- Email: [email protected]
Determination of cadmium in potassium-rich samples by combining PIXE and RBS measurements
NIMI B
Nuclear Instruments and Methods in Physics Research B 82 (1993) 579-583 North-Holland
Determination of cadmium in potassium-rich PIXE and RBS measurements
Beam Interactions with Materials &Atoms
samples by combining
P. Miiller, A. Witzmann and S. Schippel Institut fiir Festkiirperphysik, D-07743 Jena, Germany
F&d&h-Schiller-Universiriit
Jena, Physik.-Astron.-Technikwiss.
Fakultiit, Max- Wien-Platz I,
Received 4 February 1993
enables the deconvolution of the interference between the Cd-L- and the in the ppm region. An evaluation of the experimental data using the results of these measurements is given. The scattering cross sections for protons on nitrogen, oxygen, silicon and potassium were determined in the energy range between 1.0 and 1.8 MeV by means of calibration standards formed by ion implantation in order to reduce the experimental error of the RBS investigation. A comparison with alternative methods confirms the accuracy and sensitivity of our measurements. The combination of PIXE and RBS measurements
K-K,-line for the quantitative analysis of Cd-concentration
1. Introduction The toxicity of cadmium in the environment is well known, but since it also has useful properties, e.g. in optical glasses, exact knowledge of the amount of this element in samples is of current interest in several fields of science. The PIXE method provides the opportunity to determine the concentration of trace elements in a fast and nondestructive way. Normally the L-lines of Cd are used for the quantitative determination of cadmium because the L-shell ionization cross section exceeds that of the K-shell by a factor of 10’ [l]. In this case, the detection limit is expected to reach the range of 1 ppm [2]. However, if the samples contain potassium, e.g. as in glass or organic substances, the interference between the Cd-La-line (3.13 keV) and the K-Km-line (3.31 keV) substantially deteriorates the detection limit for Cd. A deconvolution of these two lines is only possible if the content of potassium is well known from supplementary measurements. For most samples the K concentration can be determined by RBS. The application of RBS has the advantage that PIXE and RBS investigations, with similar accessible depths can be carried out on the same part of the sample, thus, preventing effects from inhomogeneities of the specimen. However, when using proton backscattering the cross sec-
Correspondence to: P. Miiller, Institut fur Festkiirperphysik, Friedrich-Schiller-Universitlt Jena, Physik.-Astron.-Technikwis. Fakultlt, Max-Wien-Platz 1, Jena D-07743, Germany. 0168-583X/93/$06.00
tions of light elements deviate considerably from the Rutherford cross section because of nuclear resonance scattering and nuclear potential scattering [5]. Therefore, the quantitative analysis of proton backscattering spectra requires reliable data on backscattering cross sections especially of the light elements (C, N, 0, Si). Proton backscattering at energies exceeding 1.4 MeV has been reviewed most recently by Rauhala [3-51. A fit of experimental data to analytical functions is presented by Knox et al. [6]. Although the fitted functions are quite more reliable than the Rutherford cross sections their uncertainty can be as large as 25% [6]. In order to reduce the experimental error we determined the scattering cross sections of N, 0, Si and K by means of calibration standards formed by ion implantation. The first part of this paper presents a comparison of the cross sections for scattering of protons on nitrogen, oxygen, silicon and potassium found by our measurements with the results of Rauhala and the Rutherford cross sections. These cross sections are used in the second part of the paper to calculate the matrix composition of the samples and finally the content of cadmium. 2. Experimental The calibration standards were prepared by ion implantation of N, 0, Si and K ions in glass carbon substrates. The samples were implanted using the commercial ion implanter MACIEK 325. The implantation conditions are given in table 1. After implantation a
0 1993 - Elsevier Science Publishers B.V. All rights reserved
P. Miiller et al. / PIXE and RBS determination of Cd
580
Table 1 Implantation energy and dose of the implanted elements and area1 density of the gold layer Sample
Ion
Energy keV1
Dose [cm-‘]
Area1 density (gold) [cm-*]
1 2 3 4
N+ Of Si+ K+
50 100 60 80
1 x 10” 1 x 10” 5x10t6 2x10’6
4.2 ~10’~ 6.2 x 10” 5.15x10’5 5.4 x10’4
thin gold layer was evaporated. This layer was used as a reference because the scattering cross section of protons from gold is known to obey the Rutherford formula
(!E)“;(Y.& (cos 0 + [l - (M,/M,)’
sir?@] l”)*
,. sin40[
1 - (M1/M2)’
sin201 1’2
’ (1)
with Z,, M, and E, being the atomic number, mass and energy of the projectile (in this case H+), Z, and M, the atomic number and mass of the target atom (Au). The unknown scattering cross section (da/da), of the implanted elements can be determined by
(gj1(E,4E)=-$ $f x
implanted planar silicon (PIPS) detector (25 mm2 active area, 100 pm sensitive depth, energy resolution 12 keV) was employed. The detection angle of the X-rays for the PIXE measurements was 90” and the incidem angle of the proton beam and the exit angle of the X-rays were both 45”. A 43 Km thick Mylar window was used as the exit window for the X-rays out of the scattering chamber. A Si(Li)-detector (thickness 6 mm) with a 0.1 mil Be-window detected the X-rays. The energy resolution of this detector is 170 eV. The organic samples were prepared by growing alga spirodela polyrhiza on a nutritive solution which contained Cd(NO,),. The glass samples were homogeneously doped with Cd in the glass melt.
