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Radiation Physics and Chemistry 79 (2010) 393–396

Contents lists available at ScienceDirect

Radiation Physics and Chemistry

0969-80

doi:10.1

n Corr

E-m

(I. Han)

journal homepage: www.elsevier.com/locate/radphyschem

Measurement of La, Lb and Total L X-ray fluorescence cross-sections for someelements with 40rZr53

I. Han a,n, S. Porikli b, M. Sahin c, L. Demir d

a A˘grı _Ibrahim C- ec-en University, Faculty of Arts and Sciences, Department of Physics, 04100, A

˘grı, Turkey

b Erzincan University, Faculty of Arts and Sciences, Department of Physics, 24100, Erzincan, Turkeyc Rize University, Faculty of Arts and Sciences, Department of Physics, 53100, Rize, Turkeyd Ataturk University, Faculty of Sciences, Department of Physics, 25240, Erzurum, Turkey

a r t i c l e i n f o

Article history:

Received 20 July 2006

Accepted 17 December 2009

Keywords:

XRF

cross-section

6X/$ - see front matter & 2009 Elsevier Ltd. A

016/j.radphyschem.2009.12.014

esponding author. Tel.: +90 4422314083; fax

ail addresses: ibrahimhan25@hotmail.com, ib

.

a b s t r a c t

La, Lb and total L X-ray fluorescence (XRF) cross-sections have been measured for the nine elements (Zr,

Nb, Mo, Ag, Cd, In, Sn, Sb and I) using photon energy 5.96 keV. In these the elements, La and Lb spectra

were derived from the measured L-shell spectra by fitting process. Experimental results of La, Lb and

total L X-ray fluorescence cross-sections have been compared with theoretical results. The experimental

results of L XRF cross-section are found to be in agreement with the theoretical values.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

X-ray fluorescence (XRF) spectrometry is used world-wide. Themost established technique is energy dispersive X-ray fluores-cence (EDXRF) for quantitative analysis because EDXRF isrelatively inexpensive and requires less technical effort to runthe system. A vacancy in the inner shell of an atom is produced byvarious methods; photoionization is one of them. In this method,the incident gamma photon ejects the bound electron to thecontinuum state, creating a vacancy in the inner shell. Thisvacancy is filled through radiative or nonradiative processes. Inthe radiative process, the electron from the higher shell fills theinner shell vacancy, emitting X-ray photons.

L XRF cross sections six (i=K, L, M,...) and fluorescence yields oi

(i=K, L, M,...) are important for developing more reliabletheoretical models describing the fundamental inner-shell pro-cesses. A survey of the literature to date shows that fluorescencecross section and fluorescence yields for the L shell are availablefor a large number of elements and photon energies (S-ahin et al.,2000; Durak et al., 2000; Edgardo et al., 2002). But, theexperimental works on fluorescence cross sections and fluores-cence yields of medium Z elements for L shell are less compared tothose of large number of elements. Recently, some measurementsfor the medium Z elements have been reported (Garg et al., 1992;Gurol et al., 2003; S-ahin et al., 2005). L XRF cross sections of manyelements were measured using radioisotopes as excitation source

ll rights reserved.

: +90 4422360948.

rahimhan25@gmail.com

(Markowicz et al., 1990; Singh et al., 1989; Rao et al., 1993; Mannet al., 1994).

In this present investigation, the La, Lb and total L-shell XRFcross sections for Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, and I have beenmeasured using 55Fe point source at 5.96 keV. The L X-raysemitted by samples have been counted by a Si(Li) detector. The L

XRF cross sections have been also calculated theoretically byusing atomic parameters. The measured values have beencompared with the theoretical values.

2. Experimental Measurements and Data Analysis

The experimental arrangement and the geometry used in thispresent study are shown in Fig. 1. In this arrangement a photonsource of 55Fe was used for direct excitation of targets. 55Feradioisotope source have monochromatic energy and lowintensity. Therefore, the number of background of L X-rayspectrum was low. Pure samples (5N) of thicknesses rangingfrom 35 to 65 mg/cm2 were used in the measurements. Theradiations emitted from the target were counted by a well-shielded Si(Li) detector (active diameter 3.91 mm, active area12 mm2, thickness 3 mm, Be window thickness 0.025 mm, the fullwidth at half maximum (FWHM)=160 eV at 5.96 keV) coupled toa 4096-channel analyzer. The spectrums were accumulated intime intervals ranging from 1to 10 h and the spectrums for eachtarget were recorded separately in order to obtain sufficientstatistical accuracy. A typical L X-ray spectrum of Sb acquiredwith this arrangement is shown in Fig. 2. The spectra wereanalyzed by using Microcal Origin 7.0 software program withleast-squares fit method. The FWHM of all the peaks is allowed to

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Fig. 1. Experimental set up.

