- Email: [email protected]
Measurement of K-shell absorption edge jump factors and jump ratios of some medium Z elements using EDXRF technique
Radiation Physics and Chemistry 80 (2011) 28–32
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Measurement of K-shell absorption edge jump factors and jump ratios of some medium Z elements using EDXRF technique Baltej Singh Sidhu n, A.S. Dhaliwal, K.S. Mann, K.S. Kahlon Department of Physics, Sant Longowal Institute of Engineering & Technology, Deemed-to-be-University, Longowal 148106, Sangrur, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 7 July 2010 Accepted 1 September 2010
Energy dispersive X-ray fluorescence technique (EDXRF) has been employed for measuring K-shell absorption jump factors and jump ratios in elements Mn, Fe, Co, Cu, Zn, As and Sr using an X-PIPS Si(Li) detector. 901 reflection geometry has been used to detect the emitted fluorescent K X-rays from the target elements excited by 59.54 keV gamma-rays emitted from an 241Am radioactive point source. Measured values of these parameters have been compared with different theoretically calculated as well as with other available experimental values. It is found that the present results fairly agree with theoretically calculated and experimental values within experimental uncertainties. & 2010 Elsevier Ltd. All rights reserved.
Keywords: X-ray production cross-section K-shell absorption jump ratio and jump factor
1. Introduction Absorption jump factor and jump ratios are some of the important parameters related to emission and absorption of fluorescent X-rays. For the last three decades there have been both theoretically and experimentally renewed efforts towards better understanding of the physics of emission and absorption of fluorescent X-rays because of their numerous applications in the field of radiation physics, astro-physics, atomic physics and nondestructive trace elemental analysis of samples of biological, geological, industrial and technical interest. Total atomic interaction cross-section st of a given element does not vary smoothly with incident photon energy but there are sharp discontinuities that arise whenever the incident photon energy coincides with the binding energy of the electron in K, L, M, y shells. These sharp discontinuities, also known as absorption jumps in the cross-section at the photon energy corresponding to the shell binding energies, are due to the photoelectric interaction, which increases suddenly the probability of interaction between photon and electron of a particular shell, resulting in an abrupt change in the value of photoelectric cross-section. At these absorption edges, there are two values of photoelectric absorption coefficient t, one on the higher energy side of an edge, which corresponds to the values of this coefficient due to K-shell and higher shells, and the other on the lower energy side, which is due to L-shell and higher shells. The ratio of values of photoelectric absorption coefficient on higher to lower energy sides of an edge directly gives the absorption jump ratio, and the
n
Corresponding author. Tel.: +91 1672 2305186; fax: + 91 1672 280057. E-mail address: [email protected] (B. Singh Sidhu).
0969-806X/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2010.09.001
difference in values of photoelectric absorption coefficients on both sides of an edge gives the photoelectric cross-section of particular shell/sub-shell. Similarly absorption jump factor is associated with photoelectric absorption coefficient t for different shells/subshells (i.e. tK,tLI, tLII, y) and is defined as the fraction of the total absorption that is associated with a given shell rather than for any other shell. For example, K-shell jump ratio rK is given as rK ¼
tK þðtLI þ tLII þ tLIII Þ þ . . . ðtLI þ tLII þ tLIII Þ þðtMI þ tMII þ tMIII þ . . .Þ þ. . .
ð1Þ
Similarly, K-shell absorption jump factor JK is given as JK ¼
tK tK þ ðtLI þ tLII þ tLIII Þ þ ðtMI þ tMII þ tMIII þ . . .Þ þ . . .
ð2Þ
or Jk ¼ 1rk1 where ti is photoelectric cross-section of the ith shell. Review of experimental literature on absorption jump factor and jump ratios shows that some researchers have measured the values of these parameters for K-shell of many elements with ZZ40 using different techniques viz. the gamma-ray attenuation method (Mallikarjuna et al., 2002; Kaya et al., 2007) , the Compton peak attenuation method (Ayala and Mainardi, 1996; Polat et al., 2004; Budak and Polat, 2004), the EDXRF technique (Ertugrul et al., 2002; Budak et al., 2003; Polat et al., 2005; Nayak and Badiger, 2006) and the bremsstrahlung transmission method (Bennal and Badiger, 2007). In view of this, in the present communication we report on measurements of K-shell absorption jump factors and jump ratios in elements Mn, Fe, Co, Cu, Zn, As and Sr using the EDXRF method.
