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Measurement of K-shell fluorescence cross-sections and yields of 14 elements in the atomic number range 25⩽Z⩽47 using photoionization
Radiation Physics and Chemistry 61 (2001) 19–25
Measurement of K-shell fluorescence cross-sections and yields of 14 elements in the atomic number range 254Z447 using photoionization . Rıdvan Durak*, Yu¨ksel O¨zdemır Atatu¨rk U¨niversitesi, Fen-Edebiyat Faku¨ltesi, Fizik Bo¨lu¨mu¨, 25240 Erzurum, Tu¨rkey Received 3 March 2000; accepted 23 September 2000
Abstract K-shell X-ray fluorescence cross-sections for the elements Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag have been measured at the excitation energy of the 59.54 keV g-rays from an 241Am radioactive source of strength 100 mCi. In addition, measurement of K X-ray fluorescence yields for these elements at the same excitation energy have also been carried out. The experimental results are compared with the literature experimental values, theoretical predictions, and semiempirical fits. # 2001 Elsevier Science Ltd. All rights reserved. PACS: 32.30.Rj; 34.50.Fa; 32.80.Fb; 32.80.Hd Keywords: X-ray fluorescence; Cross-sections; Photoionization; Fluorescence yields
1. Introduction K X-ray fluorescence (XRF) cross-sections and yields are required in a variety of applications including, for example, atomic physics, medical research, non-destructive elemental analysis, and industrial irradiation processing (Hubbell et al., 1994; Durak and S,ahin, 1998). In addition, comparison of measured K X-ray fluorescence cross-sections with theoretical estimates provides a check on the validity of various physical parameters such as photoionization cross-sections, and fluorescence yields. Several attempts have been made for measuring X-ray fluorescence cross-sections and yields. Earlier experimental K X-ray fluorescence cross-sections have been measured using radioisotopes as excitation sources (Garg et al., 1985). K X-ray production cross-sections have been determined theoretically for all the elements at energies ranging from 10 to 60 keV (Krause et al., *Corresponding author. Fax: +90-442-2331062. E-mail address: [email protected] (R. Durak).
1978). Some measurements of K X-ray fluorescence cross-sections for low-Z elements at low excitation energies have been reported (Rani et al., 1988; Rao et al., 1993). However, limited investigations in the case of cross-sections of intermediate-Z elements have been made at different excitation energies in the interval 8–60 keV (Singh et al., 1990; Casnati et al., 1991). K-shell fluorescence yields oK for different elements have been investigated for many years. Bambynek et al. (1972) in a review article have fitted their collection of selected most reliable experimental values in the 134Z492 range. Krause (1979) compiled oK adopted values for elements 54Z4110. Hubbell et al. (1994) have compiled more recent experimental values. Theoretical values of oK were obtained in the region 4 4Z454 by McGuire (1970a, b) and Walters and Bhalla (1971) using the Hartree–Fock–Slater model. Chen et al. (1980) used a Dirac–Hartree–Slater approach to calculate the oK values of elements in the 184Z496 range. Kostroun et al. (1971) presents computations for elements in the range 104Z470 by combining Scofield’s (1969) radiative widths with
0969-806X/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 3 5 3 - 4
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R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
radiationless transition probabilities calculated from non-relativistic hydrogenic wave functions. However, measured (Arora et al., 1981; Al-Nasr et al., 1987) and theoretical (Balakrishna et al., 1994; Sidhu et al., 1988) K-shell fluorescence yields data, especially for in the atomic number range 244Z447, are scarce. In present work, K-shell fluorescence cross-sections and yields of 14 elements (Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag) were measured by using 59.54 keV g-rays from a 100 mCi 241Am radioactive source. Results are compared with experimental results, theoretical predictions and semiempirical fits reported in literature.
constant that resulted in the best resolution was 6 ms and this value was used throughout the measurements. To keep the statistical error below 2%, X-ray fluorescence spectra were recorded in the time intervals ranging from 0.5 to 18 h. A typical K-shell X-ray spectrum of Ge is shown in Fig. 2. The spectra were analysed using the non-linear least-squares code PEAKFIT by fitting the Gaussians to the individual transitions Ka and Kb and background expressed as a polynomial.
