Coupling equations used to calculate the chemical composition of substances by X-ray fluorescence analysis can be classified as empirical, theoretical or semi-empirical based on the method for determining the coefficients of the calibration function. The advantages and disadvantages of each class of equations are discussed. Recommendations for the selecting the optimum conditions for determining empirical correction coefficients and their control during analysis are provided.
Yu. G. Lavrentiev and A. I. Kuznetsova, “Coupling Equations in X-Ray Fluorescence Analysis,” Zavodskaya Laboratoriya, Vol. 45, No. 4, 1979, pp. 315-326.
E. I. Molchanova, A. N. Smagunova and O. F. Rozova, “Comparision of Different Types of Coupling Equations in X-Ray Analysis for Materials with Non-Permanent Composition,” Journal of Analytical Chemistry, Vol. 41, No. 7, 1986, pp. 1183-1191.
G. V. Pavlinsky and N. F. Losev, “Assessment of the Fluorescence Selective Excitation in Case of Mixed Primary Radiation,” Journal of Technical Physics, Vol. 39, No. 9, 1969, pp. 1664-1675.
A. A. Finkelshtein, “The Development of XRF Models for Homogeneous and Heterogeneous Samples,” PhD Dissertation, Irkutsk, 2006, p. 40.
G. V. Pavlinsky and A. Ju. Dukhanin, “Calculation of Photo-and Auger Electron Contribution to X-Ray Fluorescence Excitation of Elements with Low Atomic Number,” X-Ray Spectrometry, Vol. 23, 1994, pp. 221-228. doi:10.1002/xrs.1300230507
G. V. Pavlinsky, “Fundamentals of X-Ray Physics,” CISP Ltd., Cambridge, 2008, 245 p.
N. F. Losev and A. N. Smagunova, “The Basics of XRF Analysis,” Khimiya, Moscow, 1982, 208 p.
H. J. Lucas-Tooth and B. J. Price, “A Mathematical Method for the Investigation of Interelement Effects in X-Ray Fluorescence Analysis,” Metallurgia, Vol. 64, No. 2, 1961, pp. 149-152.
G. R. Lachance and R. J. Traill, “Practical Solution to the Matrix Problem in X-Ray Analysis,” Canadian Spectroscopy, Vol. 11, No. 2, 1966, pр. 43-48.
A. N. Smagunova, N. F. Losev, A. G. Revenko and A. N. Mejevich, “General Chart of Development the X-Ray Spectral Analysis Methods,” Zavodskaya Laboratoriya, Vol. 40, No. 12, 1974, pp. 1461-1463.
L. M. Pan’kova, S. D. Pan’kov and A. N. Smagunova, “Assessment of the Components Interference Efficiency Using the Calibration Measurements Method during the X-Ray Fluorescence Analysis,” Zavodskaya Laboratoriya, Vol. 44, No. 8, 1978, pp. 950-953.
A. N. Smagunova, O. F. Rozova, S. D. Pan’kov and E. I. Molchanova, “Selection of the Optimum Conditions for Setting the Calibration Function during the X-Ray Fluorescence Analysis,” In: Apparatus and Methods of X-Ray Analysis, Mashinostroenie, Leningrad, Vol. 28, 1981, pp. 15-23.
E. I. Molchanova, A. N. Smagunova and O. F. Rozova, “Selection of the Optimum Conditions for Setting the Calibration Function during the X-Ray Fluorescence Analysis,” Zavodskaya Laboratoriya, Vol. 50, No. 11, 1984, pp. 25-29.
R. Plesch, “Empirical Matrix Corrections in Practical X-Ray Spectroscopy,” X-Ray Spectrometry, Vol. 5, No. 3, 1976, pp. 142-148. doi:10.1002/xrs.1300050308
A. N. Smagunova, S. D. Pan’kov, N. F. Losev and P. I. Plotnikov, “Performing Control Over the Adjusting Factors during the X-Ray Spectrum Analysis Using the Calibration Method,” Journal of Analytical Chemistry, Vol. 32, No. 1, 1977, pp. 15-20.
J. Criss and L. Birks, “Calculation Method for Fluorescent X-Ray Spectrometry. Fundamental Parameters,” Analytical Chemistry, Vol. 40, No. 7, 1968, рp. 1080-1086. doi:10.1021/ac60263a023
J. W. Criss, “Fudamental Parameters Calculations on a Laboratory Microcomputer,” Advances in X-Ray Analysis, Vol. 23, 1980, рp. 93-97. doi:10.1007/978-1-4613-3096-7_13
F. P. Paramonov, “Identification of the Elements Concentration Using the Method of Theoretical Standard Selection,” Commun. Acad. Sci. Kazakhstan Chem., No. 3, 1966, pp. 97-98.
