Annals of Nuclear Energy 37 (2010) 681–684

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Annals of Nuclear Energy

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Buildup of gamma ray photons in flyash concretes: A study

Sukhpal Singh a,*, S.S. Ghumman b, Charanjeet Singh a, Kulwant Singh Thind c, Gurmel S. Mudahar a

a Department of Physics, Punjabi University, Patiala, Indiab Department of Physics, Sant Longowal Institute of Engineering and Technology (Deemed-tobe-University), Longowal, Sangrur, Indiac Surrey, BC, Canada V3R 6W1

a r t i c l e i n f o

Article history:Received 3 July 2009Received in revised form 26 January 2010Accepted 5 February 2010Available online 11 March 2010

0306-4549/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.anucene.2010.02.006

* Corresponding author.E-mail address: sukhpal_78@rediffmail.com (S. Sin

a b s t r a c t

The gamma ray buildup factors of flyash concretes have been calculated by using Geometrical Progres-sion formula in the energy region of 0.015–15 MeV as well as up to a penetration depth of 40 mean freepaths, and have been studied as a function of incident photon energy. From the obtained results it is seenthat for a fixed penetration depth the values of buildup factor are very large in the medium energy regionand are small in the low and high energy regions. The results have been shown graphically.

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1. Introduction

The gamma ray buildup factor is a multiplicative factor used toobtain the corrected response to the uncollided photons by includ-ing the contribution of scattered photons. It can be defined as theratio of the total detector response to that of uncollided photons.The interaction processes like photoelectric effect and pair produc-tion results the complete removal of a photon that interacts withmatter but process like Compton scattering produces secondaryphotons having equal or lower energies than the incident photons.Compton scattering is the most dominant process for medium en-ergy gamma rays that produce multiply scattered photons.

White (1950) introduced the concept of buildup factor; he ob-tained experimentally the buildup factor at 1.25 MeV gamma rayenergy for water up to 16 mfp. The importance of buildup factorin attenuation studies was further recognized by Fano (1953).Since 1950, due to the availability of reasonably accurate valuesof attenuation coefficients and cross section for various media, agreat progress has been made in the computation of buildup factordata in different materials.

Different workers (Taylor, 1954; Hubbell, 1956; Capo, 1958;Hubbell, 1963a,b; Trubey, 1966; Meisberger et al., 1968; Harimaand Nishiwaki, 1972; Metghalchi, 1979; Harima, 1983; Harimaet al., 1986) provided a number of empirical fitting formulae forthe computation of buildup factor.

Morris et al. (1975) computed the buildup factor in water, alu-minum and concrete up to penetration depth of 50 mean free pathsusing the moment method and considering incident photon energyfrom a point isotropic source. Eisenhaur and Simmons (1975) cal-culated the point isotropic buildup factors in concrete for energyrange 15 keV to 15 MeV up to a penetration depth of 40 mfp using

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gh).

the moments method. Chilton et al. (1980) calculated the buildupfactors in infinite samples of air, water and concrete in the energyrange of 0.015–15 MeV and up to penetration depth of 40 mfpusing the moments method. Sakamoto et al. (1988) used the meth-od of interpolation of gamma ray buildup factor for point isotropicsource for water air concrete and lead glass. Brar et al. (1994) com-puted the exposure Buildup factor using G–P fitting formula (Har-ima et al., 1986) for bakelite, perspex and magnox-A12 for theenergy range of 0.015–15 MeV. Sidhu et al. (1999) computed theexposure buildup factors for some biological materials in the en-ergy range of 0.015–15 MeV by using G–P fitting method. Singhet al. (2003) studied the buildup factor of flyash as a function ofincident photon energy. Asano and Sakamoto (2007) calculatedthe buildup factors for two types of heavy concretes (iron con-tained and barium-contained) using Monte Carlo simulation code,EGS4 up to penetration depth of 40 mfp and photon energy rangingfrom 0.015 to 15 MeV. Recently, Singh et al. (2008) studied exper-imentally the gamma ray buildup factors in the media of high vol-ume flyash concrete and water, using a point isotropic 137Cssource.

Generally, concrete has been used as radiation shielding mate-rial because of its low price and good shielding performance. Ce-ment is one of the most cost and energy intensive components ofconcrete. The manufacturing of cement creates huge amounts ofCO2 as a by-product that poses a serious threat to the environment.Flyash, is a non-combusted by-product of coal-fired power plants,can be substituted for large portions of Portland cement, signifi-cantly improving concrete’s environmental characteristics. Theuse of large amounts of flyash in various concrete applications isa becoming a more general practice in efforts towards using largequantities of flyash. Flyash is a finally divided mixture of silica, alu-mina, and iron oxides, forms a compound similar to Portland ce-ment when mixed with lime and water. When large amount(more than 35% of cement replacement) of flyash is used in