3. Theoretical method The theoretical values of sKa and sKb X-ray fluorescence cross-sections were calculated using the equations
2. Experimental details
sKa ¼ spK ðE ÞoK fKa ;
The geometry and the shielding arrangement of the experimental set-up employed in the present work are as shown in Fig. 1. The samples were excited with an 241 Am radioisotope source at 59.54 keV with a strength of approximately 100 mCi. Spectroscopically, pure targets of MnðCH3 COOÞ2 H2 O, Fe2O3, Ni, CuBr2, ZnSO4, Ge, As, KBr, Rb2O3, Sr(NO3)2, ZrO2, Nb5O, Pd and AgC1 of thickness ranging from 3 to 35 mg/cm2 have been used for the measurement. The samples were placed at a 458 angle with respect to the direct beam and fluorescent X-rays emitted at 908 to the detector. The K X-ray spectra from various targets were recorded with a Si(Li) detector (full-width at half-maximum (FWHM)=188 eV at 5.9 keV, active area=12 mm2, sensitivity depth=3 cm, Be window thickness=12 mm) coupled to a 1024 computerized multichannel analyser. The amplifier shaping time
sKb ¼ spK ðE ÞoK fKb ;
Fig. 1. Experimental setup used for measurements of production cross-section and yields.
ð1Þ
spK ðEÞ
is the K-shell photoionization cross-section where for the given element at the excitation energy E, oK is the K-shell fluorescence yield and fKa and fKb are fractional X-ray emission rates for Ka and Kb X-rays and are defined as 1 fKa ¼ 1 þ IKb =IKa ; 1 ; fKb ¼ 1 þ IKa =IKb
ð2Þ
where IKb =IKa is the Kb to Ka X-ray intensity ratio. In the present calculations, the values of spK ðEÞ were taken from Scofield (1973) based on Hartree–Slater potential theory, and the values of oK were taken from the tables of Hubbell et al. (1994). IKb =IKa values based on relativistic Hartree–Slater theory were used for the evaluation of theoretical K X-ray fluorescence crosssections (Scofield, 1974).
Fig. 2. Typical K X-ray spectrum for Ge irradiated with 59.54 keV gamma rays from 241Am.
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
21
where minc and memt , are the attenuation coefficients (cm2/g) of incident photons and emitted characteristic X-rays, respectively (Hubbell and Seltzer, 1995). The angles of incident photons and emitted X-rays with respect to the normal at the surface of the sample y1 and y2 were equal to 458 in the present setup. In the present study, as shown in Fig. 3, the values of the factors I0 GeKi , which contain terms related to the incident photon flux, geometrical factor and the efficiency of the X-ray detector, were determined by collecting the K X-ray spectra of thin samples of Cr, Co, Ga, Se, Mo, and In, in the same geometry in which the K X-ray fluorescence cross-sections were measured and using the equation I0 GeKa ¼
Fig. 3. Plot of the factor I0 Ge vs. K X-ray energy.
4. Experimental method The experimental K X-ray fluorescence (XRF) crosssections sxKi were evaluated using the relation sxKi ¼
IKi ; I0 GemT
ð5Þ
where IKa is the net number of counts under the corresponding photopeak, eKa is the detector efficiency for Ka X-rays and TKa is the self-absorption correction factor for the incident photons and emitted Ka X-ray photons.
ð3Þ
where IKi ði¼ a; bÞ is the net number of counts under the corresponding photopeak, the product I0G is the intensity of the exciting radiation falling on the area of the target samples visible to the detector, eKi , is the detector efficiency for Ki X-rays, m is the areal mass of the sample in g/cm2 and T is the self-absorption correction factor for the incident photons and emitted K X-ray photons. T was calculated using the relation T¼
I Ka ; sKa TKa m
1 exp½ðminc sec y1 þ memt sec y2 Þm ; ðminc sec y1 þ memt sec y2 Þm
ð4Þ
5. Results and discussion The experimental values of Ka and Kb X-ray fluorescence cross-sections for 14 elements at 59.54 keV are listed in Tables 1 and 2 together with the theoretical values. Our experimental values were fitted to a secondorder P polynomial as a function of atomic number Zð An Zn Þ and fitted values of K XRF cross-sections listed in the same tables. These values have been plotted as a function of the atomic number and are shown in Fig. 4(a) and (b). The fitted coefficients are
Table 1 Experimental, theoretical and fitted Ka X-ray fluorescence cross-sections (b/atom) Z
Element
Present work
Theoretical values
Fitted exp. values
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
22.45 0.44 24.64 0.37 41.58 1.49 48.06 3.72 64.64 4.36 82.20 4.66 117.67 5.89 157.30 6.58 206.23 6.99 227.72 8.31 296.57 11.32 321.97 12.55 536.42 22.29 595.30 27.32
21.38 25.41 42.55 50.98 65.81 83.55 111.69 152.42 201.61 229.56 294.06 329.60 546.13 596.57
23.76 26.91 39.63 49.21 60.93 90.81 108.96 151.70 203.62 231.90 296.08 331.39 540.10 588.28
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
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Table 2 Experimental, theoretical and fitted Kb X-ray fluorescence cross-sections (b/atom) Z
Element
Present work
Theoretical values
Fitted exp. values
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
3.71 0.07 3.80 0.06 5.87 0.21 7.50 0.53 9.00 0.57 13.38 0.75 17.81 0.94 24.98 1.08 31.03 1.08 39.55 1.43 50.90 1.96 57.97 2.20 114.19 4.80 112.01 4.72
