ANALYTICAL CHEMISTRY, VOL. 51, NO. 14, DECEMBER 1979
2355
Major and Trace Elements Determination in Geological and Biological Samples by Energy-Dispersive X-ray Fluorescence Spectrometry Kazuko Matsumoto and Keiichiro Fuwa" Department of Chemistry, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
A rapid method is described for the determination of K, Ca, TI, Mn, Fe, Zn, and Ga in geological samples and K, Ca, Mn, Fe, Ni, Cu, and Zn in biological samples using an energy-dispersive X-ray fluorescence spectrometer. The method is based upon the linear relation between log (energy of the characteristic X-ray line) and log (fluorescent X-ray Intensity/concentration) for the elements of atomic number from 13 to 35 (AI to Br), observed when Mo radlation is employed as an excitation source and a semiconductor detector is employed. The sample preparation is simple, requiring the addition of only three Internal standard elements for calibratlon. No standard samples are necessary. Theoretical consideration for the linear relatlon together wlth the analytical results is given.
Energy-dispersive X-ray fluorescence spectrometry has been widely applied for the analyses of geological or biological samples. Although the technique is nondestructive and provides simultaneous multielement detection, tedious sample preparation and calibration procedures are often required. Usual calibration methods such as calibration with standard reference materials, standard addition, and internal standardization, require many standard samples for the correction of matrix effect. This fact does not matter when a limited number of elements in relatively simple matrix are to be determined. However, as the number of analytes increases and the matrix composition becomes more complex, it becomes more difficult and laborious to prepare a number of standard samples with appropriate matrix compositions. As a result, this tedious sample preparation largely reduces the advantage of simultaneous multielement analysis and makes the whole analytical procedure time-consuming. I n this paper, we report an analytical method which takes advantage of the characteristics of the relative excitation and detection efficiency, when using a semiconductor detector. The method is achieved by the addition of only three internal standard elements to the sample to be analyzed. This method requires only a simple preparation procedure and yet allows the determination of elements with the atomic number from 19 to 31 (K to Gal, when Mo K a and KB radiation is used as an excitation source. Satisfactory results were obtained when applied t o the analysis of standard silicate rocks and NBS SRM plant samples.
THEORY General Background. Takamatsu has recently reported t h a t a linear relation is observed between log (fluorescent intensity/concentration) and log (energy of characteristic Xray line) of the elements with the atomic number from 19 to 30 (K to Zn) in a standard silicate rock, when a semiconductor detector is employed ( I ) . Also Giauque et al. have reported the relative X-ray excitation and detection efficiencies for many elements in the case of measurements with a semiconductor detector. These efficiencies were calculated from published physical values, such as fluorescent yield, absorption 0003-2700/79/0351-2355$01.00/0
jump ratio, or detection efficiency of the dettector, and the result shows that the efficiency values vary ijmoothly as a function of atomic number; this indicates an important and interesting possibility for quantitative multielement analysis (2-4). If the system has been carefully calibrated for a given element, then an approximate result :for neighboring elements can be easily inferred from a crude plot of the 'excitation and detection efficiency-atomic number relationship. We noticed that the linear relation mentioned above is a modified expression of the function relating the relative excitation and detection efficiency with atomic number, which Giauque et al. reported, and can be derived mathematically from the latter function. The linear relation also indicates that if the line is determined by measuring the X-ray intensities of two elements with known concentrations, a quantitative multielement analysis can be achieved for the neighboring elements. The effects of the measurement and excitation conditions on the linear relation was examined in the following. Effects of Anode Material, Excitation 'Voltage, and Sample Thickness on the Linear Relation. Figure 1shows the relation between log (fluorescent Intensity/ concentration) and log (energy of characteristic X-ra,y) observed for standard silicate rock JB-1 and NBS SRM Spinach (SRM 1570). The measurement conditions were: