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Mathematical techniques for quantitative elemental analysis by energy dispersive X-ray fluorescence

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Abstract

Recent interest in the use of automated or semi-automated energy dispersive X-ray fluorescence analysis has created the need for improved mathematical techniques and computer software for use with this type of analysis. The present paper reviews the efforts to date to develop the mathematical techniques necessary for implementing: (1) the library least-squares method for the determination of characteristic elemental X-ray intensities and (2) the use of the Monte Carlo method for extending the fundamental parameters approach to radioisotope and X-ray machine exciting sources for the determination of elemental amounts.

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References

  1. L. SALMON, Nucl. Instr. Methods, 14 (1961) 193.

    Article  Google Scholar 

  2. G. D. O'KELLEY (Ed.), Proc. Symp. on the Application of Computers to Nuclear and Radiochemistry, Catlinburg, Tennessee, October, 1962, US AEC Monograph NAS-NS3107, March, 1963.

  3. E. SCHONFELD, A. H. KIBBEY, W. DAVIS, Jr., Nucl. Instr. Methods, 45 (1966) 1.

    Article  CAS  Google Scholar 

  4. J. I. TROMBKA, R. L. SCHMADEBECK, “A numerical least-square method for resolving complex pulse-height spectra”, NASA SP-3044, 1968.

  5. P. QUITTNER, Gamma-Ray Spectroscopy with Particular Reference to Detector and Computer Evaluation Techniques, Adam Hilger, Ltd., London, 1972.

    Google Scholar 

  6. F. ARINC, R. P. GARDNER, L. WIELOPOLSKI, A. R. STILES, Adv. X-Ray Anal., 19 (1976) 367.

    Google Scholar 

  7. F. ARINC, L. WIELOPOLSKI, R. P. GARDNER, “The linear least-squares analysis of X-ray fluorescence spectra of aerosol samples using pure element library standards and photon excitation”, in X-Ray Fluorescence Analysis of Environmental Samples, T. G. DZUBAY (Ed.), Ann Arbor Science Publishers, Inc., Ann. Arbor, 1977, p. 227.

    Google Scholar 

  8. R. P. GARDNER, K. VERGHESE, Analysis and Design of Radioisotope Gauges, to be published by Plenum Publishing Corporation.

  9. D. R. DUNN, R. C. KAIFER, Z. H. MCQUAID, IEEE Trans. Nucl. Sci., 19 (1972) 461.

    CAS  Google Scholar 

  10. J. M. JAKLEVIC, F. S. GOULDING, D. A. LANDIS, IEEE Trans. Nucl. Sci., 19 (1972) 392.

    Google Scholar 

  11. L. WIELOPOLSKI, R. P. GARDNER, Trans. Amer. Nucl. Soc. Suppl. No. 3, (1975) 39.

    Google Scholar 

  12. L. WIELOPOLSKI, R. P. GARDNER, Nucl. Instr. Methods, 133 (1976) 303.

    Article  CAS  Google Scholar 

  13. R. P. GARDNER, L. WIELOPOLSKI, Nucl. Instr. Methods, 140 (1977) 289.

    Article  CAS  Google Scholar 

  14. L. WIELOPOLSKI, R. P. GARDNER, Nucl. Instr. Methods, 140 (1977) 297.

    Article  CAS  Google Scholar 

  15. B. SOUCEK, “Pulse-height analysis accuracy at high rates”, Proc. Intern. Symp. on Nuclear Engineering, Paris, France, 1963, p.437.

  16. B. SOUCEK, J. Electronics Control, 16 (1964) 81.

    Google Scholar 

  17. B. SOUCEK, J. Electronics Control, 16 (1964) 91.

    Google Scholar 

  18. B. SOUCEK, Nucl. Instr. Methods, 28 (1964) 306.

    Article  Google Scholar 

  19. T. J. KENNETT, W. V. PRESTWICH, G. L. KEECH, Nucl. Instr. Methods, 29 (1964) 325.

    Article  CAS  Google Scholar 

  20. A. JASINSKI, J. LUDZIEJEWSKI, J. BIALKOWSKI, Nucl. Instr. Methods, 31 (1964) 90.

    Article  CAS  Google Scholar 

  21. R. GOLD, Rev. Sci. Instr., 36 (1965) 784.

    Article  Google Scholar 

  22. I. DELOTTO, D. DOTTI, D. MARIOTTI, Nucl. Instr. Methods, 40 (1966) 169.

    Article  CAS  Google Scholar 

  23. I. DELOTTO, D. DOTTI, Nucl. Instr. Methods, 39 (1966) 281.

    Article  Google Scholar 

  24. J. H. WILLIAMSON, Rev. Sci. Instr., 37 (1966) 736.

    Article  Google Scholar 

  25. B. SOUCEK, Rev. Sci. Instr., 36 (1965) 1582.

    Article  Google Scholar 

  26. K. KANDIAH, Problems connected with high rates in pulse counting systems, Radiation Measurements in Nuclear Power, paper 7.4, p. 420, 1966.