3.52 3.77 5.62 7.44 8.75 12.90 16.25 23.60 31.02 37.77 49.93 57.32 110.15 117.17
5.38 4.79 5.23 6.26 7.82 12.57 15.75 23.72 33.86 39.73 53.09 60.58 106.69 116.81
Table 3 P K shell fluorescence cross-sections fitted to the An Zn as a function of atomic number Parameter
Ka Kb
Fitting coefficient A0
Al
A2
642.0332 195.0689
51.5343 14.3175
1.0721 0.2692
Table 4 Uncertainties in the quantities used to determine K X-ray fluorescence cross-sections in Eq. (3) Quantity
Nature of uncertainty
IKi ði¼ a; bÞ I0 GeKi
Counting statistic Errors in different parameters used to evaluate this factor Error in the absorption coefficients at incident and emitted photon energies Non-uniform thickness
b
t
Fig. 4. Comparison of measured K X-ray production crosssections with theoretical and fitted values as a function of atomic number: (a) Ka , (b) Kb X-ray production cross-sections.
presented in Table 3. Using these fitted values, the required experimental K shell cross-sections for individual elements can be obtained for com-
Uncertainty (%) 2 5 51
1
parison and the fit will be valid in the atomic range 244Z447. The overall error in the measured K XRF crosssections is estimated to be less than 8%, which is due to the uncertainties in various physical parameters required to evaluate the experimental results. This error is the quadrature sum of the uncertainties in the different parameters used to calculate the K X-ray production cross-sections. The uncertainties in the parameters are listed in Table 4. It can be seen from Tables 1, 2 and Fig. 4(a),(b) that our measurement values are in good agreement, within the experimental uncertainties, with
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Table 5 Comparison of present experimental results and literature experimental values of the K-shell fluorescence yields Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
K-shell flourescence yields ðoK Þ Present work
Singh (1990a)
Singh (1990b)
Arora (1981)
Kumar (1987)
Pious (1992)
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
} } } } } } } } } 0.688 0.023 } } } }
} 0.336 0.006 0.418 0.011 } } } } } } } } 0.722 0.044 0.846 0.059 }
} } 0.394 0.016 0.410 0.018 0.490 0.020 } 0.590 0.024 0.586 0.023 } } 0.700 0.028 0.738 0.030 } 0.857 0.034
0.321 0.007 } } } } } } } 0.635 0.013 } } } } }
} } } } } 0.538 0.029 } } } } } } } }
Table 6 Present experimental results and theoretical predictions values of oK Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
Present work
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
Theoretical predictions Kostroun (1971)
McGuire (1970)
Walters (1971)
0.310 0.344 0.414 0.448 0.482 0.545 0.574 0.602 0.629 0.702 0.741 0.759 0.833 0.844
} 0.364 } } 0.499 } } } } } 0.740 } } 0.842
0.3276 0.3624 0.4329 0.4678 0.5014 0.5650 0.5947 0.6498 0.6987 0.7211 0.7611 0.7788 0.8491 0.8905
the calculated theoretical values. The experimental values are in general higher than theoretical results. One of the reasons for this may be a chemical effect that occurred because of imperfections and impurities of the samples. The agreement between the present results and theoretical predictions are within the range 0.2–5.7% for Ka X-ray production cross-sections and 0.1–8.8% for Kb X-ray production cross-sections. The measured values of the K shell fluorescence yield oK , in elements Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag are compared with the other available experimental (Singh et al., 1990a, b; Arora et al., 1981; Kumar et al., 1987; Pious et al., 1992),
calculated values and semiempirical fits (Hubbell et al., 1994; Bambynek et al., 1972; Krause, 1979) in Tables 5–7. The comparison with the other available experimental values, theoretical predictions and semiempirical fits are also shown graphically in Fig. 5(a)–(c). The present experimental values agree better with the semiempirical values deduced by Hubbell et al. (1994). This agreement is within 9.2% for all elements except for Br and Rb. The comparison between the experimental results and the theoretical values leads to the conclusion that either the experimental or the calculated cross-sections can be used with confidence for analytical purposes and
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
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Table 7 Present experimental results and semiempirical fits values of oK Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
Present work
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
Semiempirical fits Fitted
Hubbell (1994)
Bambynek (1972)
Krause (1979)
0.326 0.354 0.426 0.451 0.480 0.533 0.574 0.626 0.666 0.684 0.719 0.741 0.822 0.838
0.316 0.351 0.412 0.441 0.469 0.523 0.549 0.574 0.598 0.665 0.705 0.724 0.807 0.822
0.321 0.354 0.421 0.453 0.485 0.546 0.574 0.627 0.674 0.695 0.734 0.751 0.820 0.831
0.308 0.340 0.406 0.404 0.474 0.535 0.562 0.618 0.667 0.690 0.730 0.747 0.820 0.831
Fig. 5. Comparison of measured K-shell fluorescence yield as a function of the atomic number: (a) Literature experimental results, (b) theoretical predictions and (c) semiempirical fits.
