Radiation Physics and Chemistry 79 (2010) 1174–1179

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Radiation Physics and Chemistry

0969-80

doi:10.1

n Corr

E-m

(I. Han)

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

Alloying effect on K to L shell vacancy transfer probabilitiesin 3d transition metals

I. Han a,n, L. Demir b

a Faculty of Sciences and Arts, Department of Physics, Agrı _Ibrahim C- ec-en University, TR-04100 Agrı, Turkeyb Faculty of Sciences, Department of Physics, Ataturk University, TR-25240 Erzurum, Turkey

a r t i c l e i n f o

Article history:

Received 25 May 2010

Accepted 16 July 2010

Keywords:

Alloy

Alloying effect

3d Transition metal

Vacancy transfer probability

6X/$ - see front matter & 2010 Elsevier Ltd. A

016/j.radphyschem.2010.07.015

esponding author. Tel./fax: +90 4722156554

ail addresses: ibrahimhan25@hotmail.com, ib

.

a b s t r a c t

The alloying effects on K to L shell vacancy transfer probabilities (ZKL) in 3d transition metals have been

carried out by X-ray fluorescence studies of various alloy compositions. K X-ray intensity ratios of Ti, Cr,

Fe, Co, Ni, and Cu elements in the FexNi1�x, FexCr1�x, NixCr1�x, FexCryNi1�(x + y), TixNi1�x, TixCo1�x, and

CoxCu1�x alloys have been measured following excitation by 22.69 keV X-rays from a 10 mCi 109Cd

radioactive point source and ZKL values for alloying elements have been determined from these ratios.

The spectrum of characteristic K-X-ray photons from samples were detected with a high resolution

Si(Li) detector coupled to a 4 K multichannel analyzer. The present investigation makes it possible to

perform reliable interpretation of experimental K to L shell vacancy transfer probabilities for various 3d

transition metals in alloys and can also provide quantitative information about the changes of K to

L shell vacancy transfer probabilities of these metals with alloy composition.

& 2010 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. EDXRF is very useful for determination of XRFparameters such as production cross sections, fluorescence yields,intensity ratios, and vacancy transfer probabilities. Accuratevalues of these parameters are required in several fields such asatomic, molecular and radiation physics, material science,environmental science, agriculture, forensic science, dosimetriccomputations for health physics, cancer therapy, elementalanalysis, basic studies of nuclear physics, etc.

A vacancy in the inner shell of an atom is produced by variousmethods; photoionization is one of them. In this method, theincident 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. The number of X-rayphotons emitted per vacancy is known as fluorescence yield. Inthe nonradiative process, instead of an X-ray photon, an electronfrom a higher shell is emitted and such an electron is known as

ll rights reserved.

.

rahimhan25@gmail.com

the Auger electron. The number of electrons emitted per vacancyis known as the Auger yield. In these processes, the vacancy in theinner shell (the K shell) is transferred to the higher shells (L, M,etc.). The transfer of the vacancy can also occur within a subshelland such a process is known as the Coster–Kronig transition. Thenumber of L shell vacancies produced per decay of a K shellvacancy is known as the K to L vacancy transfer probability ZKL

(Bennal and Badiger, 2006).The K X-ray fluorescence parameters such as intensity ratio

and fluorescence yield of 3d transition metals is dependent on thechemical environment of these metals in their alloys (Bhuinyaand Padhi, 1993; Raj et al., 2001; Kalayci et al., 2005; Han andDemir, 2009, 2010a, b; Dagistanli et al., 2010) and compounds(Mukoyama et al., 1986; Polasik, 1998; Raj et al., 1998, 2002). TheX-ray emission spectra are known to be influenced by thechemical combination and physical properties of X-ray emittingatoms. The variety of physical properties of the 3d transitionmetals and the large number of applications of these metals andtheir compounds and alloys cause the need for understanding theX-ray fluorescence parameters such as intensity ratio, fluores-cence yields, and vacancy transfer probability of 3d transitionmetals in various systems. The main aim of present paper isrelated to investigation of alloying effects on the vacancy transferprobabilities in 3d transition metals alloys. There are a largenumber of investigations about the vacancy transfer probability(Rao et al., 1972; Puri et al., 1993; Schonfeld and Janben, 1996,2000; Ertugrul et al., 1997, 2005; Ertugrul, 2002; Sharma et al.,2005; Santra et al., 2005; Bonzi, 2006; Han et al., 2007a; Demirand S-ahin, 2007; Tuzluca et al., 2008; Reyes-Herrera and Miranda,

