Papers in Physics, vol. 6, art. 060001 (2014) Received: 19 December 2013, Accepted: 20 January 2014 Edited by: P. Weck Reviewed by: J. P. Marques, Departamento de F́ısica, Centro de F́ısica Atómica, Fac. de Ciências, Universidade de Lisboa, Portugal. Licence: Creative Commons Attribution 3.0 DOI: http://dx.doi.org/10.4279/PIP.060001 www.papersinphysics.org ISSN 1852-4249 Experimental determination of L X-ray fluorescence cross sections for elements with 45 ≤ Z ≤ 50 at 10 keV E. V. Bonzi,1, 2∗ G. B. Grad,1† R. A. Barrea3‡ Synchrotron radiation at 10 keV was used to experimentally determine the Ll, Lα, LβI , LβII , LγI and LγII fluorescence cross sections for elements with 45 ≤ Z ≤ 50, as part of an ongoing investigation at low energies. The measured data were compared with calculated values obtained using coefficients from Scofield, Krause and Puri et al. I. Introduction This work is part of a systematic investigation on elements with 45 ≤ Z ≤ 50, which has been car- ried out at different energies [1–3]. The L X-ray cross sections were measured with monoenergetic excitation beam at 10 keV. We report cross sections for each spectral line, according to the resolution of the Si(Li) solid state detector used to resolve individual component lines of the spectral emission. The experimental cross sections were grouped considering the transitions scheme, the energy of the emission lines and the detector resolution. In general, the fluorescence cross sections ob- tained in this work show the same trend with Z and broad agreement with the data published by Puri et al. [4, 5] and Krause [6, 7], calculated using ∗E-mail: bonzie@famaf.unc.edu.ar †E-mail: grad@famaf.unc.edu.ar ‡E-mail: rbarrea@depaul.edu 1 Facultad de Matemática, Astronomı́a y F́ısica, Univer- sidad Nacional de Córdoba. Ciudad Universitaria. 5000 Córdoba, Argentina. 2 Instituto de F́ısica Enrique Gaviola (CONICET), 5000 Córdoba, Argentina. 3 Physics Department, DePaul University, Chicago, IL 60614, USA. Scofield’s coefficients [8, 9]. II. Experimental Condition The measurements were carried out at the X- ray Fluorescence beam line at the National Syn- chrotron Light Laboratory (LNLS), Campinas, Brazil [10]. The components of the experimental setup were: • Silicon (111) channel cut double crystal monochromator, which can tune energies be- tween 3 and 30 keV. The energy resolution is 3·10−4 to 4·10−4 between 7 and 10 keV. • A Si(Li) solid state detector, 5 mm thick and 5 mm in diameter, with a resolution of 170 eV at 5.9 keV and a 0.0127 cm thick beryllium win- dow. The model introduced by Jaklevic and Giauque [11] was used to obtain the detector efficiency. • The whole setup is mounted on a motorized lift table, which allows the vertical positioning of the instruments within the linearly polarized part of the beam. • To limit the beam size, a motorized com- puter controlled set of vertical and horizontal 060001-1 Papers in Physics, vol. 6, art. 060001 (2014) / E. V. Bonzi et al. slits (located upstream and downstream of the monochromator) was used. A set of foil samples (rhodium, palladium, silver, cadmium, indium and tin ) was used to determine the L fluorescence cross sections of these elements. The foil samples were provided by Alfa products Inc., with a certified purity of over 99%. The foils thicknesses are shown in Bonzi et al. (see Table I) [2]. K emission lines of chlorine, calcium, titanium and iron were measured to determine the geomet- rical and the detector efficiency factors. The Kα and Lα fluorescent spectra were mea- sured by collecting 2·105 net counts for each ele- ment in order to have the same statistical counting error in all measured spectra. A system dead time, lower than 1%, was es- tablished measuring the fluorescence emission of a Ti sample, adjusting the slit at the exit of the monochromator. All samples were measured with the same slit aperture. Unwanted effects, such as piling up, were avoided using this configuration and the geometric factors were ensured to be the same for all samples. This configuration made it unneces- sary to carry out corrections for count losses, spec- tra distortions or modification of the geometrical arrangement. III. Spectra analysis The energy of the emission lines tabulated by Scofield [8, 9] and the detector resolution were con- sidered to group the L X-ray fluorescence lines. This line arrangement was used to fit the L spec- trum, where the Lβ and Lγ compound lines have been noted with a Roman subscript according to the most intense contribution line, with its corre- sponding atomic transition: • Ll = L3 − M1, • Lα = L3 − M5 + L3 − M4, • LβI = L2 −M4 +L1 −M2 +L1 −M3 +L3 −N1, • LβII = L3 − N5 + L3 − O4 + L3 − O5 + L3− O1 + L1 − M5 + L1 − M4 + L3 − N4, • LγI = L2 − N4, • LγII = L1 −N2 +L1 −N3 +L1 −O2 +L1 −O3. The background radiation was fitted using a lin- ear second order polynomial. The area of the fluorescence peaks was deter- mined as the average of the areas obtained by the adjustment using Hypermet and Gaussian func- tions. The escape peaks were fitted using a Gaus- sian function. As a consequence of the excitation with a lin- early polarized photon beam, the contribution to the background was very low. The linear polariza- tion of the incident beam produces negligible scat- tered radiation at 900 with respect to the incident beam direction. The detector position is localized at the same height of the storage ring. IV. Data Analysis The expression for the L experimental fluorescence cross sections is [13] σeLi(Eo) = ILi Io.G.�(ELi).T(Eo,ELi) (1) where σeLi(Eo) = experimental Li fluorescence cross sections of the element observed at the en- ergy Eo, with Li = Ll, Lα, LβI, LβII, LγI or LγII; ILi = measured intensity of the Li spectral line; Io.G.�(ELi) = factor comprising the intensity of the excitation beam Io; the geometry of the ex- perimental arrangement G and the detector effi- ciency �(ELi); Eo = energy of the incident beam, in this case 10 keV; ELi = energy of the Li spectral line; the data was obtained from Scofield [8]; and T(Eo,ELi) = correction factor for self absorption in an infinitely thick sample, which is T(Eo,ELi) = ( µ(Eo) sin(θ1) + µ(ELi) sin(θ2) )−1 (2) where µ(E) = mass absorption coefficient of the sample at energy E from Hubbell and Seltzer [14] and θ1 and θ2 = incidence and take off angles, equal to 45o in the current setup. In these measurements, all the samples were con- sidered as infinitely thick for X-ray fluorescence. The factor Io.G.�(E) was calculated using the following expression 060001-2 Papers in Physics, vol. 6, art. 060001 (2014) / E. V. Bonzi et al. Io.G.�(EKi) = IKi σωFKi (Eo).Ci.T(Eo,EKi) (3) where IKi = measured intensity of the K spectral line, Ci = the weight concentration of the element of interest in the sample, σωFKi (E) = K fluorescence cross sections of the el- ement observed at energy E, defined as σωFKi (Eo) = σKi(Eo).ωK.FK, with σKi(E) = K shell photoion- ization cross section for the given element at the excitation energy E, from Scofield [8], ωK = K shell fluorescence yield, from Krause [6, 7] and FK = fractional emission rate for Kα or Kβ X- rays, from Khan and Karimi [15], defined as FKα = [ 1 + IKβ IKα ]−1 ; FKβ = [ 1 + IKα IKβ ]−1 (4) T(Eo,EKi) = correction factor for self absorp- tion in the sample, Eo = energy of the incident beam and EKi = energy of the K spectral line for a given element, from Scofield [8]. The factor Io.G.�(E) was previously determined in Ref. [2], where the same geometry and detector were used. Because of this, the Io.G.�(E) energy dependence is already known and only a scale factor is needed to obtain the correct beam intensity. Four targets: Cl (NaCl), Ca (CaHPO4 · 2H2O), Ti (Ti foil) and Fe (Fe foil) emitting fluorescent X- rays in the range from 2.4 keV to 7.0 keV were used to determine the scale factor in this work. Four Kα and four Kβ lines were used to fit the scale factor. Jaklevic and Giauque’s [11] model was used to fit the detector efficiency. V. Results and Discussion L X-ray cross section values obtained in our fluo- rescence experiment and the theoretical values cal- culated by using coefficients given by Scofield [8, 9], Puri et al. [4] and Krause [7] are shown in Table 1 and Figs. 1 to 6. Puri et al. predicted theoretical Coster Kronig and fluorescence values using ab initio relativistic calculations, while Krause’s values of ωK, ωLi and 5 10 15 20 25 30 35 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number Ll Cross Sections This work Puri Krause Figure 1: Comparison of Ll cross sections. 300 400 500 600 700 800 900 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number Lα Cross Sections This work Puri Krause Figure 2: Comparison of Lα cross sections. fij were obtained by fitting experimental and the- oretical compiled data. In Krause’s tables, the the- oretical data were calculated for singly ionized free atoms while the experimental data contain contri- butions from solid state, chemical and multiple ion- ization effects. The Lα cross section values have a better agree- ment with the theoretical values when the intensity peaks are fitted with an Hipermet function instead of a Gaussian function. This happens because the Hipermet function has a tail on the left side that increases the fitted area. Moreover, the