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
satisfactory for many other applications employing the fundamental parameter approach.
Acknowledgements This work was supported by the Atatu¨rk University Research Fund, Project no. 1998-65.
References Al-Nasr, I.A., Jabr, I.J., Al-Saleh, K.A., Saleh, N.S., 1987. Measurement of Ka cross-sections and fluorescence yields for elements in the range 424Z457 using radioisotope X-ray fluorescence. Appl. Phys. A 43, 71–73. Arora, S.K., Allawadhi, K.L., Sood, B.S., 1981. Measurements of K-shell fluorescence yields in elements 284Z453. Physica B&C 111C, 71–75. Balakrishna, K.M., Nayak, N.G., Lingappa, N., Siddappa, K., 1994. K fluorescence yield measurements in rare earth and heavy elements. J. Phys. B: Mol. Phys. 27, 715–720. Bambynek, W., Crasemann, B., Fink, R.W., Freund, H.U., Mark, H., Swift, C.D., Price, R.E., Rao, P.V., 1972. X-Ray fluorescence yields, Auger, and Coster-Kronig transition probabilities. Rev. Mod. Phys. 44, 716–813. Casnati, E., Baraldi, C., Tartari, A., 1991. Measurement of K X-ray emission from Mo, Cd, and stimulated by 59.54 keV photons. Phys. Rev. A 44, 1699–1704. Chen, M.H., Crasemann, B., Mark, H., 1980. Relativistic K-shell Auger rates, level widths and fluorescence yields. Phys. Rev. A 21, 436–441. Durak, R., S, ahin, Y., 1998. Measurement of K-shell fluorescence yields of selected elements from Cs to Pb using radioisotope X-ray fluorescence. Phys. Rev. A 57, 2578–2582. Garg, M.L., Mehta, D., Kumar, S., Mangal, P.C., Trehan, P.N., 1985. Energy dependence of photon-induced Ka and Kb X-ray fluorescence cross-sections for some elements with 204Z456. X-Ray Spectrom. 14, 165–169. Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92 and 48 additional substances of dosimetric interest. NISTIR 5632. Hubbell, J.H., Trehan, P.N., Singh, N., Chand, B., Mehta, D., Garg, M.L., Garg, R.R., Singh, S., Puri, S., 1994. A review, bibliography, and tabulation of K, L, and hinger atomic shell X-ray fluorescence yields. J. Phys. Chem. Ref. Data 23, 339–364.
