ACCURACY EVALUATION OF RESULTS OBTAINED BY FUNDAMENTAL PARAMETER METHOD IN X-RAY FLUORESCENCE SPECTROMETRY*

Transcription

1 THE RIGAKU JOURNAL VOL. 7 / NO. 2 / 1990 ACCURACY EVALUATION OF RESULTS OBTAINED BY FUNDAMENTAL PARAMETER METHOD IN X-RAY FLUORESCENCE SPECTROMETRY* KATSUMI OHNO AND MICHIO YAMAZAKI National Research Institure for Metals, , Nakameguro, Meguro-ku, Tokyo 153, Japan Accuracy of the results determined using the fundamental parameter method was evaluated in X-Ray fluorescence spectrometry. In the case of homogeneous bulk specimens, the agreements between the inter-element correction factors obtained experimentally and calculated by the fundamental parameter method were excellent. In the analysis of unhomogeneous alloys such as the precipitation hardening type and duplex type alloys, the use of one or two multielement standards was recommended to obtain accurate results by the fundamental parameter method. The effects of the uncertainty of the mass attenuation coefficients obtained from literature on the error of the results calculated by the fundamental parameter method were negligibly small in the analysis of homogeneous bulk alloys. The composition and the mass thickness of a permalloy thin film on iron substrate were simultaneously determined using pure bulk standards by the fundamental parameter method. The interaction of X-rays between the thin film and the substrate was fully calculated. Keywords: X-ray fluorescence spectrometry, Fundamental-parameter method, Thin film analysis, Pure element standards, Matrix effect, Inter-element effect. 1. Introduction X-ray fluorescence spectrometry has been a very fascinating analytical tool, because it is an essentially simultaneous multielement, precise and nondestructive analytical method. However, this spectrometry is similar in empirical conversion procedure (from line intensities to composition) to other instrumental methods of analysis. The relationship is disturbed by matrix or interelement effect, though the analytical line intensity can be proportional to the concentration of the analyte for same type of samples. A series of standard reference materials, which are similar in composition and form to unknown specimens, is required to obtain the empirical relationships. However, it is very difficult-almost impossible-to prepare and characterize such standards for the analysis of new materials in development steps. The fundamental parameter method (FPmethod) has capabilities for the quantitative analysis of bulk specimens as well as thin film specimens including multi-layer thin films with a few pure element or multielement standards, because the method uses an absolute intensityconcentration algorithm. The disadvantage of the FP-method was the requirement of a computer; * Adv. X-Ray Chem. Anal. Jpn, 18 (1987) however, the recent advance in microelectronics technology allows us to use the FPmethod. The FP-method has been one of the most powerful tools for X-ray fluorescence analysis of homogeneous specimens, but this method is impossible to be applied to unhomogeneous specimens, such as briquetting powder specimens. The use of multielement standards which are similar in composition and unhomogeneity to unknown specimens was effective to reduce caused by the unhomogeneity effect. 2. Experimental Procedure 2.1 Specimens and Instruments Specimens were selected from commercially available alloys and the alloys developed at the National Research Institute for Metals. The measuring surface of specimens were polished with a series of grit to a final lap of 0.05 µmφ alumina and washed in distilled water using an ultrasonic cleaner. A Rigaku's conventional wavelength dispersive X-ray spectrometer (3070) employing Rh-target Xray tube and pulse height selection was used for the measurements of the X-ray fluorescence intensities. A JEOL's electron probe X-ray micro analyzer (JXA-733) was used for the microscopic examination of the measuring surface of the specimens. 16 The Rigaku Journal

