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New method to measure the K-shell absorption jump factor in some rare-earth elements
Analytica Chimica Acta 505 (2004) 307–314
New method to measure the K-shell absorption jump factor in some rare-earth elements a,∗ , Gökhan Budak b ˙ Recep Polat a , Orhan Içelli a
Department of Physics, Education Faculty of Erzincan, Atatürk University, Erzincan, Turkey b Department of Physics, Science and Art Faculty, Atatürk University, Erzurum, Turkey
Received 26 May 2003; received in revised form 7 October 2003; accepted 21 October 2003
Abstract The Compton scattering of 59.54 keV gamma rays by an Al scatterer has been used as a primer source at scattering angles from 48 to 118◦ by using a Si(Li) detector, and this primer gamma ray has been send to absorbers including Gd, Tb, Dy, Ho and Er. A new method has been developed to determine the K-shell absorption jump factor of elements and compounds. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding the problems with measuring the source strength and source-to-detector solid angle. In this method, the jump factor is effected from the scattering angle. Evident energies near to K-absorption edges of each lanthanide element have been determined for chosen angles, after the incident photon energy (59.5 keV) is exposed to Compton scattering from Al (secondary source). The experimental absorption jump factors are compared with the theoretical estimates and literature experimental values. © 2003 Elsevier B.V. All rights reserved. Keywords: Rare-earth elements; Jump value; Jump factor; Absorption jump ratio
1. Introduction Absorption jump factors and jump values of an elements are very useful parameters in many fields of scientific applications such as nuclear physics, cancer therapy, industrial irradiation processing, dosimetric computations for health physics and X-ray fluorescence surface chemical analysis [1,2]. Quantitative knowledge of the emission of characteristic K radiation is still of great interest for both fundamental and applied physics. Accurate experimental values offer an appropriate means for checking the validity of the assumptions included in the different formulation of atomic models that make it possible to evaluate important atomic parameters such as the absorption jump factor and fluorescence cross-section. These cross-sections are presently available for all-shell theoretical atomic photoeffect cross-section computations and tabulations in Scofield [3]. The rare-earth metals being used nowadays in X-ray applications are absent from such experimental studies. These elements have been used as a raw material for fluorescent compounds, absorp-
∗
Corresponding author. ˙ E-mail address: orhan [email protected] (O. Içelli).
0003-2670/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2003.10.061
tion material in atomic reactions, magnetic bubble material, screen-sensitivity increasing material, as well as many other applications in the chemical, glass and electronic industries. Apart from Er, other rare-earth elements used as dopants in superconductors are also characterized by X-ray techniques. Determined absorption jump factors of elements are also required for correct use of spectroscopic techniques [4]. Accurate theoretical data on jump factors for elements are calculated for use in the applications mentioning above. Some researchers [5,6] have also theoretically calculated the jump factor and jump value by using different methods. But experimental studies [7–9] on these subjects are particularly devoid of measurements. Our purpose is to improve simply, directly, reliably and rapidly an experimental method in order to determine the absorption jump factor. In our methods, we have the benefit of Compton scattering. Ref. [7] does not describe both the deconvolution process and determination process at an incident angle of 48◦ for only Er absorber. However, we show that Compton gamma rays scattering from Al element by regulating the scattering angle have been reduced at the absorption edge of the the absorber. In the case of Compton scattering of photons from electrons, the scattered photon energy depends in a unique way on the scattering angle θ. Note that the energy of the
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R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
scattered photon is a function of the energy of the incident photon as well as of θ [10]. In this study, we have measured the absorption jump factors in some rare-earth elements making use of Compton scattering and experimental results compared with different theoretical and literature experimental values.
2. Experimental method The schematic arrangement of the experimental setup used in the present work is shown in Fig. 1. Since we have used Al [11], the inaccuracies of an incoherent scattering function are minimized. Also, the Rayleigh contribution is low in the small Z targets. As seen in Fig. 1, Al has been used as a secondary target in this experimental setup. The present experimental setup has been constituted as an ideal transmission geometry and ␥-photon energy of 59.5 keV is transmitted to Al element. Later, ␥-photon rays caused by Compton scattering from Al element have been transmitted to Gd, Dy, Ho and Er elements and a Tb4 O7 powder sample used as absorber. The energy of the scattered photon is given by. E1 (1) E2 = 1 + (E1 /m0 c2 )(1 − cos θ) where E1 is energy of incident photon, m0 c2 is the electron rest-mass energy whose value is 5.11 × 105 eV, and θ is the angle between the photon directions of travel prior to and following a scattering interaction [12] (Table 1).
3. Procedures The total attenuation coefficients and K X-rays absorption jump-factors were determined by using transmission geometry. In the present experiment a Si(Li) detector (FWHM = 160 eV at 5.96 keV) was used with a multichannel analyzer for detection of X-rays. This detector was coupled to a computerized 1024-multichannel analyzer through a spectroscopic automatic fine-tuning research amplifier. To obtain statistical sensitivity, each sample has been measured by collecting the spectra from selected elements for a period of 72 × 103 s. High purity (99.9%) thin foil samples of Gd, Dy, Ho and Er elements and a powder sample of Tb4 O7 , whose mass thickness ranges from 0.164 to 0.307 g cm−2 , have been used in conjunction with a radioactive point source of 241 Am of 100 mCi (3.7 × 109 Bq) having a ␥-photon energy of 59.5 keV. In order to eliminate the particle size effect, the Tb4 O7 samples were sieved through a 400 mesh sieve, before compressing then into pellets for 15 s by using a manual hydraulic press. In ideal transmission geometry, Al element has been used as a secondary target. Incident gamma rays of Compton scattering from Al were transmitted to the absorber. In this experiment, the net counts without absorber (I0 ) and with absorber (I) were obtained at the same time and experimental conditions. The errors in the evaluation of the area under the Compton peaks are ≤2%, the determination of the thickness of the sample is ≤3%, and the counting statistics ≤1%. A typical Compton spectrum of Gd is shown in Fig. 2.