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
accuracy of r1% in counting rates. Typical spectra of Mn with Ka and Kb photopeak areas well separated by fitting the measured spectra with appropriate multi-Gaussian function using software programme are shown in Fig. 2. The cross-section for the production of Ki X-rays, sXKi , is given by
2. Method of computation and measurement 2.1. Measurement of absorption edge jump factor (JK) and jump ratio (rK) K-shell jump factor, JK, of an element has been derived using the following relation (Ertugrul et al., 2002): JK ¼
sXK a ðst sts ÞoK FK a
ð3Þ
st and sts are Ka X-ray production cross-section, total where s atomic interaction cross-section and total scattering cross-section at incident gamma-rays of energy 59.54 keV, respectively, oK is the K-shell fluorescence yield and FKa the fraction of Ka X-ray emission rates. The presently measured values of JK have been further used to extract the values of jump ratios, rK, in the elements studied using the following relation: 1 1JK
sXKi ¼ Sao
1
NKi M o2 eKi N
ð4pÞ2
X Ka,
rK ¼
29
ð4Þ
K-shell jump factors for elements Mn, Fe, Co, Cu, Zn, As and Sr have been measured by making use of the measured values of the parameters sXK a , st and FKa and by using the theoretically calculated values of sts and oK. It is to be noted here that in order to measure FKa, the cross-sections for the production of Kb X-rays sXK b have also been measured along with sXK a . Subsequent paragraphs describe the measurement of parameters sXKi (i ¼ a, b), st and FKa. 2.2. Measurement of Ka X-ray production cross-section (sXKi ) For the measurements of sXKi (i¼ a, b), target elements of Mn, Fe, Co, Cu, Zn, As and Sr in the form of circular discs of 4.5 cm diameter have been irradiated with 59.54 keV g-rays emitted from 100 mCi 241Am source in a 901 reflection geometrical setup shown in Fig. 1. Self-supporting targets of Mn, Co, As and Sr were made from their stable chemical compounds using the technique described in Arora et al. (1981) but metallic targets of Fe, Cu and Zn have also been used in the present investigation. The K-shell fluorescence X-rays emitted from targets were analyzed by Canberra X-PIPS Si(Li) detector with an active area 8 mm2 and Be window of thickness 25 mm. This detector is embedded with a collimator of width 1.1 mm. The thickness of X-PIPS Si(Li) detector chip is 500 mm. The resolution of the detector is o190 eV at 5.9 keV photon energy and is coupled to EG&G Ortec multichannel analyzer. Direct radiations from the source to the detector were prevented using graded shielding. Spectra of different elements were recorded for a time of 3 104 s and sufficient numbers of runs were taken to achieve statistical
, t bKi
i ¼ a, b
ð5Þ
where NKi is the number of X-rays falling under Ki peak, which has been counted by X-PIPS Si(Li) detector, with S being the number of gamma-rays emitted from the source, a the correction factor for absorption of gamma-rays in source and air column, N the Avogadro number, M and t are the molecular weight and thickness of target element, respectively, o1 and o2 are source– target and target–detector solid angles, respectively, and eK a is the photopeak efficiency of detector at Ka X-rays . bKi is the selfabsorption correction factor of the target and is calculated as pffiffiffi 1expððmp þ mei Þ 2tÞ p ffiffiffi ð6Þ bKi ¼ ðmp þ mei Þ 2t where mp and mei are the mass attenuation coefficients of the target element at incident photon energy and emitted Ki X-ray energies, respectively (Gerward et al., 2001). 2.3. Measurement of geometrical efficiency related factor ðSao1 o2 eKi N=ð4pÞ2 Þ Value of factor Sao1 o2 eKi N=ð4pÞ2 in expression (5), which contains the terms related to flux of 59.54 keV g-rays emitted from the source, geometrical factor and absolute efficiency of detector, has been determined in a separate experiment (Mann et al., 1991). For this purpose target elements with 22 rZr40 other than those used in the main experiment, having the same size as the main experiment targets, were irradiated with g-rays from the source. NKi is the number of X-rays falling under Ki peak emitted from the targets in this experiment and counted under the photopeak per unit time: Sao1 o2 eKi N ð4pÞ2
¼
NKi M t bKi sXKi
ð7Þ
The theoretical values of sXKi for these target elements needed in expression (7) have been calculated using the following relation:
sXKi ¼ spK oK FKi
ð8Þ
p K
where s is the K-shell photo-ionization cross-section at incident gamma-rays of energy 59.57 keV and has been taken from the tabulated values of Scofield (1973), oK the K-shell fluorescence yield (Krause , 1979) and FKi the fractional Ki X-ray emission rates (Scofield, 1974). The measured values of the factor NKi M=t bKi sXKi were then fitted to a second-degree polynomial as a function of Ki X-ray of these elements. The values of this factor at energies of Ka X-ray peak needed to determine the Ka X-ray production crosssection of elements under study were then read from the plot. 2.4. Measurement of total atomic interaction cross-sections (st)
Fig. 1. Schematic diagram of 901 reflection geometry.
