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Radiation Physics and Chemistry 78 (2009) 760–764

Contents lists available at ScienceDirect

Radiation Physics and Chemistry

0969-80

doi:10.1

� Corr

E-m

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

Determination of mass attenuation coefficients, effective atomic and electronnumbers for some natural minerals

I. Han a,�, L. Demir a, M. S-ahin b

a Ataturk University, Faculty of Arts and Sciences, Department of Physics, 25240 Erzurum, Turkeyb Rize University, Faculty of Arts and Sciences, Department of Physics, 53100 Rize, Turkey

a r t i c l e i n f o

Article history:

Received 5 December 2008

Accepted 24 March 2009

Keywords:

Mass attenuation coefficients

Effective atomic and electron number

Natural mineral and crystal

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

016/j.radphyschem.2009.03.077

esponding author. Tel.: +90 4422314083; fax

ail address: ihan@atauni.edu.tr (I. Han).

a b s t r a c t

The total mass attenuation coefficients (mm) for SiO2 {Quartz (110 1), Quartz (110 0) and Quartz

(0 0 0 1)}, KAlSi3O8 {Orthoclase (0 10), Orthoclase (10 0)}, CaSO4 �2H2O (gypsum), FeS2 (pyrite) and

Mg2Si2O6 (pyroxene) natural minerals were measured at 22.1, 25.0, 59.5 and 88.0 keV photon energies.

The g- and X-rays were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. Atomic

and electronic cross sections (st and se), the effective atomic and electron numbers or electron densities

(Zeff and Neff) were determined using the obtained mm values for investigated samples.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The quartz, orthoclase, CaSO4 �2H2O (gypsum), FeS2 (pyrite)and Mg2Si2O6 (pyroxene) are very important natural minerals.Quartz is the most abundant mineral in the Earth’s continentalcrust. Quartz crystals have piezoelectric properties and used inphonograph pickups, quartz clock, as a crystal oscillator in quartzcrystal microbalance and in thin-film monitors. Orthoclase is animportant tectosilicate mineral, which forms igneous rock andcommon in granite and related rocks. Orthoclase is used as rawmaterial for the manufacture of some glasses, ceramics andporcelain. Gypsum is a very soft mineral composed of calciumsulfate dehydrate, common in evaporate bed, sedimentary rocks,lake and sea water, hot springs, volcanic vapors, and sulfatesolutions veins. There are a large number of uses for gypsum andsome of these are drywall, plaster ingredient, plaster of paris,blackboard chalk, fertilizer and soil conditioner. Pyrite is usuallyfound associated with other sulfides or oxides in quartz veins,sedimentary rock, metamorphic rock, coal beds and fossils. Pyriteis used commercially in the production of sulfur dioxide, for use insuch applications as the paper industry, and in the manufacture ofsulfuric acid. Pyroxene is a group of important rock-formingsilicate minerals found in many igneous and metamorphicrocks. The knowledge of natural minerals’ physical parameterssuch as the mass attenuation coefficients (mm), atomic andelectronic cross sections (st and se), the effective atomic andelectron numbers or electron densities (Zeff and Neff) is useful forunderstanding their physical properties.

ll rights reserved.

: +90 4422360948.

Since the mm values are important in fundamental physics andmany applied fields, the accurate mm values for X- and g-rays inseveral materials are essential for some fields such as, nuclear andradiation physics, radiation dosimetry, biological, medical, agri-cultural, environmental and industrial. Recently, there have been agreat number of experimental and theoretical investigations todetermine mm values. The mm values for C2H4, CO2, N2, O2, CF4, Ne,H2S, HCl, Ar, Air, Mg, Al, SiO2 and (C2H5)3PO4 materials have beendetermined by Millar and Greening (1974). Hubbell (1982)tabulated the mm values for 40 elements and 45 mixtures andcompounds over the energy range from 1 keV to 20 MeV. Thesetables were reiterated with tabulation for all elements in theatomic range 1pZp92 and 48 additional substances of dosimetricinterest (Hubbell and Seltzer, 1995; Berger and Hubbell, 1987).Wang et al. (1995) measured systematically mm values in the rangeof X-ray energies between 1.486 and 15.165 keV for SiH4 and;between 8.041 and 29.109 keV for Si. Orlic et al. (1999) publishedmm values for photon energies between 100 eV and 1000 MeV. Themm values for 22 high-purity elemental materials were measuredin the X-ray energy obtained from a variable-energy X-ray sourceranging from 13 to 50 keV by a high-purity germanium detectorwith thin Be window (Angelonea et al., 2001). The mm valuesaround the K-shell absorption edge of Nb, Zr and Mo as aparametric X-ray radiation (PXR) application of monochromatichard X-ray radiation sources have been measured (Tamura et al.,2002). The mm values of Ag in the 15–50 keV energy range with alevel of between 0.27% and 0.4% away from the K-edge wereevaluated by Tran et al. (2005). Rettschlag et al. (2007)determined mm values for Pu by using a collimated-beamtransmission method in the energy range from 60 to 2615 keV.The g-ray attenuation coefficients have been measured for someheavy metal oxide borate glasses at 662 keV by Khanna et al.(1996) and for perspex, bakelite, paraffin, Al, Cu, Pb and Hg at three