  27. M. BERTOLACCINI, C. BUSSOLATI, S. COVA, I. DELOTTO, E. GATTI, Nucl. Instr. Methods, 62 (1968) 221.

    Article  Google Scholar 

  28. A. PAZMAN, Instr. Exp. Techn. 3 (1969) 658.

    Google Scholar 

  29. B. SOUCEK, M. CIMERMAN, B. BREYER, IEEE Trans. Nucl. Sci., 17 (1970) 375.

    Article  Google Scholar 

  30. E. J. COHEN, Nucl. Instr. Methods, 121 (1974) 25.

    Article  Google Scholar 

  31. S. N. FEDOTOV, N. G. VOLKOV, Nucl. Instr. Methods, 122 (1974) 463.

    Article  CAS  Google Scholar 

  32. B. A. ROSCOE, A. K. FURR, Nucl. Instr. Methods, 140 (1977) 401.

    Article  CAS  Google Scholar 

  33. P. W. NICHOLSON, Nuclear Electronics, John Wiley & Sons, New York, 1974.

    Google Scholar 

  34. H. H. CHIANG, Basic Nuclear Electronics, Wiley Interscience, New York 1969.

    Google Scholar 

  35. J. H. HAMILTON, J. C. MANTHURUTHIL, Proc. Intern. Conf. on Radioactivity in Nuclear Spectroscopy, Gordon and Breach, New York, 1972.

    Google Scholar 

  36. F. H. SCHAMBER, “A modification of the linear least-squares fitting method which provides continuum suppression”, in X-Ray Fluorescence Analysis of Environmental Samples, T. G. DZUBAY (Ed.), Ann Arbor Science Publishers, Inc., Ann Arbor, 1977, p. 241.

    Google Scholar 

  37. R. A. SEMMLER, “Determination of the background in proton-excited X-ray spectra in the absence of blanks”, in X-Ray Fluorescence Analysis of Environmental Samples, T. G. DZUBAY (Ed.), Ann Arbor Science Publishers, Inc., Ann Arbor, 1977, p. 269.

    Google Scholar 

  38. P. J. STRATHAM, X-Ray Spectrom., 5 (1976) 16.

    Article  Google Scholar 

  39. H. C. KAUFMAN, K. R. AKSELSSON, Adv. X-Ray Anal. 18 (1975) 353.

    Google Scholar 

  40. H. C. KAUFMAN, K. R. AKSELSSON, W. J. COURTNEY, Adv. X-Ray Anal., 19 (1976) 355.

    Google Scholar 

  41. R. D. WILLIS, A. B. BASKIN, R. L. WALTER, “TRACE—a least-squares fitting program for PIXE spectra”, in X-Ray Fluorescence Analysis of Environmental Samples, T. G. DZUBAY (Ed.), Ann Arbor Science Publishers, Inc., Ann Arbor, 1977.

    Google Scholar 

  42. R. J. GEHRKE, R. C. DAVIES, Anal. Chem., 47 (1975) 1537.

    Article  CAS  Google Scholar 

  43. C. E. FIORI, R. L. MYKLEBUST, K. F. J. HEINRICH, H. YAKOWITZ, Anal. Chem., 48 (1976) 172.

    Article  CAS  Google Scholar 

  44. S. J. B. REED, N. G. WARE, X-Ray Spectrom., 2 (1973) 69.

    Article  CAS  Google Scholar 

  45. D. G. W. SMITH, C. M. GOLD, D. A. TOMLINSON, X-Ray Spectrom., 4 (1975) 149.

    Article  CAS  Google Scholar 

  46. R. P. GARDNER, F. ARINC, A. R. HAWTHORNE, L. WIELOPOLSKI, G. R. BEAM, K. VERGHESE, “Mathematical techniques for X-ray analyzers”, Technical Progress Report for U.S.E.P.A. Grant No. R-802759 for the period from May 15, 1975 to May 14, 1976.

  47. F. ARINC, R. P. GARDNER, Trans. Amer. Nucl. Soc. Suppl., No. 3, 21 (1975) 37.

    Google Scholar 

  48. F. ARINC, “Mathematical methods for energy dispersive X-ray fluorescence analysis”, unpublished Ph. D. thesis, North Carolina State University, Raleigh, 1976.