3. Analytical method The determination of the Cd-concentration in a sample using the Cd-L-line is only possible if no K is present. Fig. 1 represents the problem of line interference between the Cd-L-line and the K-Km-line, if a Si(Li)-detector with a typical energy resolution of 150 to 200 eV is used. Figs. la and lb show the K-K-line duplet and the Cd-L-line with the corresponding peak areas A, and A,,, respectively. These figures represent samples which contain only K or Cd in a matrix of light elements. Fig. lc shows the problem of overlapping peaks of K and Cd. The total peak area A, is
(gJR(El), AU
(2)
where (Nz), is the number of atoms of element x per cm* (in this case, the implanted dose), A,, and A, the signal areas of gold and the implanted element, respectively. The energy shift AE accounts for the energy loss of the projectile ions when backscattered from atoms of the implanted profile (= 15 keV). Each of the samples was first investigated by 4He backscattering (1000-1700 keV) to determine accurately the implanted dose and the area1 density of the gold layer. Afterwards, the proton backscattering cross sections were determined in the energy region between 1000 and 1800 keV from the corresponding proton spectra using formula (2). The measurements for the cross section determination were carried out with a backscattering angle of 0 = 170”. The incident angle of the proton to the surface normal and the exit angle were both 5”. The energy calibration of the accelerator was performed with the *‘Al(p, y)28Si resonances at E, = 991.9 and 1392 keV. The vacuum in the scattering chamber was better than 7 x lo-’ Pa. A passivated
I
F
d
FB
6
Energy(keV)
Fig. 1. Typical spectra obtained with a Si(Li)-detector from samples with a light matrix containing potassium and cadmium ((a) only potassium, (b) only cadmium, (cl potassium and cadmium, (d) potassium, calcium, and cadmium).
P. Miller et al. / PIXE and RBS determinationof Cd
then given by A, =A,
581
Y-K.+Cd-L
i-A,,.
(3)
If the potassium concentration in the sample is well known, from RBS measurements or other, and the experimental conditions of the PIXE measurements are fixed, then it is possible to calculate the peak area A, from A,=nC,
[Nz]
A0 W,,
(4)
with channel
Xexp
(
-px(E)-
+ &(Ex) T(Ex)
ws ff
cos p
1
dE
c j-E-g
SF,(E)
dE.
i
(5) In these equations n is the number of incident particles, C, the concentration of potassium in the sample with an area1 density of [N.], AR is the solid angle of the detector and W, describes an effective X-ray production cross section [7,8]. The first part of W, describes the production of X-rays by the incoming protons and the second part by the secondary fluorescence. &(Ex) and T(E,) are the sensitivity of the detector and the transmission of any absorber foil at the X-ray energy E,, respectively. E, is the energy of the incident ions and E, is the energy of the ions which are leaving the backside of the target. For practical applications E, is approximated by E, = E, for thin targets and E, = 0 for thick targets, were no ions are transmitted. The incident angle of the proton beam is (Yand p is the exit angle of the X-rays. The function SF;:(E) is the outgoing intensity of the X-radiation of potassium in the direction of the detection p, excited in the total volume of the sample by the X-radiation of the element i in the depth x(E). For a detailed description of SF,(E) see for example refs. [7,8]. Reality, however, is much more complicated. Usually, potassium is accompanied by calcium and neither the PIXE nor the backscattering spectrum exhibit any peak which results from K or Ca alone (see figs. 2a and 2b). It is not possible to separate K and Ca by protonRBS in the 2 MeV range and therefore the result of the RBS investigation is the sum of the concentrations of these two elements CKtCa. In the PIXE spectrum, there is not only a line interference between the Cd-Land the K-K,-lines, but also between Ca-K, and K-K,. From the surface height YK+ca of the backscattering signals due to potassium and calcium the sum
channel
Fig. 2. (a) PIXE- and (b) RBS-spectra of the sample “alga spirodela polyrhiza” No. 1, including the markers of the detected elements.
