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Identification of X-Ray Diffraction Patterns of Multicomponent Mixtures

  • Jaroslav Fiala

Abstract

A single phase diffraction pattern can usually be readily identified by searching a data base of reference powder patterns, provided of course that the substance in question is present in the data base used. The real problems of phase analysis occur when the measured pattern results from a mixture of substances. Usually, no more than five constituents in a mixture may reliably be resolved 1,2 in case that there is no additional information available by means of which the number of substances that have to be taken into consideration can sufficiently be reduced. Physical reasons of this limitation are quantitatively examined and the ways how to overcome it are elucidated in the present paper.

Keywords

Quantitative Phase Analysis Froth Flotation Maximum Likelihood Factor Analysis Mixture Pattern Unknown Constituent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. Fiala, Spectral data bases for chemical compounds identification, Computer Phys.Comm. 33: 85 (1984).ADSCrossRefGoogle Scholar
  2. 2.
    E. K. Vasiliev and M. S. Nakhmanson, “Kachestvennyi Rentgenofazovyi Analiz (Qualitative X-ray Diffraction Phase Analysis)”, in Russian, Nauka, Novosibirsk (1986).Google Scholar
  3. 3.
    L. Brillouin, “Science and Information Theory”, Academic Press, New York (1956).zbMATHGoogle Scholar
  4. 4.
    M. C. Nichols, D. K. Smith, and Q. Johnson, Differential X-ray diffract tion: a theoretical basis for a technique based on wavelength variation, J.Appl.Cryst. 18: 8 (1985).CrossRefGoogle Scholar
  5. 5.
    D. G. Schulze, Identification of soil iron oxide minerals by differenttial X-ray diffraction, Soil Sci.Soc.Amer.J. 45: 437 (1981).CrossRefGoogle Scholar
  6. 6.
    R. B. Bryant, N. Curi, C. B. Roth, and D. P. Franzmeier, Use of an internal standard with differential X-ray diffraction analysis for iron oxides, Soil Sci.Soc.Amer.J. 47: 168 (1983).CrossRefGoogle Scholar
  7. 7.
    G. Brown and I. G. Wood, Estimation of iron oxides in soil clays by profile refinement combined with differential X-ray diffraction, Clay Miner. 20: 15 (1985).CrossRefGoogle Scholar
  8. 8.
    D. G. Schulze, Correction of mismatches in 2 & scales during differential X-ray diffraction, Clays Clay Miner. 34: 681 (1986).CrossRefGoogle Scholar
  9. 9.
    L. Cartz, F. G. Karioris, and M. S. Wong, Heavy ion bombardment and X’-ray powder patterns of mixtures, Rad.Effects Lett. 85: 273 (1985).CrossRefGoogle Scholar
  10. 10.
    L. Cartz, F. G. Karioris, and M. S. Wong, Analysis of mineral powder mixtures by heavy ion bombardment and X-ray diffraction, Rad.Effects Lett. 97: 235 (1986).CrossRefGoogle Scholar
  11. 11.
    I. G. Wood, L. Nichols, and G. Brown, X-ray anomalous scattering difference patterns in qualitative and quantitative powder diffraction analysis, J.Appl.Cryst. 19: 364 (1986).CrossRefGoogle Scholar
  12. 12.
    T. Hirschfeld, Computer resolution of infrared spectra of unknown mixtures, Anal.Chem. 48: 721 (1976).CrossRefGoogle Scholar
  13. 13.
    J. Fiala, Optimization of powder diffraction identification, J. Appl. Cryst. 9: 429 (1976).CrossRefGoogle Scholar
  14. 14.
    A. Bezjak, I. §mit, and V. Alujevic, Determination of the X-ray diffraction curve of amorphous phase, Croatica Chem.Acta 54: 61 (1981).Google Scholar
  15. 15.
    A. Bezjak, V. Runje, Quantitative phase analysis of the hydrothermally treated system y-Ca2Si04-Ca0, J.Amer.Ceram.Soc. 64: 129 (1981).CrossRefGoogle Scholar
  16. 16.
    F. H. Chung, Quantitative interpretation of X-ray diffraction patterns of mixtures, I. Matrix-flushing method for quantitative multicom-ponent analysis, J.Appl.Cryst. 7: 519 (1974).CrossRefGoogle Scholar
  17. 17.
