Investigation of shielding properties of some boron compounds

Annals of Nuclear Energy 55 (2013) 341–350

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Investigation of shielding properties of some boron compounds a,⇑ _ Orhan Içelli , Kulwinder Singh Mann b,⇑, Zeynel Yalçın a, Salim Orak c, Vatan Karakaya d _ Department of Physics, Faculty of Arts and Sciences, Yıldız Technical University, Istanbul, Turkey Department of Physics, D.A.V. College, Dyanad Nagar, Bathinda (Pb) 151 001, India c _ Department of Mathematics, Faculty of Arts and Sciences, Istanbul Commerce University, Üsküdar, Istanbul, Turkey d _ Department of Mathematical Engineering, Yıldız Technical University, Istanbul, Turkey a

b

a r t i c l e

i n f o

Article history: Received 15 October 2012 Received in revised form 24 December 2012 Accepted 31 December 2012

Keywords: Buildup factors Effective atomic number Boron compounds Building-materials Rayleigh/Compton ratios

a b s t r a c t Gamma and X-ray photon interaction parameters such as the equivalent atomic number (Zeq), effective atomic number Zeff, and exposure and energy absorption buildup factor have been computed for some boron compounds in the energy range of 15–100 keV. We have used WinXCom and ZXCom software to calculate the effective atomic number from Rayleigh/Compton (R/C) ratios. Finally, the selected boron compounds have been analyzed for application as radiation shielding materials. It is concluded that boric acid (M6) and concentrated colemanite (M1) have better shielding capability among the selected samples. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The gamma-ray buildup factor is a multiplicative factor used to obtain the corrected response to the uncollided photons by including the contribution of scattered photons. Buildup factor is an important parameter in distribution of photon flux in every object (Chilton et al., 1984). Experiments are planned to get aiming at achieving gamma-ray buildup factors which are generally not easy to obtain. Therefore, studies of gamma-ray buildup factors have been carried out using some calculations. Buildup factor for gamma and X-ray is an important concept that must be considered in radiation shielding and dosimeter. Buildup factor is defined as the ratio of the total detector response to that of uncollided photons. Buildup factor data is the basic requirement for point kernel calculations commonly used in shield design. Buildup factor has been classified into two categories named as energy absorption buildup factor (EABF) and exposure buildup factor (EBF). The EABF is the buildup factor in which the quantity of interest is the absorbed or deposited energy in the interacting material or the detector response function is that of absorption in the interacting material. Whereas for the EBF the quantity of interest is the exposure and the detector response function is that of the absorption in air; that is, exposure is assumed to be equivalent to the absorbed ⇑ Corresponding authors. Tel.: +90 212 383 4247; fax: +90 212 383 4106 (O. _ Içelli). _ E-mail addresses: [email protected] (O. Içelli), [email protected] (K.S. Mann). 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2012.12.024

dose in air as measured by the non-perturbing detector. In the past, many authors have reported data on photon buildup factors (Shultis and Faw, 2000; Asano and Sakamoto, 2007; Singh et al., 2008a,b; Küçük, 2010; Mann et al., 2012a,b). For instance, Asano and Sakamoto (2007) calculated the buildup factors for two types of heavy concretes (iron contained and barium-contained) using Monte Carlo simulation code, EGS4 up to penetration depth of 40 mfp and photon energy ranging from 0.015 to 15 MeV. Recently, Singh et al. (2008a) studied experimentally the gamma ray buildup factors in the medium of high volume fly ash concrete and water, using a point isotropic 137Cs source. Boron and its compounds such as concentrate colemanite, probertite, ulexite, TSW, tincal, boric acid, and Pellet waste has been used for fields related with radiation shielding. Concentrate colemanite, ulexite and tincal which can be used as shielding material for thermal and fast neutrons are raw borates. Probertite (NaCaB5O95H2O) and ulexite (NaCaB5O98H2O) possess identical chemical formula except for their water content. Probertite has the same B2O3, Na2O and CaO content with ulexite. But the water content of probertite is less than ulexite. These boron ores are commonly used as control bars for of nuclear reactors and almost in all branches of industry in different ways. The trommel sieve waste (TSW) which forms during the boron ore production is considered to be a promising building material with its use as an admixture with Portland cement and considered to be an alternative radiation shielding material, also. Thus, to be having knowledge on the chemical composition and radiation interaction properties of TSW are important in terms of compared to other building