concentration CK+ca can be calculated in the surface energy approximation using eq. (6) (see e.g. ref. [9]), Y K+Ca= nA0’
(6) where Ech is the energy width of one channel in the RBS spectrum. The peak area AF@+Ca in the PIXE spectrum is given using eqs. (41 and (51 by A++Ca
= n
[Nz]Aa’[
C, WKB + Cc, W,,,]
.
(7)
With these two equations it is possible to determine the concentration of potassium and calcium, respectively. The concentration of cadmium can then be calculated from the peak area of the overlapping Cd-Land K-Km-line. If A, is the total peak area of the (K + Cdl-lines, then AA, = & is the statistical error of this signal. For a typical spectrum from organic or glass materials measured under standard conditions (1.7 MeV H+, 100 ~.LCcharge, 1 msr solid angle) the peak area has a value of about l-5 X lo6 counts. The statistical error AA, is then nearly l-2 x 103. Using the precondition that an element is detectable if its peak area A is three times greater than the statistical
P. Miilleret al. / PIXE and RBS determinationof Cd
582
Table 2 Detection limits of cadmium in samples containing different concentrations of potassium, measured under standard conditions (1.7 MeV H+, 100 uC charge) K-concentration
[%I
Detection limit Cd-concentration
4. Experimental
[ppml
4.1. Proton scattering cross sections
110 35.5 11 3.5 1
10 1 0.1 0.01 0.001
error, which is commonly applied for the investigations of trace elements, the detection level of this element can be calculated. For the overlapping peaks in our samples we consider Cd to be detectable if the relation A,, 2 3K is fulfilled. Table 2 gives an overview of the levels for different potassium concentrations calculated for our standard conditions. These concentration I
limits are significantly lower than the detection when using the Cd-KU-line (1000 ppm).
limit
results
The scattering cross sections of nitrogen, oxygen, silicon and potassium determined by our measurements are presented in fig. 3. For comparison, the data published by Rauhala [3-5] and the Rutherford cross sections calculated by eq. (1) are added to fig. 3. A considerable deviation of the experimentally determined cross sections from the Rutherford cross section for the light elements (N, 0, Si) is obvious. The scattering cross sections for proton scattering on nitrogen in the energy region of 1150-1400 keV (between the resonances) is about 2-3 times the Rutherford cross section. The increase of the oxygen scattering cross section ranges between 1.6 and 3.7. As expected, the
I
-I
present Rrmhala
work
8.170’ e- 170.
t
1 "Si(p,plSi" 300
-
x-a
.--. .-’
presentwork e-170' RcuWa e- 170. Rutherfordcrest section e-170'
4 It..,. I
A
-‘-.-,_, . j
ol
( ’
1600
14W
1200
0
1800
I 1040
1200
16W
?A00
1600
:J
Proton energy IkeV)
x_.,presentvork e.17o' .--.Rwhdo e.170° .-. Rutherfard crossSKtiOn
BKIp,plK39
i\
R-170’
'\
x-x
presentwork e-170'
.-.
Rutherfudcr0.ssstion e.770'
'Y '\ 'Y
‘Y, ‘1
‘1 ‘L.
.‘..
-.-.
-.-.
100 -
-.-.__
tI lW4
1204
1100 Proton
energy
1603 (keVI
18W
d 0
’ mo
1200
144
16M
1600
Proton energyIkeVI
Fig. 3. Proton scattering cross sections of nitrogen (a), oxygen (b), silicon (c) and potassium cd), for comparison, data published by Rauhala et al. [3,4] and the Rutherford cross sections calculated by eq. (1) are added.
