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Yield of Lα X-rays from a light element matrix in thick-target PIXE
259
Nuclear Instruments and Methods in Physics Research B36 (1989) 259-262 North-Holland, Amsterdam
YIELD
OF L, X-RAYS
FROM
A LIGHT
ELEMENT
MATRIX
IN THICK-TARGET
PIKE.
M. KHALIQUZZAMAN P@~.sicsBepuriment, ~nive?sity oj Garyounis, Benghazi, Libya S.T. LAM,
T. OTSUBO
* and A.H. HUSSAIN
Nuclear Research Centre, Physics Department, L.G.
University
**
of Alberta, Edmonton, Canada T6G 2N5
STEPHENS-NEWSHAM
Faculty of Pharmacy,
University of Alberta, Edmonton,
Canada T6G 2N8
Received 2 June 1988 and in revised form 4 October 1988
Yields of L, X-rays from a light element matrix have been measured for elements with atomic number 52 I Z ( 92, for incident proton energy of 2.61 MeV. The experimental results have been compared with the results of numerical calculations using L X-ray production cross section data in literature. It is shown that results of such calculations can be used for analytical application using monostandards in thick-target PIXE.
1. Introducticrn In a previous study 111it was shown that a single-element standard or monostandard could be used for multielement analysis in thick-target PIXE for K X-rays. This was possible because K X-ray production cross sections could be calculated accurately from theory. This work was undertaken to investigate if a similar approach is possible for L X-rays. The calculations in the case of L X-rays are considerably more difficult as the commonly observed L-lines in Si(Li) detector spectra are composite lines originating from the L,, L,, and L,,, subshell vacancies. Recently, Cohen and Harrigan [2] have published X-ray production cross sections separately for each component of the L X-rays lines and this has made the calculation of yields for any L X-ray line feasible. Of the three lines L,, LB and L,, which are observed in energy-dispersive PIXE studies with Si(Li) detectors, the L, case is straightforward as the components of this line (L, and Lsz) originate from the Lm subshell vacancies, the transitions being L,(L,,,-M,) and L,,(L,,,-MtV). Also, the components are not too dispersed to be observed as separate lines as Z increases. This work is limited to the L, X-rays only.
* Present address: Department of Physics, National Defence Academy, Yokosuka, Kanagawa, Japan. ** Present address: Physics Department, King Fahad University of Petroleum and Minerals, Dahran, Saudi Arabia. 0168-583X/89/$03.50 (Norm-polled
Physics
0 Elsevier ~b~is~ng
Science
Publishers
Division)
B.V.
It may be noted here that using a single-element standard has the advantage that only one standard is required for the determination of all the elements present in the sample above the detection limit. Even when multielement standards are available, this method has the advantage that certified values for all the elements to be determined are not required. The monostandard method is widely used in neutron activation analysis [3]. In spite of the great inherent advantage of this method, it appears that it has not received sufficient attention in elemental analysis using thick-target PIXE.
2. Ex~~mental The experimental setup used in the present work was the same as that reported in ref. [l]. As suitable multielement standards containing a fair number of elements with 50 5 Z I 92 could not be obtained, standards were prepared using boric acid (H,BO,) as matrix material. These were prepared by mixing atomic absorbtion standard solutions with boric acid solution in water. The mixture were freeze-dried to remove the water. The samples were dried further in an oven in air at 110 o C for 48 hours. It was found that H,BO, changed to HBO, in this process. The samples were then crushed to powder. The concentrations of the elements in the matrix were in the range of - 150 ppm. For irradiation pellets of 7 mm diameter and 1 mm in the thickness were made from the powder using a hand press. These
pellets are effectively infinitely thick for the beam energy used in this work. The samples were irradiated with 10 PC of integrated charge of a proton beam from the University of Albert Van de Graaff at a nominal energy of 3 MeV. The samples were placed in air and the proton beam was extracted into air through a 1.1 mg/cm2 Kapton window. After energy loss in the Kapton window and in air, the proton energy at the target was estimated to be 2.61 MeV. The typical beam currents used were in the range of S-10 nA. Three pellets of each sample were irradiated to average over sample nonu~for~ty. The pellets were held at 45* to the beam on 35 mm slide frames. The X-rays were detected by a Kevex Si(Li) detector (3 mm thick, 80 mm2 area, 0.025 mm Be window, resolution 180 eV at 5.9 keV) held at 90° to the beam direction. Plastic absorbers equivalent to 79 mg/cm2 thickness of carbon were used in front of the detector to reduce the counting rate due to low-energy X-rays. The solid angle of the detector was approximately 10.6 X 1Oa3 sr.