    Google Scholar 

  49. B. W. BUDESINSKY, X-Ray Spectrom., 4 (1975) 166.

    Article  CAS  Google Scholar 

  50. K. GLOCKER, H. SCHREIBER, Ann. Phys., 85 (1928) 1087.

    Google Scholar 

  51. E. GILLAM, H. T. HEAL, British J. Appl. Phys., 3 (1952) 353.

    Article  CAS  Google Scholar 

  52. J. SHERMAN, Spectrochim. Acta, 7 (1955) 283.

    Article  CAS  Google Scholar 

  53. J. SHERMAN, Spectrochim. Acta, 15 (1959) 466.

    Article  Google Scholar 

  54. T. SHIRAIWA, N. FUJINO, Japanese J. Appl. Phys., 5 (1966) 886.

    Article  CAS  Google Scholar 

  55. T. SHIRAIWA, N. FUJINO, Bull. Chem. Soc. Japan, 40 (1967) 2289.

    Article  CAS  Google Scholar 

  56. T. SHIRAIWA, N. FUJINO, Adv. X-Ray Anal. 12 (1968) 446.

    Google Scholar 

  57. T. SHIRAIWA, N. FUJINO, X-Ray Spectrom., 3 (1974) 64.

    Article  CAS  Google Scholar 

  58. R. P. GARDNER, A. R. HAWTHORNE, X-Ray Spectrom., 4 (1975) 138.

    Article  CAS  Google Scholar 

  59. A. R. HAWTHORNE, R. P. GARDNER, Anal. Chem., 47 (1975) 2220.

    Article  CAS  Google Scholar 

  60. A. R. HAWTHORNE, R. P. GARDNER, Trans. Amer. Nucl. Soc. Suppl. No. 3, 21 (1975) 38.

    Google Scholar 

  61. A. R. HAWTHORNE, R. P. GARDNER, Anal. Chem., 48 (1976) 2130.

    Article  CAS  Google Scholar 

  62. S. D. RASBERRY, K. F. J. HEINRICH, Anal. Chem., 46 (1974) 81.

    Article  CAS  Google Scholar 

  63. R. P. GARDNER, L. WIELOPOLSKI, “Adaptation of the fundamental parameters Monte Carlo simulation method to EDXRF analysis with secondary fluorescer X-ray machines”, submitted for publication in Adv. X-Ray Anal., 21 (1977).

  64. F. CLAISSE, C. SAMSON, Adv. X-Ray Anal., 5 (1962) 335.

    CAS  Google Scholar 

  65. F. BERNSTEIN, Adv. X-Ray Anal. 6 (1962) 436.

    Google Scholar 

  66. P. BLANQUET, “Theory of X-ray fluorescence analysis of powdered samples and slurries”, MINERALS AND METALS, Le Bureau de Recherches Géologiques et Minières, Paris, 1964.

  67. A. LUBECKI, B. HOLYNSKA, M. WASILEWSKA, Spectrochim. Acta, 23B, (1968) 465.

    Google Scholar 

  68. P. F. BERRY, T. FURUTA, J. R. RHODES, Adv. X-Ray Anal., 12 (1969) 612.

    CAS  Google Scholar 

  69. R. P. GARDNER, D. BETEL, K. VERGHESE, Intern. J. Appl. Radiation Isotopes, 24 (1973) 135.

    Article  CAS  Google Scholar 

  70. W. L. DUNN, C. R. EFIRD, R. P. GARDNER, K. VERGHESE, X-Ray Spectrom., 4 (1975) 18.

    Article  CAS  Google Scholar 

  71. C. B. HUNTER, J. R. RHODES, X-Ray Spectrom., 1 (1972) 107.

    Article  CAS  Google Scholar 

  72. J. R. RHODES, C. B. HUNTER, X-Ray Spectrom., 1 (1972) 113.

    Article  CAS  Google Scholar 

  73. J. W. CRISS, Anal. Chem., 48 (1976) 179.

    Article  CAS  Google Scholar 

  74. A. R. HAWTHORNE, R. P. GARDNER, “A proposed model for particle-size effects in the X-ray fluorescence analysis of heterogeneous powders which includes incidence angle and non-random packing effects”, to be submitted to X-Ray Spectrom.

  75. A. R. HAWTHORNE, R. P. GARDNER, “Monte Carlo Applications to the X-ray fluorescence analysis of aerosol samples”, in X-Ray Fluorescence Analysis of Environmental Samples, T. G. DZUBAY (Ed.), Ann Arbor Science Publishers, Inc., Ann Arbor, 1977, p. 209.

    Google Scholar 

  76. A. R. HAWTHORNE, R. P. GARDNER, T. G. DZUBAY, Adv. X-Ray Anal., 19 (1975) 323.

    Google Scholar 

  77. G. R. BEAM, “Gamma-ray transport and X-ray fluorescence calculations by invariant imbedding”, unpublished M. S. thesis, North Carolina State University, Raleigh, 1977.

    Google Scholar 

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Gardner, R.P., Wielopolski, L. & Verghese, K. Mathematical techniques for quantitative elemental analysis by energy dispersive X-ray fluorescence. J. Radioanal. Chem. 43, 611–643 (1978). https://doi.org/10.1007/BF02519515

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