P. Miller et al. / PIXE and RBS determination of Cd
Table 3 Cadmium content in different samples (alga spirodela polyrhiza and glass) determined using the described procedure, compared with XRF-measurement results Sample No.
Cd-concentration
Our results
[ppm]
Reference value
Alga spirodela polyrhiza 1 2200+ 100 2 5.50+ 150 3 370+_150>
1800&-400 -Cd-K,-line no Cd-K,-line determined
Glass 1 2 3 4
2500 1600 XRF2700 measurements 900I
2400+ 100 1800+ 100 2800f 100 1050+ 100
583
The potassium, calcium and cadmium concentrations were calculated using the procedure described in section 3. The amounts of potassium and calcium are 5.75 at.% and 2.25 at.%, respectively. The Cd-concentration in this sample was calculated using the procedure described above and also from the Cd-K,peak area. We determined a content of (1800 + 400) ppm with the help of the Cd-Km-peak and a content of (2200 k 100) ppm using our procedure. Table 3 gives an overview of the Cd-contents in different samples obtained using our method. For the glass samples our measurements were compared with XRF-measurements. The comparison in table 3 shows that the results of both methods agree quite well.
5. Summary influence of nuclear effects vanishes for elements with higher atomic number and the Rutherford cross section appears to be valid for proton scattering on potassium (see fig. 3d). Also the silicon cross section below about 1400 keV is well described by the Rutherford theory. Our results for nitrogen and silicon are in good agreement with the data from Rauhala. In the case of nitrogen an additional resonance has been found at a proton energy of u 1090 keV. The oxygen cross sections from our measurements are about 10% higher than those of Rauhala [5]. 4.2. Cadmium
determination
Fig. 2 shows the typical RBS- and PIXE-spectra of the sample “alga spirodela polyrhiza”. In the RBSspectrum the elements carbon, oxygen, potassium and calcium are clearly detectable. Charge dependent measurements showed an increase of the spectrum height proportional to the collected charge. This proves that no dynamic changes occurred in the samples during the measurement. Sample No. 1 consists of 55 at.% carbon, 37 at.% oxygen and 8 at.% potassium and calcium, calculated using the scattering cross sections given in fig. 3. The PIXE-spectrum in fig. 2a shows that the sample additionally contains the following trace elements: phosphorus, sulphur, chlorine, potassium, calcium, copper, zinc, cadmium, selenium and strontium. The concentrations of Se and Sr are close to the detection level. The corresponding concentrations were calculated using the program GUPIX, developed by Campbell and Maxwell [lo]. The amounts of these elements in sample No. 1 are given as an example in the following: P 70 ppm, S 30 ppm, Cl 750 ppm, Cu 930 ppm, Zn 250 ppm, Sr 20 ppm and Se 200 ppm.
We have shown that it is possible to determine the Cd content of K containing organic and glass samples even at very low concentrations (3 10 ppm). The concentrations of K, Ca and Cd were determined by combining RBS- and PIXE-measurements using the calculation procedure for separating the K- and Ca-signals in the spectra. Moreover, the proton scattering cross sections of light elements were determined. The cross sections differ from the Rutherford formula for C, N, 0 and Si. For K no deviations occurred in the energy range of 0.9-1.8 MeV. The values determined are in good agreement with the results of Rauhala et al. [3-51.
References Dl D.D. Cohen, M. Harrigan, At. Data Nuclear Data Tables 33 (1985) 255. 121 S.A.E. Johansson and J.L. Campbell, PIXE, a Novel Technique for Elemental Analysis (Wiley, Chichester, 1988). [31 E. Rauhala, Nucl. Instr. and Meth. B40/41 (1989) 790. [41 E. Rauhala, Nucl. Instr. and Meth. B12 (1985) 447. 151 M. Luomajarvi, E. Rauhala and M. Hautala, Nucl. Instr. and Meth. B9 (1985) 255. 161 J.M. Knox, R.J. McLead, D.R. Mayo and X. Qian, Nucl. Instr. and Meth. B45 (1990) 25. t71 L. Zolnai and Gy. Szab6, Nucl. Instr. and Meth. B34 (1988) 118. [8] Gy. Szab6 and L. Zolnai, Nucl. Instr. and Meth. B36 (1989) 88. [9] G. Giitz and K. GIrtner, High Energy Ion Beam Analysis of Solids (Akademie-Verlag, Berlin, 1988). [lo] J.A. Maxwell, J.L. Campbell and W.J. Teesdale, Nucl. Instr. and Meth. B43 (1989) 218.