normal to the target surface and & is the angle between the detector axis and the normal to the target surface. The integration was carried out up to a proton energy of 0.5 MeV as this gives almost all the X-ray yield and the difficulties of stopping power calculation at low energies are avoided [I]. The stopping powers were calculated using well established prescriptions [4,5], while the mass attenuation coefficients used were from Storm and Israel [6]. The X-ray production cross section for any given element and energy were obtained by inte~olating the cross section tables from Cohen and Harrigan [2]. The yields were calculated for 1 pg of the given element in 1 g of the matrix for an integrated charge of 1 PC.
4. Results and discussion The results obtained in the present study are presented and discussed in light of the previous work [l] in the following. 4.1. Dependence of yield on atomic number
3. Numerical calculations The calculated X-ray yields were obtained by numerical evaluation of the equation for X-ray yield:
The quantities in the first square brackets represent the number of incident protons In,), the efficiency of the detector (Ed) and the solid angle of the detector (f2). The second term in square brackets represents the attenuation of the X-rays between the target and the detector. The quantities involved are the mass attenuation coefficient hij for absorber j and X-rays of element i, and the thickness xj of the absorber j. The third term in square brackets represents X-ray yields in the target that come out through the surface. The quantities involved here are the number of atoms N, of the element i per gram of the matrix material, the thickness x of the matrix at which protons of incident energy Ep are degraded to E, the mass attenuation coefficient pj for X-rays of element i, the X-ray production cross sections u,(E) at energy E and the stopping power S,(E) for the matrix for protons with energy E. The thickness x in the matrix is given by:
Jq$,,(E) ix==
Ed.5
cos 8.,
cos 0,’
(2)
where 0, is the angle between the proton beam and the
The experimental yields for L, X-rays are shown in fig. 1 as a function of Z, along with the calculated curve. The calculated curve is normalized by a factor of 0.2707 so that the calculated and measured yields of Wo coincide with each other. The systematic shift between the calculated and observed yields may arise from uncertainties in the detector solid angle, which could be determined only approximately, uncertainties in the calculation of stopping powers and in the cross section
*1
Fig. 1. Variation of the L, X-ray yield from an infinitely thick target (HBO, E, =
matrix) as a function of atomic number (Z) at
2.61 MeV. The error bars are from counting statistics and
correspond to one standard deviation. The continuous represents the normalized calculated values.
line
M. Khaliquzzaman
et al. / Yield of L, X-rays from a light element matrix
3
Fig. 2. Variation of calculated L X-ray yields as function of beam energy in a carbon matrix (not normalized); (1) E, = 3.69 MeV, (2) EP = 3.16 MeV, (3) E, 2.61 MeV, (4) EP = 2.16 MeV. data,
and
tenuated
from beam
errors energy
in
the
calculation
on the target.
that interaction
of the uncertainties
the yield could
amplify
and
the
tematic
shift in the cross section
in the evaluation uncertainties
calculated
values.
between For
are
care
sys-
data may be amplified
of the integration taken
of
the ob-
example,
in eq. (l),
of by
due to
All the four
the normalization
In any case it is the good agreement between the experimental and normalized calculated yields as a function of atomic number which is of importance in analytical applications. Such a fit means that, once the calculated yield curve is normalized at any single point of measured L, X-ray yield for an element, the curve in turn can be used to find the concentration of an unknown element. The energy dependence of La X-ray yield was studied by performing calculations at several incident proton energies. This is shown in fig. 2. The general pattern of the curves is similar to that in the case of K X-rays [l]. For small changes in incident energy the yield curves are almost parallel. This means that a certain amount of error (- 100 keV) can be tolerated in the incident energy determination, provided that the yield curves are normalized. It may be noted that the fall in the yields for 2 < 60 is due to the absorbers between the target and the detector. factor.