2 2.2 Analysis of Bulk Specimens a) Calculation of Empirical Correction Factors The fundamental relationship between X-ray fluorescence intensity and composition which was derived by Sherman [1] and modified by Shiraiwa and Fujino [2] was used for the calculation of X- ray intensity. The theoretically calculated correction factors together with the factors obtained experimentally in the following correction model for nickel-iron-chromium system are shown in Table 1. W R = 1+ α W + β W ( + W )( i j k ) i i ij j ij k 1 Where W i, W j and W k are the mass fraction of i- th, j-th and k-th coexisting elements respectively, R i is the intensity ratio against the analytical line intensity of pure i-th element, α ij is the absorption correction factor of j-th coexisting element for i-th element, and β ik is the enhancement correction factor of k-th coexisting element for i-th element. In the calculation of the FP-method, the spectral distribution of X-ray source measured by Gilfrich [3], the mass attenuation coefficients recommended by Heinrich [4] and the fluorescence yields recommended by Colby [5] were used as the fundamental parameters. The experimental values in the row labeled R/H were obtained from literature [4] and the values in the row labeled Calc. were calculated by the FPmethod, assuming binary alloy systems. The values in the parentheses were the standard error of the factors calculated. In the analysis of homogeneous bulk specimen, the results obtained by the empirical correction and the FP-method were practically accurate, because the agreement of the correction factors obtained by both methods were excellent, as shown in Table 1. b) Analysis of Unhomogenous Specimens In the analysis of unhomogeneous specimens such as the precipitation hardening and duplex type alloys, the heat treatment of the specimens before common specimen preparation was required to obtain homogeneous specimens for X- ray fluorescence spectrometry. The microstructure of a precipitation hardening superalloy (TM-185) is shown in Photo 1 as an example of unhomogeneous alloy specimens. The microstructures of the specimen as cast and that of after thermal exposure (900 C x 1500 hr) are shown as (a) and (b) in Photo 1 respectively. Eutectic γ+γ' phase (solid black), precipitated γ' phase (dark) and carbide (bright) were observed in γ-matrix in Photo 1. The i Table 1 Experimental correction factors and theoretical correction factors calculated by the fundamental parameter method for the Rasberry-Heinrich model. α β Fe Cr Fe Ni FeKα R/H Calc (0.0064) (0.0034) NiKα R/H Calc (0.0074) (0.0067) CrKα R/H (0.0082) (0.0103) RH: Referred Data [2]/ Calc.: Calculated data by the FP method Photo 1 Typical microstructure of superalloy (TM-185) numbers in the parentheses were the volume fractions of the carbides. These phases were directly identified by electron probe X-ray microanalysis and micro-beam X-ray diffractometry. Table 2 shows the average composition obtained from the direct analysis of 30 pieces of the carbides selected at random. The determined composition in the row labeled No. 1 in Table 2, corresponding with the carbides in Photo l(a), show that the carbide was MC type. The composition in the row labeled No.2, corresponding the carbides in Photo 2(b), show that MC and M 6 C type carbides were formed in the matrix. These types of carbides were also identified by the micro-beam X-ray diffractometry. The results of the specimen TM-185 (as cast) which were analyzed with a multi-element standard and pure element standards are shown in Table 3. The composition in the row labeled XRS std was determined using the multi-element standard which was similar in composition (shown in the row labeled Ref), and microstructure to the specimen. The composition in the row labeled Vol. 7. No