Total atomic interaction cross-sections st of incident gammarays in elements Mn, Fe, Co, Cu, Zn, As and Sr have been measured using the narrow beam transmission method by employing the geometry shown in Fig. 3. Incident, I0, and transmitted, I, intensities of gamma-ray photons without and with absorber were measured and the values of st for the elements under
30
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
6000 6000 Mn Kα
5000
5000
Counts
4000
Counts
4000
3000 2000
Mn Kβ
3000 1000
110
2000
120
130
140
150
160
170
Channel No.
1000
110
120
130
140 Channel No.
150
160
170
Fig. 2. Typical spectra of Mn separated with appropriate multi-Gaussian fit.
10 mm
10 mm
4 mm
3 mm
10 mm
2 mm
T
D
S 90 mm
100 mm
Lead collimators Fig. 3. Schematic diagram of linear transmission geometry.
examination have been calculated from the following relation:
st ¼
M lnðI=Io Þ N t
ð9Þ
where t is the thickness of the target element, M the atomic mass of target sample and N is Avogadro’s number. In the present measurement, the detector was properly shielded with lead and the total scatter acceptance angle was 2.971, which is o31. Therefore for this acceptance angle, scattered radiations reaching the detector can produce a ray sum error of 0.5–1.0%, which is within the tolerable limit (Midgley, 2006).
measured experimentally using relation (5) which can be rewritten as IK b NK b bK a eK a ¼ IK a NK a bK b eK b
ð11Þ
where eK a and eK b are the efficiencies of detector for Ka and Kb X-rays, respectively; others terms have the same meaning as explained earlier in expression (5) but for Kb X-rays. Finally the calculated values of oi (Krause, 1979) and sts (Gerward et al., 2001) were then used in expression (3) for obtaining the values of JK.
2.5. Measurement of intensity ratio IKb/IKa 3. Results and discussion The fraction of Ki (i¼ a, b) X-ray radiative rates, FKi, for elements under study has been measured using the following relations: IK b 1 IK a 1 FK a ¼ 1 þ and FK b ¼ 1 þ ð10Þ IK a IK b where IKa and IKb are the measured intensities of Ka and Kb X-rays of elements under study, respectively. The ratio IKb/IKa has been
The measured values of JK and rK along with the calculated values (Gerward et al., 2001; Storm and Israel, 1970; Chantler et al., 2005) for elements Mn, Fe, Co, Cu, Zn, As and Sr as well as the values for elements Cu and Zn calculated from the experimental data (Chantler et al., 2001; Rae et al., 2010) have been depicted in tabular form shown in Table 1 as well as in Figs. 4 and 5. It is found that the measured values are in good agreement with
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
31
Table 1 Present experimental, theoretical and other experimental values for JK and rK. Element
JK
Mn
Fe
rK
Experimental
Theoretical
0.878
0.877 0.875 0.882 0.876 0.873 0.878 0.874 0.872 0.875 0.871 0.868 0.868 0.870 0.867 0.868 0.866 0.863 0.865 0.857 0.855 0.854
0.874
Co
0.873
Cu
0.867
Zn
0.869
As
0.864
Sr
0.858
Other experimental
a
Experimental
Theoretical
8.196
8.130 a 8.006 b 8.458 c 8.064 a 7.889 b 8.239 c 7.936 a 7.801 b 8.025c 7.752 a 7.564 b 7.595 c 7.692 a 7.547 b 7.592 c 7.462 a 7.317 b 7.435 c 6.993 a 6.889 b 6.865 c
b c a
7.936
b c a
7.874
b c a
0.869d
7.519
0.859e
7.633
b c a b c a
7.353
b c a
7.042
b c
Other experimental
7.652d
7.103e
a
Storm and Israel (1970). Gerward (2001). c Chantler et al. (2000). d Chantler et al. (2001). e Rae et al. (2010).