Mo anode, Mcs filter, 40 kV, 50 HA, 500-mg powder sample, pressed into a disk with 3-em diameter. In both samples a good linear relation holds throughout the range from aluminuin to bromine, but rubidium and strontium showed a slight nlegative deviation in JI3-1 and definitely in spinach. Zirconium in JB-1 is largely displaced below the line. T h e slope of the line is nearly 5 or a little less. The effect of the excitation source was next examined. When comparing a Mo tube with a Mo filter and a W tube with a Cu filter for the measurements of standard silicate rocks, JB-1, BCR-1, and GSP-1, l i n e a relations were observed for both excitation sources as shown in Figure L!. When a W tube was employed, however, the linear relation holds only from aluminum to iron, and copper, ndnc, and g,dlium cannot be measured, because strong scattered primary L lines of tungsten overlap the characteristic lines of these elements. As the atomic number further increases, this h e a r relation cannot be observed any longer and strontium, rubidium, and zirconium are located far below the line. When a Mo tube was used, the linear relation is observed from aluminum to gallium. Rubidium and strontium show slight deviation in most of the cases, and zirconium s h o w large negative deviations for all. The slope of the line always falls, in the range from 4.5 to 5.0 and no distinct difference was observed for either excitation source. As the linear range is larger for a Mo tube, further experiments were carried out with a Mo tube. The effect of the voltage applied to the tube WLIS next examined, but no significant difference was observed throughout the voltage change from 25 to 50 kV. The experiments described above indicated that the linear relation holds only for those elements whose characteristic line energies are smaller than that of the anode element, and the fact that the linear 1979 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 51, NO. 14, DECEMBER 1979
2356
JB 1
Spinach(SRM 15701
Table 1. Definitions of Symbols Used in Equations
pri
XL -A
6L
I *
11
I +
i
t
i
Figure 1. Relationship between log (fluorescent intensity/concentration) and log (energy of analytical line) observed in geological and biological
samples BCR;I
JB-1
L:
%r+i'r log(keV)
__
____
x
0
GSP-1
i
3t
05
13 15
l o g :keV
>
Mo a r o c e , K o f i l t e r , 4C k V , 5 3 p A W a n o d e , Cu f i l t e r . 25 k V . 5 0 p A
Figure 2. Comparison of the calibration curves using the excitation sources, Mo anode with Mo filter and W anode with Cu filter
: .?.'
GSP-1
L L 2 L
cs
10 1 s
l o g (KeV) sample amount
0 0069
3s 0 5 log(*eL
0 031 g
%TTF l o 5 xei
3
1-7 g
5 IO og i e V )
L
0 23' g
Figure 3. Effect of sample thickness on the calibration curves
relation does not significantly depend on the applied voltage indicates that the excitation of the analyte lines is substantially achieved by the characteristic lines of the anode elements. As the effects of the excitation conditions have been examined above, the effect of sample thickness was next examined using a Mo anode and a Mo filter with the excitation conditions kept a t 40 kV, 50 FA. Standard silicate rock GSP-1 was measured as loose powder and the amount varied from 0.006 to 0.231 g. The result is summarized in Figure 3. The linear relation was not observed when the sample amount was 0.006 g, but as the amount increased from 0.006 to 0.147 g, the cps for each element also increased, indicating that the effective depth had not yet been reached, and the linearity of the data points improved. From 0.147 to 0.231 g, the cps did not increase and there was no improvement in the linearity of the calibration curve. Therefore, it can be said that linearity of the data points is observed when the sample is thick, that is, its depth is larger than or equal to the effective depth. Also
is the analyte line intensity. is the intensity of the primary beam with effective wavelength hpri. is the effective wavelength of the primary X-ray. is the wavelength of the measured analyte line. is the fluorescent yield of analyte A. is the fractional value of the measured analyte line L in its series. is the absorption-edge jump ratio of analyte A. is the concentration of analyte A. is the fractional value of the fluorescent X-ray that is directed toward a detector. is the mass absorption coefficient of analyte A for hpri. is the mass absorption coefficient of the matrix for h p d . is the mass absorption coefficient of the matrix for analyte line h L . is the incident angle of the primary beam. is the takeoff angle of fluorescent beam. is the atomic number of analyte A . is the average atomic number of matrix. is the energy of the characteristic X-ray line of analyte A.
