research article study of gamma ray exposure...

Hindawi Publishing CorporationJournal of CeramicsVolume 2013, Article ID 721606, 6 pageshttp://dx.doi.org/10.1155/2013/721606

Research ArticleStudy of Gamma Ray Exposure Buildup Factor forSome Ceramics with Photon Energy, Penetration Depth andChemical Composition

Tejbir Singh,1 Gurpreet Kaur,2 and Parjit S. Singh3

1 Department of Physics, Sri Guru Granth Sahib World University, Fatehgarh Sahib, Punjab 140407, India2Department of Physics, Maharishi Markandeshwar University, Mullana, Haryana 133207, India3 Department of Physics, Punjabi University, Patiala, Punjab 147002, India

Correspondence should be addressed to Tejbir Singh; [email protected]

Received 12 June 2012; Accepted 7 January 2013

Academic Editor: Baolin Wang

Copyright © 2013 Tejbir Singh et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Gamma ray exposure buildup factor for some ceramics such as boron nitride (BN), magnesium diboride (MgB2), silicon carbide

(SiC), titanium carbide (TiC) and ferrite (Fe3O4) has been computed using five parametric geometric progression (G.P.) fitting

method in the energy range of 0.015 to 15.0MeV, up to the penetration of 40 mean free path (mfp). The variation of exposurebuildup factors for all the selected ceramics with incident photon energy, penetration depth, and chemical composition has beenstudied.

1. Introduction

The recent nuclear reactor explosion in Japan emphasizedthe dire need of systematic and precise studies of dosi-metric parameters of different type of materials. In thenuclear reactor, multienergetic photons were released, andfor protection from these highly penetrating radiations, thickwalls of concrete were built around the nuclear reactor.However, in case of nuclear accident, these highly penetratingradiations can travel longer distances and can cause harmto living organisms. In such a situation, the extent to whichbuilding materials can provide shielding from these harmfulradiations is of utmost concern. Keeping this in mind, anattempt has beenmade to visualize the interaction of photonswith one of the building material, namely, ceramics.

Ceramics are the composite materials in which themechanical properties such as strength, modulus, toughness,wear resistance, and hardness are of primary interest. Despitepossessing the strength and modulus values which are equalto or better than metals, these materials have chemicalinertness and brittle fracture behavior. Considering suchproperties, ceramics have been selected to visualize the

feasibility of using these materials as gamma ray shieldingmaterial.

The intensity of a gamma rays beam follows Lambert-Beer law (𝐼 = 𝐼

𝑜𝑒−𝜇𝑥) under three conditions which are (i)

monochromatic radioactive source, (ii) thin absorbing mate-rial, and (iii) narrow beam geometry that should be used. Incase, any of the three conditions has been violated, this law nolonger holds. However, violation of the law can bemaintainedusing the correction factor 𝐵, which is known as buildupfactor. Different researchers have conducted experimentaland theoretical studies in different type of materials. Severalmethods (geometric progression (G.P.) fitting method [1–3]and invariant embedding method [4]) have been used forthe computation of buildup factors for different materials indifferent geometrical situations.

American Nuclear Society [2] provided a comprehensiveset of standard data for exposure buildup factor whichincludes twenty three elements, two compounds, and onemixture in the energy range of 0.015 to 15.0MeV and up tothe penetration depth of 40mfp.

In our previous works [5, 6], the various types of buildupfactors and different methods/codes available to compute

2 Journal of Ceramics

the buildup factor have been already discussed. Recently,different researchers had contributed in providing gammaray buildup factor data for different materials such as forthermoluminescent dosimetricmaterials [7], flyash concretes[8], human tissue [9], teeth [10, 11], some essential aminoacids, fatty acids, and carbohydrates [12], and samples fromthe earth, moon, and mars [13].

In the present work, G.P. fittingmethod has been adoptedto compute exposure buildup factors at some incident photonenergies in the range of 0.015 to 15MeV with penetrationdepth up to 40mfp for some ceramics.

2. Computational Work

The computational work of exposure buildup factor for theselected ceramics has been divided into three parts. Thefirst part deals with the computation of equivalent atomicnumber (𝑍eq) for the selected ceramics in the energy regionof 15.0 keV to 15.0MeV. The second part concerns with thecomputation ofG.P. fitting parameters, and finally in the thirdpart, exposure buildup factor values have been computed inthe same energy region.

