ANALYTICAL PRECISION AND ACCURACY IN X-RAY FLUORESCENCE

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THE RIGAKU JOURNAL VOL. 21 / NO. 2 / 2004, 26–38

ANALYTICAL PRECISION AND ACCURACY IN X-RAY FLUORESCENCE ANALYSIS TOMOYA ARAI Rigaku Industrial Corporation, Akaoji, Takatsuki, Osaka 569-1146 Japan The analytical precision and accuracy in x-ray spectrochemical analysis are discussed; measured x-ray intensity is always accompanied by a small counting statistical fluctuation which conforms to the Gaussian distributions with a standard deviation of the square root of the total counts. Since the measured characteristic x-rays modified with matrix effect give rise to analytical errors, it is necessary to correct their intensity of an analyzing element. After many matrix corrections derived empirically and theoretically are reviewed, analytical examples of copper and copper alloys, stainless steels and heat resistance and high temperature alloys are investigated using a comparison parameter of RMS-difference. Calibration curve method, which is induced from the relationship between calculated intensity with fundamental parameter method and measured intensity, is revealed for quantitative determinations. Segregation in solidified materials is touch upon, which is strongly related to analytical accuracy.

1.

Introduction When analytical samples are irradiated with x-rays emitted from an x-ray tube or radioactive source, fluorescent x-rays are generated in the sample and can be measured for quantitative analysis of its elements. X-ray fluorescence analysis is rapid, precise and non-destructive. X-ray intensity, which is measured from the number of accumulated counts of x-ray photons per unit time, is always accompanied by a small counting statistical fluctuation which conform to the Gaussian distribution with a standard deviation equal to the square root of the total counts. The precision of an x-ray measurement can, therefore, be predicted by the measured intensity. For example, an accumulated intensity of one million counted x-ray photons has a standard deviation of 0.1%, and for one hundred million counts the standard deviation is 0.01%. When an x-ray beam propagates through a sample, its intensity is modified by matrix element effects, including the generation of characteristic x-rays, absorption of the emitted xrays along their paths, and the enhancement effect due to secondary excitation. Studies of these modification processes and related x-ray physical phenomena lead to the derivation of mathematical correction formulae. The development of these x-ray correction methods dominates the analytical performance of the x-ray fluorescence method. 2. 26

Correction of Matrix Element Effects

The advances in x-ray fluorescence instruments and applications have led to the need for developments of practical and effective mathematical correction formulae. A number of correction methods have been developed (see for example, Lachance and Traill [1], Rasberry and Heinrich [2], etc.). Beattie and Brissey [3] derived a basic correction formula for the relationship between the intensity of characteristic xrays and the weight fraction of constituent elements, which was the product of a term containing the intensity of measured analytical xrays and a correction factor containing the concentrations of the constituent elements. A classification of the correction equations published in the literature is carried out from the standpoint of mathematical simplicity and shown in the following: 1) The correction term of constituent elements consists of a constant plus the sum of products of x-ray intensities and correction factors, or the sum of the product of weight fractions and corrections coefficients. 2) The correction factor may or may not include the term with the analyte element. 3) The correction coefficients are mostly treated as constants, which is efficient in the case of small concentration changes of matrix elements. 4) In order to develop wider applicable correction equations and improve the elimination of analytical errors, terms with variable correction coefficients are used in the correcThe Rigaku Journal

