Research ArticleInvestigation of Gamma and Neutron Shielding Parameters forBorate Glasses Containing NiO and PbO
Vishwanath P. Singh1,2 and N. M. Badiger1
1 Department of Physics, Karnatak University, Dharwad 580003, India2Health Physics Section, Kaiga Atomic Power Station-3&4, NPCIL, Karwar 581400, India
Correspondence should be addressed to Vishwanath P. Singh; [email protected]
Received 18 January 2014; Accepted 5 March 2014; Published 23 April 2014
Academic Editor: Ali Hussain Reshak
Copyright ยฉ 2014 V. P. Singh and N. M. Badiger.This is an open access article distributed under theCreative CommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in anymedium, provided the originalwork is properly cited.
Themass attenuation coefficients, ๐/๐, half-value layer, HVL, tenth-value layer, TVL, effective atomic numbers,๐๐๐ผeff, and effective
electron densities,๐๐,eff, of borate glass sample systems of (100-๐ฅ-๐ฆ) Na
2B4O7:๐ฅPbO :๐ฆNiO (where ๐ฅ and ๐ฆ = 0, 2, 4, 6, 8, and 10
weight percentage) containing PbO andNiO, with potential gamma ray and neutron shielding applications, have been investigated.The gamma ray interaction parameters, ๐/๐, HVL, TVL, ๐
๐๐ผeff, and๐๐,eff, were computed for photon energy range 1 keVโ100GeV.The macroscopic fast neutron removal cross-sections (ฮฃ
๐ ) have also been calculated. Appreciable variations were noted for all
the interaction parameters by varying the photon energy and the chemical composition of the glass samples. The better shieldingproperties of borate glass samples containing PbOwere found.These results indicated that borate glass samples are a good radiationshielding material.
1. Introduction
Interaction of energetic radiations X/๐พ-ray and neutron withthe material is essential in radiation technologies, medical,nuclear engineering, agriculture, space technology, indus-tries, and other shielding applications. Transparent radiationshielding materials have been an interesting area in nuclearengineering to provide the adequate radiation protectionas well as visibility through it. Glasses are found to per-form the double functions of being transparent to visiblelight and absorbing the radiations, thus providing radiationshielding to the observer. The silicate glasses are found tobe the most commonly commercial glasses owning to easeof fabrication and excellent transparency to the visible light[1]. The transparent property of the glass makes it useful foroptical windows in nuclear reactors and isotope technologycenters. The optical windows play a crucial role in operationand maintenance of nuclear facilities for complete visualinspection without radiation exposure.
Lead and lead glasses are easily available for shieldingof the gamma rays and neutrons due to high densities andatomic numbers [2].The high atomic number (๐) offers large
gamma ray interaction cross-section for gamma rays anddensity plays vital role in neutron interaction. Nowadays,bismuth (Bi) and barium (Ba) are playing an analogous role inradiation shielding by replacing lead. The glasses containinglow ๐ elements (H, Li, B, C, etc.) are another group of theglasses required for neutron radiation shielding producedspecially in nuclear reactors and accelerators. It has beenfound that gamma photon in reactor is in range of 0.10 to10MeV and prompt neutron energy spectrum ranges from0.18 to 12MeV with average neutron energy 1 to 2MeVduring uranium fission [3]. Therefore boron containing glassmaterials are found to be a potential candidate for neutronradiation shielding.
The absorption of gamma ray is being represented by themass attenuation coefficients, atomic cross-sections, effectiveatomic numbers, and effective electron densities. The atten-uation coefficient is defined as the probability of radiationinteraction with a material per unit length [4]. The effectiveatomic number is a convenient parameter for evaluation ofgamma ray interaction for a compound or mixtures. Theother important parameter for interaction is an electrondensity which is defined as the electrons per unit mass
Hindawi Publishing CorporationPhysics Research InternationalVolume 2014, Article ID 954958, 7 pageshttp://dx.doi.org/10.1155/2014/954958
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Table 1: Borate glass samples containing PbO andNiO for shielding.