4.2. Yield variation
with matrix
7
Fig. 3. Variation in the relative yield for L, X-rays for different matrix compositions at E = 2.61 MeV: (1) silica (SiO,), (2) HBO,, (3) H, BO,, (4) carbohydrate (CH, 0),, (5) cellulose (C,H,,O,),.
where I, is the yield in a given matrix and I, that in a carbon matrix. It is interesting to note that the relative yields for L, X-rays drop as the Z-number decreases, which is opposite to the result obtained for K X-rays [l]. The almost parallel nature of the curves for Z > 60 for light matrices containing H, B, C and 0 shows that the same calculated yield curve can be used for all the matrices studied here (for Z > 60), provided it is normalized in each case. It can also be seen that the variation in the yield is rather small, being less than 10% among the matrices studied here. However, if the matrix change is drastic, then significant changes in the
composition
The plots of calculated relative yields (I,) for five different matrices are shown in fig. 3. The relative yields have been defined as 1, = I,/&
Cm
at-
in the calculation
in the energy loss calculation.
uncertainties
the
It is also possible
the difference
served
of
261
(3)
Fig. 4. Variation of minimum detection limit in thick-target PIXE using L, X-rays as a function of atomic number (2) at E, = 2.61 MeV. The error bars are statistical errors corresponding to one standard deviation. The continuous line is the least-squares fit to the data.
262
M. Khaliquzzaman et al. / Yield
I, X-ray yields can take place. This is shown in fig. 3 when the matrix is changed to SiO,.
4.3. Minimum
detection
limits
The minimum detection limit (MDL) is defined as the amount of an element in ppm which corresponds to the number of counts equal to three standard deviations of the background. The details of MDL calculations have been explained elsewhere [l]. The MDLs for the different elements for 10 PC irradiation are shown in fig. 4 as a function of Z. The continuous curve is the least-square fit to the data. The minimum of MDL (- 10 ppm) occurs for Z around 70. The MDL can ofcourse be reduced by longer irradiation, From the cross sections’ consideration (fig. 2), it may appear that the MDL may be reduced by increasing the beam energy, but this may not necessarily be the case, because of the increase in background with the increase in beam energy [ 11.
ofL, X-rays froma light element matrix using a standard. In light element matrices the X-ray yields vary only slightly with matrix composition and as such only approximate knowledge of the matrix composition can yield resonably accurate analytical results. The authors would like to thank Mr. Dennis Ng of Faculty of Pharmacy, University of Alberta for his help in making the synthetic standards. Thanks are due to Dr. G.C. Neilson for his support and interest in the work. One of the authors (MKZ) would like to thank Dr. Mohammed T. Elfazani, Chairman of the Department of Physics, Faculty of Science, University of Garyounis, Benghazi, Libya for extending the facilities of the department where most of the computational work has been performed. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.
References
5. Conclusion.
PI M. Khaliquzzaman, S.T. Lam, D.M. Sheppard and L.G.
It has been shown that calculated L, X-ray yields for elements with Z 2 52, imbedded in light-element matrices for infinitely thick targets, are in good agreement with experimentally observed yields except for a normalization constant. As the atomic number dependence of the yields is reproduced quantitatively, such curves can be used for analytical applications, provided they are normalized at least at a single atomic number
PI D.D. Cohen, M. Harrigan, Atomic Data and Nucl. Data
Stephens-Newsham, Nucl. Ins&. and Meth. 216 (1983) 481.
Tables 34 (1986) 393. [31 A. Simonits, L. Moens, F. De Corte, A. De Wispelaere and A. Elek, J. Hoste, J. Radioanal. Chem. 60 (1980) 461. 141W. Whaling, Handbuch der Physik, vol. 38 (Springer, Berlin, 1958) p. 193. 151 H.H. Andersen and J.F. Ziegler, Hydrogen Stopping Powers and Range in All Elements. (Pergamon Press, 1977). 161 E. Storm and H.I. Israel, Nucl. Data Tables A7 (1970) 565.