considered was, whether there was any difference in the linearity when loose powder was compared with a pressed disk sample diluted with binder (dilution factor 1:l).A significant difference was not observed and subsequent experiments were carried out with a pressed disk. Theoretical Considerations for the Linear Relation. The results of the experiments mentioned above are summarized as follows: a linear relation was observed for the elements whose characteristic line energies are lower than that of the anode element. The applied voltage does not significantly affect the linearity and the deviation of each element from the line is a minimum when the sample thickness exceeds the effective depth. These facts suggest that the linear relation is observed when the excitation of the analyte lines is substantially due to the characteristic lines of the X-ray tube anode element and the contribution of the primary continuous beam to the excitation is negligibly small, compared with that of the primary characteristic lines, as is often mentioned in the linerature (5,6). A qualitative theoretical explanation for such a linear relation is attempted in the following, based on the mathematical expressions of the fluorescent X-ray intensity. The fluorescent X-ray intensity for a thick sample is given as follows (6). CAPA(hpri)CSC$ FA - 1 dR I L = ZOwAgL(1) 4~ F M ( X ~ ~ J C S C4 + PM(XL)CSC rA
+
The symbol definitions are listed in Table I. The terms, lo and dR/47r are constants and the values of gL and (rA- l ) / r A are almost constant for the elements under consideration in the present study. Although wA varies slightly from element to element, the variation is negligible, compared with that of p ' s , Accordingly, IL/CA can be approximately expressed as follows for the analyte lines in a matrix.
Introducing the Bragg-Pierce law ( f i = KZ4X3,where K is a constant, 2 is the atomic number of an absorbing element, and X is the wavelength of absorbed X-rays) into Equation 2 gives Equation 3:
(3)
ANALYTICAL CHEMISTRY, VOL. 51, NO. 14, DECEMBER 1979
In the present experiment, Xprl is Mo K a line (0.7107 A) and Xs', are large compared with Xpri. Thus A3p" is negligibly small compared with X3L for the analytes under consideration. Therefore,
Table 11. Relative Excitation and Detection Efficiency, log (ILIC,)," Calculated for Standard Silicate Rock GSP-1 (Corrected for Matrix Absorption)
(4) Removing X3prt/Z4M from the equation, since it is essentially constant, and introducing Mosley's law (A = kZ-*, where k is a constant) into Equation 4 gives
IL/CA a
Z 4 A / X 3 L a Z'OA
0:
E5A
(5)
Equation 5 can be transformed into Equation 6 by taking the logarithm of both sides. log
(IL/CA)
= 5 log
EA
+ K'
(6)
where K' is a constant. Now the linear relation is obtained. Equation 6 signifies an approximate relation between the excitation efficiency of a n analyte line and its energy, and might be called "the fifth power rule". Although Equation 6 indicates that the slope of the line is 5, it is actually slightly less than 5 in most cases. One of the reasons for this discrepancy is t h a t although we assume Aspri is negligibly small compared with X3L when obtaining Equation 4, it becomes no longer negligible as the atomic number increases and comes close to that of Mo. Accordingly, the slope of the line is a little less than 5, and rubidium and strontium are always located slightly below the line. Zirconium exhibits a serious negative deviation, because it cannot be excited by Mo K a or KP line and thus the above mentioned consideration cannot be applied to zirconium. I t is excited by continuous X-rays, whose energies are larger than t h a t of the Mo K a and KP lines and whose intensity is much smaller than that of the molybdenum characteristic line. Thus zirconium is located far below the line. Calculation of t h e Relative Excitation and Detection Efficiencies I n c l u d i n g t h e Absorption Effect. In order t o assess the effect of the approximation, done in the course of the derivation of Equation 6, on the deviations of rubidium and strontium from the line, the quantities log ( Z L / C ~were ) calculated according to the right side of Equation 7 and were compared with the measured values.
