# K Shell X-Ray Fluorescence Parameters of Some Elements in the Atomic Range40≤Z≤50

Authors: Pinar Onder; Ahmet Tursucu; Demet Demir
Journal: Science and Technology of Nuclear Installations
 (2013)

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## Abstract

The production cross sectionsσKi, the fluorescence yield WK, K shell X-ray intensity ratio IKβ/IKα, the vacancy transfer probabilities from K to L shell ηKL, and the ΓK level widths for some elements in the atomic range 40≤Z≤50 were measured. The samples were excited by 80.998 keV gamma rays from a 10 mCi 133Ba radioactive source. The K X-rays emitted by samples were detected by using a CdTe detector. These parameters have been theoretically calculated, also. The experimental values were compared with the theoretical and semiempirical values. Our experimental values closely agreed with theoretical values and other experimental values.


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## Body

## 1. Introduction

Accurate experimental values of X-ray fluorescence parameters such as the production cross sections, the fluorescence yields, the intensity ratios, the vacancy transfer probabilities, and the level widths for different elements are important because of their wide use in atomic, molecular, and radiation physics, material science, environmental science, agriculture, forensic science, dosimetric computations for health physics, cancer therapy, elemental analysis, and basic studies of nuclear physics.A vacancy in the inner shell of an atom is produced by various methods; photoionization is one of them. In this method, the incident gamma photon ejects the element electron to the continuum state, creating a vacancy in the inner shell. The fluorescence yield of an atomic shell or subshell is defined as the probability that a vacancy in that shell or subshell is filled through a radiative transition or a nonradiative transition.In recent years, several attempts have been made for measuring X-ray fluorescence cross sections and yields for different elements. Krause et al. [1] have calculated theoretical K and L XRF cross sections. Puri et al. [2] published an extensive table of K shell X-ray fluorescence cross sections for some elements in the energy range 1–200 keV. Bennal et al. [3] measured K X-ray fluorescence parameters for Ag, Cd, In, and Sn elements. Seven [4] has measured photon induced K X-ray cross sections for some heavy elements. Hubbell et al. [5] have collected more recent experimental values of σKi. Theoretical values of σKi were obtained in the region 44≤Z≤54 by McGuire [6, 7]. Chen et al. [8] used a Dirac-Hartree-Slater approach to calculate the σK values of elements in the atomic range 18≤Z≤96. Bambynek et al. [9] have fitted their collection of selected most reliable experimental values of σKi in the 13≤Z≤92 range. The Kα, Kβ, and total K X-rays fluorescence cross sections and the average fluorescence yields for six elements with 16≤Z≤23 at 5.96 keV have been measured by Sahin et al. [10]. Horakeri et al. [11, 12] determined K shell fluorescence yields by using a simple method for some elements in 62≤Z≤83 at 123.6 and 320 keV energies. Pious et al. [13] determined total K fluorescence yields by using Xe filled proportional counter for some low elements at 59.5 keV. Balakrishna et al. [14] measured K fluorescence yields using HPGe low energy photon detector for some rare earth and heavy elements with 59.5 and 279.2 keV gamma rays.Rao et al. [15] showed that the Kβ/Kα intensity ratios depend on the excitation modes in 3D elements, but they could not find such dependence for the high Z elements. Dhal and Padhi [16] have investigated relative K X-ray intensities on the elements from Mn to Sb using 59.5 keV gamma rays. Rebohle et al. [17] have measured Kβ/Kα intensity ratio for pure 3D elements. Similarly, Ertuğrul et al. [18] have measured Kβ/Kα intensity ratios in element range 22≤Z≤69 at 59.5 keV. Pawlowski et al. [19] have reported the valence electronic structure of Ti, Cr, Fe, and Co in some alloys from Kβ/Kα X-ray intensity ratios. The vacancy transfer probabilities from K to L shell ηKL were obtained by measuring the Kβ/Kα intensity ratios in 25 elements over the range 57≤Z≤92 using a 25 mCi 57Co filtered source for excitation and a Si (Li) detector by Ertugral et al. [20]. Santra et al. [21] have measured K to L shell vacancy transfer probabilities of Mo, Pd, and Cd by exciting them with the K X-rays of Ni and Sn induced by the bremsstrahlung emanating from an X-ray tube. Demir and Şahin [22] have measured K shell X-ray production cross sections and fluorescence yields for Nd, Eu, Gd, Dy, and Ho using radioisotope in the external magnetic field.The aim of this study is to determine the production cross sectionsσKi, the fluorescence yield wK, K shell X-ray intensity ratioIKβ/IKα, the vacancy transfer probabilities from K to L shell ηKL, and the ΓK level widths for some elements in the atomic range 40≤Z≤50. The samples were excited by 80.998 keV gamma rays from a 10 mCi 133Ba radioactive source. The K X-rays emitted by samples were detected by using a CdTe detector.


