Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T02:09:27.566Z Has data issue: false hasContentIssue false

Variable Step-Counting Times for Rietveld Analysis, or, Getting the Most Out of Your Experiment Time

Published online by Cambridge University Press:  06 March 2019

I.C. Madsen
Affiliation:
C.S.I.R.O. Division of Mineral Products P.O. Box 124 Port Melbourne Victoria 3207 Australia
R.J. Hill
Affiliation:
C.S.I.R.O. Division of Mineral Products P.O. Box 124 Port Melbourne Victoria 3207 Australia
Get access

Abstract

The magnitudes of the peak intensities in a powder diffraction pattern are not uniformly distributed as a function of diffraction angle. The Lorentz-polarization factor, X-ray form-factor and the thermal vibration parameters all conspire to progressively decrease the intensities of the peaks as sinθ/λ increases. In spite of this, diffraction data for Rietveld analysis is universally collected using the same counting time for each step in the pattern. As a result, peaks at high angles are collected with lower counting precision than those at low angles, despite the fact that the high-angle region has a higher density of peaks and therefore contains more information than the low-angle part of the pattern. Indeed, the intensity, position and profile of reflections at medium and high sinθ/λ are often more easily modelled since they are subject to less interference from systematic effects such as extinction, specimen transparency and α12 overlap errors. In the present work a novel variable step-counting-time regime has been devised that increases the counting times with diffraction angle in a manner inversely proportional to the intensity fall-off calculated from the Lorentz-polarization, form-factor and thermal parameters. The effect of this new data collection regime on the results of Rietveld refinement of a number of materials of varying structural complexity is discussed.

Type
I. Whole Pattern Fitting, Rietveld Analysis and Calculated Diffraction Patterns
Copyright
Copyright © International Centre for Diffraction Data 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

“International Tables for X-ray Crystallography”, 1974, Vol. IV., The Kynoch Press, Birmingham, England.Google Scholar
Angel, R.J. and Prewitt, C.T., 1986, “Crystal structure of mullite; A re-examination of the average structure”, American Mineralogist, 71, 14761482.Google Scholar
Cnllity, B.D., 1978, “Elements of X-ray Diffraction”, 2nd ed., Addison-Wesley, Reading, Massachusetts.Google Scholar
Hill, R.J. and Howard, C.J., 1986, “A Computer Program for Rietveld Analysis of Fixed Wavelength X-ray and Neutron Diffraction Patterns”, Australian Atomic Energy Commission (now ANSTO) Report AAEC/M112.Google Scholar
Hill, R.J. and Madsen, I.C., 1987, “Data Collection Strategies for Constant Wavelength Rietveld Analysis”, Powder Diffraction, 2:146.Google Scholar
Madsen, I.C. and Hdl, R.J., 1990, “QPDA - A User-Friendly, Interactive Program for Quantitative Phase and Crystal Size/Strain Analysis of Powder Diffraction Data”, Powder Diffraction, 5: 195.Google Scholar
Young, R.A., Prince, E., and Sparks, R.A., 1982, “Suggested Guide-lines for the Publication of Rietveld Analysis and Pattern Decomposition Studies”, J. Appl. Crystatlogr., 15: 357.Google Scholar
Wiles, D.B. and Young, R.A., 1981, “A New Computer Program for Rietveld Analysis of X-ray Powder Diffraction Patterns”, J. Appl. Crystallogr., 14: 149.Google Scholar