3 Table 2 Compositions of carbides precipitated as cast and thermal exposed specimens (TM-185). Sample Hf W Ta Ni Co Cr Ti Al C Wt(%) No. 1 At(%) (MC) Wt(%) At(%) M 6C) No. 2 Wt(%) At(%) (NC) Wet-Chem. Wt(%) No. 1: Carbide composition in the alloy as cast. No. 2: Carbide composition in the alloy treated 900 C x 1500 Hr. Wet-Chem.: Wet chemical analysis of the alloy. Table 3 Comparison of results (in Mass percent) of TM-185 by the fundamental parameter method using pure elements and multi-element standards. Co Ni Cr Ti W Ta Hf Al Total XRS STD Error XRS PUR Error XRS STD* Error Chem Ref ** XRS STD : Result obtained by multi-element standard. XRS PUR : Result obtained by pure element standards. XRS STD* : Result obtained by multi-element standards after thermal exposure (900 C x 1500 Hr.). XRS pur was determined using the pure element standards. The analytical errors of titanium, tantalum, tungsten and aluminum determined by using the pure element standards were larger than those determined by using the multi-element standard. The analytical result of the specimen after thermal exposure obtained by using the multi-element standard is also shown in the row labeled XRS std* in Table 3. The microstructure of this specimen is shown in Photo l(b). In spite of the change of the carbide composition, the results determined using the multielement standard were relatively good. The tantalum was determined by using a pure tantalum standard used for the analysis mentioned above. The main cause of the analytical error of these elements can be considered because these elements were the segregated in the specimen. These elements were concentrated in the carbides. As the experimental results show, the accuracy of the results obtained by the FP-method with pure element standards in X-ray fluorescence spectrometry was unsatisfactory. The use of a few multi-element standards was recommended to obtain more accurate analytical results. The results 18 of typical superalloys analyzed by the FP-method using multi-element standards are shown in Table 4 as an example df the analysis of superalloys by using the multi-element standards. To demonstrate the effect of unhomogeneity of specimens on X-ray fluorescence intensities, the relationship between aluminum contents and AlKα intensities measured for a typical homogeneous Al-Fe alloy was shown in Fig. 1. The closed circles and the solid line in Fig. 1 show the AlKα intensities obtained from the homogeneous specimen and the intensities calculated by the FPmethod respectively. The open triangles and squares show the intensities measured from the unhomogeneous specimens that were the briquetted mixture of aluminum and iron metal powders. The backscattered composition images of the measured surface of these mixed and briquet specimens are shown in Photo 2. The black and the gray particles are aluminum and iron particles respectively. Fig. 1. and Photo 2 show that the effect of unhomogeneity of the specimen on AlKα intensities was quite remarkable. It appears that AlKα intensity changes strongly depend on the particle size. AlKα intensity pro- The Rigaku Journal

4 Table 4 Results (in mass percent) of typical superalloys analyzed by the fundamental parameter method using Multi-element standards. No. Elem. Cr Co W Ti Ta Al Hf Zr Ni TM-44 Chem Bal. X-Ray Bal. TM-48 Chem Bal. X-Ray Bal. TM-78 Desin Bal. X-Ray Bal. TM-79 Desin Bal. X-Ray Bal. +: Wet chemical analysis Photo 2 Backscattered electron composition images of mixed powder samples. Fig. 1 Relation between aluminum contents and AlKa intensities in Al-Fe system : AlKα intensities measured from homogeneous samples., : AlKα intensities measured from mixed powder samples. portionally decreases to the particle size of the specimens. The intensity obtained from the briquet specimens that obtained from the homogneous one in limit when the particle size approaches under a half of the critical depth of AlKα line. c) Uncertainty of Mass Attenuation Coefficient and Analytical Error The results obtained by the FP-method with the mass attenuation coefficients obtained from Heinrich's and McMaster's table are compared in Table 5. The specimens used were proven to be homogeneous microscopically. In the analysis of the homogeneous specimens, the effect of the uncertainty of the mass attenuation coefficient on the error of the results obtained by the FP-method was negligibly small. 2.3 Analysis of Permalloy Thin Film on Iron Substrate In the case where the same elements were included in the thin film and the substrate, it was difficult to analyze the composition and the thickness of the film. Therefore the simultaneous determination of the composition and the mass thickness of thin film specimens without substrate was used as a tool in the production control [13]. In the analysis of a permalloy thin film on an iron substrate, the interaction model of X-rays between the thin film and the substrate are shown in Fig. 2. Where S is an X-ray source and D is the thickness of thin film, R 1, R 2, R 3, R 4 and R 5 are X- rays radiated from the thin film directly excited by the X-ray source; X-rays radiated from the thin film by excited coexisting elements in the film; X- rays radiated from the substrate; X-rays radiated from the substrate are indirectly excited by the some other element in the film, and X-rays radiated from the film indirectly excited some other element in the substrate respectively. The NiKα intensity which corresponds only to R 1 was calculated, because the NiK a generated in the thin film is not excited by the iron substrate. The relationships between the calculated intensities of R 1, R 2, R 3, R 4 and the sum of them for FeKα line, and the mass thickness of the thin film containing 10% and 70% of iron were shown in Fig. 3(a). The relationships between the observable FeKα intensities (R T ) and the mass thicknesses of the Vol. 7. No