tion formulae, which are affected with the third or the fourth constituent elements. 5) Least-squares methods have been used for the determination of correction coefficients and correction equations by using experimental data from a large number of standard samples. However, after the development of the fundamental parameter method, calculated intensities have been used for the derivation of correction coefficients and equations as well as for the verification of experimentally determined coefficients and equations. Since there exist many correction methods for quantitative analysis, it is necessary for practical applications to know about the characteristics of matrix correction equations for selecting the proper fitting algorithm for the analyzed sample. Rousseau [4] reviewed the concept of the influence coefficients in matrix correction method from the standpoint of theoretical and experimental approaches. The development of the fundamental-parameters method has been carried out by a number of x-ray scientists. At first, Sherman [5] studied the generation of characteristic x-rays theoretically. Shiraiwa and Fujino [6] proceeded this method even more accurately and verified it experimentally. For the spectral distribution of a primary x-ray source, they combined Kulenkampff’s formulae [7] of continuous x-rays with their own measured intensity ratios of continuous x-rays and tungsten L series x-rays from a side window x-ray tube. Criss and Birks [8] further developed the method by measuring the primary x-ray intensity distributions from side window x-ray tubes and using mini-computer systems to control x-ray fluorescent spectrometers [9]. To improve the performance of an x-ray spectrometer, a high-power end-window x-ray tube with a thin beryllium window was developed by Machlett [10]. A remarkable improvement in the analytical performances for light elements was achieved by a closely coupling of the x-ray source with the sample and a high transmittance window. In order to accomplish a reliable fundamental parameter method, the primary xray distributions from end window x-ray tubes were measured by Arai, Shoji and Omote [11]. It was found that the output of the x-ray spectral distribution at the long wavelength region was increased. Fig. 1 shows the comparison between measured and calculated intensities of various steels and alloy metals. At low concentrations Vol. 21

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Table 1.

Measured samples in Fig. 1.

background intensity corrections should be applied and at the higher intensity ranges the measured intensity requires a counting loss correction. Samples used in Fig. 1 are shown in Table 1. Rousseau [12] inspected coefficients, equations and methods of matrix corrections for high accuracy analysis and wider applicable correction equations based on the method developed by Claisse and Quintin [13] and Criss [8]. Furthermore, Rigaku tried to compare measured and calculated intensities based on its own developed fundamental-parameters method. Using the primary x-ray distribution from the end window x-ray tube, precisely matching calibration curves were obtained. Using these curves, direct quantitative analysis was then carried out by iterative computer algorithms without the need of matrix correction equations. The analytical results will be shown for stainless steel and high alloy analysis. 3. Quantitative Analysis of Copper and Copper Alloys X-ray fluorescence analysis has been applied widely owing to its—in comparison with current routine wet chemical methods—high speed performance and, particularly important, non-destructive analytical procedure in industrial use. X-ray analysis of copper and copper alloys are typical examples where four-digit figure results can be expected, since the high reproducibility of X-ray intensity measurements and the minimization of segregation errors owing to a large analyzed surface influences the X-ray analytical error. Table 2 shows the relationship between the intensities of Cu-Ka x-rays and surface treatment. The intensities emitted from coarse surfaces exhibit a reduction; the intensity after surface treatment by a belt-surfacer (#400, No. 4) is nearly the same as after Lathe-treatment (∇∇∇, No. 1). In routine procedures, it is shown that the same surface treatment should be adopted. In Table 3, the simple repeatability for Cu-Ka xrays by using a Rigaku fixed channel spectrometer is shown. The coefficient of variation for 27

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Fig. 1-1. Relationship between nickel concentration and Ni-Ka intensities.

Fig. 1-4. Comparison between measured Ni-Ka intensities.

calculated

and

Fig. 1-2. Relationship between iron concentration and Fe-Ka intensities.

Fig. 1-5. Comparison between measured Fe-Ka intensities.

calculated

and

Fig. 1-3. Relationship between chromium concentration and Cr-Ka intensities.

Fig. 1-6. Comparison between measured Cr-Ka intensities.

calculated

and

The Rigaku Journal

Cu-Ka x-rays is 0.046% and the variation of ZnKa x-rays is 0.022%. Under the above conditions, the x-ray analytical results of pure brass samples are illustrated in Table 4. The spread width of calibrations curves is 0.019 wt/56–65 wt% in the case of copper and 0.024 wt%/34–44 wt% in the zinc, using the quadratic equations solved by the least squares method. In this measurement the analytical accuracy consists of the chemical analysis errors, the effects of surface treatment and the statistical fluctuations of x-ray intensities. On the right hand side of Table 4 the sums of x-ray concentrations of copper and zinc and the differences between concentration sums of

chemical and x-ray values are shown, which indicate the reliability of x-ray analytical results. In Fig. 2, the relationship between zinc concentrations and the intensities of Zn-Ka and ZnKb 1 x-rays, normalized to pure metal intensities, is illustrated. The high intensities of Zn-Ka xrays and the remarkable intensity reductions of Zn-Kb 1 x-rays are caused by the low-absorption of Zn-Ka x-rays and the high absorption of ZnKb 1 by the copper component. In Table 5, the intensity ratio of Zn-Kb 1/Zn-Ka against zinc concentrations are tabulated. When a small amount of additional elements such as tin, lead, iron and manganese is alloyed, the intensities of Zn-Ka x-rays decreases

Table 2. Relationship between x-ray intensity of Cu-Ka and surface treatments. Sample: Special brass (Cu content: 73.82 wt%) Measuring condition: spinning.