4. Data analysis
Table 1 Incident energy values on absorber Absorber
Scattering angle (θ)
K (absorption edge) (keV)
Energy of secondary source (keV)
Gd Tb Dy Ho Er
118◦ 108◦ 88◦ 68◦ 48◦
50.229 51.998 53.789 55.615 57.483
50.838 51.663 53.524 55.499 57.333
The total mass attenuation coefficients can be obtained from the differences in the count value with and without the presence of a sample. The mass attenuation coefficients are given as µ I = I0 exp − x·ρ (2) ρ
Fig. 1. Experimental set-up.
R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
309
30000 (a)
25000
Counts
20000
15000 (b)
10000
5000
0 35
40
45
50
55
60
Energy (keV) Fig. 2. Measured Compton spectra. Curve (a) unattenuated spectrum. (b) Attenuated spectrum by a Gd foil. Table 2 Tabulated total mass attenuation coefficients from 48 to 58.55 keV for Gd, Tb4 O7 , Dy, Ho and Er Total mass attenuation coefficient (cm2 g−1 ) E (keV)
Gd Exp.
48.02939 4.08754 48.14568 48.20383 48.26197 48.32012 48.37826 48.43641 48.49455 48.55270 48.61084 48.66899 48.72713 48.78528 48.84342 48.90157 48.95971 49.01786 49.07600 49.13415 49.19229 49.25044 49.30858 49.36673 49.42487 49.48302 49.54116 49.59931 49.65745 49.71560 49.77374 49.83189 49.89003 49.94818
4.63 4.61 4.46 4.46 4.71 4.64 4.46 4.37 4.11 4.36 4.33 4.72 4.45 4.46 4.50 4.58 4.24 4.40 4.51 4.14 4.52 4.54 4.52 4.48 4.60 4.07 4.49 4.42 4.49 4.77 5.73 6.60 7.21 9.34
E (keV) Theor. 4.28 4.27 4.25 4.24 4.23 4.22 4.20 4.19 4.18 4.16 4.15 4.14 4.12 4.11 4.10 4.09 4.07 4.06 4.05 4.04 4.03 4.01 4.00 3.99 3.98 3.96 3.95 3.94 3.93 3.92 3.91 3.89 3.88 3.87
50.00632 50.06447 50.12261 50.18076 50.23890 50.29705 50.35519 50.41334 50.47148 50.52963 50.58777 50.64592 50.70406 50.76221 50.82035 50.87850 50.93664 50.99479 51.05293 51.11108 51.16922 51.22737 51.28551 51.34366 51.40180 51.45995 51.51809 51.57624 51.63438 51.69253 51.75067 51.80882 51.86696 51.92511 51.98325 52.04140
Gd
Tb
Exp.
Theor.
Exp.
Theor.
10.7 13.4 15.2 15.9 18.3 19.4 21.0 21.5 20.7 20.0 20.8 20.1 20.1 20.9 20.8 19.6 20.4 19.8 19.3 18.0 19.2 18.4 18.0 19.8 18.0 17.4 18.7 18.7 17.7 17.7 16.9 18.1 18.1 17.2 17.2 17.2
3.86 3.85 3.84 3.82 18.6 18.6 18.5 18.5 18.4 18.4 18.3 18.2 18.2 18.1 18.1 18.0 18.0 17.9 17.9 17.8 17.8 17.7 17.7 17.6 17.6 17.5 17.5 17.4 17.4 17.3 17.3 17.2 17.2 17.1 17.1 17.0
4.92 4.72 4.80 4.67 4.70 4.73 4.70 4.62 4.76 4.73 4.76 4.69 4.64 4.63 4.83 4.64 4.70 4.64 4.61 4.91 4.67 4.82 4.64 4.70 5.07 5.09 5.60 6.30 7.19 7.98 8.68 10.6 12.1 13.4 14.8 16.4
4.06 4.05 4.04 4.03 4.01 4.00 3.99 3.98 3.97 3.95 3.94 3.93 3.92 3.91 3.90 3.88 3.87 3.86 3.85 3.84 3.83 3.82 3.80 3.79 3.78 3.77 3.76 3.75 3.74 3.73 3.72 3.71 3.70 3.68 3.68 17.7
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Table 2 (Continued ) Tb
52.09954 52.15769 52.21583 52.27398 52.33212 52.39027 52.44841 52.50656 52.56470 52.62285 52.68099 52.73914 52.79728 52.85543 52.91357 52.97172 53.02986 53.08801 53.14615 53.20430 53.26244 53.32059 53.37873 53.43688 53.49502 53.55317
Dy
Exp.
Theor.
16.5 16.8 16.6 17.4 15.8 17.4 17.3 16.8 15.6 17.1 16.3 15.9 14.7 15.4 14.6 16.4 14.1 14.8 13.8 14.3 14.2 14.5 14.3 13.8 13.3 14.7
17.7 17.6 17.6 17.5 17.5 17.4 17.4 17.3 17.3 17.2 17.2 17.1 17.1 17.0 17.0 16.9 16.9 16.8 16.8 16.7 16.7 16.6 16.6 16.5 16.5 16.4
Dy
53.61131 53.66946 53.72760 53.78575 53.84389 53.90204 53.96018 54.01833 54.07647 54.13462 54.19276 54.25091 54.30905 54.36720 54.42534 54.48349 54.54163 54.59978 54.65792 54.71607 54.77421 54.83236 54.89050 54.94865 55.00679
Theor.