90.0 89.5 89.0 88.5 88.0 87.5 87.0 86.5 86.0 85.5 85.0 84.5 84.0 83.5 83.0
8.6
Experimental
Experimental Storm&Israel(1970) Gerward(2001) Chantler et.al(2000) Chantler et.al(2001) Rae et.al(2010)
8.4
Storm &Israel(1970) Gerward(2001)
8.2
Chantler et.al(2000) Chantler et.al(2001)
8.0
Rae et.al(2010)
Jump ratio rK
Jump factor JKx10-02
b
7.8 7.6 7.4 7.2 7.0 6.8 6.6
24
26
28
30
32
34
36
38
40
Atomic number Z Fig. 4. Plot of absorption edge jump factor JK as a function of atomic number (Z).
the theoretically calculated as well as the other experimental values within experimental uncertainties. The overall estimated error associated with the present measurement is of the order of 6% , which includes uncertainty involved in the evaluation of different parameters such as area under photopeak (i.e. statistical error 2%), non-uniform target thickness and self-absorption correction factor 2–3%, critical geometrical factor 5%, etc. Uncertainties in the present measurements have been calculated by taking properly the propagation of errors in various measured quantities. In order to have a further check for the accuracy and reliability of calculated values, more experimental data for the values of JK and rK for elements with Zo 25 are needed and
24
26
28
30
32
34
36
38
40
Atomic number Z Fig. 5. Plot of absorption edge jump ratio rK as a function of atomic number.
moreover no measurements are available on these parameters for any of the elements except for bismuth for L and higher shells/ subshells. To the best of the authors’ knowledge, the present measurements for the aforesaid elements have been reported for the first time using the present technique.
Acknowledgement One of the authors (B.S. Sidhu) is thankful to the Sant Longowal Institute of Engineering and Technology, Longowal, for providing financial support in terms of fellowship.
32
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
References Arora, S.K., Allawadhi, K.L., Sood, B.S., 1981. K-shell photoelectric cross-section measurements. Phys. Rev. A 23, 1147–1151. Ayala, A.P., Mainardi, R.T., 1996. Measurement of K X-ray absorption jump ratio of erbium by attenuation of a Compton peak. Radiat. Phys. Chem. 47, 177–181. Bennal, A.S., Badiger, N.M., 2007. Measurement of K shell absorption and fluorescent parameters for elements Mo, Ag, Cd, In and Sn using a weak gamma source. J. Phys. B: At. Mol. Opt. Phys. 40, 2189–2199. Budak, G., Karabulut, A., Ertugrul, M., 2003. Determination of K-shell absorption jump factor for some elements using EDXRF Technique. Radiat. Meas. 37, 103–107. Budak, G., Polat, R., 2004. Measurement of the K X-ray absorption jump factors and jump ratios of Gd, Dy, Ho and Er by attenuation of a Compton peak. J. Quant. Spectrosc. Radiat. Transfer 88, 525–532. Chantler, C.T., Olsen, K., Dragoset, R.A., Chang, J., Kishore, A.R., Kotochigova, S.A., Zucker,D.S., 2005. X-Ray form factor, attenuation and scattering tables (version 2.1). [Online] Available: /http://physics.nist.gov/ffastS August 22, 2010, National Institute of Standards and Technology, Gaithersburg, MD. Chantler, C.T., Tran, C.Q., Barnea, Z., Paterson, D., Cookson, D.J., Balaic, D.X., 2001. Measurement of the X-ray mass attenuation coefficient of copper using 8.85–20 keV synchrotron radiation. Phys. Rev. A 64 062506-1–15. Ertugrul, M., Karabulut, A., Budak, G., 2002. Measurement of the K shell absorption jump factor of some elements. Radiat. Phys. Chem. 64, 1–3. Gerward, L., Guilbert, N., Jensen, B., Levring, H., 2001. X-ray absorption in matter: re-engineering XCOM. Radiat. Phys. Chem. 60, 23–24. Kaya, N., Tırasoglu, E., Apaydın, G., Aylıkcı, V., Cengiz, E., 2007. K-shell absorption jump factors and jump ratios in element between Tm (Z¼ 69) and Os (Z¼76) derived