ARTICLE IN PRESS

Radioactivepoint source

Be window

Pb

Fe

Al

Sample Si(L

i) D

etec

tor

Fig. 1. Experimental setup.

Table 1The experimental and theoretical values of mass attenuation coefficients for

investigated natural crystals.

mm (cm2/g)

Natural crystal 22.1 keV 25.0 keV 59.5 keV 88.0 keV

Exp. Theo. Exp. Theo. Exp. Theo. Exp. Theo.

Quartz(110 1) 1.65 1.11 0.23 0.13

Quartz(110 0) 1.98 1.34 0.28 0.18

Quartz(0 0 0 1) 2.21 1.44 0.28 0.20

Average 1.95 1.93 1.30 1.39 0.26 0.25 0.17 0.18

Orthoclase(0 10) 2.80 1.96 0.31 0.21

Orthoclase(10 0) 3.04 2.16 0.36 0.34

Average 2.92 2.73 2.00 1.94 0.33 0.30 0.22 0.19

Gypsum 3.71 3.61 2.61 2.56 0.32 0.35 0.23 0.21

Pyrite 11.82 11.70 7.90 8.26 0.77 0.80 0.38 0.35

Pyroxene 1.67 1.73 1.17 1.23 0.27 0.24 0.16 0.18

I. Han et al. / Radiation Physics and Chemistry 78 (2009) 760–764 761

different g-ray energies (59.54, 661.6 and 1332.5 keV) by Abdel-Rahman et al. (2000). The transmission of g-rays at the energies81, 356, 511, 662, 835, 1274 and 1332 keV has been studied on thealloys brass, bronze, steel, aluminum-silicon and lead-antimony(El-Kateb et al., 2000). The X-ray attenuation coefficients formaterials containing elements from H to Ca were measured usingcharacteristic X- and g-rays with energies 32–66 keV produced byX-ray fluorescence using a secondary excitation method, and140 keV obtained from an unsealed Tc source, respectively(Midgley, 2005). The X-ray attenuation coefficient of single-crystalsilicon has been measured to within level of uncertainty 0.5%using an energy dispersive method (Gerward, 1981). Singh et al.(1998) determined attenuation coefficients for some dilutesolutions (Li2SO4H2O, CuSO4 �5H2O, NiSO4 �6H2O, MgSO4 �7H2O,NH4Cl) at 662 keV.

The scattering and absorption of X- and g-rays are related tothe density and atomic number of an element. For compositematerials, it is also related to effective atomic number (Zeff). Sincepartial interaction cross section depends on the compositematerial of elements, a single atomic number being a character-istic of element will not describe the atomic number of compositematerial in the entire energy range. This new number forcomposite materials is called to be Zeff and varies with the energy.The Zeff is a convenient parameter for representing the attenuationof X-rays in a complex medium and particularly for the calculationof the dose in radiation therapy (Jackson and Hawkes, 1981). TheZeff value for a composite material is a very useful parameterfor some applications such as physical, technological andengineering. Some works to determine the Zeff values of compositematerials have been reported in the literature. Theoreticalexpressions to evaluate Zeff values for the individual partialphoton interaction processes have been suggested by Hine(1952). Murty (1965) has examined validity of differing expres-sions of Zeff for each absorption process in a heterogeneousmaterial and suggested a single Zeff for this material. Photonattenuation coefficients in certain tissue equivalent compounds,perspex, polyethylene, polycarbonate and teflon have beenmeasured at energies 13.37, 17.44, 22.10, 32.06 and 44.23 keVand the Zeff values for total photon interaction in these compoundswere derived from the measured coefficients (Parthasaradhi et al.,1992). Kumar and Reddy (1997) have calculated Zeff values fordifferent materials of dosimetric interest for total photon inter-action in the energy region 1 keV–20 MeV. Murty (2004) hasmeasured Zeff values for W/Cu alloys with two compositions in thephoton energy region 100–1400 keV and it has also been observedthat there were discrepancies between the measured Zeff valuesand the estimated values using Hine’s formula in the energyregion 60–380 keV by the same author Murty et al. (2000).Effective atomic numbers for photon energy absorption (ZPEAeff)and effective atomic numbers for photon interaction (ZPIeff) ofsome low-Z substances of dosimetric interest in the energy regionof 1 keV–20 MeV have been calculated (Shivaramu et al., 2001).The Zeff and effective electron number or electron density (Neff)values of some amino acids and sugars at the energies 30.8, 35.0,81.0, 145, 276.4, 302.9, 356, 383.9, 661.6, 1173 and 1332.5 keV havebeen calculated using the measured total attenuation crosssections (Gowda et al., 2005). Manjunathaguru and Umesh(2006) determined Zeff and Neff values of some biologicallyimportant compounds containing H, C, N and O in the energyrange 145–1330 keV. The mm, Zeff and thickness values for CuInSe2