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Kostroun, V.O., Chen, M.H., Crasemann, B., 1971. Atomic radiation transition probabilities to the ls state and theoretical K-shell fluorescence yields. Phys. Rev. A 3, 533–545. Krause, M.O., 1979. Atomic radiative and radiationless yields for K and L shell. J. Phys. Chem. Ref. Data 8, 307–327. Krause, M.O., Nester, C.V., Sparks Jr., C.J., Ricci, E., 1978. X-ray fluorescence cross-sections for K and L X-rays of the elements. Oak Ridge National Laboratory, Report ORNL-5399. Kumar, S., Singh, S., Mehta, D., Singh, N., Mangal, P.C., Trehan, P.N., 1987. Measurement of K X-ray fluorescence cross-sections for some elements with 234Z455 in the energy range 8–60 keV. X-ray Spectrom. 16, 203–206. McGuire, E.J., 1970a. K-shell Auger transition rates and fluorescence yields for elements Be–Ar. Phys. Rev. 185, 1–6. McGuire, E.J., 1970b. K-shell Auger transition rates and fluorescence yields for elements Ar–Xe. Phys. Rev. A 2, 273–278. Pious, J.K., Balakrishna, K.M., Lingappa, N., Siddappa, K., 1992. Total K fluorescence yields for Fe, Cu, Zn, Ge and Mo. J. Phys. B: Atom. Mol. Opt. Phys. 24, 1155–1160. Rani, A., Koshal, R.K., Chaturvedi, S.N., Nath, N., 1988. Photon-excited K X-ray fluorescence cross-sections measurements for some low Z elements. X-ray Spectrom. 17, 53–54. Rao, D.V., Cesareo, R., Gigante, G.E., 1993. Measurements of Li, La, Lb and Lg X-ray fluorescence cross-sections in heavy elements excited by 36.62, 48.30, 50.20 and 53.50 keV. X-ray Spectrom. 22, 401–405. Scofield, J.H., 1969. Radiative decay rates of vacancies in the K and L shell. Phys. Rev. 179, 9–16. Scofield, J. H., 1973. Theoretical photoionisation cross-sections from 1 to 1500 keV. Report UCRL 51326, Lawrence Livermore Laboratory, Livermore, CA. Scofield, J.H., 1974. Relativistic Hartree–Slater values for K and L X-ray emission rates. Atom. Data Nucl. Data Tables 14, 121–137. Sidhu, N.P.S., Grewal, B.S., Sahota, H.S., 1988. K-shell fluorescence yields of some elements from nuclear decay parameters. X-ray Spectrom. 17, 29–31. Singh, S., Rani, R., Mehta, D., Singh, N., Mangal, P.C., Trehan, P.N., 1990a. K X-ray fluorescence cross-sections measurements of some elements in the energy range 8–47 keV. X-ray Spectrom. 19, 155–158. Singh, S., Mehta, D., Garg, R.R., Kumar, S., Garg, M.L., Singh, N., Mangal, P.C., Hubbell, J.H., Trehan, P.N., 1990b. Average L-shell fluorescence yields for elements 564Z492. Nucl. Instr. and Meth. B 51, 5–10. Walters, D.L., Bhalla, C.P., 1971. Nonrelativistik Auger rates, X-ray rates, and fluorescence yields for the K shell. Phys. Rev. A 3, 1919–1927.
Measurement of K-shell fluorescence cross-sections and yields of 14 elements in the atomic number range 254Z447 using photoionization . Rıdvan Durak*, Yu¨ksel O¨zdemır Atatu¨rk U¨niversitesi, Fen-Edebiyat Faku¨ltesi, Fizik Bo¨lu¨mu¨, 25240 Erzurum, Tu¨rkey Received 3 March 2000; accepted 23 September 2000
Abstract K-shell X-ray fluorescence cross-sections for the elements Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag have been measured at the excitation energy of the 59.54 keV g-rays from an 241Am radioactive source of strength 100 mCi. In addition, measurement of K X-ray fluorescence yields for these elements at the same excitation energy have also been carried out. The experimental results are compared with the literature experimental values, theoretical predictions, and semiempirical fits. # 2001 Elsevier Science Ltd. All rights reserved. PACS: 32.30.Rj; 34.50.Fa; 32.80.Fb; 32.80.Hd Keywords: X-ray fluorescence; Cross-sections; Photoionization; Fluorescence yields
1. Introduction K X-ray fluorescence (XRF) cross-sections and yields are required in a variety of applications including, for example, atomic physics, medical research, non-destructive elemental analysis, and industrial irradiation processing (Hubbell et al., 1994; Durak and S,ahin, 1998). In addition, comparison of measured K X-ray fluorescence cross-sections with theoretical estimates provides a check on the validity of various physical parameters such as photoionization cross-sections, and fluorescence yields. Several attempts have been made for measuring X-ray fluorescence cross-sections and yields. Earlier experimental K X-ray fluorescence cross-sections have been measured using radioisotopes as excitation sources (Garg et al., 1985). K X-ray production cross-sections have been determined theoretically for all the elements at energies ranging from 10 to 60 keV (Krause et al., *Corresponding author. Fax: +90-442-2331062. E-mail address: [email protected] (R. Durak).