I. Han, L. Demir / Radiation Physics and Chemistry 79 (2010) 1174–1179 1175

2008; Sogut et al., 2009; Bennal et al., 2010) but this paper is firstinvestigation concerned with alloying effects on ZKL for presentalloys with Cd-109 and the measured values of ZKL for Ti, Cr, Fe,Co, Ni, and Cu elements in the FexNi1�x, FexCr1�x, NixCr1�x,FexCryNi1�(x+ y), TixNi1�x, TixCo1�x, and CoxCu1�x alloys are beingreported here for the first time.

2. Experimental details and data analysis

The measurements were carried out using high purity alloys (inpowder form). The powder material is pelletized into the size of13 mm diameter. The samples were irradiated using 22.69 keV X-raysfrom a 10 mCi 109Cd radioactive point source. For each sample,emitted X-rays were detected by a Si(Li) detector (full width at halfmaximum¼160 eV for a 5.9 keV X-ray peak, active area of 12 mm2,thickness of 3 mm, and Be window thickness of 0.025 mm) coupledwith a multichannel analyzer system and spectroscopy amplifier. Thedetector was also placed in a step-down shield made from Pb, Fe, andAl to minimize the detection of any radiation coming directly fromthe source and scattered from the surroundings. A typical K X-rayspectrum of Fe0.3Cr0.3Ni0.4 alloy is shown in Fig. 1. A careful fittingmethodology is required in order to obtain accurate values for thepeak areas in the experimental studies. In the present paper, all theX-ray spectra were carefully analyzed by means of the MicrocalOrigin 7.5 Demo Version software peak fitting program using a multi-Gaussian least-square fit method in order to determine the accuratepeak intensity. Residual plots are also shown in Fig. 1. In the region ofthe peaks, the residuals are insignificant and the r2 value for thewhole range was 0.99 signifying that the peak fitting was satisfactory.To determination of ZKL values, the K X-ray intensity ratios weredetermined from peak areas fitted to Gaussian function after applyingnecessary corrections to the data. For measured ratios corrections areneeded because of the difference in the Ka and Kb self-attenuations

600

0

5000

10000

15000

20000

25000

30000

35000

Fe K

β

Cr

K β

Cr

K α

FexCry Ni1-x x = 0.3; y = 0.3

Cou

nts

per

chan

nel

Cha

500

0

-500

Res

idua

l

600 800

800

Fig. 1. A typical K X-ray spectrum of Fe0.3Cr0.3Ni0.4 alloy excited

in the sample, difference in the efficiency of the Si(Li) detector andair absorption on the path between the sample and the Si(Li)detector window.

The vacancy transfer probabilities from K to L shell (ZKLi)

can be evaluated as the main number of primer Li subshellvacancies produced in the decay of one K shell vacancythrough radiative; ZKLi

ðRÞ and nonradiative; ZKLiðAÞ transitions

(Rao et al., 1972):

ZKLi¼ ZKLi

ðRÞþZKLiðAÞ ð1Þ

The experimental K to L shell total vacancy transfer prob-abilities, ZKL, were obtained by using following equation(Schonfeld and Janben, 1996):

ZKL ¼2�oK

1þðIKb=IKaÞð2Þ

where oK is the fluorescence yield of the K shell and IKb/IKa is theintensity ratio of the K X-rays.