Nuclear Instruments and Methods in Physics Research B36 (1989) 259-262 North-Holland, Amsterdam
YIELD
OF L, X-RAYS
FROM
A LIGHT
ELEMENT
MATRIX
IN THICK-TARGET
PIKE.
M. KHALIQUZZAMAN P@~.sicsBepuriment, ~nive?sity oj Garyounis, Benghazi, Libya S.T. LAM,
T. OTSUBO
* and A.H. HUSSAIN
Nuclear Research Centre, Physics Department, L.G.
University
**
of Alberta, Edmonton, Canada T6G 2N5
STEPHENS-NEWSHAM
Faculty of Pharmacy,
University of Alberta, Edmonton,
Canada T6G 2N8
Received 2 June 1988 and in revised form 4 October 1988
Yields of L, X-rays from a light element matrix have been measured for elements with atomic number 52 I Z ( 92, for incident proton energy of 2.61 MeV. The experimental results have been compared with the results of numerical calculations using L X-ray production cross section data in literature. It is shown that results of such calculations can be used for analytical application using monostandards in thick-target PIXE.
1. Introducticrn In a previous study 111it was shown that a single-element standard or monostandard could be used for multielement analysis in thick-target PIXE for K X-rays. This was possible because K X-ray production cross sections could be calculated accurately from theory. This work was undertaken to investigate if a similar approach is possible for L X-rays. The calculations in the case of L X-rays are considerably more difficult as the commonly observed L-lines in Si(Li) detector spectra are composite lines originating from the L,, L,, and L,,, subshell vacancies. Recently, Cohen and Harrigan [2] have published X-ray production cross sections separately for each component of the L X-rays lines and this has made the calculation of yields for any L X-ray line feasible. Of the three lines L,, LB and L,, which are observed in energy-dispersive PIXE studies with Si(Li) detectors, the L, case is straightforward as the components of this line (L, and Lsz) originate from the Lm subshell vacancies, the transitions being L,(L,,,-M,) and L,,(L,,,-MtV). Also, the components are not too dispersed to be observed as separate lines as Z increases. This work is limited to the L, X-rays only.
* Present address: Department of Physics, National Defence Academy, Yokosuka, Kanagawa, Japan. ** Present address: Physics Department, King Fahad University of Petroleum and Minerals, Dahran, Saudi Arabia. 0168-583X/89/$03.50 (Norm-polled
Physics
0 Elsevier ~b~is~ng
Science
Publishers
Division)
B.V.
It may be noted here that using a single-element standard has the advantage that only one standard is required for the determination of all the elements present in the sample above the detection limit. Even when multielement standards are available, this method has the advantage that certified values for all the elements to be determined are not required. The monostandard method is widely used in neutron activation analysis [3]. In spite of the great inherent advantage of this method, it appears that it has not received sufficient attention in elemental analysis using thick-target PIXE.
2. Ex~~mental The experimental setup used in the present work was the same as that reported in ref. [l]. As suitable multielement standards containing a fair number of elements with 50 5 Z I 92 could not be obtained, standards were prepared using boric acid (H,BO,) as matrix material. These were prepared by mixing atomic absorbtion standard solutions with boric acid solution in water. The mixture were freeze-dried to remove the water. The samples were dried further in an oven in air at 110 o C for 48 hours. It was found that H,BO, changed to HBO, in this process. The samples were then crushed to powder. The concentrations of the elements in the matrix were in the range of - 150 ppm. For irradiation pellets of 7 mm diameter and 1 mm in the thickness were made from the powder using a hand press. These
pellets are effectively infinitely thick for the beam energy used in this work. The samples were irradiated with 10 PC of integrated charge of a proton beam from the University of Albert Van de Graaff at a nominal energy of 3 MeV. The samples were placed in air and the proton beam was extracted into air through a 1.1 mg/cm2 Kapton window. After energy loss in the Kapton window and in air, the proton energy at the target was estimated to be 2.61 MeV. The typical beam currents used were in the range of S-10 nA. Three pellets of each sample were irradiated to average over sample nonu~for~ty. The pellets were held at 45* to the beam on 35 mm slide frames. The X-rays were detected by a Kevex Si(Li) detector (3 mm thick, 80 mm2 area, 0.025 mm Be window, resolution 180 eV at 5.9 keV) held at 90° to the beam direction. Plastic absorbers equivalent to 79 mg/cm2 thickness of carbon were used in front of the detector to reduce the counting rate due to low-energy X-rays. The solid angle of the detector was approximately 10.6 X 1Oa3 sr.