semiconductor and mm and Neff values for BiPbSrCaCuO super-conductor have been measured at different energies (Cevik et al.,2006; Cevik and Baltas, 2007). The mm and Zeff values for YBaCuO

and BiPbSrCaCuO superconductors at 511, 661 and 1274 keVenergies and for MgB2 superconductor at some energies between14.1 and 29.7 keV have been measured (Baltas et al., 2005, 2007).

The Zeff and Neff values of essential amino acids; histidine, leucine,lysine, methionine, phenylalanine, threonine, tryptophan andvaline have been calculated for total and partial photon interac-tions by the direct method in wide energy range from 1 keV–100GeV, using WinXCOM (Manohara and Hanagodimath, 2007).Molecular, atomic and electronic cross sections and effectiveatomic numbers have been determinated on the basis of mixturerule for some boron compounds (H3BO3 and Na2B4O7) and thetrommel sieve waste (TSW) in the energy range 15.74–40.93 keV(Icelli et al., 2008).

In the present work, the mass attenuation coefficients (mm), forsome natural minerals (Quartz (1101), Quartz (110 0), Quartz(0 0 01), Orthoclase (010), Orthoclase (10 0), Gypsum, Pyrite andPyroxene) at 22.1, 25.0, 59.5 and 88.0 keV photon energies have beenexperimentally measured and theoretically calculated. The sampleswere irradiated with 10 mCi Cd-109 and 100 mCi Am-241 radioactivepoint source using transmission arrangements. Total atomic andelectronic cross sections (st and se), effective atomic and electronnumbers or electron densities (Zeff and Neff) for these crystals havebeen calculated by means of the measured mm values. Also, thevariation of investigated parameters versus photon energy isgraphically presented. The experimental mm values have beenchecked using the results of WinXCom calculations.

2. Theory

The mass attenuation coefficients for the different materialsand energies are determined by the transmission. This process isdescribed by the following equation:

I ¼ Ioe�mmt (1)

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I. Han et al. / Radiation Physics and Chemistry 78 (2009) 760–764762

where Io denotes the photons with energy E, intensitywithout attenuation; I the photons with energy E, intensity afterattenuation; mm ¼ m/r (cm2/g) is the mass attenuation coef-ficient and t (g/cm2) is sample mass thickness (the mass per unitarea). The total mm values for materials composed of multielements is the sum of the (mm)i values of each constituentelement by the following mixture rule (Hubbell and Seltzer,1995):

mm ¼X

i

oiðmmÞi (2)

where oi is the proportion by weight and (mm)i is massattenuation coefficient of the ith element. For materials composedof multi elements, the fraction by weight is given by

oi ¼niAiP

jnjAj(3)

200.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Exp. Theo.Exp Dec2 fit of Exp.Exp Dec2 fit of Theo.

μ m (c

m2 /

g)

Energy (keV)

Pyroxene

Orthoclase

0

2

4

6

8

Orthoclase

Pyroxeneσ e (b

/ato

m)

Exp. Theo.Exp Dec2 fit of Exp.Exp Dec2 fit of Theo.

3.0

3.3

3.6

3.9

4.2

4.5

Pyroxene

Orthoclase

Exp. Theo.Exp Dec2 fit of ExpExp Dec2 fit of Theo.