The average K-shell fluorescence yields, oK, were derived fromthe measured Ki X-ray fluorescence cross sections using therelationship

oK ¼sK

sKðEÞð3Þ

where sK¼sKa+sKb is the total Ki X-ray fluorescence cross-section and sK(E) is the K-shell photoionization cross-sectiontaken from the tables published by Scofield (1973). The experi-mental Ki X-ray fluorescence cross sections were evaluated usingthe relation

sKi¼

NKi

I0GeKibtði¼ a,bÞ ð4Þ

where NKiis the net number of counts under the corresponding

photopeak, the product I0G is the intensity of the excitingradiation falling on the area of the target samples visible to the

Corr Coef = 0.99978

Ni K

β

Ni K

α

Fe K

α

nnel number

1000 1200 1400

1000 1200 1400

with 22.69 keV X-rays from 109Cd radioactive point source.

4

3.84

3.88

3.92

3.96

4.00

4.04

4.08

log(I0Gε) = A0/E3+ A1/E2 + A2/E + A3

r2 = 0.94505

A0 = 3.74655 ± 0.45629

A1 = -0.02442 ± 0.19612

A2 = 0.01561 ± 0.02702

A3 = -0.00103 ± 0.00119

log

(I0G

ε)

Energy (keV)5 6 7 8 9 10 11

Fig. 2. Plot of the factor I0Ge as a function of weighted mean K X-ray energy.

Table 1ZKL values for Fe and Ni in pure metals and FexNi1�x alloys.

Sample Experimental Theoretical

Fe Ni

Fe 1.436 – 1.439a 1.447b

Fe0.8Ni0.2 1.510 1.674 – –

Fe0.7Ni0.3 1.524 1.631 – –

Fe0.6Ni0.4 1.543 1.585 – –

Fe0.5Ni0.5 1.566 1.537 – –

Fe0.4Ni0.6 1.601 1.495 – –

Fe0.3Ni0.7 1.614 1.476 – –

Fe0.2Ni0.8 1.651 1.452 – –

Ni – 1.388 1.375a 1.388b

a Rao et al. (1972).b Schonfeld and Janben (2000).

Table 2ZKL values for Fe and Cr in pure metals and FexCr1�x alloys.

Sample Experimental Theoretical

Fe Cr

Fe 1.436 1.439a 1.447b

Fe0.9Cr0.1 1.507 1.704 – –

Fe0.7Cr0.3 1.520 1.663 – –

Fe0.5Cr0.5 1.564 1.640 – –

Cr 1.410 1.495a 1.508b

a Rao et al. (1972).b Schonfeld and Janben (2000).

Table 3ZKL values for Ni and Cr in pure and NixCr1�x alloys.

Sample Experimental Theoretical

Ni Cr

Ni 1.388 1.375a 1.388b

Ni0.8Cr0.2 1.330 1.710 – –

Ni0.6Cr0.4 1.379 1.662 – –

Ni0.5Cr0.5 1.427 1.632 – –

Ni0.4Cr0.6 1.488 1.576 – –

Ni0.2Cr0.8 1.532 1.543 – –

Cr 1.410 1.495a 1.508b

a Rao et al. (1972).b Schonfeld and Janben (2000).

I. Han, L. Demir / Radiation Physics and Chemistry 79 (2010) 1174–11791176

detector, eKi, is the detector efficiency for Ki X-rays, t is the areal

mass of the sample in g/cm2, and b is the self-absorptioncorrection factor for the incident photons and emitted K X-rayphotons. b was calculated using the relation