normal to the target surface and & is the angle between the detector axis and the normal to the target surface. The integration was carried out up to a proton energy of 0.5 MeV as this gives almost all the X-ray yield and the difficulties of stopping power calculation at low energies are avoided [I]. The stopping powers were calculated using well established prescriptions [4,5], while the mass attenuation coefficients used were from Storm and Israel [6]. The X-ray production cross section for any given element and energy were obtained by inte~olating the cross section tables from Cohen and Harrigan [2]. The yields were calculated for 1 pg of the given element in 1 g of the matrix for an integrated charge of 1 PC.
4. Results and discussion The results obtained in the present study are presented and discussed in light of the previous work [l] in the following. 4.1. Dependence of yield on atomic number
3. Numerical calculations The calculated X-ray yields were obtained by numerical evaluation of the equation for X-ray yield:
The quantities in the first square brackets represent the number of incident protons In,), the efficiency of the detector (Ed) and the solid angle of the detector (f2). The second term in square brackets represents the attenuation of the X-rays between the target and the detector. The quantities involved are the mass attenuation coefficient hij for absorber j and X-rays of element i, and the thickness xj of the absorber j. The third term in square brackets represents X-ray yields in the target that come out through the surface. The quantities involved here are the number of atoms N, of the element i per gram of the matrix material, the thickness x of the matrix at which protons of incident energy Ep are degraded to E, the mass attenuation coefficient pj for X-rays of element i, the X-ray production cross sections u,(E) at energy E and the stopping power S,(E) for the matrix for protons with energy E. The thickness x in the matrix is given by:
Jq$,,(E) ix==
Ed.5
cos 8.,
cos 0,’
(2)
where 0, is the angle between the proton beam and the
The experimental yields for L, X-rays are shown in fig. 1 as a function of Z, along with the calculated curve. The calculated curve is normalized by a factor of 0.2707 so that the calculated and measured yields of Wo coincide with each other. The systematic shift between the calculated and observed yields may arise from uncertainties in the detector solid angle, which could be determined only approximately, uncertainties in the calculation of stopping powers and in the cross section
*1
Fig. 1. Variation of the L, X-ray yield from an infinitely thick target (HBO, E, =
matrix) as a function of atomic number (Z) at
2.61 MeV. The error bars are from counting statistics and
correspond to one standard deviation. The continuous represents the normalized calculated values.
line
M. Khaliquzzaman
et al. / Yield of L, X-rays from a light element matrix
3
Fig. 2. Variation of calculated L X-ray yields as function of beam energy in a carbon matrix (not normalized); (1) E, = 3.69 MeV, (2) EP = 3.16 MeV, (3) E, 2.61 MeV, (4) EP = 2.16 MeV. data,
and
tenuated
from beam
errors energy
in
the
calculation
on the target.
that interaction
of the uncertainties
the yield could
amplify
and
the
tematic
shift in the cross section
in the evaluation uncertainties
calculated
values.
between For
are
care
sys-
data may be amplified
of the integration taken
of
the ob-
example,
in eq. (l),
of by
due to
All the four
the normalization
In any case it is the good agreement between the experimental and normalized calculated yields as a function of atomic number which is of importance in analytical applications. Such a fit means that, once the calculated yield curve is normalized at any single point of measured L, X-ray yield for an element, the curve in turn can be used to find the concentration of an unknown element. The energy dependence of La X-ray yield was studied by performing calculations at several incident proton energies. This is shown in fig. 2. The general pattern of the curves is similar to that in the case of K X-rays [l]. For small changes in incident energy the yield curves are almost parallel. This means that a certain amount of error (- 100 keV) can be tolerated in the incident energy determination, provided that the yield curves are normalized. It may be noted that the fall in the yields for 2 < 60 is due to the absorbers between the target and the detector. factor.
