- Email: [email protected]
X-ray production yield in standardized thick target PIXE
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 249 (2006) 792–795 www.elsevier.com/locate/nimb
X-ray production yield in standardized thick target PIXE Jim Heiji Aburaya, Nemitala Added *, Manfredo Harri Tabacniks, Ma´rcia de Almeida Rizzutto, Marcel Dupret Lopes Barbosa Institute of Physics, University of Sa˜o Paulo, Depto de Fı´sica Nuclear, IFUSP – Travessa R da rua do Mata˜o 187, Cidade Universita´ria, Caixa Postal 66318, CEP 05508-970, Sa˜o Paulo, SP, Brazil Available online 26 May 2006
Abstract A computer program CLARA that calculates a correction factor for thick target PIXE analysis is described. Using CLARA, the analysis of a powdered sample diluted in a light matrix can be corrected for X-ray self-absorption and beam energy loss to use the regular thin film PIXE yields. Dilutions of powders in boric acid were simulated for two extreme cases: carbon and iron powders. In the first case, a 10% addition of carbon changed a pre-defined thick target correction factor, Ri, less than 5% for all elements. On the other hand, 10% of iron changed Ri to about 7% for elements with Z > 21 but showed a 50% loss for the Al content. Using the same procedure, the analysis of Marine Sediment SRM IAEA-356 diluted to 1% in boric acid showed excellent agreement with the referenced data, although compromising somewhat the detection limits. Ó 2006 Elsevier B.V. All rights reserved. PACS: 07.05.Kf; 07.85.m; 29.30.Kv Keywords: Thick target; PIXE; X-ray
1. Introduction
2. Thick target PIXE
In thick target PIXE (TTPIXE) analysis [1] one always needs some information on the composition of the matrix, which holds the trace elements to be measured. Undetected elements (usually Z < 11) need to be guessed in some way to allow the evaluation of stopping power and X-ray absorption coefficients. To overcome some of these difficulties, matrix standardization is suggested in which the powdered sample is diluted to a few percent in a known matrix made of ‘‘light’’ elements (e.g. graphite, boric acid, etc.). Hence, at low sample dilutions, the energy loss and X-ray absorption coefficients in the matrix can be kept almost unchanged. At the same time, the TTPIXE yields Ri can be calculated promptly by simply applying a thick target correction factor to the known thin target PIXE yields ri.
PIXE analysis of thick homogeneous targets always comprises the solution of the thick target yield equation, to get the correspondence between the X-ray yield and the analyzed elementary mass, as follows:
*
Corresponding author. Tel.: +55 11 30916942; fax: +55 11 30312742. E-mail address: [email protected] (N. Added).
0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.03.141
X N 0 Q qn ei Ni ¼ 4p An q e q
Z
E E0
li cos a
rX i ðE00 Þ e q cos h SðE00 Þ
R E00
dE0 E0 SðE0 Þ
dE00 ;
ð1Þ
where Ni represents the number of detected X-rays, X/4p and ei are respectively the implicit solid angle fraction and the efficiency of the detector, N0 is the Avogadro’s number, An is the mass number, Q is the integrated charge of a beam with charge state q and initial energy E0, e is the value of the elementary charge, qn is the elementary mass density while q is the density of the sample, rX i is the X-ray production cross section, while a and h are respectively the incoming and outcoming angles relative to the surface normal. In Eq. (1), the final beam energy E is the
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
energy of the beam after emerging on the back side of the target (l/cos h) or E = 0 if the beam is going to be stopped inside the target. The algorithm generally used by the majority of the automatic thick target PIXE programs like GUPIX [2], to calculate the composition of thick homogeneous samples, assumes that the summation of the relative mass concentrations over all elements in the sample has to add up to unity. Our alternative approach employs the dilution of the powdered sample in a known matrix made of ‘‘light’’ elements minimizing significant changes in the stopping power and the mass absorption coefficient of the matrix. In fact, it allows us to define a constant thick target sensitivity factor Ri similarly to the well known thin target sensitivity factor ri. ri ¼
