SIMULTANEOUS ANALYSIS OF NICKEL, COBALT AND IRON BASE ALLOYS USING THE FUNDAMENTAL PARAMETER METHOD

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1 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN SIMULTANEOUS ANALYSIS OF NICKEL, COBALT AND IRON BASE ALLOYS USING THE FUNDAMENTAL PARAMETER METHOD Yoshiyuki Kataoka 1, Eiichi Furusawa 1, Hisayuki Kohno 1, Tomoya Arai 1, Al Martin 2, Hisashi Inoue 2, and Michael Mantler 3 1 Rigaku Industrial Corporation,14-8, Akaoji, Takatsuki, Osaka , Japan 2 Rigaku Americas Corporation, 99, New Trails Drive, The Woodlands, Texas 2 Vienna University of Technology, Wiedner Hauptstrasse 8-1, A-14 Vienna, Austria ABSTRACT The method of analysis of nickel, cobalt, and iron base alloys by using the fundamental parameter method, covering the entire concentration range with a single calibration for each element is evaluated. The results obtained were satisfactory and demonstrated that the method can be applied to the analyses of both, major and trace elements using a multi-channel spectrometer. For example,.14wt% of accuracy was obtained for nickel within a concentration range of to 1wt%. We found that tertiary excitation is significant in the analysis of chromium by contributing up to 2.4% of the total intensity; the accuracy was improved from.14wt% to.1wt% by incorporating tertiary excitation in the computation of theoretical intensities. The least squares fitting method for sensitivity calibration was studied; the method with a quadratic fit polynomial pinned to a fixed point gave the best result, covering a range from trace level to 1% with a single calibration line. The theoretical intensity overlapping correction method is effective when channels for overlapping lines are not available in a multi- channel spectrometer. INTRODUCTION X-ray fluorescence spectrometry is widely used for the analysis of nickel, cobalt and iron base alloys since it is a rapid and precise analytical method. The strong inter-element effects that appear in such analyses can be quite accurately accounted for by influence coefficient methods. However, these alloys cover a wide concentration range of several important elements, such as nickel and iron, and consequently the number of required standards can be extremely large; many calibration sets may then be required. Fundamental parameter methods which were reported in many papers since four decades ago [1,2,3] are an approach to solve the problem, however, the method is not popular in practical use. We have evaluated the analysis of nickel, cobalt and iron base alloys by using the fundamental parameter method installed in the software package of Rigaku Simultix to study the possibility of covering the entire concentration range with a single calibration for each element. In order to obtain accurate analysis results in a wide range from trace to high concentration, the spectrometer should have good counting linearity with small errors resulting from dead time correction, and high speed counting capability in order to minimize the error due to counting statistics. The contribution of tertiary excitation [1] was studied by theoretical intensity computations. Equations and fitting methods by least squares fit for the sensitivity calibration are evaluated. An overlapping correction as well as background subtraction methods for trace elements are discussed for analyses employing a multi-channel spectrometer. EXPERIMENTAL The measurements were performed by a multi-channel WDXRF spectrometer Rigaku Simultix with a Rh target end-window X-ray tube operated at 5kV and 7mA. Counting times were 2

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3 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN seconds. The detectors used for all transition elements were sealed proportional counters with a good counting linearity at up to 4kcps. 17 elements were measured simultaneously; Mn, Si, Cr, Ni, Co, Mo, Nb, Ti, Al, Fe, P, S, Cu, V, and Sn by their Kα lines, and W as well as Ta by their Lα lines. 118 standard samples of standard reference materials and pure metals were analyzed. The materials are listed in Table 1 and the concentration ranges of the standard samples are shown in Table 2. All samples were polished by using grinding papers of corundum 24 mesh. If a rougher grinding paper such as 1 mesh is used, the accuracy of the high concentration elements becomes worse. The surface of the polished samples are cleaned by using an airgun. Table 2. Concentration ranges of standard samples Table 1. Materials of measured samples Materials: Monel, Hastelloy, Waspaloy, Rene41, Nimonic, Haynes, Inconel, Stellite, MP159, 15Mn17Cr, 17-4PH, PH13-8Mo, RA33, Nitr, Maraging, Carpenter 2 Cb3, tool steels, stainless steels, binary alloys, pure metals of Ni, Co and Fe. Suppliers: NIST, Brammer, BCS, MBH, ARMI and JSS. Element Conc. range Element Conc. range Mn Al Si Fe -1 Cr P -.32 Ni -1 S -.3 Co -1 Cu Mo Ta -.75 W V Nb Sn -.9 Ti INCORPORATION OF TERTIARY EXCITATION COMPUTATION The analyzed nickel, cobalt and iron base alloys have variety of sample compositions including transition elements, and there can be a significant amount of tertiary excitation of Cr. The standard software package of the multi-channel spectrometer Simultix computes tertiary excitation routinely. The Ni-Kα, Ni-Kβ and Co-Kβ lines excited by primary X-rays excite Fe as secondary excitation, and these secondary Fe-Kα and Fe-Kβ lines excite Cr-Kα by the tertiary excitation. From calculating the theoretical intensities of Cr-Kα with and without tertiary excitation follows that the contribution of the tertiary excitation to the total intensity is up to 2.4%. The accuracy resulting from the two intensity calculation methods is compared in Table 3 and the relationship between standard values and analyzed values obtained by properly including tertiary excitation is shown in Fig. 1. The values of the accuracy were obtained from the root mean squares of the analytical errors. The analytical accuracy obtained by accounting for tertiary excitation is.1% as compared to.14% without. Analyzed Values (mass%) 4 4 Cr ( - 4 mass%) Accuracy:.1 mass% Standard Values (mass%) Figure 1. Relationship between standard and analyzed values Measured intensity (normalized) 1. Ni-Kα 2 4 Figure 2. Sensitivity calibration