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10340

30

20

15

10

5

mfp

----

----

- B

uild

up F

acto

r --

----

--- >

---------- Energy (MeV) -------->

Fig. 1. Variation of exposure buildup factors for concrete containing 10% flyash by

682 S. Singh et al. / Annals of Nuclear Energy 37 (2010) 681–684

concrete, it is called high volume flyash concrete. High volumeflyash concrete has some definite advantage over normal Portlandcement concrete in terms of higher ultimate strength, more dura-ble, requires less water, uses a waste by-product and creates fewerglobal warming gases. Since, flyash concrete can provide a goodalternative to the ordinary concrete, therefore keeping its impor-tance in mind, in the present work, six different flyash concretesconsisting 10%, 20%, 30%, 40%, 50% and 60% flyash by weight, havebeen selected. The gamma ray exposure buildup factor for thesechosen flyash concretes has been calculated using Geometrical Pro-gression formula (Harima et al., 1986). This formula is well knownto reproduce the buildup factors in the wide energy range of vari-ous materials and thickness with good accuracy.

To compute the theoretical values of exposure buildup factor,the elemental composition of the chosen flyash concretes is re-quired. The chemical composition of the flyash used in the prepa-ration of the presently chosen flyash concretes was obtained fromthe office of Punjab Pollution Control Board, Patiala. The chemicalcomposition of normal Portland cement was taken from literature.The elemental composition of the selected flyash concretes is pre-sented in Table 1.

weight with incident photon energy.

2. Computational work

In the present investigations the exposure G–P fitting parame-ters and corresponding buildup factors have been computed forsix different chosen flyash concretes in the energy range 0.015–15.0 MeV and for a penetration depth up to 40 mfp. The G–P fittingparameters were obtained by the method of interpolation from theequivalent atomic number (Zeq). All computational work carriedout is given in the following steps:

(a) Calculations of equivalent atomic number.(b) Calculations of G–P fitting parameters.(c) Calculations of buildup factor.

Firstly, the values of Compton partial attenuation coefficient(lComp) and the total attenuation coefficients (ltotal) are obtainedin cm2/g for the elements from Z = 1 to 40 and for the chosen flyashconcretes in the energy range 0.015–15 MeV, using the winXCOMcomputer program (initially developed by Berger and Hubbell(1987) later Gerward et al. (2004) transformed the XCOM to Win-dow platform, the window version being called winXCOM). Fur-ther, the ratio lComp/ltotal was obtained for all the elements andselected flyash concretes. The value of Zeq for the flyash concreteswas calculated by matching the ratio lComp/ltotal of a particularflyash concrete at a selected energy with the corresponding ratioof an element at the same energy. For those cases where the ratiovalue lies between the ratio for known elements, the value wasinterpolated using the following formula:

Zeq ¼Z1ðlog R2 � log RÞ � Z2ðlog R� log R1Þ

log R2 � log R1

Table 1Elemental composition of flyash concretes by weight.

Elements 10FA concrete 20FA concrete 30FA concre

C 0.0028 0.0057 0.0085O 0.3811 0.3923 0.4035Al 0.2030 0.1970 0.1910Si 0.0473 0.0736 0.0999Mg 0.0040 0.0041 0.0041Ca 0.2527 0.2264 0.2001Fe 0.1089 0.1009 0.0928S 0.0000 0.0001 0.0001

Here Z1 and Z2 are the atomic numbers of elements correspondingto the ratios R1 and R2 respectively and R is the ratio for the chosenflyash concrete sample at a particular energy. R1 and R2 are the tworatios of the flyash concrete sample.

Further, the standard reference ANSI/ANS-6.4.3 (1991) providesthe various G–P fitting parameters used for the calculation of expo-sure buildup factors for various elements starting from berylliumto iron in the energy range of 0.015–15.0 MeV for the penetrationdepths up to 40 mfp. Knowing the Zeq of the chosen flyash concretesample, the exposure G–P fitting parameters for exposure buildupfactor of the chosen flyash concrete samples were computed by asimilar process of interpolation as in case of the Zeq calculation.

These parameters were then used to generate exposure buildupfactors for the present flyash concretes using the following G–P fit-ting formula given by Harima et al. (1986):

BðE; xÞ ¼ 1þ ðb� 1ÞðKx � 1ÞK � 1

for K – 1

BðE; xÞ ¼ 1þ ðb� 1Þx for K ¼ 1

KðE; xÞ ¼ cxa þ dtanhðx=Xk � 2Þ � tanhð�2Þ

1� tanhð�2Þ

where x is the source–detector distance of the medium in mean freepath (mfp), b is value of the buildup factor at one mfp, K(E, x) is dosemultiplication factor which represents change in the shape of thedose weighted spectrum with increasing penetration depth and isrepresented as hyperbolic tangent function of penetration depth

te 40FA concrete 50FA concrete 60FA concrete

0.0113 0.0142 0.01700.4146 0.4258 0.43690.1850 0.1790 0.17300.1262 0.1525 0.17880.0041 0.0042 0.00420.1738 0.1475 0.12120.0847 0.0767 0.06860.0001 0.0002 0.0002

S. Singh et al. / Annals of Nuclear Energy 37 (2010) 681–684 683

in mfp, c, a, xk, d is the G–P fitting parameters that depend on theattenuating medium and the source energy.