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materials (Kurudirek et al., 2010). We are willing to determine the importance of boron compounds with respect to radiation shielding. Various researchers have indicated that there exists a direct relationship between (Zeff) and EBF–EABF. For example, Mann et al. have observed that for the samples with lower effective atomic numbers (Zeff) the values of EBF are larger, on the other hand for the samples with higher effective atomic numbers the values of EBF are comparatively small (Mann et al., 2012a). Kurudirek et al. have observed that EABF is higher than EBF due to the fact that the materials have higher (Zeff) values than that of air. Thus, when the (Zeff) increases the energy absorption in the medium will be more than absorption in air (Kurudirek and Topcuoglu 2011). From Singh et al. it can be concluded that the degree of violation of the Lambert–Beer law (value of energy absorption buildup factor) is less for the higher effective atomic number of the interacting material. Also, the energy absorption buildup factor depends strongly on the nature (Zeff) of the material in the lower energy region, becomes almost independent in the intermediate energy region and shows a little dependence in the higher energy region (Singh et al., 2008b). The effective atomic number (Zeff) is a useful parameter for the interpretation of the attenuation of X-ray or gamma radiation by a complex medium and medical radiation dosimeter. The (Zeff) is related to the radiation interaction with matter and useful in some applications such as designing radiation shielding, computing absorbed dose and buildup factor (Manohara _ et al., 2008). Içelli et al. have calculated Rayleigh/Compton (R/C) ratio and (Zeff) of boron compounds such as tincal, ulexite, probertite, boric acid, concentrate colemanite and TSW by using of ZXCOM code which is inspired from WinXCom, XCOM, respectively (Gerward et al., 2001, 2004; Berger and Hubbell, 1987, 1999). The (R/ C) ratio is not novel, but its dependence on the operation of the (Zeff) and ZXCom program is novel. The (Zeff) calculations are not only energy dependent but also angle dependent. Also, this study has introduced a new perspective in respect of determination of the (Zeff) using (R/C) ratio in order to compute buildup factors of _ samples (Içelli et al., 2012). Some precautions must be taken by shielding the radiation sources. For this reason, it is important to determine the buildup factors to make corrections for effective exposure and energy deposition in different shielding materials. The EABF which is the quantity of interest is the absorbed or deposited energy in the interacting material. EABF and EBF values has been determine by using G–P fitting method for some boron compounds and TSW in the energy range 15–100 keV up to a penetration depth of 40 mfp. The values are of primary importance for radiation shielding design (Suteau and Chiron, 2005). The values are needed to product building materials which are made up from boron compounds and TSW for gamma radiation shielding (Mortazavi et al., 2010). Also, the knowledge of shielding effectiveness of the materials made up from boron compounds and TSW is a useful parameter. The buildup factors of these samples are not found in any compilation or tabulation. The first aim of this study is determination of composition of sample by fractional weight of the that makes up it. Secondly, from the elemental composition, buildup factors can be calculated in the selected energy region up to a penetration depth of 40 mfp. The weight fraction of these samples is present in Table 1.

2. Theory The American Nuclear Society Standard Committee working group has developed a set of gamma-ray point isotropic source buildup factors as a standard reference database for 23 elements in the range Z = 4–92 and three compounds or mixtures namely,

air, water and concrete at 25 standard energies in the energy range of 0.015–15.0 MeV with suitable interval up to the penetration depth of 40 mean free path for use in shielding calculations. For now, there are no new reference data for buildup factors. Meanwhile, it should be all right to use the 1991 standard, since the possible discrepancies are expected to be small for the low-Z materials. 2.1. Calculation of effective atomic number and equivalent atomic number The calculation method proposed here is developed from the concept that a given the (Zeff) can completely define a mixture for the Rayleigh to Compton scattering ratio measurement, such a measurement like a single atom characterized by its atomic number. We have demonstrated that this formula is applicable for any material for a given scattering angle or X-ray photon energy _ (Duvauchelle et al., 1999; Içelli et al., 2012). The (Zeff) can be experimentally measured through the intensity ratio of Rayleigh to Compton (R/C) scattered peaks which are corrected for the photo-peak efficiency of the detector and the absorption of photons in the target and air. Then this ratio can be plotted as a function of atomic number and constitutes a fit curve. From this fit curve, the respective (Zeff) of the composite materials are identified. _ The choices of the (E0) and (h) must be compromised (Içelli et al., 2012). We have comprised 180° scattering angle and in the energy range of 15–100 keV. Manohara et al., 2011 is reported that at low energies, the buildup factor is markedly decreased with increasing (Zeff). So, we have selected energy range of 15–100 keV. This selection is important in terms of determination of EABF and EBF for radiation shielding effectiveness in X-ray energy region. Also, Singh et al., 2008a have attained that the value of buildup factor increases with increasing total scatter acceptance angle. The equivalent atomic number (Zeq), is a parameter assigned to a compound or mixture by giving a heavy weight to Compton scattering, since the buildup factor is a consequence of multiple scattering for which the main contribution is due to Compton scattering. We have considered 180° scattering angle because of Compton scattering is maximum. As can be seen from the literature, the only study _ about (Zeff) that dependents upon scattering angle is made by Içelli et al., 2012. The equivalent atomic number (Zeq) of a particular material has been calculated by matching the ratio (l/q)Compton/(l/q)Total of that material at a specific energy with the corresponding ratios of elements at the same energy. For the interpolation of Zeq for which the ratio (l/q)Compton/(l/q)Total lies between two successive ratios of elements, the following formula (Mann et al., 2012a,b) has been employed:

Z eq ¼

Z 1 ðlogR2  logRÞ þ Z 2 ðlogR  logR1 Þ logR2  logR1

ð1Þ

where Z1 and Z2 are the atomic numbers of elements corresponding to the ratios R1 and R2 respectively, R is the ratio for the selected boron sample at a specific energy. 2.2. Buildup factor In order to calculate the buildup factors, we have developed a new perspective. In this viewpoint, the (Zeff) values are firstly _ determined by means of Eq. (7) of Içelli et al., 2012, the (Zeff) values have been interpolated for elements having the G–P fitting parameters. After comprising for low energy range and 180° scattering angle, the buildup factors have been determined. The largest contribution to buildup factor comes from Compton scattering having a maximum at 180° scattering angle. The calculation methods for

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343

Table 1 The weight fraction of samples. Chemical compound

Concentrated colemanite (M1)

Probertite (M2)

Ulexite (M3)

TSW (M4)

Tincal (M5)

Boric acid (M6)

Pellet waste (M7)

Na2O F MgO Al2O3 SiO2 SO3 Cl K2O Cr CaO TiO2 Cr2O3 MnO2 Fe2O3 As2O3 Rb SrO Mo Y2O3 Cs BaO B2O3