4 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN SENSITIVITY CALIBRATION In the fundamental parameter method, the calibration is called sensitivity calibration, as shown in Fig. 2 for Ni-Kα. The sensitivity calibration equation is expressed by the correlation between theoretical intensity I T and measured intensity I M, using a polynomial. 2 IT = AI M + BI M + C In principle, the calibration should be linear as long as the counting linearity and the physical parameters are free from errors. Table 4 shows the root mean square of intensity errors for linear and quadratic fit. The results, expressed in percents of normalized intensities of pure metals, are similar to the error in concentration. They are very small in both, the quadratic and linear approach, with only a slightly better fit with the quadratic calibration. This proves that counting linearity errors and uncertainty of physical parameters in the FP method are both very small. Table 3. Tertiary excitation: Comparison of accuracy of Cr Computation mass% With tertiary excitation.1 Without tertiary excitation.14 Table 4. Sensitivity calibration: Comparison of polynomial orders (root mean square of intensity error, in %) Cr Fe Co Ni Linear Quadratic Conc. range (%) Table 5. Least squares fitting: Comparison of weighting methods (root mean square of intensity error of Ni, in % ) Fitting method Concentration range No weighting Precision weighting.3.16 Fixed point weighting.3.14 Another point to be discussed in calibration is the least squares fitting method. A requirement is to obtain an accurate fit from trace to 1%. Table 5 shows the root mean square of the intensity error of Ni, comparing three least squares fitting methods: no weighting, precision weighting and the fixed point method. In precision weighting, the square roots of the intensities are applied to the weighting function of the least squares fit. The fixed point method is a method we developed; it requires the fit curve to pass exactly through a selected data point. The root mean square by using no weighting for the low concentration range from to.52% is.36%. This is large compared to the other two methods. The fixed point method gave the best overall fitting for both, low and high concentration ranges. Fig. 3 shows a comparison of the fitting methods for the low concentration range. For the fixed Measured intensity 1. Element: Ni Measured intensity (normalized) X Fixed point method Fixed data point No weighting Precision weighting Figure 3. Comparison of fitting method in low concentration

5 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN point method, one data point shown in the figure was selected as the fixed data point. By using no weighting, the obtained fit-curve is far from any data point in the low concentration range. The fittings by the precision weighting and the fixed point method are almost identical in this range. The advantage of the fixed point method over the precision weighting method is that it gives good fitting even when the number of data points is one-sided in the concentration range. OVELAPPING CORRECTION AND BACKGROUND SUBTRACTION The line overlapping correction is important for trace analysis. A sample containing Ni and Co as well as a small amount of Cu is assumed. In the analysis of Cu by using the Cu-Kα line, the Ni-Kβ line interferes. Fig. 4 shows the spectrum and also the mass absorption coefficients of Ni and Co. The K absorption edge of Co is located between Ni-Kα and Ni-Kβ and both, the Cu-Kα and Ni-Kβ lines are located at the shorter wavelength side of the Co K absorption edge. Therefore the Ni-Kβ line should be used for the overlapping correction for the Cu-Kα line. However, the multi-channel spectrometer is equipped with only one channel for each element. In the case of Ni, the spectrometer is not equipped with a channel for Ni-Kβ because it is much weaker than Ni-Kα. Measured intensity (a.u.) Analyzing line: Cu-Kα Overlapping line: Ni-Kβ Ni-Kβ Co Cu-Kα 2θ(degrees) Figure 4. Mass absorption coefficients in overlapping region In order to correct the Cu-Kα intensity for the overlapping Ni-Kβ intensity in the FP method, we employed a theoretical intensity overlapping correction method and compared it to a conventional measured intensity overlapping correction. Ni Measured intensity correction method IMic = IMi LMi IMj I Mic : corrected measured intensity L Mj : overlapping correction coefficient I Mj : measured intensity of correcting line correction method ITic = ITi LTj ITj I Tic : corrected theoretical intensity L Tj : overlapping correction coefficient Co-K absorption edge Co-Kβ Analyzed values (mass%).2 Ni-Kα Mass absorption coefficient (cm 2 /g) Correcting line: Ni-Kα measured intensity Ni-Kβ theoretical intensity high Ni samples Standard values (mass%) Figure 5. Comparison of two overlapping correction methods for Cu analysis