X N0 1 ei rX ðE0 Þ: 4p An q e i
ð2Þ
Since both factors are unique for every elementary X-ray line, a thick target correction factor Fi can be defined as: R E00 dE0 l a qi cos Z E cos h E SðE0 Þ 00 0 Ri 1 rX i ðE Þ e dE00 ; ð3Þ Fi ¼ ¼ 00 ri rX i ðE0 Þ E0 SðE Þ where rX i ðE0 Þ is the ionization cross section at the initial beam energy. As a consequence, thick target PIXE elementary compositions in a powdered sample can be determined without any especial interactive calculation, by just using the calibrated thin film PIXE yields, corrected by a thick target correction factor, and a dilution factor D (the ratio of the sample and the dilution matrix masses), as described in Eq. (4). Ci ¼
1 Ni : D F i ri Q
ð4Þ
absorption coefficients are calculated using the XCOM software developed by Berger and Hubbell [9]. The only inputs needed to run CLARA are the primary and second matrix composition, the beam parameters (initial and final energy) and the in/out angles a and h. The user has to select the element and X-ray line of interest, and choose the cross section model (Johansson’s or Campbell’s polynomials [4,10]). By using a semi-empirical thin film calibration curve, CLARA allows calculating interactively thick target compositions or enables verifying the effect of the addition of any amount of an element or mixture to a pre-defined matrix in a very comprehensive way. 3.2. Samples Thick target correction factors were calculated for three kinds of matrices: graphite, boric acid (HBO3 Æ H2O) and hydroxyapatite (Ca10P6O26H2). To verify the effect of the contamination of boric acid with an ‘‘unknown’’ element two extreme limits were simulated with the addition respectively of graphite and iron, in different amounts. The hydroxyapatite was chosen to help the analysis of trace elements in teeth [11]. Test targets were made with IAEA-356 Marine Sediment reference material, milled in an agate mortar and diluted at 1%, 10% and 33% in boric acid (H3BO3, Merk, pro-analysis). All samples were carefully mixed and pressed (4 tons) to make 2 cm diameter pellets 3 mm thick. Thick target PIXE analysis was carried out using a 2.4 MeV proton beam, a 138 eV FWHM Si(Li) detector at 120° (a = 45°, h = 15°) with an 57 lm thick Be absorber. The charge compensation of the targets was achieved using a 6 V-DC open lamp filament like a simple electron gun.
Since the sample relative mass concentrations Ci are unitless, usually given in [lg g1], the thick target correction factor has units of [cm2 g1].
3.1. Software To compute the thick target correction factors, a computer program (CLARA1) was written, in which a primary matrix can be defined and contaminated with controlled amounts of some compound from a sample (second matrix). Written in Visual Basic, the program evaluates the integral in Eq. (3), using Newton-Cotes algorithm [3]. Total X-ray ionization cross sections are calculated using Johansson and Johansson [4,10] polynomial fit. X-ray intensity ratios are taken from Scofield [5] and Perujo et al. [6] while the fluorescence yields are from Bambyneck [7]. Stopping powers for protons up to 10 MeV, are calculated using the fitted curve given by Ziegler et al. [8]. Mass 1
Copies of CLARA can be obtained freely upon request.
6
5 TT correction factor (g/cm2)
3. Methodology
793
4
3
Ca absorption edge
2 P absorption edge 1
Carbon Boric Acid - H3BO4 Hydroxyapatite - Ca10P6O26H2
0 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic number (Z) Fig. 1. Thick target correction factors for Ka lines, calculated for carbon (graphite), boric acid and hidroxyapatite. TTPIXE analysis using 2.4 MeV proton beam, incident beam angle a = 45° and X-ray take off angle, h = 30°.
794
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
4. Results
IAEA-356 (reference) diluted 1% in boric acid (TTPIXE)
5
10
1.30 1.25
C 10% C 20% C 50%
F / F0
1.15
3
10
2
10
1
10
0
10
K Ca Ti V Cr Mn Fe Co Ni Cu Zn As Br Rb Sr Elements Fig. 4. Comparison of TTPIXE analysis of IAEA-356 marine sediment diluted to 1% in boric acid and certified values.