1978). Some measurements of K X-ray fluorescence cross-sections for low-Z elements at low excitation energies have been reported (Rani et al., 1988; Rao et al., 1993). However, limited investigations in the case of cross-sections of intermediate-Z elements have been made at different excitation energies in the interval 8–60 keV (Singh et al., 1990; Casnati et al., 1991). K-shell fluorescence yields oK for different elements have been investigated for many years. Bambynek et al. (1972) in a review article have fitted their collection of selected most reliable experimental values in the 134Z492 range. Krause (1979) compiled oK adopted values for elements 54Z4110. Hubbell et al. (1994) have compiled more recent experimental values. Theoretical values of oK were obtained in the region 4 4Z454 by McGuire (1970a, b) and Walters and Bhalla (1971) using the Hartree–Fock–Slater model. Chen et al. (1980) used a Dirac–Hartree–Slater approach to calculate the oK values of elements in the 184Z496 range. Kostroun et al. (1971) presents computations for elements in the range 104Z470 by combining Scofield’s (1969) radiative widths with
0969-806X/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 3 5 3 - 4
20
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
radiationless transition probabilities calculated from non-relativistic hydrogenic wave functions. However, measured (Arora et al., 1981; Al-Nasr et al., 1987) and theoretical (Balakrishna et al., 1994; Sidhu et al., 1988) K-shell fluorescence yields data, especially for in the atomic number range 244Z447, are scarce. In present work, K-shell fluorescence cross-sections and yields of 14 elements (Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag) were measured by using 59.54 keV g-rays from a 100 mCi 241Am radioactive source. Results are compared with experimental results, theoretical predictions and semiempirical fits reported in literature.
constant that resulted in the best resolution was 6 ms and this value was used throughout the measurements. To keep the statistical error below 2%, X-ray fluorescence spectra were recorded in the time intervals ranging from 0.5 to 18 h. A typical K-shell X-ray spectrum of Ge is shown in Fig. 2. The spectra were analysed using the non-linear least-squares code PEAKFIT by fitting the Gaussians to the individual transitions Ka and Kb and background expressed as a polynomial.
3. Theoretical method The theoretical values of sKa and sKb X-ray fluorescence cross-sections were calculated using the equations
2. Experimental details
sKa ¼ spK ðE ÞoK fKa ;
The geometry and the shielding arrangement of the experimental set-up employed in the present work are as shown in Fig. 1. The samples were excited with an 241 Am radioisotope source at 59.54 keV with a strength of approximately 100 mCi. Spectroscopically, pure targets of MnðCH3 COOÞ2 H2 O, Fe2O3, Ni, CuBr2, ZnSO4, Ge, As, KBr, Rb2O3, Sr(NO3)2, ZrO2, Nb5O, Pd and AgC1 of thickness ranging from 3 to 35 mg/cm2 have been used for the measurement. The samples were placed at a 458 angle with respect to the direct beam and fluorescent X-rays emitted at 908 to the detector. The K X-ray spectra from various targets were recorded with a Si(Li) detector (full-width at half-maximum (FWHM)=188 eV at 5.9 keV, active area=12 mm2, sensitivity depth=3 cm, Be window thickness=12 mm) coupled to a 1024 computerized multichannel analyser. The amplifier shaping time
sKb ¼ spK ðE ÞoK fKb ;
Fig. 1. Experimental setup used for measurements of production cross-section and yields.
ð1Þ
spK ðEÞ
is the K-shell photoionization cross-section where for the given element at the excitation energy E, oK is the K-shell fluorescence yield and fKa and fKb are fractional X-ray emission rates for Ka and Kb X-rays and are defined as 1 fKa ¼ 1 þ IKb =IKa ; 1 ; fKb ¼ 1 þ IKa =IKb
ð2Þ
where IKb =IKa is the Kb to Ka X-ray intensity ratio. In the present calculations, the values of spK ðEÞ were taken from Scofield (1973) based on Hartree–Slater potential theory, and the values of oK were taken from the tables of Hubbell et al. (1994). IKb =IKa values based on relativistic Hartree–Slater theory were used for the evaluation of theoretical K X-ray fluorescence crosssections (Scofield, 1974).
Fig. 2. Typical K X-ray spectrum for Ge irradiated with 59.54 keV gamma rays from 241Am.