from new mass attenuation coefficient measurements. Nucl. Instrum. Methods B 262, 16–23. Krause, M.O., 1979. Atomic radiative and radiationless yields for K and L shell. J. Phys. Chem. Ref. Data 8, 307–327. Mallikarjuna, M.,.L., Appaji Gowda, S.B., Gowda, R., Umesh, T.K., 2002. Study on photon interaction around the K-edge of some rare earth elements. Radiat.Phys. Chem. 65, 217–223. Mann, K.S., Mittal, R., Allawadhi, K.L., Sood, B.S., 1991. Measurement of Ll, La, Lb and Lg X-ray production cross sections in rare-earth elements by 60-keV photons. Phys. Rev. A 44, 2198–2201. Midgley, S.M., 2006. Energy resolution for X-ray linear attenuation coefficient measurements. Radiat. Phys. Chem. 75, 936–944. Nayak, S.V., Badiger, N.M., 2006. A novel method for measuring K shell photoelectric parameters of high Z elements. J. Phys. B: At. Mol. Opt. Phys. 39, 2893–2900. Polat, R., Budak, G., Gurol, A., Karabulut, A., Ertugrul, M., 2005. K-shell absorption jump factors for the elements Ag, Cs, Ba and La derived from new mass attenuation coefficient measurements using EDXRF technique. Radiat. Meas. 39, 409–415. Polat, R., Icelli, O., Budak, G., 2004. New method to measure the K-shell absorption jump factor in some rare-earth elements. Anal. Chim. Acta 505, 307–314. Rae, N.A., Chantler, C.T., Barnea, Z., 2010. X-ray mass attenuation coefficients and imaginary components of the atomic form factor of zinc over the energy range of 7.2–15.2 keV. Phys. Rev. A 81, 022904–022910. Scofield, J.H., 1973. Theoretical photoionization cross-sections from 1 to 1500 keV. Report no. UCRL 51326, Lawrence Livermore Laboratory, Livermore, CA. Scofield, J.H., 1974. Exchange correction of K X-ray emission rates. Phys. Rev. A 9, 1041–1049. Storm, E., Israel, I.H., 1970. Photon cross-section from 1 keV to 100 MeV for elements from Z ¼1 to 100. In: Nuclear Data Tables A7, pp. 565–681.
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Measurement of K-shell absorption edge jump factors and jump ratios of some medium Z elements using EDXRF technique Baltej Singh Sidhu n, A.S. Dhaliwal, K.S. Mann, K.S. Kahlon Department of Physics, Sant Longowal Institute of Engineering & Technology, Deemed-to-be-University, Longowal 148106, Sangrur, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 7 July 2010 Accepted 1 September 2010
Energy dispersive X-ray fluorescence technique (EDXRF) has been employed for measuring K-shell absorption jump factors and jump ratios in elements Mn, Fe, Co, Cu, Zn, As and Sr using an X-PIPS Si(Li) detector. 901 reflection geometry has been used to detect the emitted fluorescent K X-rays from the target elements excited by 59.54 keV gamma-rays emitted from an 241Am radioactive point source. Measured values of these parameters have been compared with different theoretically calculated as well as with other available experimental values. It is found that the present results fairly agree with theoretically calculated and experimental values within experimental uncertainties. & 2010 Elsevier Ltd. All rights reserved.
Keywords: X-ray production cross-section K-shell absorption jump ratio and jump factor
1. Introduction Absorption jump factor and jump ratios are some of the important parameters related to emission and absorption of fluorescent X-rays. For the last three decades there have been both theoretically and experimentally renewed efforts towards better understanding of the physics of emission and absorption of fluorescent X-rays because of their numerous applications in the field of radiation physics, astro-physics, atomic physics and nondestructive trace elemental analysis of samples of biological, geological, industrial and technical interest. Total atomic interaction cross-section st of a given element does not vary smoothly with incident photon energy but there are sharp discontinuities that arise whenever the incident photon energy coincides with the binding energy of the electron in K, L, M, y shells. These sharp discontinuities, also known as absorption jumps in the cross-section at the photon energy corresponding to the shell binding energies, are due to the photoelectric interaction, which increases suddenly the probability of interaction between photon and electron of a particular shell, resulting in an abrupt change in the value of photoelectric cross-section. At these absorption edges, there are two values of photoelectric absorption coefficient t, one on the higher energy side of an edge, which corresponds to the values of this coefficient due to K-shell and higher shells, and the other on the lower energy side, which is due to L-shell and higher shells. The ratio of values of photoelectric absorption coefficient on higher to lower energy sides of an edge directly gives the absorption jump ratio, and the
n
Corresponding author. Tel.: +91 1672 2305186; fax: + 91 1672 280057. E-mail address: [email protected] (B. Singh Sidhu).