3. Results and discussion

Figs. 1–6 show the variation of exposure buildup factors withincident photon energy in the range of 0.015–15 MeV at fixed pen-etration depths of 5, 10, 15, 20, 30 and 40 mfp for different flyashconcretes under considerations.

From these figures, it is observed that for incident photonenergies less than Epe (the energy at which photoelectric interac-tion cross section equals the Compton interaction cross section),the buildup factor values are relatively lower as compared to thatof neighboring higher energies for all the chosen penetrationdepths. Table 2 gives the values of Epe for the present chosenflyash concrete samples. These values have been estimated bymatching the two interaction coefficients calculated with the helpof a computer program and winXCOM. The low value of buildup

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5

10

15

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30

40

mfp

----

----

- B

uild

up F

acto

r --

----

--- >

---------- Energy (MeV) -------->

Fig. 2. Variation of exposure buildup factors for concrete containing 20% flyash byweight with incident photon energy.

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5

10

15

20

30

40mfp

----

----

- B

uild

up F

acto

r --

----

--->

---------- Energy (MeV) -------->

Fig. 3. Variation of exposure buildup factors for concrete containing 30% flyash byweight with incident photon energy.

factor is due to predominance of photoelectric effect which re-sults in the fast removal of low energy photons thereby notallowing these photons to buildup in the medium. Further, thevalue of Epe record a decrease with the increase in the flyash con-tent in the concrete.

In the energy region Epe < E < Epp (Epp is the energy value atwhich the pair production interaction cross section matches theCompton interaction cross section) the Compton effect is mostdominant process in energy degradation of the incident photon.It is observed that in the energy range 0.08–10 MeV the buildupfactor values are very high for a given penetration depth owingto the dominance of the Compton effect, which only helps in thedegradation of photon energy and not for the removal of a photoncompletely. Further, within energies �0.1–0.9 MeV there exist abroad peak showing the maximum value of buildup factor due tovery high rate of multiple scattering. Because of the multiple scat-tering of photons, they exist for a longer time in a material thatleads to a higher value of buildup factor. This implies that the con-

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5

10

15

20

30

40mfp

---------- Energy (MeV) -------->

----

----

- B

uild

up F

acto

r --

----

--->

Fig. 4. Variation of exposure buildup factors for concrete containing 40% flyash byweight with incident photon energy.

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102

103

5

10

15

20

30

40mfp

----

----

- B

uild

up F

acto

r --

----

--->

---------- Energy (MeV) -------->

Fig. 5. Variation of exposure buildup factors for concrete containing 50% flyash byweight with incident photon energy.

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5

10

15

20

30

40

mfp

----

----

- B

uild

up F

acto

r --

----

--->

---------- Energy (MeV) -------->

Fig. 6. Variation of exposure buildup factors for concrete containing 60% flyash byweight with incident photon energy.

Table 2Values of Epe and Epp for different flyash concrete samples.

Concrete sample Epe (MeV) Epp (MeV)

10%FA concrete 0.071 14.720%FA concrete 0.069 14.930%FA concrete 0.068 15.040%FA concrete 0.066 15.450%FA concrete 0.064 15.660%FA concrete 0.062 16.0

684 S. Singh et al. / Annals of Nuclear Energy 37 (2010) 681–684

tribution of secondary gamma ray photons to energy spectrawould be maximum in this energy range for all the flyash concretesunder consideration.

The pair production phenomenon dominates over Compton ef-fect for energies greater than 10 MeV, which results in loweringthe value of buildup factor value at these energies for a given mate-rial due to absorption behaviour of this process.

These generated values of gamma ray buildup factor can beused to calculate the gamma ray dose in a variety of shielding con-figurations by using the following formula:

D ¼ S0Be�lx

K4pr2

where D is the dose rate (units of dose rate), S0 is point source ofgamma rays (photons s�1), B is buildup factor (dimension less), lis linear attenuation coefficient (units of reciprocal length), x isthickness of the absorber passed through in going from source toreceptor (units of length) K is conversion from gamma ray flux todose rate and r is the distance from source to receptor (units oflength).

4. Concluding remarks

The gamma ray buildup factors of flyash concretes were calcu-lated by using Geometrical Progression formula in the energyrange of 0.015–15 MeV, and up to a penetration depth of 40 meanfree paths. The results showed that for a fixed penetration depththe values of buildup factor are very large in the medium energyrange and are small in the low and high energy regions.