11.3 12.3 14.1 15.2 16.5 15.2 16.7 15.6 17.0 16.3 16.2 16.3 14.5 14.5 14.8 14.5 16.3 13.1 14.1 13.8 14.6 13.3 12.3 13.2 13.4
3.53 3.52 3.51 16.8 16.7 16.7 16.6 16.6 16.5 16.5 16.4 16.4 16.3 16.3 16.2 16.2 16.2 16.1 16.1 16.0 16.0 15.9 15.9 15.8 15.8
Ho
55.06494 55.12308 55.18123 55.23937 55.29752 55.35566
4.38 4.80 5.02 5.66 6.74 7.94
3.88 3.42 3.55 3.96 4.27 3.94 3.74 4.28 4.18 4.03 3.85 3.93 4.20 4.07 3.86 4.16 4.10 3.79 3.69 3.63 4.19 4.04 5.10 6.56 7.65 9.56
Theor. 3.80 3.79 3.78 3.77 3.76 3.75 3.73 3.72 3.71 3.70 3.69 3.68 3.67 3.66 3.65 3.64 3.63 3.62 3.61 3.60 3.59 3.58 3.57 3.56 3.55 3.54
Ho
Exp.
Exp.
Exp.
Exp.
3.80 3.22 3.20 4.15 4.06 3.75 4.39 3.79 4.18 3.79 3.41 3.23 3.51 3.75 3.74 3.94 3.79 4.17 3.56 3.80 4.12 3.97 4.28 E (keV)
Theor. 3.44 3.43 3.42 3.41 3.40 3.39
56.05340 56.11155 56.16969 56.22784 56.28598 56.34413
Theor.
3.66 3.65 3.64 3.63 3.62 3.61 3.60 3.59 3.58 3.57 3.56 3.55 3.54 3.53 3.52 3.51 3.50 3.50 3.49 3.48 3.47 3.46 3.45 Ho
Er
Exp.
Theor.
13.3 13.2 13.3 13.1 13.3 13.3
15.6 15.5 15.5 15.4 15.4 15.4
Exp. 3.31 3.31 3.30 3.29 3.28 3.27
Theor. 3.45 3.44 3.43 3.42 3.41 3.40
R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
311
Table 2 (Continued ) Ho
55.41381 55.47195 55.53010 55.58824 55.64639 55.70453 55.76268 55.82082 55.87897 55.93711 55.99526
E (keV)
Exp.
Theor.
10.1 11.4 13.0 13.3 13.8 13.3 13.7 13.2 13.4 13.5 13.6
3.38 3.37 3.36 15.9 15.9 15.8 15.8 15.7 15.7 15.6 15.6
Exp. 3.42 3.41 5.40 7.39 9.38 11.3 12.3 13.6 13.1
Ho
Er
Exp.
Theor.
Exp.
Theor.
56.40227 56.46042 56.51856 56.57671 56.63485 56.69300 56.75114 56.80929 56.86743 56.92558 56.98372 57.04187
13.1 13.2 13.3 13.3 13.2 13.5 13.3 13.1 13.3 13.4 13.6 13.7
15.3 15.3 15.2 15.2 15.2 15.1 15.1 15.0 15.0 15.0 14.9 14.9
Theor.
E (keV)
Exp.
Theor.
E (keV)
Exp.
Theor.
3.29 3.28 3.27 3.26 3.25 3.25 3.24 15.1 15.1
57.62332 57.68146 57.73961 57.79775 57.85590 57.91404 57.97219 58.03033 58.08848
13.8 13.4 13.5 13.8 13.6 13.1 13.8 13.2 13.6
15.0 15.0 15.0 14.9 14.9 14.9 14.8 14.8 14.8
58.14662 58.20477 58.26291 58.32106 58.3792 58.43735 58.49549 58.55364
13.5 13.5 13.7 13.4 13.9 14.0 13.6 13.7
14.7 14.7 14.6 14.6 14.6 14.5 14.5 14.5
3.26 3.25 3.25 3.24 3.50 3.49 3.48 3.47 3.46 3.45 3.44 3.43
3.39 3.38 3.38 3.37 3.36 3.35 3.34 3.33 3.32 3.31 3.31 3.30
Er
57.10001 57.15816 57.21630 57.27445 57.33259 57.39074 57.44888 57.50703 57.56517
where µ is the linear attenuation coefficient (cm−1 ), ρ the density of the sample (g cm−3 ), x the mass thickness of the sample (cm), I0 the count value without the sample, and I is the count value of the radiation penetrating through the sample. To calculate the total mass attenuation in Tb4 O7 , the equation is given by µ µ µ = wi + wj + ··· (3) ρ compound ρ i ρ j where (µ/ρ)compound (cm2 g−1 ) is the experimental the total mass attenuation coefficient, (µ/ρ)i,j,k··· is the theoretical total mass attenuation coefficients of the constituent elements i, j, k of the compound, Wi,j,k··· is the proportion of each element by weight. If we wish to obtain the total mass attenuation coefficient of constituent element i, the value is given by (µ/ρ)compound − [wj (µ/ρ)j ] µ (4) = ρ i wi Theoretical values of the total mass attenuation coefficients are computed from the WinXcom program [13]. This program is based on the XCOM [14] data base and program of Berger and Hubbell [14]. XCOM and software XCOM (WinXcom) depend on applying the mixture rule to calculate the partial and total mass attenuation coefficients of all elements, compounds, and mixtures at standard as well as selected energies. For related elements and compound experimental and theoretical total mass attenuation coefficient are also presented in Table 2. If the theoretical values of Saloman [15] are compared with the Table 2 results, in particular around the K-edge
of Gd and Dy, the experimental and theoretical total mass attenuation coefficients for Gd (50.6459 keV) and Dy (52.09954 keV) in Table 2 are in general consistent with the calculated values of Saloman for Gd (at 50.65 keV, 16.04 cm2 g−1 ) and Dy (at 52 keV, 3.63 cm2 g−1 ). The calculation of the total mass attenuation coefficients is a requirement to obtain absorption jump factors with connected elements. Absorption jump values r and jump differences δ are measures of that portion of the total absorbed X-radiation that is absorbed by a specified atomic energy level. For example, K and LIII jump values are defined by. rK =
(µ/ρ)K + (µ/ρ)LI + (µ/ρ)LII + (µ/ρ)LIII + · · · (µ/ρ)LI + (µ/ρ)LII + (µ/ρ)LIII + · · · (5)
Table 3 Experimental and theoretical absorption jump factors (Jk ) Elements
E
Gd Tb Dy Ho Er
0.794 0.837 0.765 0.823 0.752
± ± ± ± ±
0.019 0.028 0.015 0.039 0.016
Ta
Tb
Tc
Literature E-value
0.795 0.793 0.791 0.788 0.786
0.802 0.793 0.791 0.786 0.791
0.827 0.819 0.818 0.812 0.818
0.824d 0.814d 0.813d 0.805d 0.817d,e
E: experimental values; T: theoretical values. a Ref. [13]. b Ref. [5]. c Ref. [6]. d Ref. [9]. e Ref. [7].