Glass sample Densities (g cmโ3) Weight percentageNa2B4O7 PbO NiO
S1 2.64 ยฑ 0.02 100 0 0S2 2.67 ยฑ 0.04 90 0 10S3 2.67 ยฑ 0.05 90 2 8S4 2.71 ยฑ 0.03 90 4 6S5 2.73 ยฑ 0.02 90 6 4S6 2.75 ยฑ 0.02 90 8 2S7 2.78 ยฑ 0.01 90 10 0
of the absorber. Mass attenuation coefficients of elements,compounds, and mixtures are taken from standard tables [5]developed as XCOM program at energies 1 keV to 100GeV.The XCOM program has been converted to user-friendlywindows platformWinXcom [6].
Various investigators have reported gamma ray interac-tion parameters of phosphate, lead, bismuth, silicate, and fly-ash glasses [2, 7โ11]. NiO is being used for making smokycolored glasses and for decolouring lead crystal glasses [12].The gamma ray attenuation coefficients of borate glasses arefound for 1173 and 1332 keV [13]. However detailed studyon gamma ray and neutron interaction for the coloredborate glasses containing NiO is not found in the literatures.This encouraged us to investigate the gamma and neutroninteraction parameters of borate glasses, potential shieldingmaterials.Therefore, we have calculated the mass attenuationcoefficients, ๐/๐, half-value layer, HVL, tenth-value layer,TVL, effective atomic numbers, ๐
๐๐ผeff, and effective electrondensities, ๐
๐,eff, of borate glass samples containing PbO andNiO given in Table 1. The study shall be useful for shieldingagainst gamma ray and neutron applications.
2. Theoretical Background andComputational Work
2.1. GammaRay Interaction Parameters. Thecompositions ofborate glass samples containing PbO and NiO are given inTable 1. The transmission of gamma ray is dependent uponthe material thickness, ๐ก, and linear attenuation coefficient,๐. The ๐ value is a parameter which is dependent uponthe absorber density, its atomic number, and energy ofincident photon. The linear attenuation coefficients of theborate glass samples are calculated by multiplication of massattenuation coefficients, ๐/๐, and density. The ๐/๐ values ofthe borate glasses are calculated by mixture rule ((๐/๐)glass =โ๐
๐๐ค๐(๐/๐)๐), where๐ค
๐is the proportion by weight and (๐/๐)
๐
is mass attenuation coefficient of the ๐th element by usingWinXcom [6].The quantity๐ค
๐is given by๐ค
๐= ๐๐๐ด๐/โ๐
๐๐๐๐ด๐
with condition โ๐๐๐ค๐= 1, where ๐ด
๐is the atomic weight of
the ๐th element and ๐๐is the number of formula units in the
compounds. The half-value layer, HVL (HVL = 0.6932/๐),and tenth-value layer, TVL (TVL = 2.303/๐), are inverselyproportional to ๐ values.
The effective atomic numbers (๐๐๐ผeff) for total photon
interaction are given by [14]
๐๐๐ผeff =
โ๐๐๐๐ด๐(๐/๐)
๐
โ๐๐๐(๐ด๐/๐๐) (๐/๐)
๐
, (1)
where ๐๐is molar fraction in the mixture, ๐ is linear
attenuation coefficient, ๐ is density, ๐/๐ is mass attenuationcoefficient, ๐ด is atomic weight, ๐ is atomic number, and theratio, ๐ด/๐, between the atomic mass and the atomic numberis approximately constant. The electron density is given by๐๐,eff = ๐๐ด๐/๐ด which is generalized as
๐๐,eff = ๐๐ด
๐๐๐๐ผeffโ๐๐๐๐ด๐
= ๐๐ด
๐๐๐ผeffโจ๐ดโฉ, (2)
where ๐๐is the number of atoms of the ๐th constituent
element, ๐ is the total number of atoms, and โจ๐ดโฉ is averageatomic mass of the glass samples.
2.2. Macroscopic Fast Neutron Removal Cross-Sections. Theeffective removal cross-section of compounds and homoge-nous mixtures is calculated using the value of ฮฃ
๐ (cmโ1)
or ฮฃ๐ /๐ (cm2/g) of the elements in the compounds by
mixture rule [4]. The detailed calculation procedure for ฮฃ๐
can be found various recent literatures for alloys [15], fly-ashbrick materials [16], bismuth borosilicate glasses [17], oxidedispersion strengthened steels [18] and building materials[19]. The ฮฃ
๐ /๐ values of elements have been taken from
Kaplan and Chilton [20, 21].
