K-shell X-ray fluorescence cross-sections and intensity ratios for some pure metals at 59.5 and 123.6 keV

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 262 (2007) 165–170 www.elsevier.com/locate/nimb

K-shell X-ray fluorescence cross-sections and intensity ratios for some pure metals at 59.5 and 123.6 keV U. Cevik a

a,*

, S. Kaya a, B. Ertugral b, H. Baltas c, S.M. Karabıdak

a

Karadeniz Technical University, Faculty of Arts and Science, Department of Physics, 61080 Trabzon, Turkey b Giresun University, Faculty of Arts and Science, Department of Physics, Giresun, Turkey c Rize University, Faculty of Arts and Science, Department of Physics, 53100 Rize, Turkey Received 22 February 2007; received in revised form 3 May 2007 Available online 12 June 2007

Abstract K-shell X-ray fluorescence cross-sections for some pure metals such as Cr, Fe, Co, Cu, Zn, Ga, Se, Y, Mo, Cd, In, Sn, Te, Ba, Ta, W and Bi have been theoretically and experimentally determined. The Cr, Fe, Co, Cu, Zn, Ga, Se, Y, Mo, Cd, In, Sn, Te and Ba metals were excited by 59.5 keV c-ray from 50 mCi 241Am radioactive source and the Ta, W and Bi targets were excited by 123.6 keV c-ray from 25 mCi 57Co radioactive source. The characteristic K X-rays emitted by samples were detected by using a super Si(Li) detector having a resolution of 150 eV at 5.9 keV. In addition, the IKb/IKa intensity ratios for these metals were studied. The obtained experimental values of the K-shell X-ray fluorescence cross-sections and the IKb/IKa intensity ratios have been compared with theoretical values. The measured values were in good agreement with theoretical values. Ó 2007 Elsevier B.V. All rights reserved. PACS: 32.30.Rj; 32.80.Cy; 32.70.n Keywords: Cross-sections; Intensity ratios; EDXRF; Super Si(Li) detector

1. Introduction The fluorescence cross-section is the indicator of probability of any event of particles within the target sample and target parts approaching towards the sample. The K-shell X-ray fluorescence cross-section was defined theoretically as the product of photoelectric cross-section and fluorescence yield and has been calculated from tabulated values of these parameters. Accurate experimental values of K X-ray fluorescence cross-sections and intensity ratios for different elements at different photoionization is important because of their wide use in atomic, molecular, radiation and health physics and in the nondestructive elemental analysis of materials using energy dispersive X-ray fluorescence (EDXRF). Moreover, comparison of measured K X-ray fluorescence cross-sections with theoretical values *

Corresponding author. Tel.: +90 462 3773591; fax: +90 462 3253195. E-mail address: [email protected] (U. Cevik).

0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.06.007

provides a check on the validity of various physical parameters such as photoionization cross-section, fluorescence yield and jump factor. Krause et al. have been calculated theoretical K and L XRF cross sections but there have been few reports on experimental measurements of XRF cross-sections [1]. In recent years, several attempts have been made for measuring X-ray fluorescence cross-sections. Bahn et al. determined K-shell cross-sections for ten elements with 18 6 Z 6 48 at two excitation energies from 109Cd and 125 I radioisotopes [2]. K X-ray fluorescence cross-sections for low-Z elements at low excitation energies have been reported by Rao et al. [3]. Puri et al. [4] published an extensive table of K-shell X-ray fluorescence cross sections for elements with 13 6 Z 6 92 for incident photon energy range 1–200 keV. Ka and Kb fluorescence cross-sections in the range 44 6 Z 6 68 at 59.5 keV were measured by Budak et al. [5]. Sahin et al. determined K X-ray fluorescence cross-section for six elements at 5.96 keV [6].

10

<1

27

13

100

50

β2

β5

β1

β3

α1

α2

Optical X-Ray Notation Notation

<1

j

State

β4

n l

Number of Electrons in Filled Orbitals

-

Quantum Numbers

Kab

U. Cevik et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 165–170

Line or Relative Edge Intensity

166

Kab

β4

β2

β5

β1

β3

α1

α2

Out of atom 2

5 5 5 5 5

2 2 1 1 0

5/2 3/2 3/2 1/2 1/2

6 4 4 2 2 (18O)

5 D5/2 52D3/2 52P3/2 52P1/2 52S1/2

OV OIV OIII OII OI

4 4 4 4 4 4 4

3 3 2 2 1 1 0

7/2 5/2 5/2 3/2 3/2 1/2 1/2

8 6 6 4 4 2 2 (32N)

42F7/2 42F5/2 42D5/2 42D3/2 42P3/2 42P1/2 42S1/2

NVII NVI NV NIV NIII NII NI

3 3 3 3 3

2 2 1 1 0

5/2 3/2 3/2 1/2 1/2

6 4 4 2 2 (18M)

32D5/2 32D3/2 32P3/2 32P1/2 32S1/2

MV MIV MIII MII MI

4 2 2 (8L)

22P3/2 22P1/2 22S1/2

LIII LII LI

2 1 3/2 2 1 1/2 2 0 1/2

1 0 1/2

2

2

1 S1/2

~

K

Nucleus Fig. 1. Transitions produced Ka and Kb X-ray.