tail of the Hipermet function used to fit the Lα peaks diminishes the area and the cross sections of the Ll peaks, accordingly. The experimental Ll cross sections show a sim- 060001-3 Papers in Physics, vol. 6, art. 060001 (2014) / E. V. Bonzi et al. Element Ll Lα LβI LβII γI LγII This work 13 ± 4 373 ± 13 163 ± 9 50 ± 5 22 ± 4 7 ± 2 Rh 45 Puri 16 438 194 30 11 7 Krause 15 396 212 27 11 10 This work 14 ± 2 450 ± 15 233 ± 10 43 ± 7 25 ± 3 11 ± 2 Pd 46 Puri 19 518 234 43 17 8 Krause 17 454 249 38 16 11 This work 19 ± 2 506 ± 13 280 ± 16 59 ± 6 28 ± 3 14 ± 3 Ag 47 Puri 22 597 277 55 22 10 Krause 19 516 295 48 21 14 This work 20 ± 3 579 ± 10 371 ± 17 70 ± 6 32 ± 2 15 ± 2 Cd 48 Puri 26 686 328 70 29 11 Krause 22 598 351 62 28 17 This work 23 ± 2 641 ± 19 447 ± 17 83 ± 5 37 ± 2 23 ± 2 In 49 Puri 30 795 386 89 37 13 Krause 26 689 413 77 36 20 This work 18 ± 4 579 ± 18 454 ± 17 164 ± 5 45 ± 2 33 ± 3 Sn 50 Puri 29 765 599 94 51 38 Krause 25 676 582 83 48 39 Table 1: Experimental and theoretical L X-ray fluorescence cross sections in Barns/atom at 10 keV. Experimental data (This work), theoretical values calculated using Scofield [8] and Puri [4] and semi- empirical coefficients obtained from Scofield [8] and Krause [6]. 100 200 300 400 500 600 700 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number LβI Cross Sections This work Puri Krause Figure 3: Comparison of LβI cross sections. ilar Z trend, compared to the data obtained using Krause and Puri et al. values. Nevertheless,in gen- eral, our results are lower than those. The Lα experimental fluorescence cross section data, Fig. 2, agree well with Krause’s values al- though for elements with higher Z, the experimen- tal values are slightly lower than those from Krause. They are even lower than Puri’s et al. values, but still showing the same trend with Z. The LβI experimental fluorescence cross sections show a very good agreement with the theoretical values when the Hipermet function is used to fit the area (see Fig. 3). The LβII measured cross sections show a simi- lar dependence on Z as both theoretical assemblies (Fig. 4). The LβI Sn experimental value is lower than the data presented by either Puri et al. or Krause and the LβII Sn experimental value is much higher than both theoretical values. This behavior might be due to the fitting process as both spectra lines are too close in energy; the LβII intensity seems to be overestimated while the LβI intensity seems to be underestimated. A similar behavior is observed for rhodium ex- perimental data although the differences with the theoretical values are much smaller than those for tin. The experimental LγI fluorescence cross sections show some differences with the Z trend of the theo- retical data: in the lower Z range, the experimental values are higher than the theoretical ones while for higher Z, this difference becomes smaller. Sn val- ues, Z = 50, show a different behavior, being lower than both calculated values (see Fig. 5). 060001-4 Papers in Physics, vol. 6, art. 060001 (2014) / E. V. Bonzi et al. 0 20 40 60 80 100 120 140 160 180 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number LβII Cross Sections This work Puri Krause Figure 4: Comparison of LβII cross sections. 0 10 20 30 40 50 60 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number LγI Cross Sections This work Puri Krause Figure 5: Comparison of LγI cross sections. The LγII experimental values show the general Z trend of the values presented by Krause and Puri et al.. The experimental values are sometimes higher or lower than the theoretical ones but the range of values is similar to them (see Fig. 6). To determine the uncertainties of the experimen- tal cross sections, the propagation of errors was car- ried out in Eq. (1). The uncertainty values are in general around 6-10%, and less than 40% in case of the Ll line. The uncertainty associated to the Io.G.�(E) fac- tor was estimated as the mean quadratic deviation of the experimental values (≤ 2%). For the fac- tor T(Eo,ELi), a propagation of errors was carried out assuming a 3% error in the values of the mass absorption coefficients, and a 2% error in the sine 0 10 20 30 40 50 45 46 47 48 49 50 C ro s s S e c ti o n [ b /a t] Z Atomic Number LγII Cross Sections This work Puri Krause Figure 6: Comparison of LγII cross sections. of the angles due to the sample positioning errors. Krause’s ωK values for elements with 45 ≤ Z ≤ 50 have an estimated error of 1%. The uncertainties of the peak areas were estab- lished as half the difference between the areas ob- tained using Gaussian and Hypermet functions to fit. These uncertainties were