b¼1�exp � ðm=rÞi=cos y1þðm=rÞe=cos y2

� �t

� �

ðm=rÞi=cos y1þðm=rÞe=cos y2

� �t

ð5Þ

where (m/r)i and (m/r)e are the mass attenuation coefficients(cm2/g) of incident photons and emitted characteristic X-rays,respectively. y1 and y2 are the angles of incident photons andemitted X-rays with respect to the normal at the surface of thesample in the present setup and t is the mass thickness ofthe sample in g/cm2. To estimate the self-absorption correctionin the sample and the absorption correction in the air path weused the mass attenuation coefficients obtained by means of acomputer program named WINXCOM (Gerward et al., 2001, 2004)which is based on the DOS-based compilation of XCOM developedby Berger and Hubbell (1987, 1999) for calculating massattenuation coefficients or photon interaction cross-section forany element, compound, or mixture at energies 1 keV to 100 GeV.This program uses mixture rule to calculate the partial and totalmass attenuation coefficients for all elements, compounds, andmixtures at standard as well as selected energies. The massattenuation coefficients (m/r)C for any chemical compound ormixture are estimated using the elemental values in the followingBragg’s-rule formula (Jackson and Hawkes, 1981):

ðm=rÞC ¼X

i

wiðm=rÞi ð6Þ

where wi is the proportion by weight of the ith constituent and(m/r)i is the mass attenuation coefficient for the ith constituent inthe compound.

In this study, the effective incident photon flux I0GeKi, whichcontains terms related to the incident photon flux, geometricalfactor, and the efficiency of the X-ray detector, was determined bymeasuring t, b, and the K X-ray intensities from different thinsamples and using theoretical sKi values in Eq. (4). The measuredI0Ge values for the present geometry were plotted as a function ofthe mean K X-ray energy in Fig. 2.

The IKb/IKa intensity ratio is obtained from the followingequation (Han et al., 2007b):

IKb

IKa¼

NKb

NKa

bKabKb

eKa

eKbð6Þ

where NKa and NKb represent the counts under the Ka and Kbpeaks, bKa and bKb are the self-absorption correction factors of the

target for both the incident and emitted photons, and eKa and eKb

are the detector-efficiency values for the Ka and Kb X-rays,respectively.

3. Results and discussion

K to L shell vacancy transfer probabilities (ZKL) for 3d transitionelements in pure metals and their different alloy compositions(for FexNi1�x, x¼0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2; for FexCr1�x,x¼0.9, 0.7, and 0.5; for NixCr1�x, x¼0.8, 0.6, 0.5, 0.4, and 0.2; forFexCryNi1�(x +y), x¼0.7, y¼0.1, x¼0.5, y¼0.2, x¼0.4, y¼0.3,x¼0.3, y¼0.3, x¼0.2, y¼0.2, and x¼0.1, y¼0.2; for TixNi1�x,x¼0.7, 0.6, 0.5, 0.4, and 0.3; for TixCo1�x, x¼0.7, 0.6, 0.5, 0.4, and0.3; for CoxCu1�x, x¼0.8, 0.7, 0.6, 0.5, 0.4, 0.3, and 0.2) weremeasured. The ZKL measured for the present samples have beentabulated in Tables 1–7. The total experimental uncertainty in themeasured ZKL values is estimated to be 3–7%. This uncertainty

Table 4ZKL values for Fe, Cr and Ni in pure metals and FexCryNi1�(x +y) alloys.

Sample Experimental Theoretical Other exp.

Fe Cr Ni

Fe 1.436 – – 1.439a 1.447b 1.44270.144c

Cr – 1.410 – 1.495a 1.508b 1.53870.123c

Ni – – 1.388 1.375a 1.388b 1.36470.123c

Fe0.7Cr0.1Ni0.2 1.419 1.744 1.653 – – –

Fe0.5Cr0.2Ni0.3 1.468 1.717 1.595 – – –

Fe0.4Cr0.3Ni0.3 1.477 1.686 1.590 – – –

Fe0.3Cr0.3Ni0.4 1.533 1.691 1.512 – – –

Fe0.2Cr0.2Ni0.6 1.611 1.711 1.438 – – –

Fe0.1Cr0.2Ni0.7 1.686 1.713 1.372 – – –

a Rao et al. (1972).b Schonfeld and Janben (2000).c Sogut et al. (2009).

