Profile Fitting for Quantitative Analysis in X-Ray Powder Diffraction

1982 ◽  
Vol 26 ◽  
pp. 141-147 ◽  
Author(s):  
Walter N. Schreiner ◽  
Ron Jenkins
Keyword(s):  
Mathematical Model ◽  
Quantitative Analysis ◽  
Phase Analysis ◽  
Powder Diffraction ◽  
Quantitative Phase Analysis ◽  
X Ray ◽  
Profile Fitting ◽  
Integration Techniques ◽  
Free Parameters ◽  
Integrated Intensities

Quantitative phase analysis by powder diffractometry requires accurate measurement of the integrated intensities of the diffracted, lines. When lines are isolated and on simple backgrounds, count integration techniques work very well. However, when one or more lines overlap the line of interest, or a complex background is present, profile fitting techniques are required in order to eliminate interferences.Profile fitting involves choosing a mathematical model to represent the expected profile shapes. Experience has shown that the profile shapes obtained with a parafocusing powder diffractometer are not easily described and many models have been tried with varying degrees of success. Generally the more free parameters allowed In the model the ‘setter the fits, although, aesthetically one would like to keep the number of free parameters to a minimum.

scholarly journals Quantitative Phase Analysis by X-ray Diffraction—Doping Methods and Applications

Crystals ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 27 ◽  
Author(s):  
Stanko Popović
Keyword(s):  
Quantitative Analysis ◽  
Phase Analysis ◽  
Powder Diffraction ◽  
Phase Fraction ◽  
Quantitative Phase Analysis ◽  
Intermetallic Alloys ◽  
X Ray Diffraction ◽  
X Ray ◽  
Quantitative Phase

X-ray powder diffraction is an ideal technique for the quantitative analysis of a multiphase sample. The intensities of diffraction lines of a phase in a multiphase sample are proportional to the phase fraction and the quantitative analysis can be obtained if the correction for the absorption of X-rays in the sample is performed. Simple procedures of quantitative X-ray diffraction phase analysis of a multiphase sample are presented. The matrix-flushing method, with the application of reference intensities, yields the relationship between the intensity and phase fraction free from the absorption effect, thus, shunting calibration curves or internal standard procedures. Special attention is paid to the doping methods: (i) simultaneous determination of the fractions of several phases using a single doping and (ii) determination of the fraction of the dominant phase. The conditions to minimize systematic errors are discussed. The problem of overlapping of diffraction lines can be overcome by combining the doping method (i) and the individual profile fitting method, thus performing the quantitative phase analysis without the reference to structural models of particular phases. Recent suggestions in quantitative phase analysis are quoted, e.g., in study of the decomposition of supersaturated solid solutions—intermetallic alloys. Round Robin on Quantitative Phase Analysis, organized by the IUCr Commission on Powder Diffraction, is discussed shortly. The doping methods have been applied in various studies, e.g., phase transitions in titanium dioxide, biomineralization processes, and phases in intermetallic oxide systems and intermetallic alloys.

Quantitative Phase Analysis of Devonian Shales by Computer Controlled X-Ray Diffraction of Spray Dried Samples

1978 ◽  
Vol 22 ◽  
pp. 181-191 ◽  
Author(s):  
Steven T. Smith ◽  
Robert L. Snyder ◽  
W. E. Brownell
Keyword(s):  
Quantitative Analysis ◽  
Phase Analysis ◽  
Powder Diffraction ◽  
Convenient Method ◽  
Quantitative Phase Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Intractable Problems ◽  
Computer Controlled ◽  
Spray Dried

Spray drying is shown to be an effective and rapid method for preparing samples for quantitative analysis by x-ray powder diffraction. Previously intractable problems like the simultaneous analysis of multiple phases in orientation prone systems can be carried out. Using this method, and a computer controlled diffractometer, five and six phase analyses of Devonian shales can be accomplished in approximately forty minutes. A rapid and convenient method for using the absorption diffraction technique for x-ray quantitative analysis is described.

