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
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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
28
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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29
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
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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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35
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
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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.
37
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The Rigaku Journal