Fig. 2. Experimental setup.

U. Cevik et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 165–170

167

300000

Mo K α 250000

Counts

200000

150000

100000

Mo K β1 50000

Mo K β2 0

1000

1100

1200

1300

1400

Channel 5000

Ta K α1

5000

Counts

4000

4000

3000 2000

Ta Kα2

Counts

3000

1000 0 0

2000

4000

Channel

2000

Ta K β1

1000

Ta K β2 0 3000

3250

3500

3750

4000

4250

4500

Channel Fig. 3. (a), (b) Typical K X-ray spectrum for Mo and Ta with

The measurement of Kb/Ka intensity ratios is important because of comparison with theoretical predictions based on atomic model. While the Ka X-rays arise from transitions from the L- to the K-shell, the Kb X-rays arise from transitions from the M-, N-, O-, etc. to the K-shell as shown in Fig. 1 [7]. In recent years, there have been various investigations on Kb/Ka intensity ratios. Rao et al. showed that the Kb/Ka intensity ratios depend on the excitation modes in 3d elements but they could not find such dependence for the high Z elements [8]. Dhal and Padhi have investigated relative K X-ray intensities on the elements from Mn to Sb using 59.5 keV c-rays [9]. Similarly, Ertugrul have measured Kb/Ka intensity ratios in element range 22 6 Z 6 69 at 59.5 keV [10]. Ertugrul and Simsek have measured K X-ray relative intensity of some high Z elements [11]. Pawlowski have reported the valence electronic

241

Am and

57

Co excitation.

structure of Ti, Cr, Fe and Co in some alloys from Kb/Ka X-ray intensity [12]. This study is, therefore, concerned with the comparison of the experimental Kb to Ka X-ray ratio and the K X-ray fluorescence cross-section values with the theoretical ones. In this paper, Ka, Kb and K X-ray fluorescence crosssections and Kb/Ka intensity ratios of 17 metals from Cr to Bi have been measured. The targets have been excited with 59.5 and 123.6 keV photons from 241Am and 57Co radioactive sources. Results are compared with available experimental data and the theoretical values. 2. Theory The theoretical K-shell X-ray fluorescence cross-sections rKi were calculated using the following equation

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U. Cevik et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 165–170

Table 1 The K-shell X-ray fluorescence cross-sections Element

Cr Fe Co Cu Zn Ga Se Y Mo Cd In Sn Te Ba Ta W Bi

Z

24 26 27 29 30 31 34 39 42 48 49 50 52 56 73 74 83

rKa (b/atom)

rKb (b/atom)

Experimental

Theoretical

Puri et al. [4]

Experimental

Theoretical

Puri et al. [4]

Experimental

Theoretical

Puri et al. [4]

16.49 ± 0.12 28.98 ± 0.34 36.18 ± 0.40 57.63 ± 0.46 71.59 ± 0.50 80.03 ± 0.68 146.53 ± 0.73 296.04 ± 1.40 418.97 ± 2.43 756.26 ± 6.07 819.91 ± 5.70 887.46 ± 6.83 1042.98 ± 5.16 1388.72 ± 10.90 515.58 ± 15.98 553.49 ± 18.81 802.44 ± 32.43

16.28 28.15 36.16 57.35 71.59 90.62 144.12 293.59 418.07 754.71 822.68 894.13 1045.70 1391.47 517.30 543.83 816.68

15.07 25.74 32.82 50.9 61.93 74.43 122.96 245.83 350.2 641.73 698 755.22 880.71 1155.86 436.26 456.47 669.31

2.02 ± 0.14 3.68 ± 0.13 4.71 ± 0.14 7.62 ± 0.16 8.90 ± 0.18 11.77 ± 0.28 22.08 ± 0.29 49.73 ± 0.54 75.84 ± 0.55 150.94 ± 1.20 166.94 ± 1.34 185.70 ± 1.57 218. 41 ± 1.93 323.45 ± 3.20 143.38 ± 3.95 154.68 ± 4.64 224.59 ± 5.63