4.2. Yield variation
with matrix
7
Fig. 3. Variation in the relative yield for L, X-rays for different matrix compositions at E = 2.61 MeV: (1) silica (SiO,), (2) HBO,, (3) H, BO,, (4) carbohydrate (CH, 0),, (5) cellulose (C,H,,O,),.
where I, is the yield in a given matrix and I, that in a carbon matrix. It is interesting to note that the relative yields for L, X-rays drop as the Z-number decreases, which is opposite to the result obtained for K X-rays [l]. The almost parallel nature of the curves for Z > 60 for light matrices containing H, B, C and 0 shows that the same calculated yield curve can be used for all the matrices studied here (for Z > 60), provided it is normalized in each case. It can also be seen that the variation in the yield is rather small, being less than 10% among the matrices studied here. However, if the matrix change is drastic, then significant changes in the
composition
The plots of calculated relative yields (I,) for five different matrices are shown in fig. 3. The relative yields have been defined as 1, = I,/&
Cm
at-
in the calculation
in the energy loss calculation.
uncertainties
the
It is also possible
the difference
served
of
261
(3)
Fig. 4. Variation of minimum detection limit in thick-target PIXE using L, X-rays as a function of atomic number (2) at E, = 2.61 MeV. The error bars are statistical errors corresponding to one standard deviation. The continuous line is the least-squares fit to the data.
262
M. Khaliquzzaman et al. / Yield
I, X-ray yields can take place. This is shown in fig. 3 when the matrix is changed to SiO,.
4.3. Minimum
detection
limits
The minimum detection limit (MDL) is defined as the amount of an element in ppm which corresponds to the number of counts equal to three standard deviations of the background. The details of MDL calculations have been explained elsewhere [l]. The MDLs for the different elements for 10 PC irradiation are shown in fig. 4 as a function of Z. The continuous curve is the least-square fit to the data. The minimum of MDL (- 10 ppm) occurs for Z around 70. The MDL can ofcourse be reduced by longer irradiation, From the cross sections’ consideration (fig. 2), it may appear that the MDL may be reduced by increasing the beam energy, but this may not necessarily be the case, because of the increase in background with the increase in beam energy [ 11.
ofL, X-rays froma light element matrix using a standard. In light element matrices the X-ray yields vary only slightly with matrix composition and as such only approximate knowledge of the matrix composition can yield resonably accurate analytical results. The authors would like to thank Mr. Dennis Ng of Faculty of Pharmacy, University of Alberta for his help in making the synthetic standards. Thanks are due to Dr. G.C. Neilson for his support and interest in the work. One of the authors (MKZ) would like to thank Dr. Mohammed T. Elfazani, Chairman of the Department of Physics, Faculty of Science, University of Garyounis, Benghazi, Libya for extending the facilities of the department where most of the computational work has been performed. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.
References
5. Conclusion.
PI M. Khaliquzzaman, S.T. Lam, D.M. Sheppard and L.G.
It has been shown that calculated L, X-ray yields for elements with Z 2 52, imbedded in light-element matrices for infinitely thick targets, are in good agreement with experimentally observed yields except for a normalization constant. As the atomic number dependence of the yields is reproduced quantitatively, such curves can be used for analytical applications, provided they are normalized at least at a single atomic number
PI D.D. Cohen, M. Harrigan, Atomic Data and Nucl. Data
Stephens-Newsham, Nucl. Ins&. and Meth. 216 (1983) 481.
Tables 34 (1986) 393. [31 A. Simonits, L. Moens, F. De Corte, A. De Wispelaere and A. Elek, J. Hoste, J. Radioanal. Chem. 60 (1980) 461. 141W. Whaling, Handbuch der Physik, vol. 38 (Springer, Berlin, 1958) p. 193. 151 H.H. Andersen and J.F. Ziegler, Hydrogen Stopping Powers and Range in All Elements. (Pergamon Press, 1977). 161 E. Storm and H.I. Israel, Nucl. Data Tables A7 (1970) 565.