Carbon diluted in boric acid
1.20
4
10
µg/g
Thick target correction factors for Ka X-ray lines, as defined in Eq. (3), were calculated for carbon (graphite), boric acid (HBO3 Æ H2O) and hidroxyapatite and are shown in Fig. 1. The strong influence of the Ca and P absorption edges for the hidroxyapatite matrix is clearly visible in Fig. 1. It is interesting to notice that the thick target correction factors for carbon and boric acid are almost constant for elements with Z > 24. The relative change of the thick target correction factor, F/F0 after the addition of different amounts of carbon or iron to a boric acid matrix is shown in Figs. 2 and 3. It can be seen that high Z contaminants (e.g. iron) may intro-
1.10 1.05 1.00 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic Number (Z) Fig. 2. Influence of carbon contaminant in boric acid in the correction factor calculation. F0 is the thick target correction factor for pure boric acid.
duce significant errors in the thick target correction factor for low Z elements. The comparison of the certified values of IAEA-356 reference material with a TTPIXE analysis of a sample diluted to 1% in boric acid and following the proposed thick target correction factors is shown in Fig. 4. Deviations from certified values are all within one experimental standard deviation, except for Rb, which is still within ±2r. It can also be noticed that the dilution sacrifices somewhat the detection limits. Elements in the range of 10 ppm concentration, normally detectable in a regular PIXE analysis, remained undetected. TTPIXE analysis of the IAEA-356 samples diluted at 10% and 33% did not show a good agreement with the certified values. This certainly poses a limit for the dilution and standard thick target correction procedure. 5. Conclusions
1.2
Fe diluted in boric acid
1.1 1.0
F / F0
0.9 0.8 0.7
Fe absorption edge
0.6 0.5 0.4 0.3
Fe 10% Fe 20% Fe 50% 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic Number (Z)
Fig. 3. Influence of iron contaminant in boric acid in the correction factor calculation. F0 is the thick target correction factor for pure boric acid.
The dilution of powdered samples in a known matrix of ‘‘light’’ elements is shown to be a quick and precise method for thick target PIXE analysis which uses a simple thick target correction factor and the well established thin film calibration yield curves. We noticed that the addition of 1 to 5% of sample material to a boric acid matrix produces little change to the thick target correction factors. As expected, the detection limits of the diluted sample PIXE analysis are worse than in regular thick target PIXE analysis. As an option, the samples can be prepared with different dilutions and the thick target correction factor can be recalculated for every new result, however this competes with the traditional approach of iterative thick target analysis. Acknowledgements The authors wish to express their gratitude to M.R. Antonio and M.V. Souza Lima for their help in
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
accelerator operation and maintenance. M.H.T., M.A.R. and N.A. acknowledge FAPESP and CNPq for financial support. References [1] J.L. Campbell, J.A. Cookson, Nucl. Instr. and Meth. B 3 (1984) 185. [2] J.A. Maxwell, J.A. Campbell, W.J. Teesdale, Nucl. Instr. and Meth. B 43 (1989) 218. [3] P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. [4] S.A.E. Johansson, T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 476. [5] J.H. Scofield, Phys. Ver. A 9 (1974) 1041.
795
[6] A. Perujo, J.A. Maxwell, W.J. Teesdale, J.L. Campbell, J. Phys. B 20 (1987) 4973. [7] S.A.E. Johansson, J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis, John Wiley & Sons, Great Britain, 1998. [8] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Vol. 1, Pergamon Press, New York, 1985. [9] M.J. Berger, J.H. Hubbell, XCom Photon Cross Sections on a Personal Computer, Center for Radiation Research NBS (National Bureau of Standards), Gaithersburg, 1988. [10] J.L. Campbell, J.A. Cookson, H. Paul, Nucl. Instr. and Meth. 212 (1983) 427. [11] M.A. Rizzutto, N. Added, M.H. Tabacniks, R. Liguori Neto, J.C. Acquadro, L.P. Machado, M. Vilela, T.R.C.F. Oliveira, R.A. Markarian, M. Mori, Nucl. Instr. and Meth. B 190 (2002) 186.