3. Results and Discussion
In the present investigation, themass attenuation coefficients,๐/๐, half-value layer, HVL, tenth-value layer, TVL, effectiveatomic numbers,๐
๐๐ผeff, and effective electron densities,๐๐,eff,of borate glasses containing PbO and NiO were calculated.The variation of ๐/๐, HVL, TVL, ๐
๐๐ผeff, and ๐๐,eff is shownin Figures 1โ5 respectively. The macroscopic fast neutronremoval cross section of the borate glasses is given in theTable 5.
3.1. Mass Attenuation Coefficients. The variation of massattenuation coefficients, ๐/๐, of the borate glass samples withphoton energy ranging from 1 keV to 100GeV is shown inFigure 1. From Figure 1 one can observe that the ๐/๐ valuesof the borate glass samples are very high in photoelectricabsorption region, reduce gradually, and become lowest inCompton scattering region. After it again starts increasingand becomes constant at around photon energy of 100MeVin pair production region, various peaks in ๐/๐ values areobserved for the glasses in photoelectric absorption regiondue to ๐พ-edge absorption (1.072, 8.333, and 8.8 keV), ๐ฟ-edgeabsorption (1.008, 1.586, 1.52, and 1.304 keV), and ๐-edgeabsorption (3.851, 3.554, 3.066, 2.586, and 2.484 keV). The๐พ,๐ฟ, and ๐ absorption energy values of the constituent ele-ments (Na, Ni, and Pb) are given in Table 2. The borate glasssample containing maximum PbO composition (S
7) shows
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Table 2: Photon energies (in keV) of absorption edges of ๐พ, ๐ฟ, and๐.
Element ๐
Energy (keV)
๐พ๐ฟ ๐
๐ฟ1
๐ฟ2
๐ฟ3
๐1
๐2
๐3
๐4
๐5
B 5 โ โ โ โ โ โ โ โ โO 8 โ โ โ โ โ โ โ โ โNa 11 1.072 โ โ โ โ โ โ โ โNi 28 8.333 1.008 โ โ โ โ โ โ โPb 82 8.800 1.586 1.520 1.304 3.851 3.554 3.066 2.586 2.484
Table 3: Effective atomic numbers (๐๐๐ผeff) of borate glasses at different energies (MeV) for total photon interaction.
Glass sample โจ๐โฉ ๐๐๐ผeff
lower๐๐๐ผeff
upper๐๐๐ผeff
10โ3 10โ2 10โ1 100 101 102 103 104 105
S1 7.47 7.54 9.03 7.69 9.02 7.60 7.54 7.66 7.92 7.95 7.94 7.94S2 8.00 7.75 14.31 8.38 14.04 8.20 7.75 7.99 8.49 8.54 8.53 8.53S3 8.00 7.84 21.46 8.47 15.25 12.48 7.86 8.24 9.08 9.15 9.14 9.14S4 8.02 7.95 27.76 8.56 16.52 16.30 7.96 8.49 9.66 9.75 9.74 9.73S5 8.04 8.03 33.30 8.65 17.84 19.71 8.07 8.74 10.23 10.35 10.33 10.32S6 8.06 8.12 38.22 8.74 19.22 22.79 8.18 8.99 10.79 10.93 10.91 10.90S7 8.08 8.22 42.86 8.85 20.81 25.76 8.29 9.25 11.39 11.55 11.52 11.52
Photon energy (MeV)10โ3 10โ2
10โ2
10โ1
10โ1
100
100
101
101
102
102
103
103
104
104
105
S1S2S3S4
S5S6S7
Mas
s atte
nuat
ion
coeffi
cien
t (cm
2/g
)
(100-x-y) Na2B4O7 : xPbO : yNiO (where x and y = 0, 2, 4, 6, 8, and 10)
Figure 1: Variation of mass attenuation coefficients of the borateglasses containing PbO and NiOwith photon energy for range 1 keVto 100GeV.
multiple peaks due to๐พ, ๐ฟ, and๐ absorption edges whereasborate glass sample without PbO and NiO (S
1) is found to
be with single peak due to Na element. These variationscan be explained by the partial photon interactions such asphotoelectric absorption for low-energy, Compton scatteringfor intermediate-energy, and pair production (nuclear andelectric) for high-energy regions.