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R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
where µ/ρ is the mass-absorption coefficient at the given energy for any given substance. In subsequent developments, absorption jump values, r, will be used to calculate absorption jump factors, j, i.e. the probability jλi that an incident photon will eject electrons from a K, L, M,. . . energy level. For example, the probability that a K-level electron of element i will be ejected rather than one from an L or M level is given by rK − 1 rK
(6)
5. Result and discussion It is evident from the tables that the experimental results are, in general, consistent with the theoretical data. The experimental total mass attenuation coefficients of Gd, Tb, Dy, Ho and Er around the K absorption edges versus photon energy are also graphically presented in Figs. 3–7. In this
2 -1 µ /ρ (cm .g )
10
1
Experimental WinXCom
Gd 0,1 48
49
50
51
52
Photon Energy (keV) Fig. 3. Mass attenuation coefficients of Gd around the K absorption edge.
10
µ/ρ (cm2.g-1)
jK =
Experimental values and theoretical absorption jump factors are summarized in Table 3.
1
Experimental WinXCom
Tb 0,1 50
51
52
53
Photon Energy (keV) Fig. 4. Mass attenuation coefficients of Tb around the K absorption edge.
R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
313
µ/ρ (cm2.g-1)
10
1
Experimental WinXCom
Dy 0,1 53
54
55
Photon Energy (keV) Fig. 5. Mass attenuation coefficients of Dy around the K absorption edge.
present method, Compton scattering of gamma rays from low atomic number elements including Al at definite angles is possible with ideal transmission geometry to be obtained energies near the absorption edges of absorbers. Choice of angle is very important in ideal transmission geometry. The incident photon energy can be transmitted to the absorber after choosing a definite angle for each element. As a result, the agreement between the theoretical and present experimental values leads to the conclusion that the new method is reliable, useful, and practical. Besides, the
present method will benefit those using radioisotope X-ray fluorescence techniques for data analysis. To reach a more definitive conclusion about the absorption jump factor and confirm the sensitivity of the present method, we plan to extend these measurements to various elements, compounds and even alloys as related to different primer energies. The most important section of this method be regulated according to angle of energy with the help of Eq. (1). The present method is simple, direct and rapid for the determination of absorption jump factors.
µ//ρ (cm2.g-1)
10
1
Experimental WinXCom
Hb 0,1 54
55
56
Photon Energy (keV) Fig. 6. Mass attenuation coefficients of Ho around the K absorption edge.
57
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R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
µ/ρ (cm2.g-1)
10
1
Experimental WinXCom
Er 0,1 56
57
58
Photon Energy (keV) Fig. 7. Mass attenuation coefficients of Er around the K absorption edge.
References [1] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freumd, H. Mark, C.D. Swift, R.E. Price, Mod. Phys. 44 (1972) 716. [2] D.V. Rao, R. Cesareo, G.E. Gigante, Appl. Phys. A 62 (1996) 381. [3] J.H. Scofield, UCRL-51326 (1973). [4] H. Ottomar, H. Erbele, P. Matussek, I. Michel-Piper, Assay Adv. X-Ray Anal. 30 (1987) 285. [5] W.H. McMaster, N. Kerr Del Grande, J.H. Mallett, J.H. Hubbell, UCRL-50174 (1969) Sec. II. Rev. 1. [6] N. Broll, X-Ray Spectrom. 15 (1986) 271.
[7] A.P. Ayala, R.T. Mainardi, Radiat. Phys.Chem. 47 (2) (1996) 177. [8] M.L. Mallikarjuna, S.B. Appaji Gowda, R. Gowda, T.K. Umesh, Radiat. Phys. Chem. 65 (2002) 217. [9] G. Budak, A. Karabulut, M. Ertu˘orul, Radiat. Meas. 37 (2003) 103. [10] F. Yang, H.H. Joseph, Modern Atomic and Nuclear Physics, Singapore, 1996, p. 247. ˙ [11] O. Içelli, S. Erzeneoˇglu, Spectrochim. Acta B 57 (2002) 1317. [12] A.H. Compton, Phys. Rev. 21 (1923) 483. [13] L. Gerward, N. Guilbert, K. Bjorn Jensen, H. Levring, Radiat. Phys. Chem. 60 (2001) 23. [14] M.J. Berger, J.H. Hubbell, NBSIR 87-3597 (1987). [15] E.B. Saloman, J.H. Hubbell, J.H. Scofield, Atomic Data Nucl. Data Tables (1988) 1–197.