1.91 3.41 4.38 6.94 8.85 11.54 20.78 49.79 75.52 151.30 167.31 184.44 223.35 315.85 138.34 146.31 231.69

2.02 3.58 4.57 7.02 8.74 10.87 19.98 45.99 69.34 139.18 153.47 168.8 202.55 281.26 116.9 123.08 189.48

18.00 ± 0.38 31.30 ± 0.47 40.21 ± 0.52 62.04 ± 0.62 78.54 ± 0.78 98.76 ± 1.48 164.78 ± 1.32 341.54 ± 2.73 490.62 ± 3.43 904.32 ± 6.33 989.17 ± 7.91 1077.49 ± 6.46 1268.11 ± 7.61 1705.92 ± 11.94 662.16 ± 19.86 706.47 ± 21.19 1053.58 ± 26.19

18.19 31.56 40.54 64.29 80.44 102.16 164.90 343.38 493.59 906.01 989.98 1078.57 1269.05 1707.32 655.64 690.13 1048.37

17.09 29.32 37.39 57.92 70.67 85.3 142.94 291.82 419.54 780.91 851.47 924.02 1083.26 1437.12 553.16 579.55 858.79

rKa ¼ rPK ðEÞxK fKa ;

ð1Þ

rPK ðEÞxK fKb ;

ð2Þ

rKb ¼

where rPK ðEÞ is the K-shell photoionization cross-section for the given element at the excitation energy E, xK is K shell fluorescence yield and fKa and fKb are fractional Xray emission rates for Ka and Kb X-rays and are defined as 1

ð3Þ

1

ð4Þ

fKa ¼ ð1 þ I Kb =I Ka Þ ; fKb ¼ ð1 þ I Ka =I Kb Þ ;

where IKb/IKa is the Kb to Ka X-ray intensity ratio. In the present theoretical calculations, the values of rPK ðEÞ were taken from XCOM [13], xK K-shell fluorescence yield have been taken from the recent standard fitted values of Krause [14], fKa and fKb were obtained from a table published by Broll [15]. The K-shell X-ray fluorescence cross-sections were determined experimentally by following equation rKi ¼

rKa+rKb (b/atom)

N Ki ; I 0 GeKi bKi t

The IKb/IKa intensity ratio values have been calculated using the following relation, I Kb N Kb bKa eKa ¼ ; I Ka N Ka bKb eKb

ð7Þ

where NKa and NKb are counts observed under the peaks corresponding to Ka and Kb X-rays, respectively. eKa and eKb are the efficiencies of the detector for the Ka and Kb series of X-rays. bKa and bKb are the target self-absorption correction factors for incident and emitted radiation. The peak areas were determined after the Ka and Kb photopeak areas were separated by fitting the measured spectra with multi-Gaussian function plus polynomial backgrounds using Microcal Origin 7.0 software program. The absolute efficiency e of the X-ray detector was determined by collecting the X-ray spectra of samples of Cr, Fe, Co, Cu, Zn, Se, Y, Cd, In, Sn, Te, Ba, La, Nd, Sm, Eu, Gd, Yb, W, Tl, Pb, Bi, U in the same experimental set-up using 241 Am and 57Co radioisotope sources.

ð5Þ

where NKi is the number of counts under Ki X-ray peak of the given elements, I0G is the intensity of the exciting radiation at the experimental geometry, eKi is the efficiency for the K X-rays and b is the self-absorption correction factor given by the following relation h  i linc lemit 1  exp  cos þ t h1 cos h   2 b¼ ; ð6Þ linc lemit þ t cos h1 cos h2 where t (g/cm2) is the mass thickness of the sample, linc and lemit is the sample mass attenuation coefficients for the incident and emitted energies, respectively, from XCOM. h1 and h2 are the angles of the incident and emitted photon with respect to the normal of the target surface.

3. Experiment The experimental setup and the geometry used in the measurements are shown schematically in Fig. 2. Indicated pure metals were supplied commercially by Aldrich and Alfa Aesar. High purity (99.99%) samples of Cr, Fe, Co, Cu, Zn, Ga, Se, Y, Mo, Cd, In, Sn, Te, Ba, Ta, W and Bi with thickness of 108 mg cm2 have been used for the measurement. The samples were excited with 241Am and 57 Co radioisotope sources emitting 59.5 and 123.6 keV energy. The samples were then placed at 45° angles with respect to the direct beam and fluorescent X-rays emitted 90° to the detector. The K X-ray spectra from various materials were recorded with the collimated super Si(Li) detector