0
2
4
6
8
10
12
14
16
18
HV
L (c
m)
OR
HSILBMIT
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
Figure 2: Variation of half-value layer of the borate glasses contain-ing PbO and NiO with photon energy for range 1 keV to 100GeV.
Initially at 1 keV energy, the values of ๐/๐ are very large(order of 103) which decrease sharply. At low-energy range(0.01MeV < ๐ธ < 0.1MeV), the maximum value of ๐/๐was found. The values of ๐/๐ of all the borate glass samplesbecome of order of 10โ1 as photon energy reaches 100 keV.Hence the ๐/๐ values decrease rapidly in low-energy region.This shows the dominance of photoelectric absorption in low-photon energy region. It can also be observed that there is
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Table 4: Effective electron densities (๐๐,eff) of borate glasses at different energies (MeV) for total photon interaction.
Glass sample โจ๐โฉ ๐๐,eff
lower๐๐,eff
upper๐๐,eff ร 10
23
10โ3 10โ2 10โ1 100 101 102 103 104 105
S1 2.92 3.05 3.65 3.11 3.65 3.07 3.05 3.10 3.20 3.21 3.21 3.21S2 3.04 3.04 5.61 3.28 5.50 3.21 3.04 3.13 3.33 3.35 3.34 3.34S3 3.00 3.04 8.32 3.28 5.91 4.84 3.05 3.20 3.52 3.55 3.54 3.54S4 2.97 3.04 10.60 3.28 6.32 6.24 3.05 3.25 3.70 3.73 3.73 3.72S5 2.94 3.03 12.58 3.27 6.74 7.45 3.05 3.30 3.86 3.91 3.90 3.90S6 2.91 3.03 14.25 3.26 7.16 8.50 3.05 3.35 4.02 4.07 4.07 4.06S7 2.88 3.02 15.78 3.25 7.65 9.48 3.05 3.40 4.19 4.25 4.24 4.24
Table 5: Macroscopic fast neutron removal cross-section of the borate glasses.
(a)
Ele. S1 S2 S3 S4PD ฮฃ
๐ (cmโ1) PD ฮฃ
๐ (cmโ1) PD ฮฃ
๐ (cmโ1) PD ฮฃ
๐ (cmโ1)
Na 6.03๐ธ โ 01 2.06๐ธ โ 02 5.86๐ธ โ 01 2.00๐ธ โ 02 5.77๐ธ โ 01 1.97๐ธ โ 02 5.77๐ธ โ 01 1.97๐ธ โ 02
B 5.67๐ธ โ 01 3.26๐ธ โ 02 5.51๐ธ โ 01 3.17๐ธ โ 02 5.43๐ธ โ 01 3.12๐ธ โ 02 5.42๐ธ โ 01 3.12๐ธ โ 02
O 1.47๐ธ + 00 6.02๐ธ โ 02 1.43๐ธ + 00 5.88๐ธ โ 02 1.42๐ธ + 00 5.84๐ธ โ 02 1.44๐ธ + 00 5.89๐ธ โ 02
Ni 0.00๐ธ + 00 0.00๐ธ + 00 9.81๐ธ โ 02 1.86๐ธ โ 03 7.73๐ธ โ 02 1.47๐ธ โ 03 5.79๐ธ โ 02 1.10๐ธ โ 03
Pb 0.00๐ธ + 00 0.00๐ธ + 00 0.00๐ธ + 00 0.00๐ธ + 00 4.89๐ธ โ 02 5.09๐ธ โ 04 9.77๐ธ โ 02 1.02๐ธ โ 03
2.64 0.1134 2.67 0.1124 2.67 0.1112 2.71 0.1118(b)
Ele. S5 S6 S7PD ฮฃ
๐ (cmโ1) PD ฮฃ
๐ (cmโ1) PD ฮฃ
๐ (cmโ1)
Na 5.72๐ธ โ 01 1.95๐ธ โ 02 5.68๐ธ โ 01 1.94๐ธ โ 02 5.73๐ธ โ 01 1.95๐ธ โ 02
B 5.38๐ธ โ 01 3.09๐ธ โ 02 5.34๐ธ โ 01 3.07๐ธ โ 02 5.39๐ธ โ 01 3.10๐ธ โ 02
O 1.44๐ธ + 00 5.89๐ธ โ 02 1.44๐ธ + 00 5.89๐ธ โ 02 1.43๐ธ + 00 5.84๐ธ โ 02
Ni 3.83๐ธ โ 02 7.28๐ธ โ 04 1.90๐ธ โ 02 3.61๐ธ โ 04 0.00๐ธ + 00 0.00๐ธ + 00
Pb 1.45๐ธ โ 01 1.51๐ธ โ 03 1.92๐ธ โ 01 2.00๐ธ โ 03 2.43๐ธ โ 01 2.53๐ธ โ 03
2.73 0.1116 2.75 0.1113 2.78 0.1115PD: partial density.