New method to measure the K-shell absorption jump factor in some rare-earth elements a,∗ , Gökhan Budak b ˙ Recep Polat a , Orhan Içelli a
Department of Physics, Education Faculty of Erzincan, Atatürk University, Erzincan, Turkey b Department of Physics, Science and Art Faculty, Atatürk University, Erzurum, Turkey
Received 26 May 2003; received in revised form 7 October 2003; accepted 21 October 2003
Abstract The Compton scattering of 59.54 keV gamma rays by an Al scatterer has been used as a primer source at scattering angles from 48 to 118◦ by using a Si(Li) detector, and this primer gamma ray has been send to absorbers including Gd, Tb, Dy, Ho and Er. A new method has been developed to determine the K-shell absorption jump factor of elements and compounds. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding the problems with measuring the source strength and source-to-detector solid angle. In this method, the jump factor is effected from the scattering angle. Evident energies near to K-absorption edges of each lanthanide element have been determined for chosen angles, after the incident photon energy (59.5 keV) is exposed to Compton scattering from Al (secondary source). The experimental absorption jump factors are compared with the theoretical estimates and literature experimental values. © 2003 Elsevier B.V. All rights reserved. Keywords: Rare-earth elements; Jump value; Jump factor; Absorption jump ratio
1. Introduction Absorption jump factors and jump values of an elements are very useful parameters in many fields of scientific applications such as nuclear physics, cancer therapy, industrial irradiation processing, dosimetric computations for health physics and X-ray fluorescence surface chemical analysis [1,2]. Quantitative knowledge of the emission of characteristic K radiation is still of great interest for both fundamental and applied physics. Accurate experimental values offer an appropriate means for checking the validity of the assumptions included in the different formulation of atomic models that make it possible to evaluate important atomic parameters such as the absorption jump factor and fluorescence cross-section. These cross-sections are presently available for all-shell theoretical atomic photoeffect cross-section computations and tabulations in Scofield [3]. The rare-earth metals being used nowadays in X-ray applications are absent from such experimental studies. These elements have been used as a raw material for fluorescent compounds, absorp-
∗
Corresponding author. ˙ E-mail address: orhan [email protected] (O. Içelli).
0003-2670/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.aca.2003.10.061
tion material in atomic reactions, magnetic bubble material, screen-sensitivity increasing material, as well as many other applications in the chemical, glass and electronic industries. Apart from Er, other rare-earth elements used as dopants in superconductors are also characterized by X-ray techniques. Determined absorption jump factors of elements are also required for correct use of spectroscopic techniques [4]. Accurate theoretical data on jump factors for elements are calculated for use in the applications mentioning above. Some researchers [5,6] have also theoretically calculated the jump factor and jump value by using different methods. But experimental studies [7–9] on these subjects are particularly devoid of measurements. Our purpose is to improve simply, directly, reliably and rapidly an experimental method in order to determine the absorption jump factor. In our methods, we have the benefit of Compton scattering. Ref. [7] does not describe both the deconvolution process and determination process at an incident angle of 48◦ for only Er absorber. However, we show that Compton gamma rays scattering from Al element by regulating the scattering angle have been reduced at the absorption edge of the the absorber. In the case of Compton scattering of photons from electrons, the scattered photon energy depends in a unique way on the scattering angle θ. Note that the energy of the
308
R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
scattered photon is a function of the energy of the incident photon as well as of θ [10]. In this study, we have measured the absorption jump factors in some rare-earth elements making use of Compton scattering and experimental results compared with different theoretical and literature experimental values.
2. Experimental method The schematic arrangement of the experimental setup used in the present work is shown in Fig. 1. Since we have used Al [11], the inaccuracies of an incoherent scattering function are minimized. Also, the Rayleigh contribution is low in the small Z targets. As seen in Fig. 1, Al has been used as a secondary target in this experimental setup. The present experimental setup has been constituted as an ideal transmission geometry and ␥-photon energy of 59.5 keV is transmitted to Al element. Later, ␥-photon rays caused by Compton scattering from Al element have been transmitted to Gd, Dy, Ho and Er elements and a Tb4 O7 powder sample used as absorber. The energy of the scattered photon is given by. E1 (1) E2 = 1 + (E1 /m0 c2 )(1 − cos θ) where E1 is energy of incident photon, m0 c2 is the electron rest-mass energy whose value is 5.11 × 105 eV, and θ is the angle between the photon directions of travel prior to and following a scattering interaction [12] (Table 1).
3. Procedures The total attenuation coefficients and K X-rays absorption jump-factors were determined by using transmission geometry. In the present experiment a Si(Li) detector (FWHM = 160 eV at 5.96 keV) was used with a multichannel analyzer for detection of X-rays. This detector was coupled to a computerized 1024-multichannel analyzer through a spectroscopic automatic fine-tuning research amplifier. To obtain statistical sensitivity, each sample has been measured by collecting the spectra from selected elements for a period of 72 × 103 s. High purity (99.9%) thin foil samples of Gd, Dy, Ho and Er elements and a powder sample of Tb4 O7 , whose mass thickness ranges from 0.164 to 0.307 g cm−2 , have been used in conjunction with a radioactive point source of 241 Am of 100 mCi (3.7 × 109 Bq) having a ␥-photon energy of 59.5 keV. In order to eliminate the particle size effect, the Tb4 O7 samples were sieved through a 400 mesh sieve, before compressing then into pellets for 15 s by using a manual hydraulic press. In ideal transmission geometry, Al element has been used as a secondary target. Incident gamma rays of Compton scattering from Al were transmitted to the absorber. In this experiment, the net counts without absorber (I0 ) and with absorber (I) were obtained at the same time and experimental conditions. The errors in the evaluation of the area under the Compton peaks are ≤2%, the determination of the thickness of the sample is ≤3%, and the counting statistics ≤1%. A typical Compton spectrum of Gd is shown in Fig. 2.