the main contribution to the experimental errors of the cross section. VI. Conclusions In this investigation, the L X-ray fluorescence cross sections of a group of elements with 45 ≤ Z ≤ 50 were measured using a synchrotron radiation source for monoenergetic beams at 10 keV. The polar- ization properties of the monoenergetic excitation beam and the high resolution of the detector sys- tem allowed to reduce the scattered radiation thus obtaining a better signal to noise ratio and a better accuracy for the experimental cross sections. The cross sections of Ll, Lα, LβI, LβII, LγI and LγII lines were measured considering a more detailed group than the usual sets. In Table 1, the comparison between the experimental fluorescence cross section values with the theoretical values cal- culated using coefficients from Scofield [8, 9], Puri et al. [4] and Krause [6] are shown. Our experimental values are in general in good agreement with the calculated data using Scofield’s [8, 9] and Krause’s [6] coefficients. The L cross sections present uncertainties around 6-10% and the less intensive Ll peaks show uncer- 060001-5 Papers in Physics, vol. 6, art. 060001 (2014) / E. V. Bonzi et al. tainties that in some cases come close to 40%, be- ing the fitting uncertainty the most important error source. The use of the Hypermet function is very conve- nient to fit the Lα and Lβ peaks (see Table 1). The solid state detector used in our experiments does not have enough energy resolution to resolve each spectral line. A higher resolution detection system would be desirable in order to analyze each spectral line separately. The Coster Kronig coefficients present large fluc- tuations in this atomic range and that is the cause of the observed discrepancies. Acknowledgements - This work was carried out under grants provided by SeCyT U.N.C. (Ar- gentina). Research partially supported by LNLS - National Synchrotron Light Laboratory, Brazil. [1] E V Bonzi, R A Barrea, Experimental L X-ray fluorescence cross sections for elements with 45 ≤ Z ≤ 50 at 7 keV by synchrotron radia- tion photoionization, X-ray Spectrom. 34, 253 (2005). [2] E V Bonzi, N M Badiger, G B Grad, R A Bar- rea, R G Figueroa, Measurement of L X-ray fluorescence cross sections for elements with 45 ≤ Z ≤ 50 using synchrotron radiation at 8 keV, Nucl. Instrum. Meth. B 269, 2084 (2011). [3] E V Bonzi, N M Badiger, G B Grad, R A Barrea, R G Figueroa, L X-ray fluorescence cross sections experimentally determined for elements with 45 ≤ Z ≤ 50 at 9 keV, Appl. Radiat. Isotopes 70, 632 (2012). [4] S Puri, D Mehta, B Chand, N Singh, P N Tre- han, L shell fluorescence yields and costerkro- nig transition probabilities for the elements with 25 ≤ Z ≤ 96, X-ray Spectrom. 22, 358 (1993). [5] S Puri, B Chand, D Mehta, M L Garg, S Nir- mal, P N Trehan, K and L shell X-ray fluores- cence cross sections, Atom. Data Nucl. Data 61, 289 (1995). [6] M O Krause, Atomic radiative and radiation- less yields for K and L shells, J. Phys. Chem. Ref. Data 8, 307 (1979). [7] M O Krause, C W Nestor, C J Sparks, E Ricci, X-ray fluorescence cross sections for K and L- rays of the elements, Oak Ridge National Lab- oratory, Report 5399 (1978). [8] J H Scofield, Theoretical photoionization cross sections from 1 to 1500 keV, Lawrence Liv- ermore National Laboratory, Report 51326 (1973). [9] J H Scofield, Relativistic Hartree Slater values for K and L X-ray emission rates, Atom. Data Nucl. Data 14, 121 (1974). [10] C A Perez, M Radtke, H Tolentino, F C Vicentin, R T Neuenshwander, B Brag, H J Sanchez, M Rubio, M I S Bueno, I M Raimundo, J R Rohwedder, Synchrotron radi- ation X-ray fluorescence at the LNLS: Beam- line instrumentation and experiments, X-ray Spectrom. 28, 320 (1999). [11] J M Jaklevic, R D Giauque, Handbook of X-ray spectrometry: Methods and techniques, Eds. R Van Grieken, A Markowicz, Marcel Dekker, New York (1993). [12] M C Leypy, J Plagnard, P Stemmler, G Ban, L Beck, P Dhez, Si(Li) detector efficiency and peak shape calibration in the low energy range using synchrotron radiation, X-ray Spectrom. 26, 195 (1997). [13] D V Rao, R Cesareo, G E Gigante, L X-ray fluorescence cross sections of heavy elements excited by 15.20, 16.02, 23.62 and 24.68 keV photons, Nucl. Instrum. Meth. 83, 31 (1993). [14] J H Hubbell, S M Seltzer, Tables of X-ray mass attenuation coefficients and mass-energy ab- sorption coefficients from 1 KeV to 20 MeV for elements Z=1 to 92 and 48 additional sub- stances of dosimetric interest, NISTIR, Report 5632 (1995). [15] Md R Khan, M Karimi, Kβ/Kα ratios in en- ergy dispersive X-ray emission analysis, X-ray Spectrom. 9, 32 (1980). 060001-6