Table 5ZKL values for Ti and Ni in pure metals and TixNi1�x alloys.

Sample Experimental Theoretical

Ti Ni

Ti 1.568 1.548a 1.566b

Ti0.7Ni0.3 1.568 1.679 – –

Ti0.6Ni0.4 1.599 1.599 – –

Ti0.5Ni0.5 1.615 1.583 – –

Ti0.4Ni0.6 1.622 1.491 – –

Ti0.3Ni0.7 1.664 1.479 – –

Ni 1.388 1.375a 1.388b

a Rao et al. (1972).b Schonfeld and Janben (2000).

Table 6ZKL values for Ti and Co in pure metals and TixCo1�x alloys.

Sample Experimental Theoretical/Other exp.

Ti Co

Ti 1.568 1.566a 1.58670.127b

Ti0.7Co0.3 1.616 1.650 – –

Ti0.6Co0.4 1.631 1.623 – –

Ti0.5Co0.5 1.629 1.575 – –

Ti0.4Co0.6 1.621 1.579 – –

Ti0.3Co0.7 1.679 1.482 – –

Co 1.384 1.418a 1.42070.142b

a Schonfeld and Janben (2000).b Sogut et al. (2009).

Table 7ZKL values for Co and Cu in pure metals and CoxCu1�x alloys.

Sample Experimental Theoretical/Other exp.

Co Cu

Co 1.384 1.418a 1.42070.142b

Co0.8Cu0.2 1.481 1.672 – –

Co0.7Cu0.3 1.498 1.623 – –

Co0.6Cu0.4 1.515 1.565 – –

Co0.5Cu0.5 1.560 1.527 – –

Co0.4Cu0.6 1.586 1.484 – –

Co0.3Cu0.7 1.621 1.447 – –

Co0.2Cu0.8 1.656 1.397 – –

Cu 1.387 1.357a 1.34270.121b

a Schonfeld and Janben (2000).b Sogut et al. (2009).

I. Han, L. Demir / Radiation Physics and Chemistry 79 (2010) 1174–1179 1177

arises from the uncertainties in various parameters used to thedetermination of the ZKL values including errors due to theevaluation of peak area, detector efficiency, self-absorptionfactors, and target thickness measurements.

The ZKL values obtained for pure Ti, Fe, Cr, Ni, Cu, and Co metals(Tables 1–7) are compatible with the results of Rao et al. (1972),Schonfeld and Janben (2000), and Sogut et al. (2009). In this study,the ZKL values of Ti, Cr, Fe, Cu, Ni, and Co in different compositionalloys were performed using the K X-ray intensity ratios andK shell fluorescence yields. The present agreement betweenexperimental results and the theoretical and other experimentalvalues shows that using these parameters for determination of ZKL

is very useful. Figs. 3–5 is drawn for graphical presentation ofvalues in Tables 1–7 and shows change of ZKL values as a functionof their own concentrations in FexNi1�x, FexCryNi1�(x +y) andCoxCu1�x, alloys, respectively. It can be seen from these tables andfigures that for both binary and ternary alloys, changes of ZKL

values with element concentration in alloy are similar.As seen in Tables 1–7, the ZKL values for 3d metals in alloys are

significantly different from that of the pure metal. This deviationis related to the electron rearrangement between 3d and 4s, 4p

0.21.3

1.4

1.5

1.6

1.7

1.8

Fe in FexNi1-x

Ni in FexNi1-xK

to L

she

ll va

canc

y tr

ansf

er p

roba

bilit

ies

(�K

L)

own metal concentration

0.4 0.6 0.8 1.0

Fig. 3. The change of K to L shell vacancy transfer probabilities (ZKL) for Fe and Ni

as a function of their own concentrations in FexNi1�x alloys.