6 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN I Tj : theoretical intensity of correcting line In general, the measured intensity correction method above is used for the overlapping correction. The theoretical overlapping correction method [4] is based on a scheme where the theoretical intensity of the measured line is corrected by the theoretical intensities of the overlapping lines. The theoretical intensities of the correcting lines are re-calculated in each iteration step by using the most recently calculated composition. Non-measured lines can be included in the correcting lines for the theoretical intensity correction. Fig. 5 shows a comparison of the two overlapping correction methods for Cu analysis. The dark marks indicate the correction by using Ni-Kβ theoretical intensities and the light marks are for Ni-Kα measured intensities. The light marks appearing near the lower left corner are from samples with high Ni contents. The accuracy of Cu analysis based on corrections by theoretical Ni-Kβ intensities is.5% and the accuracy by using the Ni-Kα measured intensities is.1% in the concentration range of to.2% as shown in Table 6. The accuracy is improved by the theoretical Ni-Kβ intensity correction. Similar cases of line overlapping and corrections by Kβ lines appear in the analysis of Cr, Mn, Fe,Co, and Ni. Table 6. CuKα/NiKβ overlapping correction: Accuracy of Cu analysis, in mass% Concentration range of Cu -.2% -33% Ni-Kβ theoretical intensity.5.2 Ni-Kα measured intensity.1.21 Divergence slit Sample Analyzing crystal Peak Special type receiving slit Figure 6. Fixed channel with background measurement BG Detector When analyzing trace elements, the variation of the background intensity can not be ignored. The employed multi-channel spectrometer has unique background measurement channels. Fig. 6 shows the schematics of the channel. It has a curved crystal and special receiving slit which can be switched for measuring peak and background. Thereby both, peak and background, can be measured using this special fixed channel. Fig. 7 illustrates sensitivity calibrations for Sn-Kα obtained with and without the fixed channel with background measurement function. Fig. 7(a) shows a plot without background correction Sn-Kα Sn-Kα Gross intensity Accuracy:.35 mass% (a) No background correction Net intensity 8 Accuracy:.2 mass% (b) With background correction Figure 7. Background correction for Sn

7 Copyright JCPDS-International Centre for Diffraction Data 27 ISSN using gross measured intensities. Fig. 7(b) shows the result after background correction using net intensities. The accuracy in concentration is improved by the background correction. The following equation is used for the background correction: I Net = I Gross - ki BG RESULTS Table 7 lists a summary of the accuracy for all 17 measured elements using 118 standards. The accuracy of Cr is.1% for the range from to 39.48%. The accuracy of Ni is.14% for the range from to 1%. The accuracy of Co is.71% and for Fe it is.176%. Regarding Fe, the accuracy was obtained by including Fe base alloys. The Fe concentrations of Fe base alloys were calculated as the balance and the accuracy is therefore not reliable. The maximum concentrations of Mn, Mo, W, and Cu are also very high, up to about 33%. We could obtain good accuracy for these elements. There are serious overlappings in the analysis of P and S. The concentrations of the elements causing the overlappings, such as Mo, W, Co and Cu, are extremely high and the amount of overlapping is much larger than the intensity of P and S. CONCLUSION Table 7. Accuracy of Ni, Co and Fe base alloy analysis Element Mn Si Cr Ni Co Mo W Nb Ti Al Fe P S Cu Ta V Sn Concentration range Accuracy (.18) Accurate analysis of Ni, Co and Fe base alloys for the elements ranging from traces to major constituents by using single sensitivity calibration could be achieved with the fundamental parameter method. Computation of tertiary excitation improves the accuracy for those elements where the contribution is significant. Sensitivity calibration using quadratic and our fixed point least squares fit covers a range from trace level to 1% with a single calibration line. The theoretical intensity overlapping correction method is effective when channels for the overlapping lines are not available in a multi-channel spectrometer. Background can be corrected for by using a channel with background measurement capability, for trace element analysis. REFERENCES 1. Sherman, J.; Spectrochimica Acta, 1955, 7, Shiraiwa,T., Fujino, N.,:Japanese Journal of Applied Physics, 1966, 5, Criss. J, Birks L.; Analytical Chemistry, 1968, Yamada Y., Kataoka Y., Kawahara N., Kohno H., Martin, J.; Advances in X-ray Analysis, 22, 45,