400

0

100

200

300

400

500 raw data Lα1,2 Lβ1 Lβ2 Lγ1,2 low-energy tail background

cps

Channel Number

Lα1,2

Lβ1

Lβ2

450 500 550 600 650 700

Fig. 2. A Typical spectrum of Sb.

I. Han et al. / Radiation Physics and Chemistry 79 (2010) 393–396394

vary independently in the fitting procedure. The uncertainty inthe area of the Li X-ray peak was evaluated by weighted method.The net peak areas were separated by fitting the measured spectrawith multi-Gaussian function plus polynomial backgrounds. Dueto the overlap of the La and Lb lines in the lighter elements XRFspectra, it was necessary to fix the positions of the Gaussiancomponents of the fit to their respective known energies.

The experimental L XRF cross sections have been calculatedusing the following relationship,

sLi¼

ILi

I0GeLibLi

tð1Þ

where ILi is the observed intensity (area under the photopeak)corresponding to Li group of X-rays, I0 is the intensity of incidentradiation, G is a geometrical factor, eLi is the detector effiency forthe Li group of X-rays and bLi is the self-absorption correctionfactor for the target material, t is the thickness (g cm�2 ) of thesample.

The values of bLi have been calculated by using the followingequation,

bLi ¼1�exp½�ðmincsecy1þmemtsecy2Þt�

ðmincsecy1þmemtsecy2Þtð2Þ

where mi and me are the total mass absorption coefficient of targetat incident and emitter radiation (Li X-ray) energy, respectively, y1

and y2 are the angles of incident and emitter radiation withsample surface respectively. The values of mi and me are takenfrom the tables of Hubbell and Seltzer (1995).

In this study, the effective incident photon flux IoGe, whichcontain terms related to the incident photon flux, geometrical

factor and the efficiency of the X-ray detector, was determined bymeasuring t; bKi and the K X-ray intensities from thin samples ofP, S, Cl, K, Ca, Ti and V and using theoretical sKi values in Eq. (3).

IoGeLi ¼IKi

sKibKitð3Þ

where the various terms have the same meaning as thoseexplained in Eq. (1), except that sKi is the Ki X-ray productioncross section of target taken from the table of Scofield (1973). Thetheoretical K XRF cross sections (ski) were calculated using thefundamental parameter equation

sKi ¼ sK ðEÞoK FKiði¼ a;bÞ ð4Þ

where sK(E) is the K-shell photoionization cross section for thegiven elements at excitation energy E, oK is the K-shellfluorescence yields. In the present calculations, the values ofsK(E) were taken from Scofield (1973) and the values of oK weretaken from by Hubbel et al. (1994). Fki is the fractional X-rayemission rate for Ki X-rays and FKa and FKb are defined as;

FKa ¼ ð1þ IKb=IKaÞ�1

and

FKb ¼ ð1þ IKa=IKbÞ�1

ð5Þ

where IKb/IKa is the intensity ratio. These ratios were obtainedfrom the table published by Scofield (1974).

The theoretical values of La, Lb and total L XRF cross sectionsare calculated using the following expressions;

sxL ¼ sL1o1þðsL2þsL1f12Þo2

þ½sL1ðf13þ f12f23ÞþsL2f23þsL3�o3

sLa ¼ ðsL1f13þsL1

f12f23þsL2f23þsL3

Þo3F3a

sLb ¼ sL1o1F1bþðsL1

f12þsL2Þo2F2b

þðsL1f13þsL1

f12f23þsL2f23þsL3

Þo3F ð6Þ

where sL1, sL2, and sL3 are the L subshell photoionization crosssections taken from the table of Scofield (1973), o1, o2, and o3

are the fluorescence yields of Li subshell taken from the table ofScofield (1972), f12, f13 and f23 are the Coster–Kronig transitionprobabilities taken from the table of Krause (1979). Fnk (F3a, F2b,F1b,y) are the fraction of the radiative width of the subshell Li (i=1, 2, 3) contained in the kth spectral line, for example F3a is thefraction of L X-rays originating from the L3, transition thatcontribute to the La peak.