0.040 – 1.601 0.258 2.271 0.112

8.976 – 1.236 0.311 1.510 0.121 0.045 0.061 – 25.773 – – – 0.209

5.945 – 5.243 0.146 7.797 0.127

2.975 1.775 25.387 1.259 18.592 0.520 0.051 0.708 – 32.550 0.045 0.093 0.054 0.585 0.010 0.032 2.917 – 0.011 0.178 0.068 12.19

22.013 – 9.523 0.371 7.742 0.423 0.078 0.157 – 6.555 – – – 0.066 0.006 0.012 0.994 – – – – 52.06

– – 7.063 2.533 5.218 7.802 – – 7.073 1.587 – – – 9.270 – – – 3.254 – – – 56.200

7.802 1.556 23.00 1.351 20.37 0.430 0.041 1.111

0.034 – 49.233 0.030 – – 0.264 – – 2.197 – – – – 43.96

0.021 – 34.841 – – 0.028 0.071 0.012 – 1.549 – – – – 44.22

0.012 5.856 – – – – 55.89

27.17 0.053 0.032 0.624 0.016 0.040 3.359

0.152 12.88

Table 2 The G–P fitting parameters for concentrated colemanite (M1). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.020 1.040 1.119 1.255 1.427 1.607 1.912 2.183

0.375 0.381 0.388 0.417 0.482 0.565 0.738 0.853

0.235 0.205 0.215 0.204 0.179 0.144 0.083 0.053

11.996 21.649 13.963 14.598 14.571 14.586 14.789 13.423

0.152 0.292 0.115 0.113 0.100 0.081 0.049 0.043

1.020 1.040 1.119 1.265 1.462 1.700 2.437 3.046

0.406 0.351 0.387 0.405 0.474 0.567 0.623 0.801

0.202 0.233 0.216 0.213 0.181 0.140 0.136 0.073

11.616 21.950 13.887 14.739 14.670 15.269 13.232 13.515

0.105 0.325 0.117 0.124 0.101 0.077 0.086 0.060

buildup factor are presented the first time in this study. In this method, at first R/C-(Zeff) value pairs are completed, and secondly the interpolations of the G–P fitting parameters are obtained, and finally the buildup factors are derived. It is possible to determine EABF and EBF of alloys, compounds, mixtures and minerals with this method. Most striking aspect of this method is that buildup factor for admixtures can be obtained hereafter easily. Calculation stages are shown step by step: 2.2.1. Calculation of geometric progression (G–P) fitting parameters In order to calculate the G–P fitting parameters a similar interpolation procedure was adopted as in that of the equivalent atomic number. The G–P fitting parameters for various elements were taken from the tabulation (ANSI, 1991) standard reference database which provides the G–P fitting parameters for elements from beryllium to iron in the energy region 0.015–15 MeV up to 40 mfp. The G–P fitting buildup factor coefficients of the used materials were calculated by interpolation (cubic spline) as follows

C¼

C 1 ðlogZ 2  logZ eff Þ þ C 2 ðlogZ eff  logZ 1 Þ logZ 2  logZ 1

ð2Þ

Here C1 and C2 are the values of the coefficients (GP fitting parameters) corresponding to the atomic numbers of Z1 and Z2, respectively, at a given energy and (Zeff) is the effective atomic number of the given material. The G–P fitting method has been used by different researchers for studying different solvents, polymers, human teeth and tissue substitute materials respectively. Singh et al. (2008b, 2009) and

Kurudirek and Topcuoglu (2011) an attempt has also made to perform a comparative study on the basis of different properties of selected silicates (G–P fitting coefficients, EABF and EBF, so as to obtain the suitable material for purpose of shielding utilizing interaction of gamma radiations with selected samples. 2.2.2. Calculation of energy absorption buildup factors For using in the calculation of the EABF and EBF, G–P the EABF and EBF coefficients are also available from the tables (ANSI, 1991) for elements with atomic number of (Be) to (U), as well as water, air and concrete. A buildup factor function is given:

BðE; xÞ ¼ 1 þ ðb  1ÞðK x  1Þ=ðK  1Þ; BðE; xÞ ¼ 1 þ ðb  1Þx;

K–1

K ¼ 1:

Here x is the source-to-detector distance in the medium (in mfp); b is the value of buildup factor at 1 mfp. The parameter K represents the photon dose multiplication and the change in the shape of the spectrum and K is defined as: a

KðE; xÞ ¼ cx þ d

  tanh Xx  2  tanhð2Þ k

½1  tanhð2Þ

ð3Þ

Here E is the incident photon energy and a, b, c, d and Xk are fitting parameters. The values of these parameters depend on the nature of attenuating medium and incident photon energy (E). They are given in the form of tables in ANSI, 1991; at different values of E and penetration depths. So the EABF and EBF can be

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

344 Table 3 The G–P fitting parameters for probertite (M2). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.031 1.040 1.115 1.232 1.369 1.503 1.739 1.950

0.395 0.386 0.387 0.410 0.457 0.526 0.656 0.814

0.207 0.202 0.215 0.208 0.191 0.161 0.111 0.059

15.106 20.912 13.896 14.581 14.398 14.424 14.395 14.510

0.138 0.281 0.116 0.116 0.108 0.090 0.062 0.041

1.031 1.041 1.115 1.239 1.399 1.578 2.138 2.716

0.371 0.357 0.387 0.402 0.447 0.527 0.541 0.699

0.235 0.229 0.215 0.212 0.195 0.155 0.170 0.107

13.974 21.161 13.890 14.624 14.493 15.372 13.497 13.300

0.164 0.304 0.116 0.121 0.111 0.085 0.101 0.076

Table 4 The G–P fitting parameters for ulexite (M3). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.026 1.048 1.155 1.328 1.539 1.745 2.157 2.387