## 2. Experimental Procedure

The experimental setup and the geometry used in the measurements are shown in Figure1.Figure 1
The experimental setup.All samples were irradiated with 80.998 keV gamma rays from a 10 mCi133Ba radioactive source. The samples were placed at a 45° angle with respect to the direct beam, and fluorescent X-rays emitted at 90° to the direct beam were detected by the collimated CdTe detector. An AMPTEK XR-100T-CdTe detector of crystal dimensions 3×3×1 mm3 was used in this work. A 250 μm Be window is in front of the detector. The characteristic properties of CdTe detector are given in Table 1.Table 1
The characteristic properties of CdTe detector.
Atomic number
Density, g/cm3
Band gap, eV
Average electron-hole pair eV
Average electron-hole pair Mobility at 25°C, cm2/(V·sec), eV
Average lifetime, sec
n
*
p
*
n
*
p
*
48.5
6.06
1.47
4.43
1100
100
10−6
10−7The preamp signals were processed by Ampteks digital processors, including PX4, DP4, and X123, using trapezoidal shaping and no rise-time discrimination. The digital processors include a multichannel analyzer, power supplies, closed-loop temperature regulation, and the bias voltage for the detector. The data were taken at 224 K and at 502 V bias. The data were acquired by the ADMCA.EXE software provided with Amptek’s digital processors. Spectrum analysis was carried out using the XRFFP software, developed jointly by Amptek and by Cross Roads Scientific. Special analysis algorithms have been developed for CdTe, which are incorporated with the commercially available package. The background spectra were measured in the laboratory, using a lead filter with a thickness of 30 mm. It was observed that the background level in the lead filter is smaller than that in a room. Thus, the detector was shielded by a filter of lead to obtain a thin beam of photons and to prevent undesirable radiation. 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 for data acquisition and peak analysis. The mean of ten channels at each side of the peaks was used to calculate the background and to define the net peak area. The peak areas were determined after the peaks were fitted either with pure Gaussians or Gaussians with exponential tails using the Microcal Origin 7.5 Software. A typical K shell X-ray spectrum of Sn target is shown in Figure2.Figure 2
Typical K X-rays spectrum of Sn target.The experimental production cross sectionsσKi were evaluated using the relation
(1)σKi=NKiI0GεKiβKim(i=α,β),
where NKi is the measured intensity, I0 is intensity of incident radiation, G is a geometrical factor, εKi is the efficiency of the detector at the average K X-ray energy of the element, m is the mass per unit area of the element in g/cm2, and βKi is the self-absorption correction for the target material, which accounts for the absorption in the sample of the incident photons and the emitted characteristic X-rays. The values of βKi have been calculated by using the following expression:
(2)βKi=1-exp[-(μ1/sinθ+μ2/sinϕ)m](μ1/sinθ+μ2/sinϕ)m,
where μ1 and μ2 are the mass attenuation coefficients (from [26]) of incident photons and emitted characteristic X-rays, respectively; the angles of the incident photons and emitted X-rays with respect to the surface of samples are θ and ϕ, respectively.The value of the factorsI0GεKi, which contain terms related to the incident photon flux, geometrical factor, and the efficiency of the detector, was determined by collecting the K X-ray spectra of thin samples of Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, and Sn with the mass thickness 0.031–0.865 g/cm2 in the same geometry and using the following equation:
(3)I0GεKi=NKiσKimβKi,
where NKi is the net number of counts under the corresponding photopeak, mi is the thickness of target in g/cm2, and βKi is the self-absorption correction factor for the target material, which accounts for the absorption in the target of the incident photons and the emitted characteristic X-rays. The theoretical production cross sections σKi were evaluated using the relation
(4)σKi=σKωKfKi,
where σK is the K shell photoionization cross section for the given elements at the excitation energy E. The values of σK used in these calculations were taken from the report by Scofield [27]. wK is the K shell fluorescence yield. The values of wK were taken from the annotated bibliography of Krause [23]. fKi is the fractional X-ray emission rate for Ki X-rays taken from Scofield [24].The semiempirical K shell fluorescence yieldswK were measured according to the following equation:
(5)ωK=σKσK(E),
where σK is the total K X-ray fluorescence cross section obtained experimentally and σK(E) is the theoretical K shell photoionization cross section of a given element for the excitation energy E [27].The experimental K shell X-ray intensity ratiosIKβ/IKα were evaluated using the equation
(6)IKβIKα=N(Kβ)N(Kα)β(Kα)β(Kβ)ε(Kα)ε(Kβ),
where N(Kα) and N(Kβ) are net counts observed under the peaks corresponding to Kα and Kβ X-rays, respectively, β(Kα) and β(Kβ) are the sample self-absorption correction factors for the incident photon and emitted K X-rays photons, and ε(Kα) and ε(Kβ) are photopeak efficiency values of the detector.The experimental K to L shell total vacancy transfer probabilitiesηKL were calculated by using the following equation [28]:
(7)ηKL=2-ωK1+(IKβ/IKα),
where ωK is the fluorescence yield and IKβ/IKα is the intensity ratio of the K X-rays. The K level width was measured using the following relation:
(8)ΓK=ΓK(R)wK,
where ΓK(R) is the radiative transition rate.