Nef

f (*1

023 e

lekt

ron/

cm3 )

30 40 50 60 70 80 90

20Energy (keV)

30 40 50 60 70 80 90

20Energy (keV)

30 40 50 60 70 80 90

Fig. 2. Typical plot of measured mm, st, se, Zeff and Neff for orthoclase and pyroxene. (a) Va

total electron cross sections (se), (d) effective atomic numbers (Zeff), (e) effective electron

a function of effective atomic numbers (Zeff).

where Ai is the atomic weight of the ith element and ni is thenumber of formula units. The total atomic cross sections (st) formaterials can be obtained from the measured values of mm usingthe following relation (Wang et al., 1995):

st ¼mmN

NA(4)

where N is the atomic mass of materials and NA is the Avogadro’snumber. The total electronic cross section (se) for the individualelement are calculated using the following equation (Singh et al.,2002):

se ¼1

NA

X f iNi

ZiðmmÞi ¼

st

Zeff(5)

where fi denotes the fractional abundance of the element i withrespect to the number of atoms such that f1+f2+f3+?+fi ¼ 1, Zi isthe atomic number of ith element. The st and se are related to the

0

20

40

60

80

100

120

Orthoclase

Pyroxene

Exp TheoExp Dec2 fit of Exp.Exp Dec2 fit of Theo.

σ t (b

/ato

m)

10

12

14

16

Pyroxene

Orthoclase

Exp. Theo.Exp Dec2 fit of ExpExp Dec2 fit of Theo.

Z eff

9

3.0

3.5

4.0

4.5

Nef

f (*1

023 e

lctro

n/cm

3 )

Orthoclase

Pyroxene

Exp.Theo.Fitted

20Energy (keV)

30 40 50 60 70 80 90

20Energy (keV)

30 40 50 60 70 80 90

Zeff

10 11 12 13 14 15 16

riation of mass attenuation coefficients (mm), (b) total atomic cross sections (st), (c)

numbers (Neff) versus photons energies and (f) effective electron numbers (Neff) as

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Table 2The experimental and theoretical values of total atomic cross section (st), total

electronic cross section (se), effective atomic number (Zeff) and effective electron

number (Neff) for investigated natural crystals.

Natural crystal 22.1 keV 25.0 keV 59.5 keV 88.0 keV

Exp. Theo. Exp. Theo. Exp. Theo. Exp. Theo.

st (b/atom)

Quartz 64.88 64.21 43.25 46.24 8.65 8.32 5.66 5.99

Orthoclase 103.85 97.09 71.13 69.00 11.74 10.67 7.11 6.76

Gypsum 88.42 86.04 61.97 61.01 7.63 8.34 5.48 5.00

Pyrite 785.17 777.19 524.77 548.69 51.15 53.14 24.58 23.25

Pyroxene 54.39 56.35 37.46 40.06 8.47 7.82 5.54 5.86

se (b/atom)

I. Han et al. / Radiation Physics and Chemistry 78 (2009) 760–764 763

effective atomic number (Zeff) of the material through thefollowing relation (Singh et al., 2002):

Zeff ¼st

se(6)

The effective electron number (Neff) can be written as follows:

Neff ¼NA

NZeff

Xni ¼

mm

se(7)

The theoretical mm values for present crystals were obtained bythe WinXcom program (Gerward et al., 2001). This programdepends on applying the mixture rule to calculate the partial andtotal mass attenuation coefficients for all elements, compoundsand mixtures at standard as well as selected energies.

Quartz 5.28 5.24 3.65 3.79 0.80 0.79 0.54 0.58

Orthoclase 6.98 6.82 4.79 4.89 0.88 0.87 0.58 0.53

Gypsum 5.65 5.45 3.84 3.96 0.79 0.80 0.57 0.59

Pyrite 34.14 34.21 23.36 24.13 2.34 2.37 1.12 1.08

Pyroxene 4.80 4.78 3.34 3.47 0.77 0.76 0.54 0.58

Zeff

Quartz 12.28 12.26 11.85 12.21 10.83 10.59 10.41 10.25

Orthoclase 14.87 14.24 14.86 14.12 13.39 12.29 12.17 12.70

Gypsum 15.65 15.78 16.15 15.40 9.69 10.42 9.68 8.51

Pyrite 23.00 22.72 22.46 22.74 21.87 22.38 21.90 21.46

Pyroxene 11.32 11.79 11.20 11.55 11.00 10.26 10.25 10.16

Neff (*1023 electron/cm3)