U. Cevik et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 165–170

(FWHM = 150 eV at 5.9 keV) manufactured by Canberra with an active area of 30 mm2 , thickness 3 mm and Be window thickness 25 lm. The output from the preamplifier, with pulse pile-up rejection capability, was fed to a multichannel analyzer interfaced with a personal computer provided with suitable software (Genie 2000) for data acquisition and peak analysis program. The live time was

2

σκα= 308.492-20.150Z+0.0608Z +0.0115Z

Kα fluorescence cross-section (b/at)

1600

3

at 59.5 keV

1400 1200 1000

σκα = -1466.005+35.520Z at 123.6 keV

800 600 400 Experimental

200

Theoretical

0 20

25

30

35

40

45

50

55

60

65

70

75

80

85

Atomic number (Z) 2

Kβ fluorescence cross-section (b/at)

3

σκ β = -129.483+14.474Z-0.573Z +8.170*10-3 Z at 59.5 keV

350 300

σκ β = -437.729+7.981Z at 123.6 keV

250 200 150 100

Experimental

50

Theoretical

0 20

25

30

35

40

45

50

55

60

65

70

75

80

85

169

selected to be 2000 s for all elements. The peak areas have been calculated from the spectrum obtained for each measurement. Fig. 3 shows a typical K X-ray spectrum of Mo and Ta metals. 4. Results and discussion Experimental, theoretical and Puri et al. [4] values of Ka, Kb and total K-shell fluorescence cross-sections for some pure metals at 59.5 and 123.6 keV are listed in the Table 1. These values have been plotted as a function of the atomic number in Fig. 4(a)–(c). It can be seen from Table 1 and Fig. 4 that experimental values are in good agreement with the theoretical ones within the experimental uncertainties. The deviations between the theoretical and experimental values are found to be 0.3%, 2% and 0.5% for rKa, rKb and rKa,b, respectively. The reason for larger deviation between the theoretical and the experimental values for rKb is statistically poor due to lower intensity of the Kb line in comparison with the Ka line. The average deviation of our experimental values from Puri et al. [4] values were found to be 8%, 5% and 8%, respectively. This deviation can be attributed that while Puri et al. used K-shell photoionization cross-sections tabulated by Scofield [16] in the calculations, we used Hubbell and Seltzer [13] values. Furthermore, IKb/IKa X-ray intensity ratios have been determined using the same experimental set-up for the same elements. Experimental values of the IKb/IKa intensity ratios and theoretical values are plotted as a function of the atomic number in the Fig. 5. For each metal, the Kb to Ka X-ray intensity ratios increase evidently with increase atomic number. The experimental K X-ray IKb/IKa intensity ratios are also in agreement with the theoretical values calculated for these elements as given in Table 2. The average deviation from the experimental values of Hansen et al. [17] was found to be 3% in calculating the intensity ratio. The deviation was found to be 0.9% in the most reliable the theoretical values of Scofield [18]. Our results show

Atomic number (Z) -2

0.36

3

IK β /IK α = -0.0536 + 0.00612Z - 3.470*10 -5Z2-5.203*10-8Z3

0.34 0.32

1600 1400 1200

σκα,β = -2176.052+38.9146Z at 123.6 keV

1000 800 600

IKβ /IKα intensity ratio

Kα, β fluorescence cross-section (b/at)

2

σκα,β= 276.401-13.735Z-0.300Z +1.78*10 Z at 59.5 keV

1800

0.30 0.28 0.26 0.24 0.22 0.20 0.18 0.16

400 200

Experimental

0.14

Theoretical

0.12

0

Experimental Theoretical Fitted

0.10

20

25

30

35

40

45

50

55

60

65

70

75

80

85

Atomic number (Z) Fig. 4. (a), (c) The variation of experimental and theoretical Ka, Kb and total K-shell fluorescence cross-section values versus atomic number.

20

30

40

50

60

70

80

90

Atomic number (Z) Fig. 5. The variation of experimental, theoretical and fitted IKb/IKa intensity ratio values as a function of atomic number.