0.373 0.428 0.394 0.443 0.524 0.630 0.758 0.919

0.232 0.178 0.214 0.194 0.160 0.118 0.082 0.037

13.879 16.368 14.252 14.411 14.715 14.773 13.330 13.748

0.157 0.131 0.116 0.108 0.089 0.064 0.050 0.041

1.026 1.048 1.156 1.336 1.579 1.972 2.720 3.370

0.388 0.421 0.392 0.442 0.530 0.537 0.711 0.899

0.217 0.184 0.218 0.193 0.154 0.166 0.102 0.043

12.752 16.285 14.070 14.650 15.335 13.776 13.447 13.663

0.128 0.104 0.121 0.107 0.082 0.087 0.069 0.045

Table 5 The G–P fitting parameters for TSW (M4). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.022 1.040 1.121 1.238 1.387 1.535 1.793 1.984

0.354 0.391 0.389 0.412 0.464 0.538 0.682 0.820

0.257 0.199 0.215 0.207 0.187 0.156 0.102 0.058

11.983 20.106 14.016 14.586 14.450 14.474 14.518 14.352

0.174 0.269 0.115 0.115 0.106 0.087 0.058 0.041

1.022 1.041 1.121 1.246 1.417 1.615 2.231 2.764

0.413 0.363 0.388 0.403 0.455 0.540 0.567 0.714

0.192 0.225 0.216 0.213 0.191 0.151 0.159 0.102

11.254 20.298 13.885 14.656 14.546 15.341 13.414 13.331

0.083 0.280 0.117 0.122 0.108 0.082 0.096 0.074

Table 6 The G–P fitting parameters for tincal (M5). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.052 1.109 1.327 1.654 2.130 2.470 2.909 3.043

0.379 0.413 0.461 0.581 0.644 0.795 1.024 1.202

0.223 0.200 0.184 0.133 0.121 0.071 0.009 0.029

11.690 13.827 14.466 15.453 14.167 14.899 13.607 12.449

0.115 0.106 0.098 0.069 0.065 0.056 0.022 0.007

1.051 1.109 1.336 1.691 2.250 2.781 3.728 4.198

0.409 0.416 0.456 0.573 0.635 0.781 1.041 1.254

0.197 0.196 0.187 0.136 0.126 0.077 0.004 0.042

11.440 14.532 14.429 15.506 13.746 13.149 14.318 12.829

0.091 0.105 0.098 0.071 0.069 0.052 0.017 0.004

calculated easily for elements between (Be) and (U). The G–P fitting parameters for the selected samples have been listed in Tables 2–8, respectively.

attenuation coefficient is an energy dependent parameter; therefore the mean free path also varies depending on the incident photon energy.

2.2.3. Mean free path (mfp) The thickness/penetration depth of interacting material is measured in the units of mean free path, where one mean free path (mfp) represents the average traveled distance between two successive interactions of photons, which results in decreasing the intensity of incident photon beam by the factor of 1/e. It is equal to the reciprocal of linear attenuation coefficient. Since, the linear

3. Experimental procedure 3.1. Sample preparation Except for Pellet waste, procedure for the other samples is sim_ ilar with previous study (Içelli et al., 2012). The sludge part in the reactor which is produced during manufacture of borax from

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345

Table 7 The G–P fitting parameters for Boric Acid (M5). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.024 1.039 1.099 1.193 1.313 1.456 1.737 1.950

0.359 0.353 0.367 0.397 0.433 0.508 0.655 0.814

0.249 0.220 0.232 0.214 0.202 0.168 0.111 0.059

12.775 25.840 13.684 14.551 14.230 14.350 14.390 14.510

0.170 0.353 0.132 0.121 0.115 0.094 0.063 0.041

1.024 1.040 1.099 1.196 1.337 1.522 2.134 2.716

0.404 0.319 0.367 0.398 0.420 0.509 0.540 0.699

0.201 0.254 0.232 0.211 0.209 0.162 0.170 0.107

11.827 26.437 13.684 14.430 14.320 15.420 13.500 13.300

0.098 0.448 0.132 0.116 0.121 0.089 0.101 0.076

Table 8 The G–P fitting parameters for Pellet waste (M6). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

b

c

a

Xk

d

b

c

a

Xk

d

1.025 1.040 1.125 1.255 1.413 1.572 1.840 2.051

0.360 0.405 0.390 0.417 0.476 0.552 0.704 0.831

0.248 0.191 0.214 0.204 0.182 0.150 0.094 0.057

12.869 17.952 14.080 14.599 14.530 14.531 14.624 14.041

0.169 0.238 0.115 0.113 0.102 0.084 0.054 0.042

1.024 1.041 1.125 1.265 1.447 1.659 2.312 2.858

0.402 0.379 0.388 0.405 0.467 0.554 0.589 0.743

0.203 0.215 0.217 0.213 0.185 0.145 0.150 0.093

11.906 17.993 13.883 14.741 14.628 15.303 13.343 13.393

0.101 0.217 0.118 0.124 0.104 0.079 0.092 0.069

Table 9 Effective atomic numbers for samples (Zeff). Energy (keV)

Colemanite (M1)

Probertite (M2)

Ulexite (M3)

TSW (M4)

Tincal (M5)

Boric acid (M6)

Pellet waste (M7)