Nuclear Instruments and Methods in Physics Research B 82 (1993) 579-583 North-Holland
Determination of cadmium in potassium-rich PIXE and RBS measurements
Beam Interactions with Materials &Atoms
samples by combining
P. Miiller, A. Witzmann and S. Schippel Institut fiir Festkiirperphysik, D-07743 Jena, Germany
F&d&h-Schiller-Universiriit
Jena, Physik.-Astron.-Technikwiss.
Fakultiit, Max- Wien-Platz I,
Received 4 February 1993
enables the deconvolution of the interference between the Cd-L- and the in the ppm region. An evaluation of the experimental data using the results of these measurements is given. The scattering cross sections for protons on nitrogen, oxygen, silicon and potassium were determined in the energy range between 1.0 and 1.8 MeV by means of calibration standards formed by ion implantation in order to reduce the experimental error of the RBS investigation. A comparison with alternative methods confirms the accuracy and sensitivity of our measurements. The combination of PIXE and RBS measurements
K-K,-line for the quantitative analysis of Cd-concentration
1. Introduction The toxicity of cadmium in the environment is well known, but since it also has useful properties, e.g. in optical glasses, exact knowledge of the amount of this element in samples is of current interest in several fields of science. The PIXE method provides the opportunity to determine the concentration of trace elements in a fast and nondestructive way. Normally the L-lines of Cd are used for the quantitative determination of cadmium because the L-shell ionization cross section exceeds that of the K-shell by a factor of 10’ [l]. In this case, the detection limit is expected to reach the range of 1 ppm [2]. However, if the samples contain potassium, e.g. as in glass or organic substances, the interference between the Cd-La-line (3.13 keV) and the K-Km-line (3.31 keV) substantially deteriorates the detection limit for Cd. A deconvolution of these two lines is only possible if the content of potassium is well known from supplementary measurements. For most samples the K concentration can be determined by RBS. The application of RBS has the advantage that PIXE and RBS investigations, with similar accessible depths can be carried out on the same part of the sample, thus, preventing effects from inhomogeneities of the specimen. However, when using proton backscattering the cross sec-
Correspondence to: P. Miiller, Institut fur Festkiirperphysik, Friedrich-Schiller-Universitlt Jena, Physik.-Astron.-Technikwis. Fakultlt, Max-Wien-Platz 1, Jena D-07743, Germany. 0168-583X/93/$06.00
tions of light elements deviate considerably from the Rutherford cross section because of nuclear resonance scattering and nuclear potential scattering [5]. Therefore, the quantitative analysis of proton backscattering spectra requires reliable data on backscattering cross sections especially of the light elements (C, N, 0, Si). Proton backscattering at energies exceeding 1.4 MeV has been reviewed most recently by Rauhala [3-51. A fit of experimental data to analytical functions is presented by Knox et al. [6]. Although the fitted functions are quite more reliable than the Rutherford cross sections their uncertainty can be as large as 25% [6]. In order to reduce the experimental error we determined the scattering cross sections of N, 0, Si and K by means of calibration standards formed by ion implantation. The first part of this paper presents a comparison of the cross sections for scattering of protons on nitrogen, oxygen, silicon and potassium found by our measurements with the results of Rauhala and the Rutherford cross sections. These cross sections are used in the second part of the paper to calculate the matrix composition of the samples and finally the content of cadmium. 2. Experimental The calibration standards were prepared by ion implantation of N, 0, Si and K ions in glass carbon substrates. The samples were implanted using the commercial ion implanter MACIEK 325. The implantation conditions are given in table 1. After implantation a
0 1993 - Elsevier Science Publishers B.V. All rights reserved
P. Miiller et al. / PIXE and RBS determination of Cd
580
Table 1 Implantation energy and dose of the implanted elements and area1 density of the gold layer Sample
Ion
Energy keV1
Dose [cm-‘]
Area1 density (gold) [cm-*]
1 2 3 4
N+ Of Si+ K+
50 100 60 80
1 x 10” 1 x 10” 5x10t6 2x10’6
4.2 ~10’~ 6.2 x 10” 5.15x10’5 5.4 x10’4
thin gold layer was evaporated. This layer was used as a reference because the scattering cross section of protons from gold is known to obey the Rutherford formula
(!E)“;(Y.& (cos 0 + [l - (M,/M,)’
sir?@] l”)*
,. sin40[
1 - (M1/M2)’
sin201 1’2
’ (1)
with Z,, M, and E, being the atomic number, mass and energy of the projectile (in this case H+), Z, and M, the atomic number and mass of the target atom (Au). The unknown scattering cross section (da/da), of the implanted elements can be determined by
(gj1(E,4E)=-$ $f x
implanted planar silicon (PIPS) detector (25 mm2 active area, 100 pm sensitive depth, energy resolution 12 keV) was employed. The detection angle of the X-rays for the PIXE measurements was 90” and the incidem angle of the proton beam and the exit angle of the X-rays were both 45”. A 43 Km thick Mylar window was used as the exit window for the X-rays out of the scattering chamber. A Si(Li)-detector (thickness 6 mm) with a 0.1 mil Be-window detected the X-rays. The energy resolution of this detector is 170 eV. The organic samples were prepared by growing alga spirodela polyrhiza on a nutritive solution which contained Cd(NO,),. The glass samples were homogeneously doped with Cd in the glass melt.