170

U. Cevik et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 165–170

Table 2 Our experimental Kb/Ka intensity ratios values are compared with the most probable experimental values Hansen, with theoretical values of Scofield and Khan Element

Z

Experimental

Hansen [17]

Scofield [18]

Khan [19]

Fitted values

Cr Fe Co Cu Zn Ga Se Y Mo Cd In Sn Te Ba Ta W Bi

24 26 27 29 30 31 34 39 42 48 49 50 52 56 73 74 83

0.132 ± 0.005 0.135 ± 0.007 0.137 ± 0.008 0.136 ± 0.005 0.136 ± 0.005 0.143 ± 0.006 0.167 ± 0.006 0.191 ± 0.007 0.197 ± 0.006 0.212 ± 0.007 0.219 ± 0.008 0.221 ± 0.009 0.226 ± 0.009 0.238 ± 0.010 0.271 ± 0.012 0.274 ± 0.012 0.295 ± 0.014

0.113 0.128 0.132 0.134 0.135 – 0.151 – 0.193 0.215 0.219 0.226 0.230 0.237 – – —

0.136 0.139 – 0.138 0.141 – 0.162 – 0.198 – – 0.223 – 0.243 0.268 0.270 —

0.133 0.134 0.135 0.137 0.139 – 0.161 – 0.195 0.216 0.218 0.222 0.227 0.237 – – —

0.123 0.131 0.135 0.144 0.147 0.152 0.164 0.183 0.194 0.213 0.216 0.220 0.226 0.237 0.276 0.276 0.292

good agreement with Khan and Karim [19] and average deviation from our experimental values was found to be 0.5%. The overall error in the measurement of Ka, Kb and total K-shell fluorescence cross-sections and intensity ratios are estimated to be <5%. The errors arise from the following factors: Self absorption correction (<2%), efficiency correction (<3%) and background correction (<3%). In the calculations, pile up and escape peak effects could be neglected because of very small effects in the experiment. The electronic structure of a given metal in a compound is found to be different from that of pure metal because of the presence of alien metal atoms. In the present measurements, only pure metals such as Cr, Fe, Co, Cu, Zn, Ga, Se, Y, Mo, Cd, In, Sn, Te, Ba, Ta, W and Bi were used to neglect chemical environment effect from alien atoms. But, the chemical effect on the Kb/Ka ratios still exists due to the atoms of the same element. The theoretical values are obtained for free atom. On the other hand, the electronic structures of metals are different from that of the free atom. Although the metallic atom is neutral, it is surrounded by the atoms of the same element and its valence electrons are in conduction band. However, the chemical effect on the Kb/Ka ratios for this reason is very small. So, we try to obtain the best experimental result respect to theoretical ones. Consequently, the agreement between the experimental results and the theoretical values leads to the conclusion that the present method will be beneficial for determining fluorescence cross-sections and intensity ratios. Thus, the

obtained data can be helpful for radioisotope XRF method for elemental analysis. References [1] M.O. Krause, C.W. Nestor, C.J. Sparks and E. Ricci, Oak Ridge National Laboratory Report No. ORNL-5399, 1978. [2] C. Bahn, S.N. Chaturvedi, N. Nah, X-Ray Spectrom. 10 (1981) 28. [3] D.V. Rao, R. Cesareo, G.E. Gigante, X-Ray Spectrom. 22 (1993) 401. [4] S. Puri, B. Chand, D. Mehta, M.L. Garg, N. Singh, P.S. Trehan, At. Data Nucl. Data Tables 61 (1995) 289. [5] G. Budak, A. Karabulut, L. Demir, Y. Sahin, Phys. Rev. A 3 (1999) 2015. [6] M. Sahin, L. Demir, G. Budak, Appl. Radiat. Isotopes 63 (2005) 141. [7] E.P. Bertin, Principles and Practice of X-Ray Spectrometric Analysis, second ed., Planum Press, New York-London, 1975. [8] V.N. Rao, S.B. Reddy, G. Satyanarayana, D.L. Sastry, Physica B, C 143 (1986) 375. [9] B.B. Dhal, H.C. Padhi, Phys. Rev. A 50 (1994) 1096. ¨ . So¨gu¨t, O ¨ . Simsek, E. Bu¨yu¨kkasap, J. Phys. B 34 [10] M. Ertugrul, O (2001) 909. ¨ . Simsek, J. Phys. B 35 (2002) 601. [11] M. Ertugrul, O [12] F. Pawlowski, M. Polasik, S. Raj, H.C. Padhi, D.K. Basa, Nucl. Instr. and Meth. B 195 (2002) 367. [13] J .H. Hubbell, S.M. Seltzer, National Institute of Standards and Technology Center for Radiation Research, Document No. NISTIR, 1995, p. 5632. [14] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [15] N. Broll, X-Ray Spectrom. 15 (1986) 271. [16] J.H. Scofield, Lawrence Livermore Laboratory Reports UCRL51326, 1973. [17] J.S. Hansen, H.U. Freund, R .W. Fink, Nucl. Phys. A 142 (1970) 604. [18] J.H. Scofield, Phys. Rev. A 9 (1974) 1041. [19] M.R. Khan, M. Karimi, X-Ray Spectrom. 9 (1980) 32.