Table 3. Simultix.

Precision of x-ray intensity of copper and zinc in brass. Sample: BS-33, Equipment: Rigaku

Table 4. Quantitative analysis of copper and zinc in brass. Equipment: Rigaku Simultix (40 kV–5 mA, 40 sec. FT), Surface treatment of the samples: Milling finish.

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Fig. 2. Relationship among concentration. measured and calculated x-ray intensity of various alloys.

Table 5. samples.

Intensity ratios of Zn-Kb 1 / Zn-Ka in brass

owing to the high absorption by these elements. This is shown in Fig. 2 for the case of NBS brass samples, which include small amounts of such additional elements, and for nickel silver alloy samples. Because of their short wavelengths, Sn-K and Pb-L x-rays can excite Cu-K and Zn-K x-rays, whereby an increase of measured intensities of Cu-Ka and Zn-Ka xrays can be expected. However, secondary excitation can be disregarded, as the concentration of tin and lead is low. The similarity of low absorption by nickel, copper and zinc is responsible for small correction coefficients of Cu-Ka and Zn-Ka x-rays in nickel. In order to review the analytical accuracy of numerous reports, a comparison parameter is introduced, defined as the root mean square between chemical analyses and non-corrected or corrected x-ray values (abbreviated as RMS-difference). Table 6 shows the RMS-difference of copper and copper alloys, which were reported by many researchers. Bareham and Fox [14] developed their own xray spectrometer and analyzed copper and copper alloys. In order to compensate for the matrix effects, beforehand the concentrations of the additional elements were measured, which underwent inconsiderable influence by matrix 30

effects. Then the calibration curves for Cu-Ka and Zn-Ka x-rays were prepared with classifications based on the concentration of the additional elements, and used for the determination of accurate concentrations of copper and zinc. It was a noticeable result that the analytical accuracy of pure brass samples shown in 1b in Table 6-1 was small. Lucas-Tooth and Price [15] showed the analytical accuracy of corrected copper concentrations in brass samples and Lucas-Tooth and Pyne [16] indicated that the ten-times repeatability for copper concentrations with fresh surface measurements in a day was 0.065 wt%; the analytical accuracy was equal to this repeatability. Ishihara, Koga, Yokokura and Uchida [17] prepared calibrations of special brass and special bronze for the x-ray determination based on a simple calibration method. Rousseau and Bouchard [18] verified the correction equations derived by Claisse and Quintin [13] and Criss [8] using calculated intensities based on the fundamental parameter method and x-ray measurements of NBS copper alloys. A detailed comparison of measured and calculated x-ray intensities was given. Iwasaki and Hiyoshi [19] studied the segregation of bronze alloys. The analytical results of original cast samples analyzed by means of xray and ICP methods were compared with those of recast samples which were prepared with a centrifugal casting machine. RMS-differences in Table 8 show the x-ray analytical results between the originally casted and recasted samples. In the case of high concentrations of lead, large differences between cast and recast samples were found in copper and lead analyses. In tin analysis, however, small differences are denoted between them. In zinc analysis a small reduction of the zinc concentration arises from escaping vapor, exhibiting small differences. Rigaku measured pure brass samples using the Rigaku sequential and fixed channel spectrometers. The analytical accuracies of copper and zinc using Rigaku fixed channel simultaneous spectrometers are superior to those of Rigaku sequential spectrometers. As the counting circuits of the fixed channel spectrometer handle a high throughput of electronic signals from x-ray photons, high precision measurements can be carried out in short time. The analytical examples of copper and copper alloys indicated that high precision measurements are possible and four-digits analyses are exhibited; inhomogeneity-effects like the segThe Rigaku Journal

Table 6-1. RMS-difference in copper and copper alloy analysis. The upper value is the RMS-difference and the lower is the concentration range of the element in each cell.