slight variation of ๐/๐ of all the selected borate glass samplesat particular photon energy. It is due to the reason thatphotoelectric absorption is dependent on photon energy andatomic number as ๐ of the elements and ๐4.5/๐ธ3.5. All theborate glass samples under investigation contain differentconstituent elements (
5B,8O,11Na,28Ni, and
82Pb) with
different weight fractions of elements. The slight differencesin the weight fraction of elements result in insignificantvariation of ๐/๐ values in photoelectric absorption region.
With increase in photon energy (above 100 keV), thereduction rate of the ๐/๐ is observed to be very slow (10โ1 to10โ2). It was observed that the variation is negligible between0.5 and 5MeV where Compton scattering dominates. Itis because the interaction cross-section is linearly depen-dent on ๐. With further increase in photon energy (above50MeV), it was found that the ๐/๐ values start increasingand become constant at around 100MeV. This is because thepair production process in nuclear field,๐/๐
(npp), and electronfield, ๐/๐
(epp), starts at threshold energies of 1.022MeV and2.044MeV and thereafter increases with increase in the
incident photon energy. In this high-energy region, a slightvariation at particular incident photon energy was againobserved due to their different chemical compositions. Itmay be due to the cross-sections for pair production processin nuclear field and for triplet production depending onatomic numbers ๐2 and ๐, respectively. It is to be notedthat although pair production processes initiate at photonenergy 1.022MeV, they require more incident photon energyto overcome Compton scattering.
3.2. HVL and TVL Values. The variation of half-value layer,HVL, and tenth-value layer, TVL, of the borate glass sampleswith photon energy ranging from 1 keV to 100GeV is shownin Figures 2 and 3. We have plotted HVL and TVL ofordinary (OR), hematite-serpentine (HS), ilmenite-limonite(IL), basalt-magnetite (BM), and ilmenite (IT) [22] alongwith borate glass samples for comparison.
3.3. Effective Atomic Numbers. The variation of effectiveatomic numbers, ๐
๐๐ผeff, for total photon interaction and
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0
10
20
30
40
50
60
TVL
(cm
)
OR
HSILBMIT
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
Figure 3: Variation of tenth-value layer of the borate glassescontaining PbO and NiO with photon energy for range 1 keV to100GeV.
noncoherent interaction of the borate glass samples forphoton energy ranging from 1 keV to 100GeV is shown inFigures 4(a) and 4(b). The average effective atomic numbers,โจ๐โฉ, lower and upper values of effective atomic numbers atenergies 10โ3, 10โ2, 10โ1, 100, 101, 102, 103, 104, and 105 are givenin Table 3. At low-energy range (0.01MeV < ๐ธ < 0.05MeV),the maximum value of ๐
๐๐ผeff was found. At intermediateenergies (0.05MeV< ๐ธ < 5MeV), where Compton scatteringis themain photon interaction process,๐
๐๐ผeff is approximatelyequal to the arithmeticmean of the atomic number calculatedfrom the chemical formula of the glass samples, โจ๐โฉ =(1/๐)โ
๐๐๐๐ง๐. At high energies, (๐ธ > 50MeV), ๐
๐๐ผeff is againconstant but smaller than in the low-energy region. It isobserved that there is a good agreement between ๐
๐๐ผeff at10MeV (Table 3) and the mean atomic number, โจ๐โฉ, derivedfrom the chemical composition of the glass samples, whereCompton scattering is the main photon interaction process.