4. Data analysis
Table 1 Incident energy values on absorber Absorber
Scattering angle (θ)
K (absorption edge) (keV)
Energy of secondary source (keV)
Gd Tb Dy Ho Er
118◦ 108◦ 88◦ 68◦ 48◦
50.229 51.998 53.789 55.615 57.483
50.838 51.663 53.524 55.499 57.333
The total mass attenuation coefficients can be obtained from the differences in the count value with and without the presence of a sample. The mass attenuation coefficients are given as µ I = I0 exp − x·ρ (2) ρ
Fig. 1. Experimental set-up.
R. Polat et al. / Analytica Chimica Acta 505 (2004) 307–314
309
30000 (a)
25000
Counts
20000
15000 (b)
10000
5000
0 35
40
45
50
55
60
Energy (keV) Fig. 2. Measured Compton spectra. Curve (a) unattenuated spectrum. (b) Attenuated spectrum by a Gd foil. Table 2 Tabulated total mass attenuation coefficients from 48 to 58.55 keV for Gd, Tb4 O7 , Dy, Ho and Er Total mass attenuation coefficient (cm2 g−1 ) E (keV)
Gd Exp.
48.02939 4.08754 48.14568 48.20383 48.26197 48.32012 48.37826 48.43641 48.49455 48.55270 48.61084 48.66899 48.72713 48.78528 48.84342 48.90157 48.95971 49.01786 49.07600 49.13415 49.19229 49.25044 49.30858 49.36673 49.42487 49.48302 49.54116 49.59931 49.65745 49.71560 49.77374 49.83189 49.89003 49.94818
4.63 4.61 4.46 4.46 4.71 4.64 4.46 4.37 4.11 4.36 4.33 4.72 4.45 4.46 4.50 4.58 4.24 4.40 4.51 4.14 4.52 4.54 4.52 4.48 4.60 4.07 4.49 4.42 4.49 4.77 5.73 6.60 7.21 9.34
E (keV) Theor. 4.28 4.27 4.25 4.24 4.23 4.22 4.20 4.19 4.18 4.16 4.15 4.14 4.12 4.11 4.10 4.09 4.07 4.06 4.05 4.04 4.03 4.01 4.00 3.99 3.98 3.96 3.95 3.94 3.93 3.92 3.91 3.89 3.88 3.87
50.00632 50.06447 50.12261 50.18076 50.23890 50.29705 50.35519 50.41334 50.47148 50.52963 50.58777 50.64592 50.70406 50.76221 50.82035 50.87850 50.93664 50.99479 51.05293 51.11108 51.16922 51.22737 51.28551 51.34366 51.40180 51.45995 51.51809 51.57624 51.63438 51.69253 51.75067 51.80882 51.86696 51.92511 51.98325 52.04140
Gd
Tb
Exp.
Theor.
Exp.
Theor.
10.7 13.4 15.2 15.9 18.3 19.4 21.0 21.5 20.7 20.0 20.8 20.1 20.1 20.9 20.8 19.6 20.4 19.8 19.3 18.0 19.2 18.4 18.0 19.8 18.0 17.4 18.7 18.7 17.7 17.7 16.9 18.1 18.1 17.2 17.2 17.2
3.86 3.85 3.84 3.82 18.6 18.6 18.5 18.5 18.4 18.4 18.3 18.2 18.2 18.1 18.1 18.0 18.0 17.9 17.9 17.8 17.8 17.7 17.7 17.6 17.6 17.5 17.5 17.4 17.4 17.3 17.3 17.2 17.2 17.1 17.1 17.0
4.92 4.72 4.80 4.67 4.70 4.73 4.70 4.62 4.76 4.73 4.76 4.69 4.64 4.63 4.83 4.64 4.70 4.64 4.61 4.91 4.67 4.82 4.64 4.70 5.07 5.09 5.60 6.30 7.19 7.98 8.68 10.6 12.1 13.4 14.8 16.4
4.06 4.05 4.04 4.03 4.01 4.00 3.99 3.98 3.97 3.95 3.94 3.93 3.92 3.91 3.90 3.88 3.87 3.86 3.85 3.84 3.83 3.82 3.80 3.79 3.78 3.77 3.76 3.75 3.74 3.73 3.72 3.71 3.70 3.68 3.68 17.7
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Table 2 (Continued ) Tb
52.09954 52.15769 52.21583 52.27398 52.33212 52.39027 52.44841 52.50656 52.56470 52.62285 52.68099 52.73914 52.79728 52.85543 52.91357 52.97172 53.02986 53.08801 53.14615 53.20430 53.26244 53.32059 53.37873 53.43688 53.49502 53.55317
Dy
Exp.
Theor.
16.5 16.8 16.6 17.4 15.8 17.4 17.3 16.8 15.6 17.1 16.3 15.9 14.7 15.4 14.6 16.4 14.1 14.8 13.8 14.3 14.2 14.5 14.3 13.8 13.3 14.7
17.7 17.6 17.6 17.5 17.5 17.4 17.4 17.3 17.3 17.2 17.2 17.1 17.1 17.0 17.0 16.9 16.9 16.8 16.8 16.7 16.7 16.6 16.6 16.5 16.5 16.4
Dy
53.61131 53.66946 53.72760 53.78575 53.84389 53.90204 53.96018 54.01833 54.07647 54.13462 54.19276 54.25091 54.30905 54.36720 54.42534 54.48349 54.54163 54.59978 54.65792 54.71607 54.77421 54.83236 54.89050 54.94865 55.00679
Theor.