2.1. Computations of Equivalent Atomic Numbers (𝑍𝑒𝑞). For

the computation of𝑍eq, the values of Compton partial attenu-ation coefficient (𝜇Comp) and the total attenuation coefficients(𝜇total) were obtained in cm

2/g for the selected ceramics in theenergy range of 0.015 to 15.0MeV using WinXCom program[14]. The values of 𝑍eq for the selected ceramics were com-puted by matching the ratio 𝑅 (𝜇Comp/𝜇total) of a particularceramics at a selected energy with the corresponding ratio ofan element at the same energy. In case the value of ratio liesbetween two ratios for known successive elements, the value𝑍eq was then interpolated using the following logarithmicinterpolation formula [6]:

𝑍eq =𝑍1(log𝑅

2− log𝑅) + 𝑍

2(log𝑅 − log𝑅

1)

(log𝑅2− log𝑅

1)

, (1)

where 𝑍1and 𝑍

2are the atomic numbers of elements corre-

sponding to the (𝜇Comp/𝜇total) ratios, 𝑅1 and 𝑅2, respectively,and 𝑅 (𝜇Comp/𝜇total) is the ratio for the selected ceramic at aparticular energy, which lies between ratios 𝑅

1and 𝑅

2.

2.2. Computations of G.P. Fitting Parameters. AmericanNational Standards [2] provided the exposure G.P. fittingparameters of 23 elements (

4Be-8O,11Na-16S,18Ar-20Ca,26Fe,

29Cu, Mo, Sn, La, Gd, W,

82Pb, and

92U), one compound

(water), and two mixtures (air and concrete) in the energyrange of 0.015 to 15.0MeV and up to a penetration depth of40mfp.The computed values of𝑍eq for the selected ceramicswere used to interpolate G.P. fitting parameters (𝑏, 𝑐, 𝑎, 𝑋

𝑘,

and 𝑑) for the exposure buildup factor using the followinglogarithmic interpolation formula [6]:

𝑃 =

𝑃1(log𝑍

2− log𝑍eq) + 𝑃2 (log𝑍eq − log𝑍1)

log𝑍2− log𝑍

1

, (2)

where 𝑍1and 𝑍

2are the elemental atomic numbers between

which the equivalent atomic number 𝑍eq of the chosenceramic lies.𝑃

1and𝑃2are the values of G.P. fitting parameters

corresponding to the atomic numbers 𝑍1and 𝑍

2, respec-

tively, at a given energy. Using the interpolation formula,G.P. fitting parameters for exposure buildup factors werecomputed at the selected incident photon energies for thechosen ceramics.

2.3. Computations of Buildup Factors. The computed G.P.fitting parameters (𝑏, 𝑐, 𝑎, 𝑋

𝑘, and 𝑑) were used to compute

the exposure buildup factors for the selected ceramics inincident photon energy range of 0.015 to 15.0MeV and upto the penetration depth of 40mfp using following equations[2–4]:

𝐵 (𝐸, 𝑥) = 1 +𝑏 − 1

𝐾 − 1(𝐾𝑥− 1) , for 𝐾 = 1,

𝐵 (𝐸, 𝑥) = 1 + (𝑏 − 1) 𝑥, for 𝐾 = 1,(3)

where

𝐾 (𝐸, 𝑥) = 𝑐𝑥𝑎+ 𝑑

tanh (𝑥/𝑋𝑘− 2) − tanh (−2)

1 − tanh (−2),

for 𝑥 ⩽ 40mfp.(4)

3. Results and Discussion

The variation of exposure buildup factor with the incidentphoton energy in the range of 0.015 to 15.0MeV has beenshown in Figure 1 for BN at some of the penetration depths(1, 5, 10, 20, 30, and 40mfp). For the fixed penetration depthof 1mfp, at lower incident photon energy (0.015MeV), thevalue of energy absorption buildup factor is small, and itincreases with the increase in incident photon energy, reachesamaximumvalue in the intermediate energy region, and afterthat starts decreasing with the further increase in the incidentphoton energy.