3.4. Effective Electron Densities. The variation of effectiveelectron densities, ๐
๐,eff, for total interaction and noncoher-ent interaction of the borate glass sampleswith photon energyranging from 1 keV to 100GeV is shown in Figures 5(a) and5(b). The average effective electron density, โจ๐
๐โฉ, lower and
upper values of effective electron densities at specific energiesas 10โ3, 10โ2, 10โ1, 100, 101, 102, 103, 104, and 105 are given inTable 4. The variations of ๐
๐,eff with photon energy for totalinteraction processes (Figures 5(a) and 5(b)) were similar tothat of ๐
๐๐ผeff and can be explained in similar manner.
3.5. Macroscopic Fast Neutron Removal Cross-Section. Themacroscopic fast neutron removal cross-sections ฮฃ
๐ (cmโ1)
of the borate glass samples are given in Table 5. It was
5
10
15
20
25
30
35
40
45
50Total
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
Effec
tive a
tom
ic n
umbe
r (ZPI
eff)
(a)
5
10
15
20
25
30
35
40
45
50Noncoherent
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
Effec
tive a
tom
ic n
umbe
r (ZPI
eff)
(b)
Figure 4: Variation of effective atomic numbers of the borate glassescontaining PbO and NiO with photon energy for range 1 keV to100GeV.
observed that the ฮฃ๐ was highest (0.1134) for S
1whereas all
the remaining borate glasses range from 0.1112 to 0.1118.The highest value of ฮฃ
๐ for S1was observed due to zero
contribution of Pb and Ni elements. It can be concludedthat borate glass sample (S
1) is a superior neutron shielding
material. Moreover, the borate glass alonemay not be suitablefor gamma ray shielding; therefore borate glasses containingPbO and NiO are suitable glass shielding materials forgamma ray and neutron. Since oxide containing glasses
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Total
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
2.0
ร1024
2.0
2.0
1.0
1.0
1.0
0.8
0.6
0.4
0.2
Effec
tive e
lect
ron
dens
ities
(Ne,e
ff)
(a)
Noncoherent
Photon energy (MeV)10โ3 10โ2 10โ1 100 101 102 103 104 105
S1S2S3S4
S5S6S7
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Effec
tive e
lect
ron
dens
ity (N
e,eff
)
ร1024
(b)
Figure 5: Variation of effective electron densities of the borateglasses containing PbO and NiOwith photon energy for range 1 keVto 100GeV.
are having roughly constant ฮฃ๐ , borate glass containing
10% PbO (S7) would be preferable gamma ray as well
as neutron shielding. The ฮฃ๐ value of borate glass sam-
ple (S1) was found to be higher than ordinary concrete
whereas other borate glass samples (S2โ โ โ S7) were lower
than it.
4. Conclusions
In the present investigation, themass attenuation coefficients,๐/๐, half-value layer, HVL, tenth-value layer, TVL, effectiveatomic numbers,๐
๐๐ผeff, and effective electron densities,๐๐,eff,of borate glass samples containing PbO and NiO werecalculated for photon energy 1 keV to 100GeV. The macro-scopic fast neutron removal cross-sectionswere calculated forneutron energy 2โ12MeV.These parameters were found to bevarying with the photon energy and chemical compositionsof the glass samples.These results shall be useful for shieldingapplications against gamma ray and neutron.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
References
[1] W. S. Rothwell, Radiation Shielding Window Glasses, Bull. PE-50, Coming Glass Works, Coming, New York, NY, USA, 1958.
[2] K. J. Singh, N. Singh, R. S. Kaundal, and K. Singh, โGamma-ray shielding and structural properties of PbO-SiO2 glasses,โNuclear Instruments andMethods in Physics Research B, vol. 266,no. 6, pp. 944โ948, 2008.
[3] G. Samuel and S. Alexander,Nuclear Reactor Engineering, vol. 1,4th edition, 2004.
[4] J. Wood, Computational Methods in Reactor Shielding, Perga-mon Press, New York, NK, USA, 1982.
[5] M. J. Berger, J. H. Hubbell, S. M. Seltzer et al., โXCOM: photoncross sections database,โ NIST Standard Reference Database(XGAM) NBSIR 87-3597, 2010, http://www.nist.gov/pml/data/xcom/index.cfm.