15 20 30 40 50 60 80 100

15.7612 15.5668 10.4602 11.7038 12.7250 14.0916 15.4682 15.8031

15.5590 16.0155 11.7563 12.0598 12.6212 13.6250 15.4824 16.5973

15.2741 15.2102 10.6716 11.5573 12.3495 13.5181 14.9610 15.4122

15.9276 16.5799 12.6567 12.9377 13.4605 14.3414 15.7170 16.4797

12.2354 9.3826 9.3424 9.8401 10.277 10.9412 12.0657 12.7131

15.6093 16.5482 11.8508 12.4447 13.6278 15.8048 16.9888 21.8836

15.6729 16.3340 12.5351 12.7503 13.2237 14.0582 15.4663 16.2726

Mean

13.9475

14.2146

13.6193

14.7626

9.6935

15.5948

14.5391

Table 10 Equivalent atomic numbers for samples (Zeq). Energy (keV)

Colemanite (M1)

Probertite (M2)

Ulexite (M3)

TSW (M4)

Tincal (M5)

Boric acid (M6)

Pellet waste (M7)

15 20 30 40 50 60 80 100

14.5281 15.5485 15.8552 16.0530 16.1994 16.3104 16.4586 16.5628

12.8087 15.4960 15.9881 16.3157 16.5498 16.7299 16.9907 17.1663

13.4529 14.3262 14.6151 14.8036 14.9390 15.0477 15.1928 15.2914

14.1067 15.4387 15.7524 16.2357 16.4141 16.5507 16.7477 16.8929

10.4769 11.3489 11.5967 11.7639 11.8902 11.9929 12.1272 12.2231

13.7683 15.8508 16.4604 16.8167 17.0792 17.2800 17.5660 17.7684

13.7410 15.2867 15.6273 16.0234 16.2063 16.3456 16.5425 16.6851

Mean

15.9395

16.0057

14.7086

16.0174

11.6775

16.5737

15.8072

tincalconite, called the Pellet waste (PW), is discharged to a waste canal. The same procedures have been performed for the other samples with XRD (X-ray Diffractometry) system pattern were gi_ ven in Içelli et al., 2012 for Pellet waste. 4. Results and discussion In this study, we have determined the values of the (Zeff) for some boron bearing waste materials by ZXCOM program in the energy ranging from 15 to 100 keV. By using this program, (Zeff) can

be calculated based on R/C ratio for elements, compounds, alloys and admixture. Then, for the materials we concerned, a, b, c, d and Xk parameters are obtained from interpolation. In this procedure, the (Zeff) is used as independent variable for E; 15, 20, 30, 40, 50, 60, 80, 100 keV and various x values. After then, we have calculated the EABF and EBF. The (Zeff) of these Boron compounds obtained from Rayleigh to Compton scattering ratio (R/C) has been calculated by using to ZXCom. After determining (Zeff), then EABF and EBF were computed. This calculation procedure is a novel approach to these factors.

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

346

1.2 1.18

−−−>

1.12

−−−

1.14

EBF

1.16

(b) 1.22

15 keV

1.2

M1 M2 M3 M4 M5 M6 M7

1.18 1.16

EABF −−−>

1.22

1.1

1.14

15 keV M1 M2 M3 M4 M5 M6 M7

1.12 1.1

−−−

(a)

1.08

1.08

1.06

1.06

1.04

1.04 1.02

1.02 0

20

40

0

--- Penetration depth (mfp) ---> 4 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 2.2 2

(d)

30 keV M1 M2 M3 M4 M5 M6 M7

3 2.8 2.6 2.4

−−− EABF −−−>

−−−

EBF

−−−>

(c)

20

40

--- Penetration depth (mfp) --->

1.8

2.2 2

30 keV M1 M2 M3 M4 M5 M6 M7

1.8 1.6

1.6 1.4

1.4

1.2

1.2

1

0

20

0

40

--- Penetration depth (mfp) --->

(f)

60 keV

M1 M2 M3 M4 M5 M6 M7

10

1

1

0

20

0

40

--- Penetration depth (mfp) --->

(g)

800

M1 M2 M3 M4 M5 M6 M7

700

EABF −−−>

600

200

−−−

−−−

EBF −−−>

40

(h) 100 keV

300

20

--- Penetration depth (mfp) --->

500

400

40

60 keV

−−− EABF −−−>

10

M1 M2 M3 M4 M5 M6 M7

−−−

EBF −−−>

(e)

20

--- Penetration depth (mfp) --->

500

100 keV M1 M2 M3 M4 M5 M6 M7

400 300 200

100 100 0

0 0

20

--- Penetration depth (mfp) --->

40

-100

0

20

40

--- Penetration depth (mfp) --->

Fig. 1. Variation of EBF and EABF with mean free path for all samples at selected energies; (a and b) 15 keV, (c and d) 30 keV, (e and f) 60 keV and (g and h) 100 keV.