In lower and higher energy regions photo-electric andpair productions are most dominant processes (in whichcomplete absorption of photon takes place), which result inminimum value of buildup factor. While in the interme-diate energy region, Compton scattering is the dominantphoton interaction process, which results only in the energydegradation of the photon and not the complete absorption.Hence the photons will pile up and give rise to peak. Similartrend has been observed at higher penetration depths of theceramic.

The dominant range of Compton scattering process canbe expressed in the range of 𝐸photo-Comp and 𝐸Comp-pair prodwhere 𝐸photo-Comp represents the energy for which bothphotoelectric absorption and Compton scattering showalmost equal value for mass attenuation coefficient. Whereas𝐸Comp-pair prod represents the energy for which both Comp-ton scattering and pair production processes show equaldominance. For boron nitride (least𝑍eq ceramic), the value of𝐸photo-Comp is about 23 keV (the corresponding value of massattenuation coefficient (𝜇

𝑚) at which energy is 0.160 cm2/g)

Journal of Ceramics 3

BN

Penetration depth1mfp5mfp10mfp

20 mfp30mfp40 mfp

Expo

sure

build

up fa

ctor

Incident photon energy (MeV)

100

101

102

103

104

105

100

101

10−1

10−2

Figure 1: Variation of exposure buildup factor with incident photonenergy for BN.

and the value of 𝐸Comp-pair prod is 28MeV (the correspondingvalue of mass attenuation coefficient (𝜇

𝑚) at which energy is

0.68×10−2 cm2/g). Whereas for ferrite (highest𝑍eq ceramic),

the value of 𝐸photo-Comp is about 100 keV (the correspondingvalue of mass attenuation coefficient (𝜇

𝑚) at which energy

is 0.14 cm2/g), and the value of 𝐸Comp-pair prod is 12MeV(the corresponding value of mass attenuation coefficient(𝜇𝑚) at which energy is 0.13 × 10−1 cm2/g). Since, the

exposure buildup factor is the result of multiple Comptonscattering processes, hence the study of buildup factor is ofutmost importance between the values of 𝐸photo-Comp and𝐸Comp-pair prod. Similarly, for other ceramics like magnesiumdiboride, silicon carbide, titanium carbide, and ferrite, thedominant range for Compton scattering process lies inbetween 15.0 keV and 15.0MeV.

Further, it has been also observed that the ceramics withlow 𝑍eq show large Compton scattering dominant range (asin case of BN), whereas for ceramics with comparatively high𝑍eq, Compton scattering dominance region is less (as in casesof ferrite and titanium carbide). Exposure buildup factor as afunction of penetration depth up to 40 mean free path forthe selected ceramics has been shown in Figure 2 for BN atsome of the selected incident photon energies (0.015, 0.10,0.50, 5.00, and 15.0MeV). It has been observed that at all theselected energies, exposure buildup factor increases with theincrease in penetration depth of BN. It may be due to thereason that as thickness of ceramic increases, the probabilityof multiple Compton scatterings also increases, and hence

the exposure buildup factor increases. Similar trend has beenobserved for other ceramics.

However, the increasing rate was found to be slow forlower andhigher incident photon energies, and rapid increasewas observed in case of intermediate energy region. Theslower increasing rate in the lower and higher energy regionswas due to the dominance of different photon absorptionprocesses in these energy regions (photoelectric effect inthe lower energy region and pair production in the higherenergy region) which results in the complete absorptionof gamma photons in the interacting medium, whereas inthe intermediate energy region the dominant process isthe Compton scattering, which results only in the energydegradation of photons. Hence, there is a finite possibility ofthe photon to reach the detector even for the large penetrationdepths of the ceramics, and hence maximum violation ofLambert-Beer equation has been observed.

Further, the increasing rate of exposure buildup factorwith the penetration depth is more rapid up to the certainincident photon energy (0.1MeV), where the Compton scat-tering process is most dominant process, and after this theincreasing rate of exposure buildup factor becomes slower forhigher energies.