Nuclear Instruments and Methods in Physics Research B 249 (2006) 792–795 www.elsevier.com/locate/nimb
X-ray production yield in standardized thick target PIXE Jim Heiji Aburaya, Nemitala Added *, Manfredo Harri Tabacniks, Ma´rcia de Almeida Rizzutto, Marcel Dupret Lopes Barbosa Institute of Physics, University of Sa˜o Paulo, Depto de Fı´sica Nuclear, IFUSP – Travessa R da rua do Mata˜o 187, Cidade Universita´ria, Caixa Postal 66318, CEP 05508-970, Sa˜o Paulo, SP, Brazil Available online 26 May 2006
Abstract A computer program CLARA that calculates a correction factor for thick target PIXE analysis is described. Using CLARA, the analysis of a powdered sample diluted in a light matrix can be corrected for X-ray self-absorption and beam energy loss to use the regular thin film PIXE yields. Dilutions of powders in boric acid were simulated for two extreme cases: carbon and iron powders. In the first case, a 10% addition of carbon changed a pre-defined thick target correction factor, Ri, less than 5% for all elements. On the other hand, 10% of iron changed Ri to about 7% for elements with Z > 21 but showed a 50% loss for the Al content. Using the same procedure, the analysis of Marine Sediment SRM IAEA-356 diluted to 1% in boric acid showed excellent agreement with the referenced data, although compromising somewhat the detection limits. Ó 2006 Elsevier B.V. All rights reserved. PACS: 07.05.Kf; 07.85.m; 29.30.Kv Keywords: Thick target; PIXE; X-ray
1. Introduction
2. Thick target PIXE
In thick target PIXE (TTPIXE) analysis [1] one always needs some information on the composition of the matrix, which holds the trace elements to be measured. Undetected elements (usually Z < 11) need to be guessed in some way to allow the evaluation of stopping power and X-ray absorption coefficients. To overcome some of these difficulties, matrix standardization is suggested in which the powdered sample is diluted to a few percent in a known matrix made of ‘‘light’’ elements (e.g. graphite, boric acid, etc.). Hence, at low sample dilutions, the energy loss and X-ray absorption coefficients in the matrix can be kept almost unchanged. At the same time, the TTPIXE yields Ri can be calculated promptly by simply applying a thick target correction factor to the known thin target PIXE yields ri.
PIXE analysis of thick homogeneous targets always comprises the solution of the thick target yield equation, to get the correspondence between the X-ray yield and the analyzed elementary mass, as follows:
*
Corresponding author. Tel.: +55 11 30916942; fax: +55 11 30312742. E-mail address: [email protected] (N. Added).
0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.03.141
X N 0 Q qn ei Ni ¼ 4p An q e q
Z
E E0
li cos a
rX i ðE00 Þ e q cos h SðE00 Þ
R E00
dE0 E0 SðE0 Þ
dE00 ;
ð1Þ
where Ni represents the number of detected X-rays, X/4p and ei are respectively the implicit solid angle fraction and the efficiency of the detector, N0 is the Avogadro’s number, An is the mass number, Q is the integrated charge of a beam with charge state q and initial energy E0, e is the value of the elementary charge, qn is the elementary mass density while q is the density of the sample, rX i is the X-ray production cross section, while a and h are respectively the incoming and outcoming angles relative to the surface normal. In Eq. (1), the final beam energy E is the
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
energy of the beam after emerging on the back side of the target (l/cos h) or E = 0 if the beam is going to be stopped inside the target. The algorithm generally used by the majority of the automatic thick target PIXE programs like GUPIX [2], to calculate the composition of thick homogeneous samples, assumes that the summation of the relative mass concentrations over all elements in the sample has to add up to unity. Our alternative approach employs the dilution of the powdered sample in a known matrix made of ‘‘light’’ elements minimizing significant changes in the stopping power and the mass absorption coefficient of the matrix. In fact, it allows us to define a constant thick target sensitivity factor Ri similarly to the well known thin target sensitivity factor ri. ri ¼