The values of wA were based on those in ref. 7 and absorption edge jump ratios, mass-absorption coefficients, and fractional values were taken from the literature ref. 8 and 9. The calculation was performed for USGS standard silicate rock GSP2, assuming that the matrix composition is C 45%, 0 24.2%, Si 15.7%,A1 4.070, and Fe 1.5%. Although the result shows a good agreement for the elements from potassium to gallium, measured values for rubidium and strontium are still smaller than the calculated ones. For the explanation of this discrepancy, the detection efficiency of a semiconductor detector has to be taken into consideration. For the radiation between 3 and 15 eV striking a 5-mm thick silicon detector with a 7.5-pm thick beryllium window, the detection efficiency is unity ( 1 , 6). However, the total detection efficiency is also affected by the geometry of the detector and collimator employed for the analysis. For analysis without a fine collimator placed in front of the detector, a fraction of the radiation strikes the detector at an angle of less than 90' and impinges upon the detector near the periphery of the sensitive region. This reduces the detector efficiency to 0.79,0.90, and 0.98 for Sr K a (14.14 keV), As K a (10.35 keV), and Cu K a (8.04 keV) X-rays, respectively (2).
2357
line
calculated
measured
K Ka, Ca K a , Ti K a , Mn K a , Fe K a , CU K a , Zn K O , Ga K a , Rb Ka, Sr K a ,
0.559 0.805 1.221 1.795 1.989 2.418 2.545 2.652 3.176 3.245
0.537 0.796 1.252 1.696 1.989 2.446 2.600 2.713 3.179 3.232
a The values are normalized b y setting the calculated value for Fe K a ,equal to the measured value for Fe K Q , .
The second factor affecting the values of log (ZL/CA)for rubidium and strontium is the contribution of the primary continuous X-rays to the excitation. Although we a s u m e that the elements are excited by approximately monochromatic Mo K a and KP lines in deriving the log (IL/(;*) - log ( E A ) linear relation, relatively strong continuous radiation actually exists which consists of energies just below the Mo K a line and is not eliminated by a Mo filter. Although this radiation contributes to the excitation of the elements with lower energy mass-absorption edge to a certain extent, rubidium and strontium are not excited by it, because their K absorption edge energies are higher than this portion of the radiation. As a result, Giauque e t al. reported the mass absorption coefficients for strontium and bromine are reduced by 9.7 and 1.8%, respectively ( 2 ) . Taking all these effects into account, the quantities log (IL/CA) are corrected, assuming, by interpolation, that the geometrical factor is 0.81 and 0.79 for R b K a and Sr K a , respectively, and the effect of the continuous X-ray for rubidium and strontium excitation is 9.0% and 9.7%, respectively. The results, shown in Table 11, show a good agreement between the calculated and measured values. CALIBRATION METHOD A rapid analytical method for the determination of major and trace elements in geological and biological samples has been developed utilizing the linear relation. This method requires the addition of a t least two appropriate internal standard elements. The linear line is determined by adding two elements with known concentration. The slope and intersection of the line are calculated as follows:
A=
B=
1%
(IL/CA)l
log ( I L l C A h
1%
-
log
(IL/CA)l
(EA12 -
1%
(EA)1
1% (Ed2 - 1% 1% ( E A 1 2 - 1%
(IL/CA)2
log
(8) (EA)1
(9)
(EA11
where A and B are the slope and the intersection of the line, respectively, and the subscripts 1 and 2 refer to the elements added. Once the line is determined, the concentration of the neighboring element i is determined by Equation 10.