Table 6-2.

Evaluating conditions of the analysis in the Table 6-1.

regation generated during the solidification process of molten metals influences the analytical accuracy. 4. Quantitative Analysis of Stainless Steels The analytical problems of stainless steels are typical for x-ray fluorescent spectrochemical analysis. The primary x-ray excitations and the matrix effects in the samples should be investigated precisely. The primary excitation is dominated by the intensity distribution of continuous and characteristic x-rays and therefore related to the target material and the design of the employed x-ray tube. The matrix effects are comVol. 21

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posed of absorption and secondary enhancement effects; they modify the generated x-rays in the sample and give rise to analytical errors. In the case of matrix effects in stainless steels, where the Ni-K x-rays and primary x-rays are absorbed by chromium and iron, the absorption correction is sensitive to changes of the concentrations of chromium and iron. Fe-Ka x-rays are enhanced by secondary excitation from Ni-K x-rays and chromium absorbs Fe-Ka x-rays. Furthermore, Cr-Ka x-rays are enhanced by K x-rays of iron and nickel. Complex matrix effects between Ni-K, Fe-K and Cr-K x-rays occur thereby in the sample [33]. Several energetic coincidences of characteris31

Table 7-1. RMS-difference in stainless steel analysis. The upper value is the RMS-difference and the lower is the concentration range of the element in each cell.

Table 7-2.

Evaluating conditions of the analysis in the Table 7-1.

tic x-rays require spectral corrections for lineoverlaps, including Mn-Ka x-rays with Cr-Kb 1 xrays, Co-Ka with Fe-Kb 1, S-Ka with Mo-La and P-Ka with Mo-L l. In Table 7 the analytical accuracy based on several reported papers is compiled and RMSdifferences are adopted. Sugimoto [20] proposed a matrix effect correction method on the basis of the use of weight fractions of con32

stituent elements and also studied the correction method using the intensities of constituent elements. It was clarified that the use of weight fractions and measured intensities of the constituent elements is equivalent from the standpoint of analytical accuracy. For the derivation of the correction equation, he referred to the papers of Beattie and Brissey [3], Anderman [21] and Burcham [22]. The correction equation conThe Rigaku Journal

sists of products of an intensity term of measured x-rays and correction factors, however the iron term was excluded in either case of weight fraction or intensity corrections, but the correction terms of nickel and chromium were included. For the sake of clarifying the starting point of the studies, the chemical analysis errors were shown and are tabulated in Table 8. The x-ray analytical errors are two or three times as large as those of the chemical analysis. Lachance and Traill [23] derived simple correction equations based on the weight fractions of the constituent elements. The weight fraction of an analyzed element was proportional to the x-ray intensity which carries the correction factor of one plus the sum of the products of weight fraction and correction coefficients, “a ”, of the constituent elements. Most of the “a ”-coefficients could be calculated by using absorption coefficients, and the results in Table 7 indicate the effectiveness of assuming constant “a ” correction coefficients. Shiraiwa and Fujino [24] studied the generation process of x-ray fluorescent x-rays and completed the fundamental parameter method after Sherman studies [5]. The physical process of the generation of x-rays was analyzed precisely. For obtaining the primary x-ray tube spectrum, they combined continuous x-rays and the L-series of characteristic x-rays from tungsten. After calculating the intensities of fluorescent x-rays, correction equations were derived for the analysis of low alloy and stainless steels. In Table 7 the RMS-difference of stainless steels are shown. After Criss and Birks measured the primary xray intensity distributions, they developed the fundamental parameter method and compared three correction methods [8]. The first one was the purely experimentally determined correction method based on the commonly used equations, the second was a correction equation method using monochromatic x-rays selected for excitation of the characteristic x-rays, and the third method was a correction calculation using the fundamental parameter method. In Table 7, the results of the first calculation are shown. In 1978, Criss and Birks developed a new computer program NRLXRF combining fundamental parameter calculations and experimentally derived corrections for applications with a wider range of constituents and more accurate analyses. RMS-differences measured in 1978 are improved from the results in 1968. Mochizuki [25] derived a unique correction Vol. 21

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Table 8. steels.