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

(a)

(b)

4.0

−−−− EBF −−−−>

3.5

3.0

4.5

1mfp M1 M2 M3 M4 M5 M6 M7

4.0

−−−− EABF −−−−>

4.5

2.5

2.0

3.5 3.0

1mfp M1 M2 M3 M4 M5 M6 M7

2.5 2.0 1.5

1.5

1.0

1.0

20

30

40

50

60

70 80 90 100

20

−−− Energy (keV) −−−>

(d)

5mfp M1 M2 M3 M4 M5 M6 M7

10

1

40

50

60

70 80 90 100

60

70 80 90 100

60

70 80 90 100

60

70 80 90 100

5mfp

10

M1 M2 M3 M4 M5 M6 M7

1

20

30

40

50

60

70 80 90 100

20

−−− Energy (keV) −−−>

2

10

(f)

15mfp M1 M2 M3 M4 M5 M6 M7

10

1

0

10

M1 M2 M3 M4 M5 M6 M7

1

10

0

30

40

50

60

70 80 90 100

20

(h)

40mfp M1 M2 M3 M4 M5 M6 M7

40

50

40mfp 3

10

−−−− EABF −−−−>

2

30

−−− Energy (keV) −−−>

−−− Energy (keV) −−−>

10

50

10

20

3

40

15mfp 2

10

(g)

30

−−− Energy (keV) −−−>

−−−− EABF −−−−>

(e)

−−−− EBF −−−−>

30

−−− Energy (keV) −−−>

−−−− EABF −−−−>

−−−− EBF −−−−>

(c)

−−−− EBF −−−−>

347

10

2

10

1

10

0

10

M1 M2 M3 M4 M5 M6 M7

1

10

0

10

20

30

40

50

60

−−− Energy (keV)−−−>

70 80 90 100

20

30

40

50

−−− Energy (keV) −−−>

Fig. 2. Variation of EBF and EABF with incident photon energy for all samples at selected penetration depths; (a and b) 1 mfp, (c and d) 5 mfp, (e and f) 15 mfp and (g and h) 40 mfp.

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

348

compounds is displayed for range 5–40 mfp. In Fig. 2, values of EABF and EABF for all samples are combined. The concentrated colemanite (M1) has good shielding effectiveness but for higher energies the boric acid (M6) shows good shielding properties. From this point of view, the present study is expected to be helpful in radiation shielding based on calculations the EABF and EBF after determined the weight fractions of some boron compounds. Mann et al., 2012b have verified that value of EBF depends strongly on the chemical composition and attained inverse relationship between EBF and (Zeff). Explanation of, in the samples studied, least (Zeff) possesses the maximum value of EBF. We have verified that this state for boric acid (M6). The values of EABF and EBF have been listed for 5–40 mfp values in the range of 15–100 keV at Tables 11–17. It has been observed from Tables 11–17 that the values of EABF and EBF gradually increase with increasing of mean free path (mfp) and energy. This may be due to the reason that with the increase in penetration depth, the probability of multiple scattering goes on increases and creating more photons in the material thereby increasing the values of buildup factors. The dependence of values of buildup factors on the penetration depth and energy of incident gamma ray photon is useful to study the gamma ray shielding properties of materials. The present work has verified that from the selected samples, while boric acid have exhibited good shielding properties for higher energy, but concentrated colemanite shows well shielding

In this study, the (Zeff) for these given compounds related to R/C ratio demonstrated for only 180° angle of incidence value and in the range of 15–100 keV. The (Zeff), EABF and EBF values of samples such as boron compounds are needed to be determined precisely before their applications especially in industry, radioisotope monitoring, cross-section studies of absorption, scattering and attenuation of radiation, designs of radiation shielding, calculations of absorbed dose in radiotherapy and many other radioactive applications. Furthermore, it can be also utilized in the computation of absorbed dose in radiation therapy, etc. The EABF and EBF values are very useful in choosing a substitute composite material in place of an element for that energy depending on the requirement (Han and Demir, 2009). For the selected samples, (Zeff) and (Zeq) are present in Tables 9 and 10, respectively. Boron compounds thermalize and absorb neutrons effectively, so they are appropriate for shielding of neutrons and other radiations such as neutron-absorbent solutions. In Fig. 1, values of EABF and EABF for all samples are given. It is indicated that the shielding effectiveness is independent of penetration depth at low energy range (15–100 keV). As seen literature, Mann et al., 2012a,b have attained the dependence EBF and EABF on (Zeff) and (Zeq) in energy region 0.015–0.7 MeV. For all penetration depths boric acid (M6) and concentrated colemanite (M1) shows good and tincal (M5) shows poor shielding effectiveness according to other samples. In Fig. 2, energy dependence of EABF and EBF for present boron Table 11 Buildup factors for concentrated colemanite (M1). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.020 1.040 1.119 1.255 1.427 1.607 1.912 2.183

1.043 1.081 1.249 1.565 2.059 2.720 4.328 6.124

1.055 1.100 1.317 1.743 2.475 3.564 6.706 10.973

1.064 1.113 1.370 1.884 2.820 4.303 9.023 16.392

1.070 1.124 1.411 2.002 3.125 4.991 11.393 22.404

1.074 1.134 1.456 2.145 3.528 6.017 15.760 34.386

1.082 1.128 1.492 2.244 3.825 6.840 19.840 48.370

1.020 1.040 1.119 1.265 1.462 1.700 2.437 3.046

1.043 1.079 1.249 1.577 2.130 2.974 5.590 9.372

1.054 1.099 1.318 1.756 2.560 3.909 8.613 17.032

1.062 1.113 1.370 1.899 2.915 4.708 11.738 25.815

1.068 1.125 1.412 2.020 3.227 5.446 14.977 35.786

1.073 1.139 1.456 2.161 3.639 6.578 20.401 55.346

1.081 1.134 1.492 2.252 3.935 7.394 27.244 78.620

Table 12 Buildup factor for probertite (M2). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.031 1.040 1.115 1.232 1.369 1.503 1.739 1.950