3. Analytical method The determination of the Cd-concentration in a sample using the Cd-L-line is only possible if no K is present. Fig. 1 represents the problem of line interference between the Cd-L-line and the K-Km-line, if a Si(Li)-detector with a typical energy resolution of 150 to 200 eV is used. Figs. la and lb show the K-K-line duplet and the Cd-L-line with the corresponding peak areas A, and A,,, respectively. These figures represent samples which contain only K or Cd in a matrix of light elements. Fig. lc shows the problem of overlapping peaks of K and Cd. The total peak area A, is
(gJR(El), AU
(2)
where (Nz), is the number of atoms of element x per cm* (in this case, the implanted dose), A,, and A, the signal areas of gold and the implanted element, respectively. The energy shift AE accounts for the energy loss of the projectile ions when backscattered from atoms of the implanted profile (= 15 keV). Each of the samples was first investigated by 4He backscattering (1000-1700 keV) to determine accurately the implanted dose and the area1 density of the gold layer. Afterwards, the proton backscattering cross sections were determined in the energy region between 1000 and 1800 keV from the corresponding proton spectra using formula (2). The measurements for the cross section determination were carried out with a backscattering angle of 0 = 170”. The incident angle of the proton to the surface normal and the exit angle were both 5”. The energy calibration of the accelerator was performed with the *‘Al(p, y)28Si resonances at E, = 991.9 and 1392 keV. The vacuum in the scattering chamber was better than 7 x lo-’ Pa. A passivated
I
F
d
FB
6
Energy(keV)
Fig. 1. Typical spectra obtained with a Si(Li)-detector from samples with a light matrix containing potassium and cadmium ((a) only potassium, (b) only cadmium, (cl potassium and cadmium, (d) potassium, calcium, and cadmium).
P. Miller et al. / PIXE and RBS determinationof Cd
then given by A, =A,
581
Y-K.+Cd-L
i-A,,.
(3)
If the potassium concentration in the sample is well known, from RBS measurements or other, and the experimental conditions of the PIXE measurements are fixed, then it is possible to calculate the peak area A, from A,=nC,
[Nz]
A0 W,,
(4)
with channel
Xexp
(
-px(E)-
+ &(Ex) T(Ex)
ws ff
cos p
1
dE
c j-E-g
SF,(E)
dE.
i
(5) In these equations n is the number of incident particles, C, the concentration of potassium in the sample with an area1 density of [N.], AR is the solid angle of the detector and W, describes an effective X-ray production cross section [7,8]. The first part of W, describes the production of X-rays by the incoming protons and the second part by the secondary fluorescence. &(Ex) and T(E,) are the sensitivity of the detector and the transmission of any absorber foil at the X-ray energy E,, respectively. E, is the energy of the incident ions and E, is the energy of the ions which are leaving the backside of the target. For practical applications E, is approximated by E, = E, for thin targets and E, = 0 for thick targets, were no ions are transmitted. The incident angle of the proton beam is (Yand p is the exit angle of the X-rays. The function SF;:(E) is the outgoing intensity of the X-radiation of potassium in the direction of the detection p, excited in the total volume of the sample by the X-radiation of the element i in the depth x(E). For a detailed description of SF,(E) see for example refs. [7,8]. Reality, however, is much more complicated. Usually, potassium is accompanied by calcium and neither the PIXE nor the backscattering spectrum exhibit any peak which results from K or Ca alone (see figs. 2a and 2b). It is not possible to separate K and Ca by protonRBS in the 2 MeV range and therefore the result of the RBS investigation is the sum of the concentrations of these two elements CKtCa. In the PIXE spectrum, there is not only a line interference between the Cd-Land the K-K,-lines, but also between Ca-K, and K-K,. From the surface height YK+ca of the backscattering signals due to potassium and calcium the sum
channel
Fig. 2. (a) PIXE- and (b) RBS-spectra of the sample “alga spirodela polyrhiza” No. 1, including the markers of the detected elements.