11.3 12.3 14.1 15.2 16.5 15.2 16.7 15.6 17.0 16.3 16.2 16.3 14.5 14.5 14.8 14.5 16.3 13.1 14.1 13.8 14.6 13.3 12.3 13.2 13.4
3.53 3.52 3.51 16.8 16.7 16.7 16.6 16.6 16.5 16.5 16.4 16.4 16.3 16.3 16.2 16.2 16.2 16.1 16.1 16.0 16.0 15.9 15.9 15.8 15.8
Ho
55.06494 55.12308 55.18123 55.23937 55.29752 55.35566
4.38 4.80 5.02 5.66 6.74 7.94
3.88 3.42 3.55 3.96 4.27 3.94 3.74 4.28 4.18 4.03 3.85 3.93 4.20 4.07 3.86 4.16 4.10 3.79 3.69 3.63 4.19 4.04 5.10 6.56 7.65 9.56
Theor. 3.80 3.79 3.78 3.77 3.76 3.75 3.73 3.72 3.71 3.70 3.69 3.68 3.67 3.66 3.65 3.64 3.63 3.62 3.61 3.60 3.59 3.58 3.57 3.56 3.55 3.54
Ho
Exp.
Exp.
Exp.
Exp.
3.80 3.22 3.20 4.15 4.06 3.75 4.39 3.79 4.18 3.79 3.41 3.23 3.51 3.75 3.74 3.94 3.79 4.17 3.56 3.80 4.12 3.97 4.28 E (keV)
Theor. 3.44 3.43 3.42 3.41 3.40 3.39
56.05340 56.11155 56.16969 56.22784 56.28598 56.34413
Theor.
3.66 3.65 3.64 3.63 3.62 3.61 3.60 3.59 3.58 3.57 3.56 3.55 3.54 3.53 3.52 3.51 3.50 3.50 3.49 3.48 3.47 3.46 3.45 Ho
Er
Exp.
Theor.
13.3 13.2 13.3 13.1 13.3 13.3
15.6 15.5 15.5 15.4 15.4 15.4
Exp. 3.31 3.31 3.30 3.29 3.28 3.27
Theor. 3.45 3.44 3.43 3.42 3.41 3.40
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Table 2 (Continued ) Ho
55.41381 55.47195 55.53010 55.58824 55.64639 55.70453 55.76268 55.82082 55.87897 55.93711 55.99526
E (keV)
Exp.
Theor.
10.1 11.4 13.0 13.3 13.8 13.3 13.7 13.2 13.4 13.5 13.6
3.38 3.37 3.36 15.9 15.9 15.8 15.8 15.7 15.7 15.6 15.6
Exp. 3.42 3.41 5.40 7.39 9.38 11.3 12.3 13.6 13.1
Ho
Er
Exp.
Theor.
Exp.
Theor.
56.40227 56.46042 56.51856 56.57671 56.63485 56.69300 56.75114 56.80929 56.86743 56.92558 56.98372 57.04187
13.1 13.2 13.3 13.3 13.2 13.5 13.3 13.1 13.3 13.4 13.6 13.7
15.3 15.3 15.2 15.2 15.2 15.1 15.1 15.0 15.0 15.0 14.9 14.9
Theor.
E (keV)
Exp.
Theor.
E (keV)
Exp.
Theor.
3.29 3.28 3.27 3.26 3.25 3.25 3.24 15.1 15.1
57.62332 57.68146 57.73961 57.79775 57.85590 57.91404 57.97219 58.03033 58.08848
13.8 13.4 13.5 13.8 13.6 13.1 13.8 13.2 13.6
15.0 15.0 15.0 14.9 14.9 14.9 14.8 14.8 14.8
58.14662 58.20477 58.26291 58.32106 58.3792 58.43735 58.49549 58.55364
13.5 13.5 13.7 13.4 13.9 14.0 13.6 13.7
14.7 14.7 14.6 14.6 14.6 14.5 14.5 14.5
3.26 3.25 3.25 3.24 3.50 3.49 3.48 3.47 3.46 3.45 3.44 3.43
3.39 3.38 3.38 3.37 3.36 3.35 3.34 3.33 3.32 3.31 3.31 3.30
Er
57.10001 57.15816 57.21630 57.27445 57.33259 57.39074 57.44888 57.50703 57.56517
where µ is the linear attenuation coefficient (cm−1 ), ρ the density of the sample (g cm−3 ), x the mass thickness of the sample (cm), I0 the count value without the sample, and I is the count value of the radiation penetrating through the sample. To calculate the total mass attenuation in Tb4 O7 , the equation is given by µ µ µ = wi + wj + ··· (3) ρ compound ρ i ρ j where (µ/ρ)compound (cm2 g−1 ) is the experimental the total mass attenuation coefficient, (µ/ρ)i,j,k··· is the theoretical total mass attenuation coefficients of the constituent elements i, j, k of the compound, Wi,j,k··· is the proportion of each element by weight. If we wish to obtain the total mass attenuation coefficient of constituent element i, the value is given by (µ/ρ)compound − [wj (µ/ρ)j ] µ (4) = ρ i wi Theoretical values of the total mass attenuation coefficients are computed from the WinXcom program [13]. This program is based on the XCOM [14] data base and program of Berger and Hubbell [14]. XCOM and software XCOM (WinXcom) depend on applying the mixture rule to calculate the partial and total mass attenuation coefficients of all elements, compounds, and mixtures at standard as well as selected energies. For related elements and compound experimental and theoretical total mass attenuation coefficient are also presented in Table 2. If the theoretical values of Saloman [15] are compared with the Table 2 results, in particular around the K-edge
of Gd and Dy, the experimental and theoretical total mass attenuation coefficients for Gd (50.6459 keV) and Dy (52.09954 keV) in Table 2 are in general consistent with the calculated values of Saloman for Gd (at 50.65 keV, 16.04 cm2 g−1 ) and Dy (at 52 keV, 3.63 cm2 g−1 ). The calculation of the total mass attenuation coefficients is a requirement to obtain absorption jump factors with connected elements. Absorption jump values r and jump differences δ are measures of that portion of the total absorbed X-radiation that is absorbed by a specified atomic energy level. For example, K and LIII jump values are defined by. rK =
(µ/ρ)K + (µ/ρ)LI + (µ/ρ)LII + (µ/ρ)LIII + · · · (µ/ρ)LI + (µ/ρ)LII + (µ/ρ)LIII + · · · (5)
Table 3 Experimental and theoretical absorption jump factors (Jk ) Elements
E
Gd Tb Dy Ho Er
0.794 0.837 0.765 0.823 0.752
± ± ± ± ±
0.019 0.028 0.015 0.039 0.016
Ta
Tb
Tc
Literature E-value
0.795 0.793 0.791 0.788 0.786
0.802 0.793 0.791 0.786 0.791
0.827 0.819 0.818 0.812 0.818
0.824d 0.814d 0.813d 0.805d 0.817d,e
E: experimental values; T: theoretical values. a Ref. [13]. b Ref. [5]. c Ref. [6]. d Ref. [9]. e Ref. [7].