1.064 1.082 1.241 1.507 1.881 2.343 3.402 4.847

1.082 1.101 1.308 1.663 2.206 2.941 4.856 8.014

1.095 1.114 1.358 1.786 2.475 3.454 6.203 11.231

1.104 1.125 1.398 1.888 2.707 3.918 7.515 14.575

1.114 1.134 1.440 2.010 3.001 4.566 9.689 20.823

1.117 1.127 1.475 2.092 3.222 5.080 11.649 26.713

1.031 1.041 1.115 1.239 1.399 1.578 2.138 2.716

1.063 1.080 1.241 1.517 1.935 2.530 4.208 7.104

1.081 1.100 1.308 1.674 2.270 3.179 5.966 11.727

1.095 1.115 1.358 1.798 2.547 3.719 7.699 16.663

1.106 1.127 1.398 1.901 2.785 4.207 9.427 21.898

1.113 1.140 1.440 2.022 3.083 4.923 12.140 30.881

1.119 1.134 1.475 2.102 3.298 5.408 15.302 41.537

Table 13 Buildup factor for ulexite (M3). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.026 1.048 1.155 1.328 1.539 1.745 2.157 2.387

1.054 1.104 1.330 1.760 2.430 3.323 5.412 7.584

1.070 1.131 1.426 2.020 3.055 4.624 8.939 14.734

1.082 1.149 1.501 2.230 3.587 5.792 12.666 23.342

1.091 1.163 1.561 2.407 4.070 6.913 16.670 33.468

1.098 1.177 1.632 2.624 4.757 8.743 24.460 55.101

1.102 1.178 1.684 2.782 5.274 10.280 34.167 79.924

1.026 1.048 1.156 1.336 1.579 1.972 2.720 3.370

1.054 1.103 1.331 1.777 2.538 3.697 7.204 12.007

1.069 1.131 1.428 2.041 3.193 5.092 11.959 23.730

1.080 1.150 1.504 2.252 3.738 6.424 17.054 37.851

1.088 1.166 1.565 2.432 4.231 7.751 22.550 54.507

1.094 1.187 1.632 2.659 4.963 9.975 32.613 90.040

1.102 1.196 1.685 2.816 5.474 12.486 44.743 131.937

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

349

Table 14 Buildup factor for TSW (M4). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.022 1.040 1.121 1.238 1.387 1.535 1.793 1.984

1.046 1.083 1.255 1.523 1.933 2.455 3.677 5.024

1.060 1.102 1.325 1.684 2.284 3.124 5.394 8.407

1.070 1.116 1.379 1.812 2.575 3.702 7.015 11.893

1.077 1.126 1.422 1.919 2.828 4.229 8.627 15.552

1.081 1.134 1.469 2.046 3.152 4.982 11.409 22.454

1.090 1.126 1.506 2.133 3.394 5.581 13.957 29.150

1.022 1.041 1.121 1.246 1.417 1.615 2.231 2.764

1.046 1.081 1.255 1.533 1.992 2.662 4.617 7.412

1.059 1.101 1.326 1.696 2.354 3.392 6.731 12.427

1.067 1.116 1.380 1.826 2.653 4.005 8.855 17.858

1.073 1.128 1.422 1.933 2.912 4.563 11.010 23.703

1.080 1.141 1.469 2.060 3.242 5.393 14.492 34.017

1.090 1.135 1.506 2.142 3.481 5.967 18.699 46.345

Table 15 Buildup factor for tincal (M5). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.052 1.109 1.327 1.654 2.130 2.470 2.909 3.043

1.108 1.237 1.780 2.878 4.666 6.896 11.305 14.685

1.137 1.305 2.058 3.780 7.003 11.959 24.342 37.466

1.159 1.356 2.282 4.546 9.327 17.480 41.031 71.137

1.173 1.396 2.473 5.256 11.764 23.628 61.715 117.273

1.188 1.441 2.721 6.381 16.352 35.833 112.464 249.086

1.212 1.477 2.907 7.213 21.475 47.349 178.726 442.737

1.051 1.109 1.336 1.691 2.250 2.781 3.728 4.198

1.109 1.237 1.794 2.960 5.009 8.043 15.959 23.478

1.139 1.305 2.074 3.882 7.545 14.054 35.007 62.049

1.159 1.355 2.299 4.660 10.066 20.628 59.203 118.646

1.173 1.396 2.492 5.378 12.675 27.832 89.101 195.784

1.188 1.443 2.743 6.505 17.399 41.965 163.661 422.721

1.212 1.475 2.935 7.323 22.900 60.132 258.441 749.592

Table 16 Buildup factor for Boric Acid (M6). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.024 1.039 1.099 1.193 1.313 1.456 1.737 1.950

1.050 1.076 1.202 1.413 1.718 2.182 3.392 4.847

1.065 1.093 1.258 1.534 1.967 2.684 4.837 8.014

1.076 1.106 1.301 1.629 2.170 3.108 6.173 11.231

1.084 1.116 1.335 1.707 2.341 3.486 7.475 14.575

1.089 1.130 1.368 1.796 2.548 3.997 9.628 20.823

1.096 1.131 1.397 1.856 2.706 4.401 11.567 26.713

1.024 1.040 1.099 1.196 1.337 1.522 2.134 2.716

1.050 1.075 1.202 1.418 1.758 2.341 4.193 7.104

1.064 1.092 1.258 1.540 2.012 2.880 5.938 11.727

1.073 1.105 1.301 1.635 2.219 3.322 7.657 16.663

1.080 1.116 1.335 1.712 2.394 3.717 9.371 21.898

1.086 1.132 1.368 1.802 2.600 4.285 12.056 30.881

1.096 1.132 1.397 1.865 2.751 4.659 15.182 41.537

Table 17 Buildup factor for Pellet waste (M7). Energy (MeV)

