Analysis of Coating Weight and Iron Content for Iron-Zinc Alloy Coatings by Using X-ray Fluorescence with Multiple Regression

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1 Journal of the Korean Physical Society, Vol. 42, No. 2, March 2003, pp Analysis of Coating Weight and Iron Content for Iron-Zinc Alloy Coatings by Using X-ray Fluorescence with Multiple Regression Jae-Hwa Hong Sensor & Instrumentation Team, Research Institute of Industrial Science & Technology, Pohang Soon-Ju Kwon Department of Materials Science and Engineering, Pohang Institute of Science & Technology, Pohang (Received 18 November 2002) Zinc-iron alloy coatings are produced by annealing of zinc-coated steels, in which the iron and the zinc are interdiffued to form iron-zinc alloy. The analysis of the coating weight and the iron content within the coating is very important since they are closely related to the corrosion properties. However, it is difficult to measure these alloy coatings by using the conventional X-ray fluorescence (XRF) method because iron is contained both in the coatings and the substrate. Furthermore, there is some concern that the non-uniform concentration of iron within the coatings may result in significant errors in the XRF analysis. The difference in probing depth for Zn Kα and Zn Lα lines can be used to separate the iron contained in the coating from that in the steel. The critical coating weights for the Zn Kα and the Zn Lα lines were determined by fitting the line intensities of zinc electroplated coatings, and the coating weights of commonly produced zinc-iron alloy coatings were found to be higher than the critical coating weight for the Zn Lα line and lower than that for the Zn Kα line. A multiple regression method was successfully applied with the Zn Kα and the Zn Lα line intensities for the determination of the coating weight. The iron contents in the coatings were determined by using the Zn Lα line only. With the proposed method, a coating weight accuracy to 0.57 g/m 2 and an iron content to 0.57 % was achieved for a number of commercially produced zinc-iron alloy coatings. PACS numbers: Jb Keywords: XRF, Zinc-iron, Alloying coating I. INTRODUCTION Zinc-iron alloy coatings have been widely used, especially in automobile panels, because they have superior corrosion resistance and can be easily painted and welded [1]. It is important to determine the coating weight (coating thickness) and iron content because the coating weight is a major factor in corrosion resistance and because the ductility or formability of the coating is closely related to the iron content. The determination of the coating weight and the iron content in zinc-iron alloy coatings has usually been carried out by using a wet chemical analysis [2]. If the X-ray fluorescence method can be applied to these coatings, the analysis time should be shortened considerably. Although the X-ray fluorescence method has been successfully applied to measure coating weights and compositions of various coatings [3 5], it is difficult to analyze hongjh@rist.re.kr Fax: , Tel: galvannealed coatings by using the conventional X-ray fluorescence method because the iron is contained both in the coating and in the substrate. Furthermore, the inhomogeneity of the iron concentration within the coating might result in errors in the analytical values. Tanabe et al. [6] proposed a method using two incident and takeoff angles for the determination of the iron content for galvannealed coatings. That method utilizes the differences in X-ray pass lengths with known X-ray absorption coefficients of the coatings. Yamamoto et al. [7] developed a method using X-ray diffraction combined with X-ray fluorescence. They determined the iron content by measuring X-ray diffraction angle using the fact that the lattice parameters of Zn-Fe inter-metallic compounds vary with iron content. However, both of these methods require special equipment to detect the fluorescence line intensities at different takeoff angles or diffraction peaks at different angles. Furthermore, none of the above-mentioned methods can simultaneously or accurately determine the coating weight and the iron content. Matsumoto et al. [8] were the first to use the Zn Kα

