' of the Rietveld refinement with regard to SREF. In particular, it is shown that the interpretation of the electron density of the tremolite structure by SREF is model dependent. By assuming that the site-scattering values from SREF should be as close as possible to those from electron microprobe analysis, as a crucial constraint for the correct description of the final crystal-chemical model, it is found that it is best satisfied by using partially ionized scattering curves (SCs) for O and Si, and neutral SCs (neutral oxygen curves or NOCs) for other atoms. This combination leads to the best fit to the diffraction data. Moreover, it is found that Rietveld refinement using NOCs produces the best structural results, in excellent agreement with SREF. It is worth noting that, due to the complexity of the diffraction pattern and the fairly large number of freely refinable parameters, refinements with different combinations of SCs produce results almost indistinguishable from a statistical point of view, albeit showing significant differences from a structural point of view.

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