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
21
where minc and memt , are the attenuation coefficients (cm2/g) of incident photons and emitted characteristic X-rays, respectively (Hubbell and Seltzer, 1995). The angles of incident photons and emitted X-rays with respect to the normal at the surface of the sample y1 and y2 were equal to 458 in the present setup. In the present study, as shown in Fig. 3, the values of the factors I0 GeKi , which contain terms related to the incident photon flux, geometrical factor and the efficiency of the X-ray detector, were determined by collecting the K X-ray spectra of thin samples of Cr, Co, Ga, Se, Mo, and In, in the same geometry in which the K X-ray fluorescence cross-sections were measured and using the equation I0 GeKa ¼
Fig. 3. Plot of the factor I0 Ge vs. K X-ray energy.
4. Experimental method The experimental K X-ray fluorescence (XRF) crosssections sxKi were evaluated using the relation sxKi ¼
IKi ; I0 GemT
ð5Þ
where IKa is the net number of counts under the corresponding photopeak, eKa is the detector efficiency for Ka X-rays and TKa is the self-absorption correction factor for the incident photons and emitted Ka X-ray photons.
ð3Þ
where IKi ði¼ a; bÞ is the net number of counts under the corresponding photopeak, the product I0G is the intensity of the exciting radiation falling on the area of the target samples visible to the detector, eKi , is the detector efficiency for Ki X-rays, m is the areal mass of the sample in g/cm2 and T is the self-absorption correction factor for the incident photons and emitted K X-ray photons. T was calculated using the relation T¼
I Ka ; sKa TKa m
1 exp½ðminc sec y1 þ memt sec y2 Þm ; ðminc sec y1 þ memt sec y2 Þm
ð4Þ
5. Results and discussion The experimental values of Ka and Kb X-ray fluorescence cross-sections for 14 elements at 59.54 keV are listed in Tables 1 and 2 together with the theoretical values. Our experimental values were fitted to a secondorder P polynomial as a function of atomic number Zð An Zn Þ and fitted values of K XRF cross-sections listed in the same tables. These values have been plotted as a function of the atomic number and are shown in Fig. 4(a) and (b). The fitted coefficients are
Table 1 Experimental, theoretical and fitted Ka X-ray fluorescence cross-sections (b/atom) Z
Element
Present work
Theoretical values
Fitted exp. values
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
22.45 0.44 24.64 0.37 41.58 1.49 48.06 3.72 64.64 4.36 82.20 4.66 117.67 5.89 157.30 6.58 206.23 6.99 227.72 8.31 296.57 11.32 321.97 12.55 536.42 22.29 595.30 27.32
21.38 25.41 42.55 50.98 65.81 83.55 111.69 152.42 201.61 229.56 294.06 329.60 546.13 596.57
23.76 26.91 39.63 49.21 60.93 90.81 108.96 151.70 203.62 231.90 296.08 331.39 540.10 588.28
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
22
Table 2 Experimental, theoretical and fitted Kb X-ray fluorescence cross-sections (b/atom) Z
Element
Present work
Theoretical values
Fitted exp. values
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
3.71 0.07 3.80 0.06 5.87 0.21 7.50 0.53 9.00 0.57 13.38 0.75 17.81 0.94 24.98 1.08 31.03 1.08 39.55 1.43 50.90 1.96 57.97 2.20 114.19 4.80 112.01 4.72
3.52 3.77 5.62 7.44 8.75 12.90 16.25 23.60 31.02 37.77 49.93 57.32 110.15 117.17
5.38 4.79 5.23 6.26 7.82 12.57 15.75 23.72 33.86 39.73 53.09 60.58 106.69 116.81
Table 3 P K shell fluorescence cross-sections fitted to the An Zn as a function of atomic number Parameter
Ka Kb
Fitting coefficient A0
Al
A2
642.0332 195.0689
51.5343 14.3175
1.0721 0.2692
Table 4 Uncertainties in the quantities used to determine K X-ray fluorescence cross-sections in Eq. (3) Quantity
Nature of uncertainty
IKi ði¼ a; bÞ I0 GeKi
Counting statistic Errors in different parameters used to evaluate this factor Error in the absorption coefficients at incident and emitted photon energies Non-uniform thickness
b
t
Fig. 4. Comparison of measured K X-ray production crosssections with theoretical and fitted values as a function of atomic number: (a) Ka , (b) Kb X-ray production cross-sections.