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

EBF

EABF

1

5

10

15

20

30

40

1

5

10

15

20

30

40

1.025 1.040 1.125 1.255 1.413 1.572 1.840 2.051

1.050 1.085 1.262 1.565 2.015 2.589 3.924 5.380

1.065 1.105 1.335 1.743 2.408 3.346 5.885 9.213

1.077 1.119 1.391 1.885 2.735 4.004 7.763 13.274

1.085 1.129 1.435 2.003 3.021 4.610 9.657 17.619

1.090 1.133 1.485 2.147 3.396 5.498 13.025 25.967

1.097 1.124 1.523 2.246 3.674 6.207 16.143 34.557

1.024 1.041 1.125 1.265 1.447 1.659 2.312 2.858

1.051 1.083 1.262 1.577 2.082 2.820 4.984 8.039

1.064 1.105 1.335 1.757 2.488 3.652 7.433 13.873

1.074 1.120 1.392 1.900 2.824 4.356 9.927 20.347

1.080 1.133 1.436 2.021 3.117 5.003 12.486 27.484

1.087 1.143 1.484 2.163 3.500 5.981 16.698 40.676

1.097 1.139 1.523 2.254 3.776 6.672 21.908 56.583

for lower energy. Also, this fact confirmed by Figs. 1 and 2. These materials can be used purely or as mixture in concrete for making effective shields against gamma rays. We suggested that the effectiveness of shielding against the ionizing radiations will be enhanced by using concrete with high percentage of boric acid and concentrated coleminate. As seen literature, Korkut et al., 2012 have reported that the increased concentrations of boron atoms can enhance the neutron shielding property of selected samples. As obtained result, we have reported boric acid (M6) as the most best shielding material and as seen Table 1 boric acid

have the most high compositions of B2O3. More interesting is the following, we have reported that TSW is too poor shielding and the most low compositions of B2O3. Gencel et al., 2010a,b Okuno 2005 and Okuno et al ., 2009 and 2009 have attained that affected by the increasing concentration of colemanite shielding properties of concrete. Akkurt et al., 2010, have verified for Zeolite. We have suggested boric acid (M6) in the terms of effect of increasing B2O3 composition on the radiation shielding of concrete because of EBF of boric acid (M6) is litter than concentrated colemanite (M1).

_ O. Içelli et al. / Annals of Nuclear Energy 55 (2013) 341–350

350

Throughout this work, in order to do optimizations, we use the following symbols for the both (EABF) and (EBF); for tincal (ATnk and BTnk ), ulexite (ATnk and BTnk ), etc. for present materials. For example, for the ulexite, we use symbol of elements for power of matrix.

Max : ðAUn1 : AUn7 Þ ¼ BUn1

This work was supported by the Yıldız Technical University under award Number 2011-01-01-KAP02. References

n¼1:8

MaxðBU11 : BU81 Þ ¼ C Un1 MaxðC U11 ; C Tn1 ; C n Þ ¼ 749:6 Min : ðAUn1 : AUn7 Þ ¼ BUn1 n¼1:8

Acknowledgment

ðn ¼ 1; . . . ; 8Þ

MinðBU11 : BU81 Þ ¼ C Un1 MinðC U11 ; C Tn1 ; C n Þ ¼ 41:5 ðn ¼ 1; . . . ; 8Þ

ð4Þ

According to results of optimization process, it is concluded that tincal provides bigger buildup factor than boric acid and concentrated colemanite. Thus boric acid and concentrated colemanite are more convenient for shielding shows. 5. Conclusion The (Zeff) and Rayleigh/Compton ratio for boron compounds have been calculated with ZXCom which programs in the FORTRAN language. It is most important that ZXCom may be participated to literature after XCOM, WinXCom, and NXCom (El-Khayatt, 2011). In order to calculate the buildup factors, we have developed a new perspective. This viewpoint is containing to determine the (Zeff). The (Zeff) values have been interpolated for elements by the G–P fitting parameters. It is possible to determine EABF and EBF of material such as alloys, compounds, mixtures and minerals with this method. The studies of EABF and EBF determined using ZXCom will continue unabated. The inverse relationship between EABF–EBF and the (Zeff)–(Zeq) is justified that material with maximum value of (Zeff)–(Zeq) possesses the minimum exposure buildup factor or vice versa. Among the selected materials, boric acid offers maximum value for these mean (Zeff)–(Zeq) as seen Tables 9 and 10. There is a non-linear correlation between EABF–EBF and the (Zeff)–(Zeq). For photon energies less than 100 keV, among the selected samples, tincal (with lower the h(Zeff)i–h(Zeq)i) provides bigger buildup factor and hence poor shielding from gamma radiation. But boric acid and (with bigger the h(Zeff)i–h(Zeq)i) provides lower buildup factor, thus it shows good shielding properties. As confirmed from optimization operation, from the present work it has been verified that from the selected samples, boric acid and concentrated colemanite have exhibited good shielding properties. Also, this fact confirmed by Figs. 1 and 2. These materials can be used as pure directly or as mixture in concrete for making shields against gamma rays. We suggested that the concrete with high percentage of boric acid and concentrated colemanite will be very efficient material for shielding against the ionizing radiations. In the lower energy region the EABF and EBF depends strongly on the nature of the material and chemical composition that contribute to formation of the (Zeff)–(Zeq). The EABF and EBF are important that for researchers working to develop new shielding materials for ionizing radiations in radiological laboratories, nuclear reactors and nuclear medicine fields. The present study is expected to be helpful to develop new shielding materials used in radiation dosimetry, diagnostics, and radiotherapy. At the same time the dependence the EABF and EBF on the penetration depth and energy of incident gamma ray photon is useful for further study the gamma ray shielding properties of the selected samples.

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