where Ci is the concentration of the analyte. EXPERIMENTAL To illustrate the capability of the method, biological and geological standard samples were analyzed. For the analyses of NBS SRM,Orchard Leaves, Tomato Leaves, and Spinach, NaCl and GeOs were added at the ca. 0.1% level for the determination of elements from potassium to zinc and the linear lines were calculated using the concentration and X-ray intensities of chlorine
2358
ANALYTICAL CHEMISTRY, VOL. 51, NO. 14, DECEMBER 1979
Table IV. Analyses of Standard Rocks, GSP-1 and G - 2
Table 111. Analyses of NBS Plant SRMs
GSP-1, ppm
Orchard Leaves (SRM 1571), ppm this work internal internal standard, certified value Si, Cr, Se Sc, Ni, Ge K
18100 t 790
Ca Mn
21000 i 850 110 i 9 3352 1 4
Fe
cu Zn K
Ca Mn Fe cu Zn K Ca Mn Fe Ni cu Zn
13.7 24.7
i i
1.3 2.2
16600 i 21100 i 85 i 338 i
780
14700
850
20900 I 91i 300 I 12i 25i
10
16
25.3 i 2.5
z
Tomato Leaves (SRM 1573), ppm 47900 T 600 51600 i 580 44600 i 26500 t 720 29200 i 7 5 0 30000 i 2231 7 266 i 8 238 + 623 I10 831 i 10 690: 12.2 i 1 . 3 11: 72.8 * 2.0 78.0 t 2 . 1
300 300 4
20 1
3 300 300 7
25 1
~~
Spinach (SRM 157O), ppm 40400 I 620 46500 i 500 35600 -. 300 11900 t 860 14OOO i 370 13500 I 300 184 i i o 165i 3 165 1 6 525 t 11 597 i 6 550 ILO 5.4
i
[GI
1.0
12.6 t 1 . 4 52.9 i 2.2
60.1 t 2.0
121 2 50: 2
and germanium. However, analytically satisfactory results were not obtained from these calibration lines, so in the second attempt, three elements were added. Two sets of three elements were tested; one set was silicon, chromium, and selenium, and the other set was scandium, nickel, and germanium. All the elements except selenium were added as finely powdered oxides to 0.5 g of the sample. For selenium, NazSeOl was added. The resultant concentration for each element was Si 5 % , Cr 0.170, Se 0.07%, Sc 0.2%, Ni 0.1%, and Ge 0.1%. The sample was mixed for 30 min in a polystyrene container with a mixer, No. 8000, Spex Industries, and then pressed at 2800 kg/cm2 into a disk with a diameter of 3 cm. For the analyses of USGS standard silicate rocks, GSP-1 and G-2, scandium, nickel, and germanium were added as oxides together with the binder (Somer-blend, Somer Lab. Inc.), with which the samples were diluted 2 times. The concentration of each element was Sc 0.0870, Ni 0.08%, and Ge 0.0870,respectively. The apparatus used for measurements was a TEFA 6110 system, Ortec Inc., with a Mo anode and a Mo filter. The exciting and fluorescent beams both made angles of about 45' with the sample plane. The X-ray tube was operated at 40 kV unless otherwise stated and the anode current was adjusted for each sample so that the total counting rate did not exceed lo4 cps. X-ray spectra were obtained using an 28 mm2 Si(Li) detector having 160-eV resolution fwhm a t 5.9 keV. Data accumulation time was usually 2000 s, and the spectra were analyzed on a PDP 11/05 computer using a peak fitting program, which unfolds the overlapping peaks, assuming the X-ray peak shape is pseudo Gaussian. K q line intensities were used throughout the analytical calculations.