0969-806X/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2010.09.001
difference in values of photoelectric absorption coefficients on both sides of an edge gives the photoelectric cross-section of particular shell/sub-shell. Similarly absorption jump factor is associated with photoelectric absorption coefficient t for different shells/subshells (i.e. tK,tLI, tLII, y) and is defined as the fraction of the total absorption that is associated with a given shell rather than for any other shell. For example, K-shell jump ratio rK is given as rK ¼
tK þðtLI þ tLII þ tLIII Þ þ . . . ðtLI þ tLII þ tLIII Þ þðtMI þ tMII þ tMIII þ . . .Þ þ. . .
ð1Þ
Similarly, K-shell absorption jump factor JK is given as JK ¼
tK tK þ ðtLI þ tLII þ tLIII Þ þ ðtMI þ tMII þ tMIII þ . . .Þ þ . . .
ð2Þ
or Jk ¼ 1rk1 where ti is photoelectric cross-section of the ith shell. Review of experimental literature on absorption jump factor and jump ratios shows that some researchers have measured the values of these parameters for K-shell of many elements with ZZ40 using different techniques viz. the gamma-ray attenuation method (Mallikarjuna et al., 2002; Kaya et al., 2007) , the Compton peak attenuation method (Ayala and Mainardi, 1996; Polat et al., 2004; Budak and Polat, 2004), the EDXRF technique (Ertugrul et al., 2002; Budak et al., 2003; Polat et al., 2005; Nayak and Badiger, 2006) and the bremsstrahlung transmission method (Bennal and Badiger, 2007). In view of this, in the present communication we report on measurements of K-shell absorption jump factors and jump ratios in elements Mn, Fe, Co, Cu, Zn, As and Sr using the EDXRF method.
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
accuracy of r1% in counting rates. Typical spectra of Mn with Ka and Kb photopeak areas well separated by fitting the measured spectra with appropriate multi-Gaussian function using software programme are shown in Fig. 2. The cross-section for the production of Ki X-rays, sXKi , is given by
2. Method of computation and measurement 2.1. Measurement of absorption edge jump factor (JK) and jump ratio (rK) K-shell jump factor, JK, of an element has been derived using the following relation (Ertugrul et al., 2002): JK ¼
sXK a ðst sts ÞoK FK a
ð3Þ
st and sts are Ka X-ray production cross-section, total where s atomic interaction cross-section and total scattering cross-section at incident gamma-rays of energy 59.54 keV, respectively, oK is the K-shell fluorescence yield and FKa the fraction of Ka X-ray emission rates. The presently measured values of JK have been further used to extract the values of jump ratios, rK, in the elements studied using the following relation: 1 1JK
sXKi ¼ Sao
1
NKi M o2 eKi N
ð4pÞ2
X Ka,
rK ¼
29
ð4Þ
K-shell jump factors for elements Mn, Fe, Co, Cu, Zn, As and Sr have been measured by making use of the measured values of the parameters sXK a , st and FKa and by using the theoretically calculated values of sts and oK. It is to be noted here that in order to measure FKa, the cross-sections for the production of Kb X-rays sXK b have also been measured along with sXK a . Subsequent paragraphs describe the measurement of parameters sXKi (i ¼ a, b), st and FKa. 2.2. Measurement of Ka X-ray production cross-section (sXKi ) For the measurements of sXKi (i¼ a, b), target elements of Mn, Fe, Co, Cu, Zn, As and Sr in the form of circular discs of 4.5 cm diameter have been irradiated with 59.54 keV g-rays emitted from 100 mCi 241Am source in a 901 reflection geometrical setup shown in Fig. 1. Self-supporting targets of Mn, Co, As and Sr were made from their stable chemical compounds using the technique described in Arora et al. (1981) but metallic targets of Fe, Cu and Zn have also been used in the present investigation. The K-shell fluorescence X-rays emitted from targets were analyzed by Canberra X-PIPS Si(Li) detector with an active area 8 mm2 and Be window of thickness 25 mm. This detector is embedded with a collimator of width 1.1 mm. The thickness of X-PIPS Si(Li) detector chip is 500 mm. The resolution of the detector is o190 eV at 5.9 keV photon energy and is coupled to EG&G Ortec multichannel analyzer. Direct radiations from the source to the detector were prevented using graded shielding. Spectra of different elements were recorded for a time of 3 104 s and sufficient numbers of runs were taken to achieve statistical