presented in Table 3. Using these fitted values, the required experimental K shell cross-sections for individual elements can be obtained for com-
Uncertainty (%) 2 5 51
1
parison and the fit will be valid in the atomic range 244Z447. The overall error in the measured K XRF crosssections is estimated to be less than 8%, which is due to the uncertainties in various physical parameters required to evaluate the experimental results. This error is the quadrature sum of the uncertainties in the different parameters used to calculate the K X-ray production cross-sections. The uncertainties in the parameters are listed in Table 4. It can be seen from Tables 1, 2 and Fig. 4(a),(b) that our measurement values are in good agreement, within the experimental uncertainties, with
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
23
Table 5 Comparison of present experimental results and literature experimental values of the K-shell fluorescence yields Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
K-shell flourescence yields ðoK Þ Present work
Singh (1990a)
Singh (1990b)
Arora (1981)
Kumar (1987)
Pious (1992)
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
} } } } } } } } } 0.688 0.023 } } } }
} 0.336 0.006 0.418 0.011 } } } } } } } } 0.722 0.044 0.846 0.059 }
} } 0.394 0.016 0.410 0.018 0.490 0.020 } 0.590 0.024 0.586 0.023 } } 0.700 0.028 0.738 0.030 } 0.857 0.034
0.321 0.007 } } } } } } } 0.635 0.013 } } } } }
} } } } } 0.538 0.029 } } } } } } } }
Table 6 Present experimental results and theoretical predictions values of oK Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
Present work
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
Theoretical predictions Kostroun (1971)
McGuire (1970)
Walters (1971)
0.310 0.344 0.414 0.448 0.482 0.545 0.574 0.602 0.629 0.702 0.741 0.759 0.833 0.844
} 0.364 } } 0.499 } } } } } 0.740 } } 0.842
0.3276 0.3624 0.4329 0.4678 0.5014 0.5650 0.5947 0.6498 0.6987 0.7211 0.7611 0.7788 0.8491 0.8905
the calculated theoretical values. The experimental values are in general higher than theoretical results. One of the reasons for this may be a chemical effect that occurred because of imperfections and impurities of the samples. The agreement between the present results and theoretical predictions are within the range 0.2–5.7% for Ka X-ray production cross-sections and 0.1–8.8% for Kb X-ray production cross-sections. The measured values of the K shell fluorescence yield oK , in elements Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Sr, Zr, Nb, Pd and Ag are compared with the other available experimental (Singh et al., 1990a, b; Arora et al., 1981; Kumar et al., 1987; Pious et al., 1992),
calculated values and semiempirical fits (Hubbell et al., 1994; Bambynek et al., 1972; Krause, 1979) in Tables 5–7. The comparison with the other available experimental values, theoretical predictions and semiempirical fits are also shown graphically in Fig. 5(a)–(c). The present experimental values agree better with the semiempirical values deduced by Hubbell et al. (1994). This agreement is within 9.2% for all elements except for Br and Rb. The comparison between the experimental results and the theoretical values leads to the conclusion that either the experimental or the calculated cross-sections can be used with confidence for analytical purposes and
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
24
Table 7 Present experimental results and semiempirical fits values of oK Z
25 26 28 29 30 32 33 35 37 38 40 41 46 47
Element
Mn Fe Ni Cu Zn Ge As Br Rb Sr Zr Nb Pd Ag
Present work
0.354 0.007 0.330 0.005 0.412 0.015 0.412 0.029 0.482 0.032 0.537 0.030 0.605 0.032 0.648 0.028 0.691 0.024 0.690 0.025 0.751 0.029 0.734 0.028 0.806 0.034 0.829 0.038
Semiempirical fits Fitted
Hubbell (1994)
Bambynek (1972)
Krause (1979)
0.326 0.354 0.426 0.451 0.480 0.533 0.574 0.626 0.666 0.684 0.719 0.741 0.822 0.838
0.316 0.351 0.412 0.441 0.469 0.523 0.549 0.574 0.598 0.665 0.705 0.724 0.807 0.822
0.321 0.354 0.421 0.453 0.485 0.546 0.574 0.627 0.674 0.695 0.734 0.751 0.820 0.831
0.308 0.340 0.406 0.404 0.474 0.535 0.562 0.618 0.667 0.690 0.730 0.747 0.820 0.831
Fig. 5. Comparison of measured K-shell fluorescence yield as a function of the atomic number: (a) Literature experimental results, (b) theoretical predictions and (c) semiempirical fits.
R. Durak, Y. O¨zdemir / Radiation Physics and Chemistry 61 (2001) 19–25
satisfactory for many other applications employing the fundamental parameter approach.
Acknowledgements This work was supported by the Atatu¨rk University Research Fund, Project no. 1998-65.
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