concentration CK+ca can be calculated in the surface energy approximation using eq. (6) (see e.g. ref. [9]), Y K+Ca= nA0’
(6) where Ech is the energy width of one channel in the RBS spectrum. The peak area AF@+Ca in the PIXE spectrum is given using eqs. (41 and (51 by A++Ca
= n
[Nz]Aa’[
C, WKB + Cc, W,,,]
.
(7)
With these two equations it is possible to determine the concentration of potassium and calcium, respectively. The concentration of cadmium can then be calculated from the peak area of the overlapping Cd-Land K-Km-line. If A, is the total peak area of the (K + Cdl-lines, then AA, = & is the statistical error of this signal. For a typical spectrum from organic or glass materials measured under standard conditions (1.7 MeV H+, 100 ~.LCcharge, 1 msr solid angle) the peak area has a value of about l-5 X lo6 counts. The statistical error AA, is then nearly l-2 x 103. Using the precondition that an element is detectable if its peak area A is three times greater than the statistical
P. Miilleret al. / PIXE and RBS determinationof Cd
582
Table 2 Detection limits of cadmium in samples containing different concentrations of potassium, measured under standard conditions (1.7 MeV H+, 100 uC charge) K-concentration
[%I
Detection limit Cd-concentration
4. Experimental
[ppml
4.1. Proton scattering cross sections
110 35.5 11 3.5 1
10 1 0.1 0.01 0.001
error, which is commonly applied for the investigations of trace elements, the detection level of this element can be calculated. For the overlapping peaks in our samples we consider Cd to be detectable if the relation A,, 2 3K is fulfilled. Table 2 gives an overview of the levels for different potassium concentrations calculated for our standard conditions. These concentration I
limits are significantly lower than the detection when using the Cd-KU-line (1000 ppm).
limit
results
The scattering cross sections of nitrogen, oxygen, silicon and potassium determined by our measurements are presented in fig. 3. For comparison, the data published by Rauhala [3-5] and the Rutherford cross sections calculated by eq. (1) are added to fig. 3. A considerable deviation of the experimentally determined cross sections from the Rutherford cross section for the light elements (N, 0, Si) is obvious. The scattering cross sections for proton scattering on nitrogen in the energy region of 1150-1400 keV (between the resonances) is about 2-3 times the Rutherford cross section. The increase of the oxygen scattering cross section ranges between 1.6 and 3.7. As expected, the
I
-I
present Rrmhala
work
8.170’ e- 170.
t
1 "Si(p,plSi" 300
-
x-a
.--. .-’
presentwork e-170' RcuWa e- 170. Rutherfordcrest section e-170'
4 It..,. I
A
-‘-.-,_, . j
ol
( ’
1600
14W
1200
0
1800
I 1040
1200
16W
?A00
1600
:J
Proton energy IkeV)
x_.,presentvork e.17o' .--.Rwhdo e.170° .-. Rutherfard crossSKtiOn
BKIp,plK39
i\
R-170’
'\
x-x
presentwork e-170'
.-.
Rutherfudcr0.ssstion e.770'
'Y '\ 'Y
‘Y, ‘1
‘1 ‘L.
.‘..
-.-.
-.-.
100 -
-.-.__
tI lW4
1204
1100 Proton
energy
1603 (keVI
18W
d 0
’ mo
1200
144
16M
1600
Proton energyIkeVI
Fig. 3. Proton scattering cross sections of nitrogen (a), oxygen (b), silicon (c) and potassium cd), for comparison, data published by Rauhala et al. [3,4] and the Rutherford cross sections calculated by eq. (1) are added.
P. Miller et al. / PIXE and RBS determination of Cd
Table 3 Cadmium content in different samples (alga spirodela polyrhiza and glass) determined using the described procedure, compared with XRF-measurement results Sample No.