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where µ/ρ is the mass-absorption coefficient at the given energy for any given substance. In subsequent developments, absorption jump values, r, will be used to calculate absorption jump factors, j, i.e. the probability jλi that an incident photon will eject electrons from a K, L, M,. . . energy level. For example, the probability that a K-level electron of element i will be ejected rather than one from an L or M level is given by rK − 1 rK
(6)
5. Result and discussion It is evident from the tables that the experimental results are, in general, consistent with the theoretical data. The experimental total mass attenuation coefficients of Gd, Tb, Dy, Ho and Er around the K absorption edges versus photon energy are also graphically presented in Figs. 3–7. In this
2 -1 µ /ρ (cm .g )
10
1
Experimental WinXCom
Gd 0,1 48
49
50
51
52
Photon Energy (keV) Fig. 3. Mass attenuation coefficients of Gd around the K absorption edge.
10
µ/ρ (cm2.g-1)
jK =
Experimental values and theoretical absorption jump factors are summarized in Table 3.
1
Experimental WinXCom
Tb 0,1 50
51
52
53
Photon Energy (keV) Fig. 4. Mass attenuation coefficients of Tb around the K absorption edge.
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313
µ/ρ (cm2.g-1)
10
1
Experimental WinXCom
Dy 0,1 53
54
55
Photon Energy (keV) Fig. 5. Mass attenuation coefficients of Dy around the K absorption edge.
present method, Compton scattering of gamma rays from low atomic number elements including Al at definite angles is possible with ideal transmission geometry to be obtained energies near the absorption edges of absorbers. Choice of angle is very important in ideal transmission geometry. The incident photon energy can be transmitted to the absorber after choosing a definite angle for each element. As a result, the agreement between the theoretical and present experimental values leads to the conclusion that the new method is reliable, useful, and practical. Besides, the
present method will benefit those using radioisotope X-ray fluorescence techniques for data analysis. To reach a more definitive conclusion about the absorption jump factor and confirm the sensitivity of the present method, we plan to extend these measurements to various elements, compounds and even alloys as related to different primer energies. The most important section of this method be regulated according to angle of energy with the help of Eq. (1). The present method is simple, direct and rapid for the determination of absorption jump factors.
µ//ρ (cm2.g-1)
10
1
Experimental WinXCom
Hb 0,1 54
55
56
Photon Energy (keV) Fig. 6. Mass attenuation coefficients of Ho around the K absorption edge.
57
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µ/ρ (cm2.g-1)
10
1
Experimental WinXCom
Er 0,1 56
57
58
Photon Energy (keV) Fig. 7. Mass attenuation coefficients of Er around the K absorption edge.
References [1] W. Bambynek, B. Crasemann, R.W. Fink, H.U. Freumd, H. Mark, C.D. Swift, R.E. Price, Mod. Phys. 44 (1972) 716. [2] D.V. Rao, R. Cesareo, G.E. Gigante, Appl. Phys. A 62 (1996) 381. [3] J.H. Scofield, UCRL-51326 (1973). [4] H. Ottomar, H. Erbele, P. Matussek, I. Michel-Piper, Assay Adv. X-Ray Anal. 30 (1987) 285. [5] W.H. McMaster, N. Kerr Del Grande, J.H. Mallett, J.H. Hubbell, UCRL-50174 (1969) Sec. II. Rev. 1. [6] N. Broll, X-Ray Spectrom. 15 (1986) 271.
[7] A.P. Ayala, R.T. Mainardi, Radiat. Phys.Chem. 47 (2) (1996) 177. [8] M.L. Mallikarjuna, S.B. Appaji Gowda, R. Gowda, T.K. Umesh, Radiat. Phys. Chem. 65 (2002) 217. [9] G. Budak, A. Karabulut, M. Ertu˘orul, Radiat. Meas. 37 (2003) 103. [10] F. Yang, H.H. Joseph, Modern Atomic and Nuclear Physics, Singapore, 1996, p. 247. ˙ [11] O. Içelli, S. Erzeneoˇglu, Spectrochim. Acta B 57 (2002) 1317. [12] A.H. Compton, Phys. Rev. 21 (1923) 483. [13] L. Gerward, N. Guilbert, K. Bjorn Jensen, H. Levring, Radiat. Phys. Chem. 60 (2001) 23. [14] M.J. Berger, J.H. Hubbell, NBSIR 87-3597 (1987). [15] E.B. Saloman, J.H. Hubbell, J.H. Scofield, Atomic Data Nucl. Data Tables (1988) 1–197.