F3a ¼½GðM4�L3ÞþGðM5�L3Þ�

G3ð7Þ

where F3a is the sum of the radiative transition rate whichcontribute to the La line associated with the hole filling in the L3

subshell, G3 is the theoretical total radiative transition rate of theL subshell, G(M4�L3) is the radiative transition rate from the M4

shell to the L3 shell and G(M5�L3) is the radiative transition ratefrom the M5 shell to the L3 shell. The radiative transition rates formany elements have been calculated from table of Scofield(1974). All other Fny are similarly defined.

3. Result and discussion

Accurate experimental values of XRF cross sections for variouselements at different photoionization energies are importantbecause of their extensive use in atomic, molecular, radiation andmedical physics, material science, environmental science, agri-culture, forensic science, dosimetric computations for healthphysics, cancer therapy. They are also used in practical applica-tions, such as elemental analysis by the X-ray emission technique,

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I. Han et al. / Radiation Physics and Chemistry 79 (2010) 393–396 395

and basic studies of the nuclear and atomic processes leading tothe emission of X-rays and irradiation processes.

In this study, the La, Lb and total L XRF cross sections for nineelements (Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, I) were measured.Experimental and theoretical L XRF cross sections for the elementsmentioned above were listed in Table 1. They are plotted asfunctions of the atomic number in Fig. 3. The values of the L XRFcross sections increase with the increasing atomic numbers. Theunit of all cross sections is barns/atom. It is evident from Table 1and Fig. 3 that the experimental values for all elements are ingeneral, agreement with theoretical values within experimentalerror. The present agreement between the theoretical and theexperimental values leads to the conclusion that these presentdata will benefit using radioisotope XRF technique in applied

400

1000

2000

3000

4000

5000

6000

σ Lα

Atomic number

Exp.Theo.

0

2000

4000

6000

8000

10000

σ Lx

Exp. Theo.

42 44 46 48 50 52 54

40Atomic number

42 44 46 48 50 52 54

Fig. 3. The Li XRF cross sections v

Table 1Experimental and theoretical values of L XRF cross-section for some elements in the a

sLa sLb

Element Exp. Theo. Exp.

Zr 753767 710 4027Nb 847776 876 4837Mo 1097798 1035 5827Ag 22587203 2092 12417Cd 25707231 2410 16737In 30787277 2769 20897Sn 34467310 2851 24947Sb 38597347 3303 30927I 48327434 4322 38837

fields also EDXRF spectrometry for determination the L XRF crosssections are very useful. The L XRF cross sections can be calculatedtheoretically by using photoionization cross sections, fluorescenceyields, and fractional emission rates. Uncertainties in thesetabulated quantities largely reflect the error in the L XRF crosssections. For this reason, most users prefer the experimentalvalues of the cross sections whenever large discrepancies areobserved between theoretical and experimental results. Theoverall errors in the present measurements of L XRF crosssections are estimated to be 8–12%. The errors are attributed touncertainties in the different parameters used to evaluate L XRFcross sections, namely, the evaluation of peak areas (�3–6%), I0Ge(�6–8%), target thickness measurement (�2%) and absorptioncorrection factor (�2%).

0

500

1000

1500

2000

2500

3000

3500

4000

4500

σ Lβ

Exp. Theo.

0

2000

4000

6000

8000

10000

σLα

σLβ

σX

σ Exp

.

40Atomic number

42 44 46 48 50 52 54

40Atomic number

42 44 46 48 50 52 54

L

alues versus atomic number.

tomic range 40rZr53 (barns/atom).

sLx

Theo. Exp. Theo.

36 414 12097108 1171

43 517 13817124 1408

52 612 17547157 1670

111 1331 37257335 3668

150 1600 46867421 4307

188 1887 54957494 5006

224 2435 63697573 5750

278 2780 74367669 6627

349 3633 94187847 8700

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I. Han et al. / Radiation Physics and Chemistry 79 (2010) 393–396396

For quantitative analytical applications, it is necessary to knowthe different relative intensities of the photons which contributeto the fluorescence. In the overlapped peaks, net peak areas aredetermined using peak fitting procedures. As a result, there is fairagreement between the theoretical and the experimental values,the peak fitting processes being of considerable importance inseparating out individual contributions from the mixed peaks.

References

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Edgardo, V.B., Barrea, R.A., 2002. Measurements of L X-ray fluorescence crosssections for rare earths at 15.2 keV. Rad. Phys. Chem., 63129–63134.

Garg, R.R., Puri, S., Singh, S., Mehta, D., Shahi, J.S., Garg, M.L., Singh, N., Mangal, P.C.,Trehan, P.N., 1992. Measurements of L X-ray fluorescence cross sections andyields for elements in the atomic range 41rZr52 at 5.96 keV. Nucl. Instrum.Methods B 72, 147–152.

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