All the selected ceramics have different chemical compo-sition and hence different equivalent atomic number (𝑍eq).So, to study the chemical composition dependence of differ-ent ceramics on exposure buildup factor, exposure buildupfactor for all the selected ceramics has been plotted against theincident photon energy at fixed penetration depths of 1, 5, 10,and 40mfp and has been shown in Figures 3, 4, 5, and 6. Fromthese figures, it has been observed that for all the selectedceramics, exposure buildup factor values are small at lowerincident photon energies as well as higher incident photonenergies and show maximum values in the intermediateenergy region. Itmay be due to the same reason of dominanceof different partial photon interaction processes in differentenergy regions. Among the selected ceramics, ferrite (highest𝑍eq) shows the minimum value for the exposure buildupfactor, whereas maximum values are observed for boronnitride (lowest 𝑍eq). It may be due to the reason that ferrite,which is a ceramic of oxygen (𝑍 = 8, weight fraction = 0.30)and iron (𝑍 = 26, weight fraction = 0.70), has the maximumequivalent atomic number due to the major contribution ofiron. Whereas boron nitride consists of boron (𝑍 = 5, weightfraction = 0.44) and nitrogen (𝑍 = 7, weight fraction = 0.56)and has the minimum equivalent atomic number. From thisobservation, it can be concluded that exposure buildup factoris inversely proportional to the equivalent atomic number ofthe ceramics at lower penetration depths (below 10mfp).

In Figure 5, for the fixed penetration depth of 10mfpof all the selected ceramics and for incident photon energyabove 3MeV, different ceramics show almost same valuesfor exposure buildup factor. It signifies that, above certainincident photon energy (about 3MeV), exposure buildupfactor becomes almost independent of the chemical com-position of the interacting material. Further, the selectedceramics mostly follow different crystal structures such asBN, SiC, and MgB

2follow hexagonal, TiC follows cubic,

and Fe2O3follows rhombohedral structure. Since different


Energy (MeV)0.0150.10.5

0 10 20 30 40

515

Expo

sure

build

up fa

ctor

Penetration depth (mfp)

BN

100

101

102

103

104

105

Figure 2: Variation of exposure buildup factor with penetrationdepth of BN.

1

7

6

5

4

3

2

Expo

sure

build

up fa

ctor

Incident photon energy (in MeV)

Penetration depth = 1mfpBNMgB2

SiC

TiCFe3O4

100

101

10−1

10−2

Figure 3: Variation of exposure buildup factor with incident photonenergy for all ceramics at 1mfp.

Expo

sure

build

up fa

ctor



SiC

TiCFe3O4

100

100

101

102

101

10−1

10−2


Expo

sure

build

up fa

ctor



SiC

TiCFe3O4

100

100

101

101

102

103

10−1

10−2


Journal of Ceramics 5Ex

posu

rebu

ildup

fact

or


BNMgB2

SiC

TiCFe3O4

Penetration depth = 40 mfp

100

100

101

101

102

103

105

104

10−1

10−2


ceramics follow different crystal structure, the same valuesfor exposure buildup factor above 3MeV photon energy andat the penetration depth of 10mfp suggest that exposurebuildup factor becomes independent of crystal structure.

However, in Figure 6, which shows the variation of expo-sure buildup factor for all the selected ceramics at the fixedpenetration depths of 40mfp, reversal in the trend of expo-sure buildup factor values has been observed above 3MeV.That is above the incident photon energy of 3MeV, exposurebuildup factor shows maximum values for ferrite (highest𝑍eq ceramic) and minimum values for boron nitride (lowest𝑍eq ceramic); that is, the exposure buildup factor becomesdirectly proportional to the equivalent atomic number of theceramic. It may be due to the reason that pair productioninitiates from 1.022MeV, and its dominance increases withthe increase in photon energy, and it results in the formationof an electron and a positron. For smaller penetration depths(below 10 mean free path) of the ceramics, these particlesescape either from the material or after multiple collisionwithin the ceramic comes to rest and further annihilates, thatis, creates two secondary gamma rays of 0.511MeV, whichescapes from the ceramic material. With the increase in pen-etration depth (above 10mfp), these secondary gamma rays(due to annihilation) contribute in increasing the intensity ofprimary gamma rays and try to compensate for the decreasein primary gamma rays due to pair production. With thefurther increase in the penetration depth, that is, for largerpenetration depths, the probability of creation of secondarygamma rays increases, and hence the contribution of these

secondary gamma rays towards exposure buildup factor alsoincreases.

4. Conclusions

From the present studies, the following conclusions can bedrawn.

(i) Exposure buildup factor increases with the increase inpenetration depth (40mfp).

(ii) Exposure buildup factor shows the following differenttrends with incident photon energy.