Chemical analysis errors of stainless

method. At first, the intensities of Cr-Ka x-rays were measured using binary alloys of iron and chromium; after nickel was added, the influence of nickel to Cr-Ka x-rays was investigated. Abe [26] discussed the analysis of stainless steels based on the JIS correction method which was authorized by the committee of the iron and steel institute in Japan. Because an end window x-ray tube equipped with a thin beryllium window and a rhodium target was used, the analytical results of light elements were accurate enough for industrial applications. Three kinds of correction coefficients in the JIS formula were used and independently determined. RMS-differences in Table 7 are the mean values of three correction calculations. The spread degrees of RMS-differences using each correction coefficients are very similar to the mean values of RMS difference in Table 7. The ASTM group [27] adopted a simple calibration method for x-ray analysis of stainless steels. X-ray analytical values in the reports were pooled among five laboratories joint to the ASTM group. Ito, Sato and Narita [28] concluded that there were no differences between analytical results of a -coefficients methods and the JIS correction method for stainless steel analysis. For the overlap-correction of Cr-Kb 1 x-rays with Mn-Ka x-rays, they tried to use the weight fraction of chromium and the intensity of Cr-Ka x-rays, and showed that elimination of Cr-Kb 1 x-ray influences the manganese weight fraction in any case. Rousseau and Bouchard [18] compared measured x-ray intensities with those calculated by the fundamental parameter method. A confrontation figure of measured and calculated xray intensities was shown. After the ClaisseQuintin [13] and Criss-Birks [8] equations were inspected using the calculated intensities, the modified equations based on the ClaisseQuintin equation were derived by means of adding the third correction terms to the Lachance-Trail equation. Many NBS samples were analyzed and good analytical results were obtained. 33

Gunicheva, Finkelshtein and Afonin [29] analyzed NBS standard samples and private samples using the Claisse-Quintin equation with some modifications. Fairly good accuracy for nickel and chromium was obtained. Broll, Caussin and Peter [30] studied fundamental parameter methods for the determination of matrix correction equations and the Lachance-Traill equation; they developed a method with some modifications for quantitative determinations and showed analytical results of BAS stainless steels. Rigaku analyzed stainless steel samples supplied by NBS, BAS and JIS. For matrix corrections they adopted the Rigaku fundamental-parameters method for the calculation of x-ray intensities and prepared calibration curves from measured and calculated x-ray intensities. By using the established calibration curves, weight fractions of constituent elements were calculated by means of iterative algorithms. Although confidence problems originating from the physical constants exist in the calculated intensities, the calculated analysis values can be accepted on the basis of RMS-differences shown in Table 7. 5. Quantitative Analysis of Heat Resistance and High Temperature Alloys Abbott [31], who was the first developer of a commercial x-ray fluorescent spectrometer, presented a strip chart record of high alloy steel (16-25-6) (see Fig. 3). In Fig. 4 the measurement of NBS 1155 high alloy steel with a today’s instrument is illustrated. Since the fluorescent intensities and spectral resolution are sufficiently high for practical applications, the difference between these two pictures exhibits the historical progress of 50-years development. As pointed out by Abbott, the x-ray method is well suitable for analyzing heat resistance and high temperature alloys which consist of nickel, cobalt, iron, and chromium as major constituents, and low concentrations of varying other elements. Because the concentrations of the constituent elements influences the metallurgical properties of high temperature and heat resistance alloys, quantitative determination requires high precision. Studies of RMS-differences are shown in Table 9. Rickenbach [32] showed the precision and accuracy of nickel and chromium analysis. The measured precision of nickel and chromium in an A286 metal was shown as the composite error within a day and extending several days. The mean value of the nickel error was 34

Fig. 3. [31].

Spectrum of 16-25-6 alloy taken by Abbott

Fig. 4. Spectrum of NBS1155 taken by using Rigaku ZSX 100e.

0.03 wt%/26.2 wt% and for chromium it was 0.023 wt%/14.5 wt%. They are one-fifth of the RMS-differences in Table 9. It was noted that no matrix corrections were required for specimens with only small concentration variations. Lucas-Tooth and Pyne [16] discussed a formula where the correction factor is a constant plus the sum of products of the individual x-ray intensities of the constituent elements with correction coefficients. RMS-differences of 0.07 wt% in chromium and 0.032 wt% in manganese were reported. A third report sponsored by the ASTM committee in 1964 was presented by Gillieson, Reed, Milliken and Young [33]. Simultaneously, a report about spectrochemical analysis of high temperature alloys by spark excitation was given. Referring to the matrix correction methThe Rigaku Journal

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Table 9-2.