, t bKi
i ¼ a, b
ð5Þ
where NKi is the number of X-rays falling under Ki peak, which has been counted by X-PIPS Si(Li) detector, with S being the number of gamma-rays emitted from the source, a the correction factor for absorption of gamma-rays in source and air column, N the Avogadro number, M and t are the molecular weight and thickness of target element, respectively, o1 and o2 are source– target and target–detector solid angles, respectively, and eK a is the photopeak efficiency of detector at Ka X-rays . bKi is the selfabsorption correction factor of the target and is calculated as pffiffiffi 1expððmp þ mei Þ 2tÞ p ffiffiffi ð6Þ bKi ¼ ðmp þ mei Þ 2t where mp and mei are the mass attenuation coefficients of the target element at incident photon energy and emitted Ki X-ray energies, respectively (Gerward et al., 2001). 2.3. Measurement of geometrical efficiency related factor ðSao1 o2 eKi N=ð4pÞ2 Þ Value of factor Sao1 o2 eKi N=ð4pÞ2 in expression (5), which contains the terms related to flux of 59.54 keV g-rays emitted from the source, geometrical factor and absolute efficiency of detector, has been determined in a separate experiment (Mann et al., 1991). For this purpose target elements with 22 rZr40 other than those used in the main experiment, having the same size as the main experiment targets, were irradiated with g-rays from the source. NKi is the number of X-rays falling under Ki peak emitted from the targets in this experiment and counted under the photopeak per unit time: Sao1 o2 eKi N ð4pÞ2
¼
NKi M t bKi sXKi
ð7Þ
The theoretical values of sXKi for these target elements needed in expression (7) have been calculated using the following relation:
sXKi ¼ spK oK FKi
ð8Þ
p K
where s is the K-shell photo-ionization cross-section at incident gamma-rays of energy 59.57 keV and has been taken from the tabulated values of Scofield (1973), oK the K-shell fluorescence yield (Krause , 1979) and FKi the fractional Ki X-ray emission rates (Scofield, 1974). The measured values of the factor NKi M=t bKi sXKi were then fitted to a second-degree polynomial as a function of Ki X-ray of these elements. The values of this factor at energies of Ka X-ray peak needed to determine the Ka X-ray production crosssection of elements under study were then read from the plot. 2.4. Measurement of total atomic interaction cross-sections (st)
Fig. 1. Schematic diagram of 901 reflection geometry.
Total atomic interaction cross-sections st of incident gammarays in elements Mn, Fe, Co, Cu, Zn, As and Sr have been measured using the narrow beam transmission method by employing the geometry shown in Fig. 3. Incident, I0, and transmitted, I, intensities of gamma-ray photons without and with absorber were measured and the values of st for the elements under
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B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
6000 6000 Mn Kα
5000
5000
Counts
4000
Counts
4000
3000 2000
Mn Kβ
3000 1000
110
2000
120
130
140
150
160
170
Channel No.
1000
110
120
130
140 Channel No.
150
160
170
Fig. 2. Typical spectra of Mn separated with appropriate multi-Gaussian fit.
10 mm
10 mm
4 mm
3 mm
10 mm
2 mm
T
D
S 90 mm
100 mm
Lead collimators Fig. 3. Schematic diagram of linear transmission geometry.
examination have been calculated from the following relation:
st ¼
M lnðI=Io Þ N t
ð9Þ
where t is the thickness of the target element, M the atomic mass of target sample and N is Avogadro’s number. In the present measurement, the detector was properly shielded with lead and the total scatter acceptance angle was 2.971, which is o31. Therefore for this acceptance angle, scattered radiations reaching the detector can produce a ray sum error of 0.5–1.0%, which is within the tolerable limit (Midgley, 2006).
measured experimentally using relation (5) which can be rewritten as IK b NK b bK a eK a ¼ IK a NK a bK b eK b
ð11Þ
where eK a and eK b are the efficiencies of detector for Ka and Kb X-rays, respectively; others terms have the same meaning as explained earlier in expression (5) but for Kb X-rays. Finally the calculated values of oi (Krause, 1979) and sts (Gerward et al., 2001) were then used in expression (3) for obtaining the values of JK.