2 -414- Journal of the Korean Physical Society, Vol. 42, No. 2, March 2003 and the Zn Lα line intensities and to apply them to Zn- Ni and Fe-Zn alloy electroplated coatings. However, the determination of the coating weight and the iron content for galvannealed steels has not been reported yet. Since galvannealed coatings are produced by the heat treatment of zinc-coated (galvanized) steels, they have layered structures of several zinc-iron intermetallic phases, which are totally different from those in electroplating steels. In this paper, we report the measurement results for the coating weights and the iron contents of commonly produced galvannealed steels, which contain about 10 wt.% iron. Both the Zn Kα and the Zn Lα lines were used to determine the coating weight whereas only the Zn Lα line was used to determine the iron content. The accuracies determined by using a multiple regression method were compared with those obtained by using a wet chemical method. II. EXPERIMENT 1. Sample Preparation From industrially produced galvannealing lines, galvannealed steels with coating weights ranging from 42.9 g/m 2 to 76.2 g/m 2 and iron contents ranging from 9.13 wt.% Fe to 13.6 wt.% Fe were collected for reference samples. The coating weight means the weight on a unit area, and the term coating thickness is frequently used in the field of X-ray fluorescence. However, the weight on a unit area (ρ t, ρ = density, t = thickness) is measured by X-ray fluorescence. It is convenient to use coating weight when the density varies with the coating composition. The zinc-coated steels used for the determination of the critical coating weight were electrodeposited on steel substrates in a chloride solution. Five, 50-mm-diameter samples were punched from the same batch. The coating weight of the reference samples at the center position were determined by averaging the remaining 4 samples by measuring the difference of weight before and after dissolving the samples in diluted hydrochloric acid (known as the gravimetric method). The iron content was determined by using the ICP (inductively coupled plasma) method. Table 1 shows the measured coating weights and alloying degrees. Table 1. Coating weight and iron content of galvannealed reference samples. Sample No. Coating weight Alloying degree (g/m 2 ) (Fe%) Table 2. XRF analytical conditions. X-ray tube Detector Analyzing crystal Incident angle Takeoff angle Measuring time Sample rotation Chamber vacuum Lα Rh target, 50 kv-50 ma, Be window Scintillation counter for Zn Kα Flow proportional counter (P-10 gas) for Zn Lα LiF (200) for Zn Kα RAP (001) for Zn Lα sec for Zn Kα, 40 sec for Zn Lα 30 rpm Torr III. RESULTS AND DISCUSSION 1. Critical Coating Weight for Zn Kα and Zn 2. XRF Measurements The intensities of Zn Kα and Zn Lα radiations were measured using a wavelength-dispersive, simultaneoustype X-ray fluorescence spectrometer (Rigaku, Simultix 12). The measurement conditions are listed in Table 2. Figure 1 shows the Zn Kα and the Zn Lα line intensity as a function of the Zn coating weight for Zn electroplated coatings. When the coating weight is small, the intensity of the Zn Kα line increases linearly and then saturates slowly. The intensities of the Zn Lα line behave similarly, but the saturating coating weight is much smaller than that of the Zn Kα line.

3 Analysis of Coating Weight and Iron Content for Iron-Zinc Alloy Coatings Jae-Hwa Hong and Soon-Ju Kwon Fig. 2. Schematic drawing of fluorescence X-rays from galvannealed steel. Fig. 1. Intensity of Zn Kα and Zn Lα line as a function of coating weight. Closed circles represent Zn Kα, and open circles represent Zn Lα line. Table 3. Results for the fitting parameters and the critical coating weights for the Zn Kα and Zn Lα lines. Fitting I a Critical coating weight parameter (g/m 2 ) Zn Kα Zn Lα The critical coating weight, t, at which the ratio of the intensity I to the infinite thickness intensity I is 0.99 can be calculated using the XRF intensities and by fitting to the equation I = I [1 exp( a t)], where, a is a fitting parameter and t is the coating weight. Table 3 shows the results for the fitting parameters and for the critical coating weight. The critical coating weight for Zn Lα line was g/m 2, which means the Zn Lα intensity is not a function of the coating weight but only a function of Zn% (or iron content) when the sample coating weight is greater than g/m 2. The critical coating weight was measured at g/m 2 for the Zn Kα line. The coating weight of commonly produced galvannealed coatings varied from about from 40 g/m 2 to about 80 g/m 2, which is higher than the critical coating weight for the Zn Lα line and lower than the critical coating weight for the Zn Kα line. In this range of coating weights, the Zn Kα line intensity is a function of coating weight as well as the iron content of the coating layer. If the coating weight is above the critical coating weight of the Zn Kα line, we cannot determine the coating weight effectively by using the Zn Kα line intensity. 2. Coating Weight Determination by Multiple Regression When the primary X-rays are incident on galvannnealed steel, several fluorescence X-rays are emitted, as shown in Fig. 2. The intensities of Zn Kα line are given as I ZnKα = k ZnKα I 0 W Zn [1 exp{ (µλ F e Zn / sin φ + µznkα F e Zn / )ρ F e Zn t] µ λ F e Zn / sin φ + µznkα F e Zn /, (1) where I ZnKα : intensity of Zn Kα line from galvannealed steel, I 0 : intensity of incident X-rays, W Zn : Zn content in the galvannealed steel, ρ F e Zn : density of the coating, φ, ϕ: incident and takeoff angles, k ZnKα : mass absorption coefficient, µ λ F e Zn : mass absorption coefficient of the incident X- rays on the coating, µ ZnKα F e Zn : mass absorption coefficient of the Zn Kα line in the coating, t: thickness of the coating. The equations for the Zn Lα line are obtained by replacing the subscript Kα by Lα. Equation (1) becomes Eq. (2) by using a Taylor expansion and an approximation: I ZnKα = k ZnKα I 0 W Zn [ ρ F e Zn t 1 {( µ λ F e 2 sin φ + µznkα ) F e + ( µ λ Zn µλ F e + µznkα µ ZnKα ) } F e WZn ρ 2 sin φ sin φ F e Zn t 2]. (2) Equation (2) leads to Eq. (3) when the mass absorption coefficients and the incident and takeoff angles are constant: I ZnKα = a (Zn%) x F e Zn + b (Zn%) x 2 F e Zn + c (Zn%) 2 x 2 F e Zn + d, (3)