V. P. Afonin and T. N. Gunicheva, “X-Ray Fluorescence Analysis of Ores and Minerals,” Nauka, Novosibirsk, 1977, 256 p.
V. P. Afonin, “X-Ray Fluorescence Analysis of Minerals,” Journal of Analytical Chemistry, Vol. 41, No. 9, 1986, pp. 1541-1556.
G. V. Pavlinsky and L. I. Vladimirova, “Approximate Model for Calculation of X-Ray Fluorescence Intensity and Its Use in XRF Spectrometry,” X-Ray Spectrometry, Vol. 28, No. 4, 1999, pp. 183-193. doi:10.1002/(SICI)1097-4539(199905/06)28:3 3.0.CO;2-9
V. Ya. Borkhodoev, “X-Ray Fluorescence Analysis of Ores by the Fundamental Parameter Method,” SVK NII DVO RAN, Magadan, 1999, 280 p.
T. Shiraiwa and N. Fujino, “Theoretical Correction for Coexistent Elements in Fluorescent X-Ray Analysis of Alloy,” Advances in X-Ray Analysis, Vol. 11, 1968, pp. 63-64. doi:10.1007/978-1-4684-8676-6_5
Yu. I. Velichko, B. D. Kalinin, A. N. Mezhevich, R. I. Plotnikov and A. G. Revenko, “Dependence Analysis of Theoretical Corrections and Chemical Composition of Sample during the Steel X-Ray Spectral Analysis,” Zavodskaya Laboratoriya, Vol. 43, No. 4, 1977, pp. 437-442.
T. Gunicheva, A. Finkelshtein and V. Afonin, “A Matrix Effect Correction Algorithm for X-Ray Fluorescence Analysis of Steels,” X-Ray Spectrometry, Vol. 19, No. 6, 1990, pр. 237-242. doi:10.1002/xrs.1300190507
R. Tertian, “The Claisse-Quintin and Lachance-Claisse Alpha Correction Algorithms and Their Modifications. A Critical Examination,” X-Ray Spectrometry, Vol. 15, No. 4, 1986, рp. 251-258.
G. Anderman, “Semitheoretical Approach to Interelement Correction Factors in Secondary X-Ray Emission Analysis,” Analytical Chemistry, Vol. 38, No. 1, 1966, pр. 82-86. doi:10.1021/ac60233a022
G. V. Pavlinsky, N. F. Losev, T. N. Gunicheva and A. G. Revenko, “Method of X-Ray Fluorescence Analysis Using the Successive Corrections on the Base of Standards-Binars,” In: Apparatus and Methods of X-Ray Analysis, Mashinostroenie, Leningrad, Vol. 4, 1969, pp. 184-190.
A. G. Revenko, G. V. Pavlinsky and N. F. Losev, “New Variant of Calibration Method in X-Ray Fluorescence Analysis,” Zavodskaya Laboratoriya, Vol. 36, No. 4, 1970, pp. 675-680.
W. K. De Jongh, “X-Ray Fluorescence Analysis Applying Theoretical Matrix Correction Stainless Steel,” X-Ray Spectrometry, Vol. 2, No. 4, 1973, pp. 151-158. doi:10.1002/xrs.1300020404
P. A. Pella, G. Y. Tao and G. R. Lachance, “Intercomparison of Fundamental Parameter Interelemen Correction Methods,” X-Ray Spectrometry, Vol. 15, No. 4, 1986, pp. 251-258. doi:10.1002/xrs.1300150407
N. Broll, “Quantitative X-Ray Fluorescence Analysis. Theory and Practice of the Fundamental Coefficient Method,” X-Ray Spectrometry, Vol. 15, No. 4, 1986, pр. 271-285. doi:10.1002/xrs.1300150410
R. M. Rousseau, “A Comprehensive Alpha Coefficient Algorithm (a Second Version),” X-Ray Spectrometry, Vol. 15, No. 3, 1987, pp. 103-108. doi:10.1002/xrs.1300160303
R. M. Rousseau, “Corrections for Matrix Effects in X-Ray Fluorescence Analysis—A Tutorial,” Spectrochimica Acta, Part B, Vol. 61, 2006, pp. 759-777. doi:10.1016/j.sab.2006.06.014
E. I. Molchanova, A. N. Smagunova, T. N. Gunicheva, A. V. Smagunov, N. A. Azmuko and A. L. Pospelov, “Dependence of Correct Results of X-Ray Fluorescence Steel Analysis and Selected Method of Registering the Influence of Chemical Samples Composition on the Value of α-Ratios in Theoretical Bind-Equation,” Journal of Analytical Chemistry, Vol. 50, No. 6, 1995, pp. 595-599.