## 3. Results and Discussion

The overall error in the present measurements is estimated to be 4-5%. This error is the quadrature sum of the uncertainties in the different parameters used to evaluate the K shell fluorescence parameters, that is, target thickness (≤1%), the evaluation of the peak area (≤3%), detector efficiencyI0GεKij (≤3%), and absorption correction factor (≤2%).The experimental values ofσKα and σKβ production cross sections in the atomic range 40≤Z≤50 for 80.998 keV are listed in Table 2. The σKα and σKβ production cross sections versus atomic number were plotted in Figures 3 and 4, also.Table 2
The experimentalσKα and σKβ production cross sections.
Sample
ExperimentalσKα
TheoreticalσKα
ExperimentalσKβ
TheoreticalσKβ
Zr
118.374
118.374
20.561
20.562
Nb
137.257
137.257
24.322
24.322
Mo
148.251
148.252
26.818
26.819
Ru
172.576
172.577
32.358
32.358
Rh
202.336
202.336
38.565
38.565
Pd
222.744
222.745
43.056
43.057
Ag
244.202
244.203
47.961
47.961
Cd
267.368
267.369
55.016
53.340
Sn
316.684
316.685
64.274
65.269Figure 3
The variation inσKα production cross sections as a function of atomic number.Figure 4
The variation inσKβ production cross sections as a function of atomic number.These theoretical values were calculated by using K X-ray emission rates based on relativistic Hartree-Slater theory [24]. The present experimental results of K shell X-ray production cross sections are only compared with the calculated theoretical values. The deviations between the theoretical and experimental values are found to be 0.0006% and 3% for σKαand σKβ, respectively. The reason for larger deviation between the experimental and the theoretical values for σKα is statistically poor due to lower intensity of the Kβ line in comparison with the Kα line.The K shell fluorescence yieldsωK for these elements were calculated and listed in Table 3 together with theoretical values. The theoretical values were taken from Krause [23]. The average K shell fluorescence yields are plotted as function of the atomic number in Figure 5, also. Our experimental values have differences of 0.35–0.47% with Krause [23]. This may be due to the fact that when the elements of K X-ray energies increase, the detector efficiency decreases.Table 3
K shell X-ray fluorescence yields.
Sample
w
K experimental
Krause (1979) [23]
Zr
0.730
0.730
Nb
0.747
0.747
Mo
0.765
0.765
Ru
0.749
0.749
Rh
0.808
0.808
Pd
0.820
0.820
Ag
0.831
0.831
Cd
0.847
0.843
Sn
0.859
0.862Figure 5
K X-ray fluorescence yields versus atomic number.The experimental values ofIKβ/IKα X-ray intensity ratios for these elements were calculated from (6) and listed in Table 4. The experimental values of the IKβ/IKα intensity ratios are plotted as a function of the atomic number in Figure 6. As seen from Figure 6, the IKβ/IKα X-ray intensity ratios increase evidently with increase in atomic number. The experimental IKβ/IKα intensity ratios are also in agreement with the theoretical values calculated for these elements as given in Table 4. Our experimental values have differences of 0.5–3% with Scofield’s [24].Table 4
