Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T17:37:56.412Z Has data issue: false hasContentIssue false
  • English
  • Français

The Use of Reference Intensity Ratios in X-Ray Quantitative Analysis

Published online by Cambridge University Press:  10 January 2013

Robert L. Snyder
Robert L. Snyder
Affiliation:
Institute for Ceramic Superconductivity, New York College of Ceramics at Alfred University, Alfred, New York 14802, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Each of the RIR based methods for carrying out quantitative X-ray powder diffraction analysis are described and a consistent set of notation is developed. The so called “standardless” analysis procedures are shown to be a special case of the internal-standard method of analysis where the normalizing assumption is used. All analytical methods, other than the Rietveld whole pattern matching procedure, require the use of explicitly measured standards, typically in the form of RIR values. However, if only semi-quantitative results can be tolerated, the standards may be obtained by using published RIR and relative intensity values. The exciting new techniques of whole pattern fitting and Rietveld constrained quantitative analysis are also described in RIR notation and shown also to be forms of the internal-standard method with the normalization assumption. The quantitative results obtained from Rietveld quantitative analysis are derived from computed standards in the form of computed, normalized, RIRN values. The normalization assumption in Rietveld analysis allows the exclusive use of computed standards and comes as close to a “standardless” analysis as one can achieve: relying on the absence of amorphous material and on the validity of the structural models. Relationships are given for obtaining quantitative analysis from these RIRN values obtainable from the least-squares scale factors.

Type
Research Article
Information
Powder Diffraction , Volume 7 , Issue 4 , December 1992 , pp. 186 - 193
Copyright
Copyright © Cambridge University Press 1992