4 -416- Journal of the Korean Physical Society, Vol. 42, No. 2, March 2003 Table 4. Comparison of the coating weights measured by using the XRF and the ICP methods. Sample No. Coating weight Coating weight Deviations of coating Deviations of coating by using Eq. (3) by using Eq. (4) weight using Eq. (3) weight using Eq. (4) and (g/m 2 ) (g/m 2 ) and chemical method (%) chemical method (%) Average where x F e Zn (= ρ F e Zn t) is the coating thickness and a, b, c, and d are coefficients, d being the background term. If we solve the quadratic equation of Eq. (3) with respect to x, we can determine the coating weight by using the Zn Kα line intensity and the Zn %. Another way of determining the coating weight is to simply make a multiple regression equation by using the Zn Kα and the Zn Lα line intensities expressed as Eq. (4). In this study, the coating weight is expressed from the Zn Kα line intensities in a 2nd-order polynomial form and the Zn Lα line intensities in a linear form. We add the interaction term as Zn Kα multiplied by Zn Lα: x = a + b I ZnKα + c I 2 ZnKα + d I ZnLα + e I ZnKα I ZnLα, (4) where x is the coating thickness, I ZnKα and I ZnLα are the Zn Kα and Zn Lα line intensities, respectively, and a, b, c and d are regression coefficients. In this study, industrially produced galvannealed coatings with coating weights from 42 g/m 2 to 77 g/m 2 were analyzed. Table 4 shows the results of the analysis. We can calculate the coating weight by solving Eq. (3), where the Zn % is replaced by a linear regression of Zn Lα line intensity. The average deviation for the coating weights, which was obtained by using Eq. (3), was 1.53 % whereas the average deviation obtained by using Eq. (4) was 1.33 %. These results indicate that the theoretical calculation of the Zn Kα line intensity is not precisely accurate when applied to galvannealed coatings. The main reason is the in-depth inhomogeneity of the samples. For a number of galvannealed coatings, a plot of coating weight determined by the Zn Kα and the Zn Lα lines with the multiple regression equation, Eq. (4), against the coating weight determined by using a gravimetric method is shown in Fig. 3. A very good correlation coefficient of more than 0.99 is obtained, suggesting that this method can be used for routine analysis of galvannealed coatings. 3. Determination of Iron Content Fig. 3. Comparison of coating weights determined by using XRF method to those determined by using the ICP method.

5 Analysis of Coating Weight and Iron Content for Iron-Zinc Alloy Coatings Jae-Hwa Hong and Soon-Ju Kwon combined with the multiple regression. IV. CONCLUSIONS Fig. 4. Comparison of the iron contents determined by using the XRF method to those determined by using the ICP method. Figure 4 shows the relationship between the iron concentration of galvannealed steel and the Zn Lα line intensities. The calibration curve was constructed from the linear regression equation. The iron content of galvannealed samples can be determined from the Zn Lα line intensities when the coating weight is greater than the Zn Lα critical coating weight. The coating weight range of industrially produced galvannealed coatings is normally above the Zn Lα critical coating weight of g/m 2. Thus, the Zn Lα line intensity is a function of only the Zn %, not of the coating weight. The analytical accuracy was 0.57 %. The results were satisfactory for routine measurement of galvannealed samples, so this method can be used as a replacement for wet chemical methods, such as chemical titration or ICP. The average deviations were not significantly increased when we added the Zn Kα line intensity as a second parameter The critical coating weights of the Zn Kα and the Zn Lα line intensities were experimentally determined to be g/m 2 and g/m 2, respectively, and were applied in conjunction with the multiple regression method to analyze the galvannealed coatings. The average deviation of the coating weight determined by using the gravitational method is 0.57 g/m 2. The iron concentration was determined by using the Zn Lα line intensity to a concentration accuracy of 0.57 %. The XRF analysis and proposed multiple regression method using Zn Kα and Zn Lα line intensities can be successfully used to determine both the coating weight and the iron content of industrially produced galvannealed coatings. REFERENCES [1] A. R. Marder, Prog. Mat. Sci. 45, 191 (2000). [2] Kil Dong Lee, J. Korean Phys. Soc. 38, 33 (2001). [3] T. C. Huang, X-Ray Spectrum. 20, 29 (1991). [4] M. H. J. Bekkers and H. A. van Sprang, X-ray Spectrum 26, 122 (1997). [5] W. H. Lee, B. S. Cho, B. J. Kang, J. Y. Kim, J. G. Lee, C. O. Jeong and Y. G. Kim, J. Korean Phys. Soc. 40, 11 (2002). [6] H. Tanabe, K. Imai, H. Kato, A. Honda, O. Fujita and N. Taguchi, NKK Giho 135, 43 (1991). [7] A. Yamamoto, W. Tanimoto, N. Makiishi and Y. Matsumura, Kawasaki Steel Giho 21, 107 (1989). [8] Y. Matsumoto, N. Fujino and S. Tsuchiya, Trans. ISIJ 28, 957 (1988).