Evaluating conditions of the analysis in the Table 9-1.

Table 9-1. RMS-difference in heat resistance steel and high temperature alloy analysis. The upper value is the RMS-difference and the lower is the concentration range of the element in each cell.

ods by Lucas-Tooth and Price [15] and LucasTooth and Pyne [16], they applied a correction on the basis of x-ray intensities of the constituent elements. For higher accuracy, the measured intensities of aluminum and silicon constituents should be added in order to improve the matrix correction. Lachance and Traill [23] studied simple matrix correction equations that were one plus the sum of products of the weight fraction of constituent elements and correction coefficients. Based on the analysis of high nickel alloys that are selected from the application report, RMSdifferences were calculated and are shown in Table 9. On the basis of the Lachance-Traill equations, Caldwell [34] derived two kinds of correction equations. The first one was a fixed correction coefficient equation and the second one was a variable correction coefficient equation for wider concentration applications, on which the third or fourth constituent elements exerted reform. RMS-differences of major constituents in variable correction coefficient calculations improved those of the fixed correction coefficient method. Ito, Sato and Narita [35] studied the JIS correction equations that consist of the product of a factor containing a quadratic polynomial of the intensity of the measured x-rays, and a matrix correction factor. The coefficients of the intensity part were determined by least- squares algorithms from binary alloys with known chemical composition or from mathematical models; the second factor is one plus the sum of products of the weight fractions of the constituent elements and correction coefficients. Excluded are the terms containing the base constituent and the measured elements. In practical applications for nickel base alloys the correction coefficients of light and heavy elements from iron-based alloys were used; for the analysis of the major constituent elements, chromium, iron, and cobalt in nickel base alloys, the correction coefficients were determined experimentally. Griffiths and Webster [36] discussed the derivation of matrix correction equations in detail. They adopted the modified Lachance-Traill equation, in which the calibration constants of the x-ray intensity terms were determined by regression analysis and the correction factors were calculated with a program theoretically derived by de Jongh [37]. The two kinds of RMS-differences of authenticated sample analysis are shown in Table 9. The values in the 36

upper line are the calculated results based on normal matrix correction in the ALPHAS program, and the second values in the lower line are derived with the use of correction coefficients calculated under the condition of a fixed 60 : 20 : 20 constituent sample. Itoh, Sato, Ide and Okochi [38] studied the analysis of high alloys using the product of apparent concentrations and one plus the sum of products of weight fractions of the constituent elements and theoretically calculated correction coefficients. They compared the correction methods and clarified that there were no differences between them; based on their experimental findings they proposed a correction method which was authorized by the JIS committee. The results of analytical accuracy were two or more times higher than those of x-ray analytical precision. Rigaku analyzed high nickel alloys of NBS and specially prepared samples. For the matrix correction, they adopted the Rigaku fundamental parameter method and prepared calibration curves, which were used for the determination of the constituent elements. The RMS-differences in these studies were fairly small. 6. Segregation Influencing Analytical Accuracy The influence of inhomogeneity phenomena on the analytical accuracy is one of the most important factors. The internal soundness of an ingot which was studied by Marburg [39] bequeathed that the inhomogeneity induced in the cooling process from molten metals intimated strong effects to analytical problems to be solved. Stoops and McKee [40] studied the reduction of analytical accuracy for titanium concentrations owing to segregation of nickel base alloys of M252 (19 wt% chromium, 10 wt% cobalt, 10 wt% molybdenum, 2.5 wt% titanium, 3 wt% iron, 1 wt% aluminum, 0.15 wt % carbon and 0.35 wt% silicon). Since a major portion of titanium can be found in the grain boundaries of carbide or carbon-nitride particles, the differences between regular chemical and x-ray analysis values indicate a wider distribution, which is 5 to 10% of the amount of titanium present. When chemical analysis is carried out using samples scooped up from the x-ray analytical surface, x-ray values are nearly equal to that of chemical analysis, i.e., 0.5–1% of the amount of titanium present. It is well known that in the rapidly cooled steel low concentration manganese and impuThe Rigaku Journal