X N0 1 ei rX ðE0 Þ: 4p An q e i
ð2Þ
Since both factors are unique for every elementary X-ray line, a thick target correction factor Fi can be defined as: R E00 dE0 l a qi cos Z E cos h E SðE0 Þ 00 0 Ri 1 rX i ðE Þ e dE00 ; ð3Þ Fi ¼ ¼ 00 ri rX i ðE0 Þ E0 SðE Þ where rX i ðE0 Þ is the ionization cross section at the initial beam energy. As a consequence, thick target PIXE elementary compositions in a powdered sample can be determined without any especial interactive calculation, by just using the calibrated thin film PIXE yields, corrected by a thick target correction factor, and a dilution factor D (the ratio of the sample and the dilution matrix masses), as described in Eq. (4). Ci ¼
1 Ni : D F i ri Q
ð4Þ
absorption coefficients are calculated using the XCOM software developed by Berger and Hubbell [9]. The only inputs needed to run CLARA are the primary and second matrix composition, the beam parameters (initial and final energy) and the in/out angles a and h. The user has to select the element and X-ray line of interest, and choose the cross section model (Johansson’s or Campbell’s polynomials [4,10]). By using a semi-empirical thin film calibration curve, CLARA allows calculating interactively thick target compositions or enables verifying the effect of the addition of any amount of an element or mixture to a pre-defined matrix in a very comprehensive way. 3.2. Samples Thick target correction factors were calculated for three kinds of matrices: graphite, boric acid (HBO3 Æ H2O) and hydroxyapatite (Ca10P6O26H2). To verify the effect of the contamination of boric acid with an ‘‘unknown’’ element two extreme limits were simulated with the addition respectively of graphite and iron, in different amounts. The hydroxyapatite was chosen to help the analysis of trace elements in teeth [11]. Test targets were made with IAEA-356 Marine Sediment reference material, milled in an agate mortar and diluted at 1%, 10% and 33% in boric acid (H3BO3, Merk, pro-analysis). All samples were carefully mixed and pressed (4 tons) to make 2 cm diameter pellets 3 mm thick. Thick target PIXE analysis was carried out using a 2.4 MeV proton beam, a 138 eV FWHM Si(Li) detector at 120° (a = 45°, h = 15°) with an 57 lm thick Be absorber. The charge compensation of the targets was achieved using a 6 V-DC open lamp filament like a simple electron gun.
Since the sample relative mass concentrations Ci are unitless, usually given in [lg g1], the thick target correction factor has units of [cm2 g1].
3.1. Software To compute the thick target correction factors, a computer program (CLARA1) was written, in which a primary matrix can be defined and contaminated with controlled amounts of some compound from a sample (second matrix). Written in Visual Basic, the program evaluates the integral in Eq. (3), using Newton-Cotes algorithm [3]. Total X-ray ionization cross sections are calculated using Johansson and Johansson [4,10] polynomial fit. X-ray intensity ratios are taken from Scofield [5] and Perujo et al. [6] while the fluorescence yields are from Bambyneck [7]. Stopping powers for protons up to 10 MeV, are calculated using the fitted curve given by Ziegler et al. [8]. Mass 1
Copies of CLARA can be obtained freely upon request.
6
5 TT correction factor (g/cm2)
3. Methodology
793
4
3
Ca absorption edge
2 P absorption edge 1
Carbon Boric Acid - H3BO4 Hydroxyapatite - Ca10P6O26H2
0 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic number (Z) Fig. 1. Thick target correction factors for Ka lines, calculated for carbon (graphite), boric acid and hidroxyapatite. TTPIXE analysis using 2.4 MeV proton beam, incident beam angle a = 45° and X-ray take off angle, h = 30°.
794
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
4. Results
IAEA-356 (reference) diluted 1% in boric acid (TTPIXE)
5
10
1.30 1.25
C 10% C 20% C 50%
F / F0
1.15
3
10
2
10
1
10
0
10
K Ca Ti V Cr Mn Fe Co Ni Cu Zn As Br Rb Sr Elements Fig. 4. Comparison of TTPIXE analysis of IAEA-356 marine sediment diluted to 1% in boric acid and certified values.