References

ANSI, 1991. American National Standard Gamma-Ray Attenuation Coefficient andBuildup Factors for Engineering Materials. ANSI/ANS-6.4.3.

Asano, Y., Sakamoto, Y., 2007. Gamma Ray Buildup Factors for Heavy Concretes.JAEAData/Code 2007-006.

Berger, M.J., Hubbell, J.H., 1987/1999. XCOM: Photon Cross-Sections Database, WebVersion 1.2, National Institute of Standards and Technology, Gaithersburg, MD20899, USA. <http://physics.nist.gov/xcom> (Originally published as NBSIR 87-3597 ‘‘XCOM: Photon Cross Sections on a Personal Computer’’).

Brar, G.S., Sandhu, A.K., Singh, M., Mudahar, G.S., 1994. Exposure buildup factors forbakelite, perspex and magnox-A12 up to 40 mfp using the interpolationmethod. Radiat. Phys. Chem. 44, 459–466.

Capo, M.A., 1958. Polynomial Approximation of Gamma Ray Buildup Factors for aPoint Isotropic Source. APEX-510, General Electric Company.

Chilton, A.B., Eisenhaur, C.M., Simmons, G.L., 1980. Photon point source buildupfactor for air, water and iron. Nucl. Sci. Eng. 73, 97–107.

Eisenhaur, C.M., Simmons, G.L., 1975. Point isotropic gamma ray buildup factors inconcrete. Nucl. Sci. Eng. 56, 263–270.

Fano, U., 1953. Gamma-ray attenuation. Part II – Analysis of penetration. Nucleonics11, 55–61.

Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2004. WinXCom – A program forcalculating X-ray attenuation coefficients. Radiat. Phys. Chem. 71, 653–654.

Harima, Y., Nishiwaki, Y., 1972. An approximation of gamma-ray buildup factors bytransmission dose buildup geometrical progression. Nucl. Eng. Des. 23, 209–227.

Harima, Y., 1983. An approximation of gamma ray buildup factors by modifiedgeometrical progression. Nucl. Sci. Eng. 83, 299–309.

Harima, Y., Sakamoto, Y., Tanaka, S., Kawai, M., 1986. Validity of the geometric-progression formula in approximating the gamma ray buildup factors. Nucl. Sci.Eng. 94, 24–35.

Hubbell, J.H., 1956. Dose Due to Distributed Gamma-Ray Sources, NBS Report, 4928.Hubbell, J.H., 1963a. A power series buildup factor formulation. Application to

rectangular and off-axis disk source problems. J. Res. Nat. Bur. Stand. C 67, 291–306.

Hubbell, J.H., 1963b. Dose fields from plane sources using point-source data.Nucleonics 21, 144–148.

Meisberger, L.L., Keller, R.J., Shalek, R.J., 1968. The effective attenuation in water ofthe gamma rays of gold198, iridium192, cesium137, radium226 and cobalt60.Radiology 90, 953–957.

Metghalchi, M., 1979. On the polynomial form of gamma-ray buildup factorfunctions. Nucl. Sci. Eng. 70, 207–209.

Morris, E.E., Chilton, A.B., Vetter, A.F., 1975. Tabulation and empirical representationof infinite medium gamma-ray buildup factors for mono-energetic pointisotropic sources in water, aluminum and concrete. Nucl. Sci. Eng. 56, 171–178.

Sakamoto, Y., Tanaka, S., Harima, Y., 1988. Interpolation of gamma ray buildupfactors for point isotropic source with respect to atomic number. Nucl. Sci. Eng.100, 33–42.

Sidhu, G.S., Singh, P.S., Mudahar, G.S., 1999. A study of energy and effective atomicnumber dependence of the exposure buildup factors in biological materials. J.Radiol. Prot. 20, 53–68.

Singh, K., Singh, C., Singh, J., Singh, P.S., Mudahar, G.S., 2003. Flyash: a radiationshielding material. Ind. J. Phys. 77A, 41–45.

Singh, S., Kumar, A., Singh, C., Thind, K.S., Mudahar, G.S., 2008. Effect of finite sampledimensions and total scatter acceptance angle on the gamma ray buildup factor.Ann. Nucl. Energy 35, 2414–2416.

Taylor, J.J., 1954. Application of Gamma Ray Buildup Data to Shield Design. WAPD-RM 217, Bettis Atomic Power Laboratory.

Trubey, D.K., 1966. A Survey of Empirical Functions Used to Fit Gamma-Ray BuildupFactors. ORNL-RSIC-10, Oak Ridge National Laboratory.

White, G.R., 1950. The penetration and diffusion of 60Co gamma-rays in water usingspherical geometry. Phys. Rev. 80, 154–156.