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

Alexander, L. E., Klug, H. P. & Kummer, E. (1948). J. Appl. Phys. 19, 742.Google Scholar
Bezjak, A. (1961). X-ray-Quantitative Analysis of Multiphase Systems. Croatica Chemica Acta 33, 197–199.Google Scholar
Bish, D. L. & Howard, S. A. (1988). Quantitative phase analysis using the Rietveld method. J. Appl. Crystallogr. 21, 86–91.CrossRefGoogle Scholar
Chung, F. H. (1974a). Quantitative Interpretation of X-ray Diffraction Patterns. I. Matrix-flushing method of quantitative multicomponent analysis. J. Appl. Crystallogr. 7, 519–525.CrossRefGoogle Scholar
Chung, F. H. (1974b). Quantitative Interpretation of X-ray Diffraction Patterns. II. Adiabatic principle of X-ray diffraction analysis of mixtures. J. Appl. Ctystallogr. 7, 526–31.CrossRefGoogle Scholar
Chung, F. H. (1975). Quantitative Interpretation of X-ray Diffraction Patterns. III. Simultaneous Determination of a Set of Reference Intensities. J. Appl. Crystallogr. 8, 17–19.CrossRefGoogle Scholar
Cline, J. P. & Snyder, R. L. (1983). The Dramatic Effect of Crystallite Size on X-ray Intensities. Adv. in X-ray Anal. 26, 111–118.Google Scholar
Cline, J. P. & Snyder, R. L. (1985). Powder Characteristics Affecting Quantitative Analysis. In Advances in Material Characterization II, p131–144, Snyder, R. L., Condrate, R. A. & Johnson, P. F., editors, Plenum Press, New York.Google Scholar
Cline, J. P. & Snyder, R. L. (1987). The Effects of Extinction on X-ray Powder Diffraction Intensities. Adv. in X-ray Anal. 30, 447–456.Google Scholar
Copeland, L. E. & Bragg, R. H. (1958). Quantitative X-ray Diffraction Analysis. Anal. Chem. 30, 196–206.CrossRefGoogle Scholar
Gehringer, R. C., McCarthy, G. J., Garvey, R. G., & Smith, D. K. (1983). X-ray diffraction intensity of oxide solid solutions: Application to qualitative and quantitative phase analysis. Adv. X-ray Anal. 26, 119–128.Google Scholar
Hill, R. J. and Howard, C. J. (1987). Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Crystallogr. 20, 467–474.CrossRefGoogle Scholar
Howard, S. A. & Snyder, R. L. (1989). The Use of Direct Convolution Products in Profile and Pattern Fitting Algorithms I. Development of the Algorithms, J. Appl. Crystallogr. 22, 238–243.CrossRefGoogle Scholar
Hubbard, C. R., Evans, E. H. & Smith, D. K. (1976). The Reference Intensity Ratio, I/IC. for Computer Simulated Patterns, J. Appl. Crystallogr. 9, 169–174.CrossRefGoogle Scholar
Hubbard, C. R. and Snyder, R. L., (1983). Reference Intensity Ratio-Measurement and Use in Quantitative XRD, Pow. Diff. 3, 74.CrossRefGoogle Scholar
Hubbard, C. R., Robbins, C. R. & Snyder, R. L. (1983). XRD Quantitative Analysis using the NBS*QUANT82 System. Adv. X-ray Anal. 26, 149–157.Google Scholar
Hubbard, C. R. & Snyder, R. L. (1988). Reference Intensity Ratio-Measurement and Use in Quantitative XRD. Pow. Diff. 3, 74–78.CrossRefGoogle Scholar
Karlak, F. & Burnett, D. S. (1966). Quantitative Phase Analysis by X-ray Diffraction. Anal. Chem. 38, [12] 1741–1745.Google Scholar
Klug, H. P. & Alexander, L. E. (1974). X-ray Diffraction Procedures. John Wiley and Sons, New York, 2nd ed.Google Scholar
O'Connor, B. H. and Raven, M. D. (1988). Application of the Rietveld refinement procedure in assaying powdered mixtures. Pow. Diff. 3, 2–6.CrossRefGoogle Scholar
Rietveld, H. M. (1969). A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 2, 65–71.Google Scholar
Smith, D. K., Nichols, M. C. & Zolensky, M. E., (1982). POWD10. A FORTRAN IV program for calculating X-ray powder diffraction patterns - version 10. The Pennsylvania State University, University Park, Pa.Google Scholar
Smith, D. K., Johnson, G. G. Jr., & Ruud, C. O., (1986). Clay mineral analysis by automated powder diffraction analysis using the whole diffraction pattern. Adv. X-ray Anal. 29, 217–224.Google Scholar
Smith, D. K., Johnson, G. G. Jr, Scheible, A., Wims, A. M., Johnson, J. L. & Ullmann, G. (1987). Quantitative X-ray powder diffraction method using the full diffraction pattern. Pow. Diff. 2, 73–77.Google Scholar
Smith, D. K., Johnson, G. G. Jr, and Wims, A. M. (1988). Use of full diffraction pattern spectra, both experimental and calculated, in quantitative powder diffraction analysis. Aust. J. Phys. 41, 311–321.Google Scholar
Smith, D. K., Johnson, G. G. Jr, Kelton, M. J. & Anderson, C. A. (1989). Chemical constraints in quantitative X-ray powder diffraction for mineral analysis of the sand silt fractions of sedimentary rocks. Adv. X-ray Anal.Google Scholar
Smith, D. K., (1992). Advances in Qualitative and Quantitative XRD Analysis by Whole-Pattern Methods. Adv. X-ray Anal. 35, in press.Google Scholar
Smith, S. T., Snyder, R. L. & Brownell, W. E., (1979a). Minimization of Preferred Orientation in Powders by Spray Drying. Adv. X-ray Anal. 22, 77–88.Google Scholar
Smith, S. T., Snyder, R. L. & Brownell, W. E. (1979b). Quantitative Phase Analysis of Devonian Shales by Computer Controlled X-ray diffraction of spray dried samples. Adv. X-ray Anal. 22, 181–191.Google Scholar
Snyder, R. L. & Bish, D. L. (1989). Quantitative Analysis, in Modern Powder Diffraction, Bish, D. L. and Post, J. E. ed. p101–144.Google Scholar
Snyder, R. L. and Carr, W. L. (1974). A Method of Determining the Preferred Orientation of Crystallites Normal to a Surface. Surfaces and Interfaces of Glass and Ceramics, ed., Frechette, V. D. p.85–99.CrossRefGoogle Scholar
Snyder, R. L., Hubbard, C. R. & Panagiotopoulos, N. C. (1981). AUTO: A Real Time Diffractometer Control System. NBSIR 81-2229.Google Scholar
Snyder, R. L., Hubbard, C. R. & Panagiotopoulos, N. C. (1982). A Second Generation Automated Powder Diff. Control System. Adv. X-ray Anal 25, 245–160.Google Scholar
Snyder, R. L. & Hubbard, C. R. (1984). NBS*QUANT84: A System for Quantitative Analysis by Automated X-ray Powder Diffraction. NBS Internal Publication.Google Scholar
Visser, J. W. & deWolff, P. M. (1964). Absolute Intensities. Report 641.109, Technisch Physische Dienst, Delft, Netherlands.Google Scholar
Wiles, D. B. & Young, R. A. (1981). A new computer program for Rietveld analysis of X-ray powder diffraction patterns. J. Appl. Crystallogr. 14, 149–151.Google Scholar