(a) For the entire energy region (0.015–15.0MeV),in case of small penetration depths (below10mfp), exposure buildup factor is inverselyproportional to the 𝑍eq.

(b) In the higher energy region (above 3MeV forthe selected ceramics), there exists a penetrationdepth (about 10mfp in the present case), forwhich exposure buildup factor becomes almostindependent of the 𝑍eq or the chemical compo-sition of the ceramics.

(c) In the higher energy region (above 3MeV),for large penetration depths (above 15mfp),exposure buildup factor becomes directly pro-portional to 𝑍eq.

Among the selected ceramics, ferrite (Fe3O4) offers better

gamma ray shielding.

References

[1] Y. Sakamoto, S. Tanaka, and Y. Harima, “Interpolation ofgamma ray build-up factors for point isotropic source withrespect to atomic number,”Nuclear Science and Engineering, vol.100, pp. 33–42, 1988.

[2] American National Standard Institute, “Gamma-ray attenua-tion coefficients and buildup factors for engineering materials,”Report ANSI/ANS 6.4.3, 1991.

[3] Y. Harima, Y. Sakamoto, S. Tanaka, and M. Kawai, “Validity ofthe geometrical progression formula in approximating gamma-ray buildup factors,” Nuclear Science and Engineering, vol. 94,pp. 24–35, 1986.

[4] A. Shimizu and H. Hirayama, “Calculation of gamma-raybuildup factors up to depths of 100mfp by the method ofinvariant embedding,” Nuclear Science and Technology, vol. 40,pp. 192–200, 2003.

[5] P. S. Singh, T. Singh, and P. Kaur, “Variation of energyabsorption buildup factors with incident photon energy andpenetration depth for some commonly used solvents,” Annalsof Nuclear Energy, vol. 35, pp. 1093–1097, 2008.

[6] T. Singh, N. Kumar, and P. S. Singh, “Chemical compositiondependence of exposure buildup factors for some polymers,”Annals of Nuclear Energy, vol. 36, no. 1, pp. 114–120, 2009.

[7] S. R. Manohara, S. M. Hanagodimatha, and L. Gerwardb,“Energy absorption buildup factors for thermoluminescentdosimetric materials and their tissue equivalence,” RadiationPhysics and Chemistry, vol. 79, no. 5, pp. 575–582, 2010.


[8] S. Singh, S.S. Ghumman, C. Singh, K. S. Thind, and G. S.Mudahar, “Buildup of gamma ray photons in flyash concretes:a study,” Annals of Nuclear Energy, vol. 37, pp. 681–684, 2010.

[9] M. Kurudirek, B. Dogan, M. Ingec, N. Ekinci, and Y. Ozdemir,“Gamma-ray energy absorption and exposure buildup factorstudies in some human tissues with endometriosis,” AppliedRadiation and Isotopes, vol. 69, pp. 381–388, 2011.

[10] H. C. Manjunatha and B. Rudraswamy, “Computation of expo-sure build-up factors in teeth,”Radiation Physics and Chemistry,vol. 80, no. 1, pp. 14–21, 2011.

[11] M. Kurudirek and S. Topcuoglu, “Investigation of human teethwith respect to the photon interaction, energy absorption andbuildup factor,” Nuclear Instruments and Methods in PhysicsResearch B, vol. 269, no. 10, pp. 1071–1081, 2011.

[12] M. Kurudirek and Y. Ozdemir, “A comprehensive study onenergy absorption and exposure buildup factors for someessential amino acids, fatty acids and carbohydrates in theenergy range 0.015–15MeV up to 40 mean free path,” NuclearInstruments and Methods in Physics Research B, vol. 269, no. 1,pp. 7–19, 2011.

[13] M. Kurudirek, B. Dogan, Y. Ozdemir, A. CamargoMoreira, andC. R. Appoloni, “Analysis of some Earth, Moon and Mars sam-ples in terms of gamma ray energy absorption buildup factors:Penetration depth, weight fraction of constituent elements andphoton energy dependence ,” Radiation Physics and Chemistry,vol. 80, pp. 354–364, 2011.

[14] L. Gerward, N. Guilbert, K. Bjørn Jensen, and H. Levring,“X-ray absorption in matter. Reengineering XCOM,” RadiationPhysics and Chemistry, vol. 60, no. 1-2, pp. 23–24, 2001.

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