Quartz 3.69 3.68 3.56 3.67 3.26 3.18 3.13 3.08

Orthoclase 4.18 4.00 4.18 3.97 3.77 3.46 3.42 3.57

Gypsum 6.57 6.62 6.78 6.46 4.07 4.37 4.06 3.57

Pyrite 3.46 3.42 3.38 3.42 3.29 3.37 3.30 3.23

Pyroxene 3.48 3.62 3.44 3.55 3.38 3.15 3.15 3.12

3. Experiment

The schematic arrangement of the experimental setup in thepresent work is shown in Fig. 1. The samples were irradiated by22.1, 25.0, 59.5 and 88.0 keV photons emitted by 10 mCi Cd-109and 100 mCi Am-241 radioactive point source, respectively. Foreach sample and energy, Io and I intensities which are withoutand after attenuation were measured by a Si(Li) detector(FWHM ¼ 160 eV at 5.9 keV, active area 12 mm2, thickness 3 mmand Be window thickness 0.025 mm) coupled with a multi-channel analyzer system consisting of a 16384 channels analyzerand spectroscopy amplifier. The detector was also placed in a step-down shield made from Pb, Fe and Al to minimize the detection ofany radiation coming directly from the source and scattered fromthe surroundings. The distance between the radioactive pointsource with sample and the sample and Beryllium window ofSi(Li) detector were 14 and 1 cm, respectively. The peak areas havebeen calculated from the spectrum obtained for eachmeasurement. The measurements for all types of samples werecarried out five times for each energy value.

4. Results and discussion

The measured mass attenuation coefficient (mm) values forquartz (110 1), quartz (110 0) and quartz (0 0 0 1), orthoclase(0 10), orthoclase (10 0), gypsum, pyrite and pyroxene naturalcrystals at 22.1, 25.0, 59.5 and 88.0 keV photon energies have beentabulated in Table 1 and only for two samples (orthoclase andpyroxene) were plotted in Fig. 2(a). It is clearly seen that the mm

depends on the photon energy and decreases with increasingphoton energy. As can be seen in Table 1 and Fig. 2(a), theexperimental mm values for almost all samples agree withtheoretical values calculated using the WinXCom program basedon the mixture rule. The total experimental uncertainty of the mm

values depends on the uncertainties of Io (without attenuation)and I (after attenuation) peak area evaluation, mass thicknessmeasurements and counting statistics. Typical total uncertainty inthe measured experimental mm values is estimated to be 2–3%.Measured total atomic and electronic cross section (st and se)values for natural minerals were also presented in Table 2 and fororthoclase and pyroxene plotted versus photon energy in Fig. 2(b,c), respectively. The plots of st and se with photon energy showalmost similar behavior to mm plot. Effective atomic number (Zeff )values were determined from Eqs. (4)–(6) by using the mm values,and given in Table 2. The variation of Zeff versus photon energywas also shown graphically for orthoclase and pyroxene in Fig.2(d). It is seen from Table 2 and Fig. 2(d) that Zeff values forpresent samples vary and decrease with photon energy. In thecomposite materials, the interaction (such as absorption andscattering) of g- and X-rays with these materials is related to

obtained Zeff values and photon energies. Effective electronnumbers or electron densities (Neff) for present samples weredetermined using mm and se values and given in Table 2 alsoplotted versus photon energy for orthoclase and pyroxene inFig. 2(e). It is seen from this table and figures that Neff varies withphoton energy. Fig. 2(f) gives a plot of Neff versus Zeff for thephoton energy and shows that Neff increases linearly withincreasing Zeff.

5. Conclusion

The present experimental study has been undertaken to getsome information on the mm and related parameters (Zeff, Neff, st

and se) for natural crystal. It has been demonstrated that the mm isa useful and sensitive physical quantity to determine the Zeff andNeff for natural crystal. In the interaction of photon with matter,mm values are dependent on the physical and chemical environ-ments of the sample. The obtained mm values decrease withincreasing photon energy. Also the variation of st and se withenergy is identical to mm. The Neff is closely related to the Zeff andenergy dependence of Neff and Zeff is the same. In the presentstudy, it is indicated that the mm, Zeff and Neff are useful parametersfor natural crystals. The results of this study will be helpful tounderstand better how mm values change with variation of the Zeff

and Neff values of the crystal. To our best knowledge, experimentaland theoretical investigation of the mm, st, se, Zeff and Neff forpresent natural crystals are not available in the literature.Moreover, the results of this work can stimulate both experi-mental and theoretical research for other crystals and minerals.

Acknowledgement

One of the author (I. Han) is grateful to TUBITAK for thefinancial support.

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I. Han et al. / Radiation Physics and Chemistry 78 (2009) 760–764764

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