RESULTS AND DISCUSSION T h e accuracy of the present method critically depends on the selection and the concentration of the internal standard elements added. Elements chosen should not be contained in the sample or, if any, the amount must be negligibly small compared with the added amount. Moreover, they should be selected so that the error of the linear line is a minimum for the energy range of the analyte lines. In other words, the energies of the added elements should be appropriately separated from each other for the energy range of interest, for if they lie too close to each other, compared with the whole range of analyte line energies, the error of the line would be large at both ends. Furthermore, the added elements should be selected so t h a t it might not significantly affect the total
this work, internal standard, Sc, Ni, Ge
-
recommended valuea
G-2, ppm
this work, internal standard, Sc, Ni, Ge
48800~720 45900 3 7 1 0 0 t 15100 810 13900 13800 t 3 3 5 0 t 150 3960 2460 t (330) Mn 2261 15 253 t Fe 34200 i 1100 30300 18800 i Zn 102i 7 98 104t (22) 20.4 i Ga 16.31 10.0 K Ca Ti
+
recommended valuen
730 37400 790 (13400) 160 2990 13 (260) 900 18500 7 85 22.9 9.0
The values in parentheses are the average values of m a n y reports and are not recommended ones (10 ),
matrix composition. Serious absorption or enhancement effects caused by the over-addition of the internal elements must be avoided. In the first attempt for this method, chlorine and germanium were added to standard silicate rocks for the determination of elements from aluminum to gallium. However, satisfactory results were not obtained. This is probably due to the particle size effect for chlorine X-ray line, and in order to avoid this effect, more complicated sample preparation technique, such as borate fusion for silicate rocks, is required. However, such sample preparation results in several times dilution of the sample, thus causing several trace elements not-detectable. Moreover, in the present study, emphasis is placed on the simplicity of the sample preparation and rapidity of the analysis; thus it was decided not t o change the sample preparation procedure but t o add three elements t o compensate for the possible particle size effect. Two sets of experiments were carried out, one adding scandium, nickel, and germanium, and the other adding silicon, chromium, and selenium. The results are summarized in Tables I11 and IV. The results seem better when silicon, chromium, and selenium are added as internal standards. In the case of scandium, nickel, and germanium, unfolding of the overlapped copper K a line and nickel KP line was not accurate enough, because of the strong intensity of nickel KP line compared with copper K a intensity, and thus copper could not be determined. For the analysis of silicate rocks, silicon can not be used, for it is originally contained in a large amount, thus scandium, nickel, and germanium were added. The results for the elements listed in Table I11 and IV are in good agreement with certified or recommended values. In conclusion, although the present method cannot correct for the enhancement effect of particle size effect, it provides easy correction for moderate absorption effects with minimum sample preparation. Rapid determination of the elements from potassium to gallium in biological or geological samples is possible with the accuracy of 10% or less for most elements.
LITERATURE CITED (1) T. Takamatsu, BunsekiKagaku, 27, 193 (1978). (2) . , R. D. Giauoue. F. S. Gouldina, J. M. Jaklevic, and R. H. Pehl, Anal. Chem., 45,' 671 (1973). (3) R. D. Giauque, R. B. Garrett, L. Y. Gxh, J. M. Jaklevic, and D. F. Malone, Adv. X-Ray Anal., 18, 305 (1976). 141 J. > , - M. Jaklevic and F. S.Gouldina. "X-Rav SDectrometrv". H. K. Heralotz and L: S. Birks, Eds., Vol. 2, i a r c e l Dekker, New York, 1978. (5) J. V. Gilfrich and L. S. Birks, Anal. Chem., 40, 1077 (1968). (6) E. P. Berth, "Principles and Practice of X-Ray Spectrometric Analysis", Plenum Press, New York, 1975. (7) R. W. Fink, R. C. Jopson. N. Mack, and C. D. Swift, Rev. Mod. Phys., 38, 513 (1966). (8) W. H. McMaster. N. K. Dei Grande, J. H. Mellett. and J. H. Hubbell, "Compilation of X-ray Cross Sections", University of California Lawrence Livermore Laboratory Rept. UCRL-50174, Section 11, Revision 1 (1969). (9) J. S. Hansen, H. U. Freund, and R. W. Fink, Nucl. Phys. A , 142, 604 (1970). (10) F. J. Flanagan, Geochim. Cosmochim. Acta, 37, 1189 (1973).
-
RECEIVEDfor review May 3, 1979. Accepted August 28, 1979.