    F. H. Chung, Quantitative interpretation of X-ray diffraction patterns of mixtures. II. Adiabatic principle of X-ray diffraction analysis of mixtures, J.Appl.Cryst. 7: 526 (1974).CrossRefGoogle Scholar
  18. 18.
    F. H. Chung, Quantitative interpretation of X-ray diffraction patterns of mixtures. III. Simultaneous determination of a set of reference intensities, J.Appl.Cryst. 8: 17 (1975).CrossRefGoogle Scholar
  19. 19.
    L. S. Zevin, A method of quantitative phase analysis without standards, J.Appl.Cryst. 10: 147 (1977).CrossRefGoogle Scholar
  20. 20.
    J. Fiala, Powder diffraction analysis of a three component sample, Anal.Chem. 52: 1300 (1980).CrossRefGoogle Scholar
  21. 21.
    J. Fiala, A new method for powder diffraction phase analysis, Cryst.Res. Technol. 17: 643 (1982).Google Scholar
  22. 22.
    M. Cerfiansky, Matrix formulation of the iterative method of phase analysis, J.Appl.Cryst. 20: 260 (1987).CrossRefGoogle Scholar
  23. 23.
    W. Windig, J. Haverkamp, and P. G. Kistemaker, Interpretation of sets of pyrolysis mass spectra by discriminant analysis and graphical rotation, Anal.Chem. 55: 81 (1983).CrossRefGoogle Scholar
  24. 24.
    W. Windig, E. Jakab, J. M. Richards, and H. L. C. Meuzelaar, Self-modeling curve resolution by factor analysis of a continuous series of pyrolysis mass spectra, Anal.Chem. 59: 317 (1987).CrossRefGoogle Scholar
  25. 25.
    K. G. Joreskog, J. E. Klovan, and R. A. Reyment, “Geological Factor Analysis”, Elsevier, Amsterdam (1976).Google Scholar
  26. 26.
    D.J. Aigner and A. S. Goldberger, “Latent Variables in Socio-Economic Models”, North Holland, Amsterdam (1977).zbMATHGoogle Scholar
  27. 27.
    Y. Ahmavaara, “On the Unified Fact or Theory of Mind”, S. Tiedeakatemia, Helsinki (1957).Google Scholar
  28. 28.
    P. Murray-Rust and R. Bland, Computer retrieval and analysis of molecular geometry. II. Variance and its interpretation, Acta Cryst. B34: 2527 (1978).CrossRefGoogle Scholar
  29. 29.
    H.H. Harman, “Modern Factor Analysis”, The University of Chicago Press, Chicago (1967).zbMATHGoogle Scholar
  30. 30.
    P. F. Lazarsfeld and N. W. Henry, “Latent Structure Analysis”, Houghton Mifflin, New York (1968).zbMATHGoogle Scholar
  31. 31.
    R. J. Rummel, “Applied Factor Analysis”, Northwestern University Press, Evanston (1970).zbMATHGoogle Scholar
  32. 32.
    E. R. Malinowski and D. G. Howery, “Factor Analysis in Chemistry”, John Wiley and Sons, New York (1980).zbMATHGoogle Scholar
  33. 33.
    D. Macnaughtan L. B. Rogers, and G. Wernimont, Principle-component analysis applied to chromatographic data, Anal.Chem. 44: 1421 (1972).CrossRefGoogle Scholar
  34. 34.
    A. Meisterj Estimation of component spectra by the principal components method, Anal.Chim.Acta 161: 149 (1984).CrossRefGoogle Scholar
  35. 35.
    S. Borgen and B. R. Kowalski, An extension of the multivariate component-resolution method to three components, Anal.Chim.Acta 174: 1 (1985).CrossRefGoogle Scholar
  36. 36.
    P. J. Gemperline, Target transformation factor analysis with linear inequality constraints applied to spectroscopic-chromatographic data, Anal.Chem. 58: 2656 (1986).CrossRefGoogle Scholar
  37. 37.
    K. G. Jöreskog, A general approach to confirmatory maximum likelihood factor analysis, Psychometrika 34: 183 (1969).CrossRefGoogle Scholar
  38. 38.
    C. Jochum, P. Jochum, and B. R. Kowalski, Error propagation and optimal performance in multicomponent analysis, Anal.Chem. 53: 85 (1981).CrossRefGoogle Scholar
  39. 39.
    G. E. Braun, A Monte Carlo error simulation applied to calibration-free X-ray diffraction phase analysis, J.Appl.Cryst. 19: 217 (1986).CrossRefGoogle Scholar
  40. 40.
    A. Lorber, Error propagation and figures of merit for quantification by solving matrix equations, Anal.Chem. 58: 1167 (1986).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Jaroslav Fiala
    • 1
  1. 1.Central Research Institute ŠKODAPlzeňCzechoslovakia

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