Cd-concentration
Our results
[ppm]
Reference value
Alga spirodela polyrhiza 1 2200+ 100 2 5.50+ 150 3 370+_150>
1800&-400 -Cd-K,-line no Cd-K,-line determined
Glass 1 2 3 4
2500 1600 XRF2700 measurements 900I
2400+ 100 1800+ 100 2800f 100 1050+ 100
583
The potassium, calcium and cadmium concentrations were calculated using the procedure described in section 3. The amounts of potassium and calcium are 5.75 at.% and 2.25 at.%, respectively. The Cd-concentration in this sample was calculated using the procedure described above and also from the Cd-K,peak area. We determined a content of (1800 + 400) ppm with the help of the Cd-Km-peak and a content of (2200 k 100) ppm using our procedure. Table 3 gives an overview of the Cd-contents in different samples obtained using our method. For the glass samples our measurements were compared with XRF-measurements. The comparison in table 3 shows that the results of both methods agree quite well.
5. Summary influence of nuclear effects vanishes for elements with higher atomic number and the Rutherford cross section appears to be valid for proton scattering on potassium (see fig. 3d). Also the silicon cross section below about 1400 keV is well described by the Rutherford theory. Our results for nitrogen and silicon are in good agreement with the data from Rauhala. In the case of nitrogen an additional resonance has been found at a proton energy of u 1090 keV. The oxygen cross sections from our measurements are about 10% higher than those of Rauhala [5]. 4.2. Cadmium
determination
Fig. 2 shows the typical RBS- and PIXE-spectra of the sample “alga spirodela polyrhiza”. In the RBSspectrum the elements carbon, oxygen, potassium and calcium are clearly detectable. Charge dependent measurements showed an increase of the spectrum height proportional to the collected charge. This proves that no dynamic changes occurred in the samples during the measurement. Sample No. 1 consists of 55 at.% carbon, 37 at.% oxygen and 8 at.% potassium and calcium, calculated using the scattering cross sections given in fig. 3. The PIXE-spectrum in fig. 2a shows that the sample additionally contains the following trace elements: phosphorus, sulphur, chlorine, potassium, calcium, copper, zinc, cadmium, selenium and strontium. The concentrations of Se and Sr are close to the detection level. The corresponding concentrations were calculated using the program GUPIX, developed by Campbell and Maxwell [lo]. The amounts of these elements in sample No. 1 are given as an example in the following: P 70 ppm, S 30 ppm, Cl 750 ppm, Cu 930 ppm, Zn 250 ppm, Sr 20 ppm and Se 200 ppm.
We have shown that it is possible to determine the Cd content of K containing organic and glass samples even at very low concentrations (3 10 ppm). The concentrations of K, Ca and Cd were determined by combining RBS- and PIXE-measurements using the calculation procedure for separating the K- and Ca-signals in the spectra. Moreover, the proton scattering cross sections of light elements were determined. The cross sections differ from the Rutherford formula for C, N, 0 and Si. For K no deviations occurred in the energy range of 0.9-1.8 MeV. The values determined are in good agreement with the results of Rauhala et al. [3-51.
References Dl D.D. Cohen, M. Harrigan, At. Data Nuclear Data Tables 33 (1985) 255. 121 S.A.E. Johansson and J.L. Campbell, PIXE, a Novel Technique for Elemental Analysis (Wiley, Chichester, 1988). [31 E. Rauhala, Nucl. Instr. and Meth. B40/41 (1989) 790. [41 E. Rauhala, Nucl. Instr. and Meth. B12 (1985) 447. 151 M. Luomajarvi, E. Rauhala and M. Hautala, Nucl. Instr. and Meth. B9 (1985) 255. 161 J.M. Knox, R.J. McLead, D.R. Mayo and X. Qian, Nucl. Instr. and Meth. B45 (1990) 25. t71 L. Zolnai and Gy. Szab6, Nucl. Instr. and Meth. B34 (1988) 118. [8] Gy. Szab6 and L. Zolnai, Nucl. Instr. and Meth. B36 (1989) 88. [9] G. Giitz and K. GIrtner, High Energy Ion Beam Analysis of Solids (Akademie-Verlag, Berlin, 1988). [lo] J.A. Maxwell, J.L. Campbell and W.J. Teesdale, Nucl. Instr. and Meth. B43 (1989) 218.