2.5. Measurement of intensity ratio IKb/IKa 3. Results and discussion The fraction of Ki (i¼ a, b) X-ray radiative rates, FKi, for elements under study has been measured using the following relations: IK b 1 IK a 1 FK a ¼ 1 þ and FK b ¼ 1 þ ð10Þ IK a IK b where IKa and IKb are the measured intensities of Ka and Kb X-rays of elements under study, respectively. The ratio IKb/IKa has been
The measured values of JK and rK along with the calculated values (Gerward et al., 2001; Storm and Israel, 1970; Chantler et al., 2005) for elements Mn, Fe, Co, Cu, Zn, As and Sr as well as the values for elements Cu and Zn calculated from the experimental data (Chantler et al., 2001; Rae et al., 2010) have been depicted in tabular form shown in Table 1 as well as in Figs. 4 and 5. It is found that the measured values are in good agreement with
B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
31
Table 1 Present experimental, theoretical and other experimental values for JK and rK. Element
JK
Mn
Fe
rK
Experimental
Theoretical
0.878
0.877 0.875 0.882 0.876 0.873 0.878 0.874 0.872 0.875 0.871 0.868 0.868 0.870 0.867 0.868 0.866 0.863 0.865 0.857 0.855 0.854
0.874
Co
0.873
Cu
0.867
Zn
0.869
As
0.864
Sr
0.858
Other experimental
a
Experimental
Theoretical
8.196
8.130 a 8.006 b 8.458 c 8.064 a 7.889 b 8.239 c 7.936 a 7.801 b 8.025c 7.752 a 7.564 b 7.595 c 7.692 a 7.547 b 7.592 c 7.462 a 7.317 b 7.435 c 6.993 a 6.889 b 6.865 c
b c a
7.936
b c a
7.874
b c a
0.869d
7.519
0.859e
7.633
b c a b c a
7.353
b c a
7.042
b c
Other experimental
7.652d
7.103e
a
Storm and Israel (1970). Gerward (2001). c Chantler et al. (2000). d Chantler et al. (2001). e Rae et al. (2010).
90.0 89.5 89.0 88.5 88.0 87.5 87.0 86.5 86.0 85.5 85.0 84.5 84.0 83.5 83.0
8.6
Experimental
Experimental Storm&Israel(1970) Gerward(2001) Chantler et.al(2000) Chantler et.al(2001) Rae et.al(2010)
8.4
Storm &Israel(1970) Gerward(2001)
8.2
Chantler et.al(2000) Chantler et.al(2001)
8.0
Rae et.al(2010)
Jump ratio rK
Jump factor JKx10-02
b
7.8 7.6 7.4 7.2 7.0 6.8 6.6
24
26
28
30
32
34
36
38
40
Atomic number Z Fig. 4. Plot of absorption edge jump factor JK as a function of atomic number (Z).
the theoretically calculated as well as the other experimental values within experimental uncertainties. The overall estimated error associated with the present measurement is of the order of 6% , which includes uncertainty involved in the evaluation of different parameters such as area under photopeak (i.e. statistical error 2%), non-uniform target thickness and self-absorption correction factor 2–3%, critical geometrical factor 5%, etc. Uncertainties in the present measurements have been calculated by taking properly the propagation of errors in various measured quantities. In order to have a further check for the accuracy and reliability of calculated values, more experimental data for the values of JK and rK for elements with Zo 25 are needed and
24
26
28
30
32
34
36
38
40
Atomic number Z Fig. 5. Plot of absorption edge jump ratio rK as a function of atomic number.
moreover no measurements are available on these parameters for any of the elements except for bismuth for L and higher shells/ subshells. To the best of the authors’ knowledge, the present measurements for the aforesaid elements have been reported for the first time using the present technique.
Acknowledgement One of the authors (B.S. Sidhu) is thankful to the Sant Longowal Institute of Engineering and Technology, Longowal, for providing financial support in terms of fellowship.
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B. Singh Sidhu et al. / Radiation Physics and Chemistry 80 (2011) 28–32
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