I
K
β
/
I
K
α X-ray intensity ratios.
Sample
I
K
β/IKα experimental
Scofield (1974) [24]
Zr
0.1737
0.1737
Nb
0.1772
0.1772
Mo
0.1809
0.1809
Ru
0.1875
0.1875
Rh
0.1905
0.1906
Pd
0.1932
0.1933
Ag
0.1963
0.1944
Cd
0.2057
0.1995
Sn
0.2029
0.2061Figure 6
The variation inIKβ/IKα as a function of atomic number.The experimental values ofηKL were calculated from (7), listed in Table 5, and plotted as a function of the atomic number in Figure 7. The values of the ηKL decrease with the increase in atomic numbers. K shell electrons of Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, and Sn were excited by using the radioisotope source since K-edges energie of these elements are lower than the energy of the incident photons. The vacancy created in the K shell is filled through the radiative transition or a nonradiative transition. Since the L X-ray intensity is enhanced with the K to L shell vacancy transfer, the L X-ray production cross sections of Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, and Sn increase. As seen from Table 5, the experimental values of ηKL agree with the theoretically calculated values within 0.3–5%Table 5
K-L total vacancy transfer.
Sample
η
KL experimental
Theoretical
Zr
1.082
1.062
Nb
1.064
1.045
Mo
1.046
1.029
Ru
1.053
1.000
Rh
1.001
0.987
Pd
0.989
0.975
Ag
0.977
0.964
Cd
0.956
0.953
Sn
0.946
0.934Figure 7
The variation inηKL as a function of atomic number.The experimental values ofΓK were calculated from (8), listed in Table 6 and plotted as a function of the atomic number in Figure 8. Our experimental values have differences of 0.2–0.5% with [25].Table 6
K shellΓK level widths.
Sample
Γ
K experimental
Krause and Oliver (1979) [25]
Zr
3.84
3.84
Nb
4.14
4.14
Mo
4.52
4.52
Ru
5.33
5.33
Rh
5.77
5.77
Pd
6.24
6.24
Ag
6.75
6.75
Cd
7.24
7.28
Sn
8.51
8.49Figure 8
The variation inΓK as a function of atomic number.As a result, more experimental and theoretical values for the elements from Zr to Sn are needed for full knowledge of K X-ray fluorescence parameters. These experimental values are very important for qualitative and quantitative element analysis used in the XRF technique. It is well known that characteristic X-ray lines are influenced by the chemical state of the emitting element: peak energy, peak width, relative emission rates, and satellite peak formation. Also, they are affected by the detected element speciation [29]. Thus, the obtained data can be helpful for the radioisotope XRF method for elemental analysis.



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