5 Table 5 Results (in mass percent) calculated from mass absorption coefficients in two different papers by the fundamental parameter method. Sample M.C.A. Fe Ni Cr Mn Si Mo Total Heinrich W Error NTK-316 McMaster W Error W SD Heinrich W Error YUS-4090 McMaster W Error W SD W: Composition obtained by FP method. W SD : Composition analyzed by Wet-chemical method. M.C.A.: Mass absorption coeff, obtained from the papers [4,6]. Table 6 Simultaneous determination of composition and massthickness of permalloy thin film alone and on iron substrate. Substrate None Fe-substrate FeKα OBS NiKα OBS FeKα FeKα FeKα FeKα FeKα TOTAL (49.7%) (51.6%) (50.3%) NiKα CAL (50.3%) 0.224(48.4%) (49.7%) D CALC D CALC : Mass thickness obtained by the FP-method Mass thickness certificated: 3.20 (mg/cm 2 ). Certificated composition: 50.2%Fe, 49.8%Ni. films various iron contents were shown in Fig. 4(a). Fig. 3 and 4 suggest the determination of the composition and the thickness of the film simultaneously, when the iron content of the film is less than 70%. Table 6 shows the results of the simultaneous determination of the composition and the mass thickness of the permalloy thin film on the iron substrate. It was possible to determine accurately the composition and the mass thickness of the permalloy thin films on iron substrate using the pure element standards by the FP-method. The dependence of 20 Fig. 2 Schematic diagram of typical fluorescent X-rays generated from permalloy thin film on iron substrate. the changing rate of FeKα intensities on the mass thickness of the films is also shown in Fig. 4(b). 3. Conclusion The use of the multi-element standard is recommended to obtain accurate results in the fundamental parameter method of X-ray fluorescence spectrometry, although the use of the pure element standards is more convenient in the spectrometry. The fundamental parameter method is a powerful tool for the analysis of thin film specimens, because the composition and the thickness are simultaneously determined using the pure element standards. Acknowledgment This work was performed as a part of "The Advance Gas Turbine" in "Moonlight" Energy Saving Technology project sponsored by the Agency of Industrial Science and Technology, MITI. The Rigaku Journal

6 Fig. 3 Simulated relationships between mass thickness of permalloy and FeKα intensities generated for permalloy thin film on iron substrate. Fig. 4 Simulated relations between mass thickness of various kinds of permalloy thin films on iron substrate and observable FeKα intensities. References [1] J. Sherman, Spectrochim. Acta, 7, 283 (1966). [2] T. Shiraiwaand N. Fujino, Jpn. J. App. Phys., 3, 886 (1966). [3] J. V. Gilflichand L. S. Birks, Anal. Chem., 40, 1077 (1968). [4] K. J. F. Heinrich and S. D. Rasberry, Anal. Chem., 46, 81 (1974). [5] J. W. Colby, Adv. X-Ray Anal., 11, 287 (1968). [6] K. J. F. Heinrich, "X-Ray Microprobe," p. 296 (1966), (John Wiley). [7] W. H. McMaster, "Complication of X-Ray Cross Section", Document UCRL 5074, National Information Service U.S. [8] D. Laguittton and W. Parrish, Anal.Chem., 49, 1152 (1977). [9] T. Shiraiwa and N. Fujino, Adv. X-Ray Anal., 12, 446 (1969). [10] M. Mantler, Adv. X-Ray Anal., 27, 433 (1984). [11] K. Ohno, J. Fujiwara and I. Morimoto, X-Ray Spectrom., 9, 138 (1980). [12] T. Okada and N. Akamatsu, Adv. X-Ray Chem. Anal. Japan, 17, 177 (1986). [13] Private communication from T. C. Huang and W. Parrish, IBM Almaden Research Center. Vol. 7. No