Quantitative Phase Analyses of a Slag Using X-Ray Powder Diffraction

2014 ◽  
Vol 881-883 ◽  
pp. 1241-1244
Author(s):  
Wei Jin Zeng ◽  
Chao Zeng ◽  
Wei He
Keyword(s):  
Quantitative Analysis ◽  
Phase Analysis ◽  
Powder Diffraction ◽  
Rietveld Method ◽  
Quantitative Phase Analysis ◽  
Powder Diffraction Data ◽  
X Ray ◽  
Quantitative Phase ◽  
Full Profile ◽  
Qualitative Phase

The quantitative phase analyses of a slag have been successfully carried out by using both of the full-profile Rietveld and RIR methods from X-ray powder diffraction data. The qualitative phase analysis indicates that the slag contains mayenite (CaO)12(Al2O3)7, olivine Ca2(SiO4), gehlenite Ca2Al (AlSiO7), lemite Ca2(SiO4) and hibonite CaO(Al2O3)6. The quantitative analysis from Rietveld refinement shows that the weight concentrations of mayenite, olivine, gehlenite, lemite and hibonite for the slag are 48.8(4) wt.%, 32.2(5) wt.%, 11.0(9) wt.%, 6.2(1.1) wt.% and 1.8 (1.2) wt.%, respectively. The quantitative phase analysis results obtained by Rietveld method are more precise then those by RIR method.

scholarly journals Evaluation via multivariate techniques of scale factor variability in the rietveld method applied to quantitative phase analysis with X ray powder diffraction

2006 ◽  
Vol 9 (4) ◽  
pp. 369-374 ◽  
Author(s):  
Terezinha Ferreira de Oliveira ◽  
Roberto Ribeiro de Avillez ◽  
Eugenio Kahn Epprecht ◽  
Joaquim Carlos Barbosa Queiroz
Keyword(s):  
Phase Analysis ◽  
Powder Diffraction ◽  
Rietveld Method ◽  
Scale Factor ◽  
Quantitative Phase Analysis ◽  
Multivariate Techniques ◽  
X Ray ◽  
Quantitative Phase

Effect of Testing Factors on Rietveld Quantitative Analysis of Cement-Matrix Materials

2017 ◽  
Vol 898 ◽  
pp. 2054-2059
Author(s):  
Yan Ling Gan ◽  
Su Ping Cui ◽  
Ya Li Wang ◽  
Hong Xia Guo
Keyword(s):  
Quantitative Analysis ◽  
Phase Analysis ◽  
Rietveld Method ◽  
Cementitious Materials ◽  
Cement Matrix ◽  
Quantitative Phase Analysis ◽  
Step Size ◽  
X Ray ◽  
Quantitative Phase ◽  
Scan Time

For cement-matrix materials, the microstructure plays a vital important role in the research. Recently, quantitative phase analysis of cementitious materials can be performed using the Rietveld method by fitting the calculated X-ray diffraction (XRD) profile with the observed one. The aim of this paper is to further perform the quantitative analysis by the Rietveld method and discuss the influence of testing factors on the Rietveld quantitative phase analysis. The factors included the collection range of pattern, step size and the scan time of per step. In this study, the chemical composition of the samples was determined by X-ray fluorescence (XRF) spectrometry. And their phase composition was calculated by X-ray powder diffraction and Rietveld analysis. The results showed that the collection range of pattern depended on the tested materials , and the scanning range should include the main diffraction peak of the sample. Smaller step size and longer scan time of each step made the fitting factor smaller, also the calculated pattern coincided with the measured pattern, better enhance the precision of the analyses.

scholarly journals RIR - Measurement and Use in Quantitative XRD

1988 ◽  
Vol 3 (2) ◽  
pp. 74-77 ◽  
Author(s):  
Camden R. Hubbard ◽  
Robert L. Snyder
Keyword(s):  
Quantitative Analysis ◽  
Powder Diffraction ◽  
Internal Standard ◽  
Quantitative Phase Analysis ◽  
Internal Standard Method ◽  
Reference Standard ◽  
Powder Diffraction File ◽  
X Ray ◽  
Independent Constant ◽  
General Instrument

AbstractThe Reference Intensity Ratio (RIR) is a general, instrument-independent constant for use in quantitative phase analysis by the X-ray powder diffraction internal standard method. When the reference standard is corundum, RIR is known as I/Ic; These constants are collected in the Powder Diffraction File (1987), can be calculated, and can be measured. Recommended methods for accurate measurement of RIR constants are presented, and methods of using these constants for quantitative analysis are discussed. The numerous, complex constants in Copeland and Bragg's method introduced to account for superimposed lines can be simply expressed in terms of RIR constants and relative intensities. This formalism also permits introduction of constraints and supplemental equations based on elemental analysis.

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