[6] L. Gerward, N. Guilbert, K. B. Jensen, and H. Levring,โWinXComโa program for calculating X-ray attenuation coef-ficients,โ Radiation Physics and Chemistry, vol. 71, no. 3-4, pp.653โ654, 2004.
[7] J. Kaewkhao and P. Limsuwan, โMass attenuation coefficientsand effective atomic numbers in phosphate glass containingBi2O3, PbO and BaO at 662 keV,โ Nuclear Instruments andMethods in Physics Research A, vol. 619, no. 1โ3, pp. 295โ297,2010.
[8] K. Kirdsiri, J. Kaewkhao, A. Pokaipisit, W. Chewpraditkul, andP. Limsuwan, โGamma-rays shielding properties of xPbO:(100โ x)B2O3glasses system at 662 keV,โ Annals of Nuclear Energy,
vol. 36, no. 9, pp. 1360โ1365, 2009.[9] K. Kirdsiri, J. Kaewkhao, N. Chanthima, and P. Limsuwan,
โComparative study of silicate glasses containing Bi2O3, PbO
and BaO: Radiation shielding and optical properties,โ Annals ofNuclear Energy, vol. 38, no. 6, pp. 1438โ1441, 2011.
[10] S. Singh, A. Kumar, D. Singh, K. S. Thind, and G. S. Mudahar,โBarium-borate-flyash glasses: As radiation shielding materi-als,โNuclear Instruments andMethods in Physics Research B, vol.266, no. 1, pp. 140โ146, 2008.
[11] N. Chanthima, J. Kaewkhao, and P. Limsuwan, โStudy ofphoton interactions and shielding properties of silicate glassescontaining Bi2O3, BaO and PbO in the energy region of 1 keVto 100GeV,โ Annals of Nuclear Energy, vol. 41, pp. 119โ124, 2012.
[12] W. Weyl, Coloured Glasses, Society of Glass Technology, Lon-don, UK, 1951.
Physics Research International 7
[13] A. I. Fawazi, A. A. El-Sayes, A. A. El-Latif, and M. El-Desoky, โBorate glass with lead and Nickel oxides for radiationattenuation,โ Abhath Al-Yarmouk, vol. 15, no. 2, pp. 195โ205,2006.
[14] S. R. Manohara, S. M. Hanagodimath, K. S. Thind, and L.Gerward, โOn the effective atomic number and electrondensity:a comprehensive set of formulas for all types of materials andenergies above 1 keV,โ Nuclear Instruments and Methods inPhysics Research B, vol. 266, no. 18, pp. 3906โ3912, 2008.
[15] V. P. Singh and N. M. Badiger, โGamma ray and neutronshielding properties of some soils samples: buildup factors andattenuation coefficients,โ Indian Journal of Pure and AppliedPhysics . In press.
[16] V. P. Singh and N. M. Badiger, โThe Study on gamma-ray andneutron shielding factors of fly-ash bricks materials,โ JournalRadiological Protection, vol. 34, pp. 89โ101, 2014.
[17] V. P. Singh, N. M. Badiger, N. Chanthima, and J. Kaewkhao,โEvaluation of gamma-ray exposure buildup factors and neu-tron shielding for bismuth borosilicate glasses,,โ RadiationPhysics and Chemistry, vol. 98, pp. 14โ21, 2014.
[18] V. P. Singh, N. M. Badiger, and M. E. Medhat, โAssessment ofexposure build-up factors of some oxide dispersion strength-ened steels applied inmodern nuclear engineering and designs,โNuclear Engineering and Design, vol. 270, pp. 90โ100, 2014.
[19] V. P. Singh, N. M. Badiger, and A. M. El-Khayatt, โStudyon gamma-ray exposure buildup factors of and fast neutronshielding of some building materials,โ Radiation Effects andDefects in Solids. In press.
[20] M. F. Kaplan, Concrete Radiation Shielding, Longman Scientificand Technology, England, UK, 1989.
[21] A. B. Chilten, J. K. Shultis, and R. E. Faw, Principle of RadiationShielding, Prentice-Hall, Englewood, Ill, USA, 1984.
[22] I. I. Bashter, โCalculation of radiation attenuation coefficientsfor shielding concretes,โ Annals of Nuclear Energy, vol. 24, no.17, pp. 1389โ1401, 1997.
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