0.01.2

1.4

1.6

1.8

Fe in FexCryNi1-(x+y)

Cr in FexCryNi1-(x+y)

Ni in FexCryNi1-(x+y)

K to

L s

hell

vaca

ncy

tran

sfer

pro

babi

litie

s(� K

L)

own metal concentration

0.2 0.4 0.6 0.8 1.0

Fig. 4. The change of K to L shell vacancy transfer probabilities (ZKL) for Fe and Ni

as a function of their own concentrations in FexCryNi1�(x + y) alloys (own metal

concentration refers to x for Fe, y for Cr and 1�(x+y) for Ni).

0.21.3

1.4

1.5

1.6

1.7

1.8

Co in CoxCu1-x

Cu in CoxCu1-x

K to

L s

hell

vaca

ncy

tran

sfer

pro

babi

litie

s (�

KL)

own metal concentration

0.4 0.6 0.8 1.0

Fig. 5. The change of K to L shell vacancy transfer probabilities (ZKL) for Co and Cu

as a function of their own concentrations in CoxCu1�x alloys.

I. Han, L. Demir / Radiation Physics and Chemistry 79 (2010) 1174–11791178

valence shells (delocalization) and/or charge transfer of 3delectrons from one element to another. The delocalization andcharge transfer phenomena can be in opposite directions andlarger than the others; therefore, the valance electronic arrange-ment for these alloys are different. This can cause some unevenchange in relation between the ZKL values and the own metalconcentration of 3d transition elements in alloys. Electronsremoved from the 3d state of one element influence screeningeffect on the 3d and 4s electrons and binding energies of 3d and4s electrons. Changing the screening effect and binding energiesof 3d and 4s electrons causes a change in the ZKL values of metalatoms. The number of transferred electrons from the 3d state ofone element to the 3d state of other element is different fordifferent composition, so the ZKL values of metals depend on alloycompositions. The alloying effect is clearly observed in the K to Lvacancy transfer probabilities. The changes in the ZKL with alloycompositions are in same directions for both elements in a certainalloy and generally, there is a decrease in ZKL values of metalswith increasing concentration in alloys. The origin of change inK to L vacancy transfer probabilities of 3d transition metals shouldbe interpreted in terms of the change in the electronic configura-tion of alloying metals. The 3d transition metal alloys plays animportant role in fundamental and applied research due to varietyof physical properties. The physical properties of binary andternary 3d transition metal alloys depend strongly on the valenceelectronic structure, which is responsible for the observed changein ZKL values of the Ti, Fe, Cr, Ni, Cu, and Co in different alloys.Experimental results obtained in this investigation show that ZKL

values for alloys exhibit a great dependence on alloy composition.The ZKL values for 3d transition metals are modified with alloyingof these metals, therefore ZKL are sensitive tools to investigatealloying effect. Thus, the specific alloy composition may beimportant in developing different special properties or to improvethe present characteristics of 3d transition metal alloys. Theknowledge of alloying effect on K to L shell vacancy transferprobabilities is important for determining the different andspecial features of the 3d transition metal alloys.

4. Conclusion

Present study has been performed in exploring the alloyingeffect on the K to L vacancy transfer probabilities (ZKL) of 3dtransition metals. For this reason ZKL values were measured for

pure 3d metals and their different alloy compositions. The resultsindicate that alloying effect cause significant changes in ZKL valuesin 3d transition metal alloys, in other words K to L vacancy transferprobabilities is affected by the alloying operation. This arises fromchange of valence electron structure with delocalization and/orcharge transfer in alloys. This means that physical properties of thealloy are strongly influenced by the alloy composition. Electrical,magnetic, and other properties of 3d transition metal alloys can beenhanced and controlled with certain chemical composition.Consequently, private alloy composition may enable the produc-tion of alloys with ideal physical properties for specific applica-tions. To attain more definite results and to satisfy conclusionsabout alloying effects on K to L vacancy transfer probabilities,studies should be continued for different 3d transition metal alloys.

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