Carbon diluted in boric acid
1.20
4
10
µg/g
Thick target correction factors for Ka X-ray lines, as defined in Eq. (3), were calculated for carbon (graphite), boric acid (HBO3 Æ H2O) and hidroxyapatite and are shown in Fig. 1. The strong influence of the Ca and P absorption edges for the hidroxyapatite matrix is clearly visible in Fig. 1. It is interesting to notice that the thick target correction factors for carbon and boric acid are almost constant for elements with Z > 24. The relative change of the thick target correction factor, F/F0 after the addition of different amounts of carbon or iron to a boric acid matrix is shown in Figs. 2 and 3. It can be seen that high Z contaminants (e.g. iron) may intro-
1.10 1.05 1.00 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic Number (Z) Fig. 2. Influence of carbon contaminant in boric acid in the correction factor calculation. F0 is the thick target correction factor for pure boric acid.
duce significant errors in the thick target correction factor for low Z elements. The comparison of the certified values of IAEA-356 reference material with a TTPIXE analysis of a sample diluted to 1% in boric acid and following the proposed thick target correction factors is shown in Fig. 4. Deviations from certified values are all within one experimental standard deviation, except for Rb, which is still within ±2r. It can also be noticed that the dilution sacrifices somewhat the detection limits. Elements in the range of 10 ppm concentration, normally detectable in a regular PIXE analysis, remained undetected. TTPIXE analysis of the IAEA-356 samples diluted at 10% and 33% did not show a good agreement with the certified values. This certainly poses a limit for the dilution and standard thick target correction procedure. 5. Conclusions
1.2
Fe diluted in boric acid
1.1 1.0
F / F0
0.9 0.8 0.7
Fe absorption edge
0.6 0.5 0.4 0.3
Fe 10% Fe 20% Fe 50% 13 15 17 19 21 23 25 27 29 31 33 35 37 39 Atomic Number (Z)
Fig. 3. Influence of iron contaminant in boric acid in the correction factor calculation. F0 is the thick target correction factor for pure boric acid.
The dilution of powdered samples in a known matrix of ‘‘light’’ elements is shown to be a quick and precise method for thick target PIXE analysis which uses a simple thick target correction factor and the well established thin film calibration yield curves. We noticed that the addition of 1 to 5% of sample material to a boric acid matrix produces little change to the thick target correction factors. As expected, the detection limits of the diluted sample PIXE analysis are worse than in regular thick target PIXE analysis. As an option, the samples can be prepared with different dilutions and the thick target correction factor can be recalculated for every new result, however this competes with the traditional approach of iterative thick target analysis. Acknowledgements The authors wish to express their gratitude to M.R. Antonio and M.V. Souza Lima for their help in
J.H. Aburaya et al. / Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 792–795
accelerator operation and maintenance. M.H.T., M.A.R. and N.A. acknowledge FAPESP and CNPq for financial support. References [1] J.L. Campbell, J.A. Cookson, Nucl. Instr. and Meth. B 3 (1984) 185. [2] J.A. Maxwell, J.A. Campbell, W.J. Teesdale, Nucl. Instr. and Meth. B 43 (1989) 218. [3] P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. [4] S.A.E. Johansson, T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 476. [5] J.H. Scofield, Phys. Ver. A 9 (1974) 1041.
795
[6] A. Perujo, J.A. Maxwell, W.J. Teesdale, J.L. Campbell, J. Phys. B 20 (1987) 4973. [7] S.A.E. Johansson, J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis, John Wiley & Sons, Great Britain, 1998. [8] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Vol. 1, Pergamon Press, New York, 1985. [9] M.J. Berger, J.H. Hubbell, XCom Photon Cross Sections on a Personal Computer, Center for Radiation Research NBS (National Bureau of Standards), Gaithersburg, 1988. [10] J.L. Campbell, J.A. Cookson, H. Paul, Nucl. Instr. and Meth. 212 (1983) 427. [11] M.A. Rizzutto, N. Added, M.H. Tabacniks, R. Liguori Neto, J.C. Acquadro, L.P. Machado, M. Vilela, T.R.C.F. Oliveira, R.A. Markarian, M. Mori, Nucl. Instr. and Meth. B 190 (2002) 186.