rity sulfur are dispersed and moderate analytical accuracy in manganese and sulfur determination can be found. In sufficiently annealed steel, small particles of manganese sulfide are precipitated in the grain boundaries of steel grains and the large deviations of Mn-Ka and SKa x-rays are found. Free cutting metals that are among the most widely used industrial materials are typical examples for exhibiting segregation phenomena in metals. Small metal particles like lead in steels and copper alloys influence machine processing of high-speed cutting. The following is associated with copper alloy analysis previously mentioned. Iwasaki and Hiyoshi studied lead segregation in bronze alloys [19]. According to the microscopic observations surface pictures of a cast bronze shows a mixture of ground metal of copper and lead precipitated particles and in the recast pictures the surface with scattering of lead small particles can be seen. From cast sample surface comparing with that of recast samples Cu-Ka xrays exhibit higher intensities and Pb-La x-rays show lower intensities. In recast sample surfaces, Cu-Ka x-rays show lower intensities and Pb-La x-rays are higher intensities because of absorption of Cu-Ka x-rays and the exciting of bare surfaces of many small particles of lead on analyzing surface. In the analysis of lead free cutting steels (Pb content: 0.1–0.3 wt%), small particles of lead metal (1–15 m m) are scattered in steel. T. Arai reported that simple repeatability of Pb-La x-rays is 0.003 wt% and RMS-difference of lead is 0.018 wt% [41]. The characteristics of segregation or inhomogeneity have been recognized as one of natural phenomena or the discoveries through experimental works. If some studies or works have been attained a success after long or hard works, possibilities of the second and the third success or discovery will be increased on the bases of research works and their process. 7.

Concluding Remarks Elemental analysis of materials may be absolute or relative. Gravimetric analysis is a typical example for the former, while x-ray fluorescence and optical emission methods represent the latter. In the case of a relative analysis, standard samples are required, which are attached to reliable or authenticated analytical values supported by absolute analyses. The values guaranteed by absolute analysis are the mean values of volume analysis, while x-ray analytical Vol. 21

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values represent surface analysis with an information depth of 5 to 50 micrometers. In order to reduce the analytical uncertainty, which originates from the differences between volume and surface analysis, homogeneous samples should be used. For the sake of reducing the effect of inhomogeneity on the sample surface, large analyzed surfaces of 3 to 10 centimeter squared are recommended. The results of the pure brass analysis clarify that small analytical errors and the close agreement between chemical and x-ray analysis parallel the quality of homogeneity of the analyzed samples. In the x-ray analysis of stainless steels it is possible to reduce the analytical error by means of an optimized matrix correction method. For the confidence of x-ray analysis it is necessary to analyze the iron concentration and to supervise the sum of x-ray analytical concentration values of the constituent elements. In order to perform high alloy analysis, it is necessary to have knowledge about x-ray and chemical analysis and of the metallurgical phenomena occurring in the process of the sample preparation. Since the analytical accuracy is defined by a combination of errors of chemical analysis, uncertainty in the measured x-ray intensity, and uncorrected matrix effects by the constituent elements, the observed accuracy can be reduced by effective matrix corrections adapted to x-ray analysis and elimination of other systematic errors may be activated. Rome was not built in a day!! Acknowledgments In commemoration of the receipt of the 2004 Birks award at the Denver x-ray conference, the writing of this paper was made possible with an invitation by Dr. Hideo Toraya, Director of X-ray Research Laboratory, Rigaku Corporation and Editor-in-Chief of Rigaku Journal, Dr. Ting C. Huang, Associate Editor-in-Chief and Emeritus of IBM Almaden Research Center at San Jose, CA, USA and Dr. Michael K. Mantler, Editor for the Rigaku Journal and Professor at the Vienna University of Technology, Austria. The author wishes to express his thanks to them. He also is indebted to many distinguished x-ray scientists for permitting to utilize a number of their reports. He thanks Dr. Takashi Yamada, Mr. Naoki Kawahara, Dr. Makoto Doi and Mr. Takashi Shoji for their assistance in the preparation of the paper.

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