Research Article | Open Access
Vishwanath P. Singh, N. M. Badiger, "A Comprehensive Study on Gamma-Ray Exposure Build-Up Factors and Fast Neutron Removal Cross Sections of Fly-Ash Bricks", Journal of Ceramics, vol. 2013, Article ID 967264, 13 pages, 2013. https://doi.org/10.1155/2013/967264
A Comprehensive Study on Gamma-Ray Exposure Build-Up Factors and Fast Neutron Removal Cross Sections of Fly-Ash Bricks
Geometric progression (GP) method was utilized to investigate gamma-ray exposure build-up factors of fly-ash bricks for energies from 0.015 to 15 MeV up to 40 mfp penetration depth. The EBFs of the fly-ash bricks are dependent upon the photon energy, penetration depths, and the chemical compositions of the elements. Appreciable variations in exposure build-up factor (EBF) are noted for the fly-ash bricks. The EBFs were found to be small in low and high photon energy regions whereas very large in medium energy region. EBF of the bricks is inversely proportional to equivalent atomic number below 10 mfp for entire energy region of interest 0.015 to 15 MeV. The EBFs of fly-ash, brick of mud, and common brick were similar at 1.5 MeV photon energy. The EBF of the fly-ash bricks was found to be higher than that of the brick of mud, and common brick. The fast neutron removal cross sections of the fly-ash bricks, brick of mud, and common bricks were also calculated which were found to be in the same order. It is expected that this study should be very directly useful for shielding effectiveness of fly-ash brick materials and dose estimation.
Safety inside residential and nonresidential building against the radiation is evaluated by the shielding properties by the parameters such as mass attenuation coefficients, energy absorption coefficients, and half-value layer. Gamma-ray interacts with material by photoelectric absorption, compton scattering, and pair production, which depends upon photon energy and element compositions. The intensity of a gamma-ray beam through a medium follows the Lambert Beer law under three conditions namely, (i) monochromatic rays, (ii) thin absorbing material, and (iii) narrow beam geometry. In case, any of the above conditions is not being met, this law is no longer applicable. The law can be applicable by using a correction factor, called as “build-up factor.”
The concept of build-up factor was introduced in late 1950  by obtaining experimentally the build-up factor at 1.25 MeV gamma-ray energy for water up to 16 mfp. The importance of build-up factor in attenuation studies was further recognized for multienergy gamma-rays with poor geometry . Since 1950, due to the availability of reasonably accurate values of attenuation coefficients and cross section of the various mediums, a great progress has been made in the computation of build-up factor in different types of materials such as medical, dosimetric, shielding, and radiation protection.
The build-up factor is a dimensionless multiplication factor which corrects the response of uncollided photon beam. The build-up is defined as the ratio of total value of specified radiation quantity at any point to the contribution to that value from radiation reaching the point without having undergone a collision. There are two types of build-up factors which are the quantity of interest: (a) the absorbed or deposited energy in the interacting materials and detector response function is that of absorption in the interacting medium; (b) the exposure build-up factor in which quality of interest is the exposure and detector response function is that of absorption in air . The build-up factors have been computed by various codes such as PALLAS , ADJMON-I [6, 7], ASFIT , and EGS4 . These codes are using an accurate algorithmic for the Klein-Nishina cross section which eliminated other sources of errors.
The compilation for build-up factors by various codes was reported in ANSI/ANS-6.4.3-1991 by American Nuclear Society . The data in the report covers energy range from 0.015 to 15 MeV up to penetration depth of 40 mean free path (mfp). The build-up factors in the ANS-6.4.3 are for 23 elements of atomic number, to 92. The build-up factors of ANS-6.4.3 can be calculated by invariant embedding [11, 12]. Harima et al.  developed a fitting formula, called geometric progression (GP), which gave build-up factors of the good agreement with the ANS-6.4.3. The GP fitting is more accurate than three exponential fit in the water medium. The GP fitting formula is known to be accurate within the estimated uncertainty (<5%) and Harima  had extensive historical review and reported the current gamma photon build-up factors and applications . Various researchers have investigated gamma-ray build-up factors in different materials such as concretes [14–16], gaseous mixture , human tissues , soils and ceramic [19, 20] which showed that the GP fitting is a very useful method for estimation of exposure and energy absorption build-up factors. Recently the radiation shielding by fly-ash concretes  and building materials  has been reported.
The innovative bricks using the residual fly-ash are considered high-quality building materials by the manufacturers which will potentially decrease some of the negative environmental impact of coal-fired power generation while meeting increasing demands for greener building materials [22, 23]. Fly-ash brick (FAB), an environment-friendly cost-saving building product, is an alternative to burnt clay bricks. The FAB is approximately stronger than common bricks with consistent strength. The FABs are ideally suited for internal, external, load bearing, and nonload bearing walls. FABs are durable, economical, and eco-friendly and have low water absorption (8–12%), less mortar consumption, and low energy consumption with the lowest green house impact. These bricks are not affected by environmental conditions and remain static thus ensuring longer life of the building. These bricks are economical/cost-effective and nil wastage while transporting and handling. The houses and buildings in which people are living are constructed by the bricks made up of soil and environmental-friendly fly-ashes. The potential applications of fly-ash are shielding materials , glasses [25, 26], X-ray shielding , electromagnetic radiation in X-band and Ku-band shielding , and houses and building construction [22, 23].
In view of radiation safety inside the houses or buildings constructed by FAB, a theoretical gamma-ray exposure build-up factor (EBF) and fast neutron removal cross section have been calculated. We have calculated the EBF of eight types of FABs, brick of mud (BOM), and common brick (COB) by GP fitting in the photon energy range from 0.015 to 15 MeV up to 40 mfp. Comparative analysis shows that higher build-up factors exist for FABs and lower fast neutron removal cross sections. High EBF proves that FABs are poor gamma shielding for the construction of houses and buildings. The study reveals that brick of mud and common brick are low-cost safe building materials against radiation. It should be noted that this study is valuable in shielding analysis and estimation of emergency dose.
2. Computation Method
The elemental compositions of the fly-ash bricks are given in Table 1 . These fly-ash bricks samples are prepared by a formula (Lime)0.15 (Gypsum)0.05 (Fly Ash) (Soil), where the values of range from 0.4 to 0.7. Two other bricks of mud (BOM) and common brick (COM) are also analyzed for comparison of shielding properties for gamma-ray and neutron. The build-up calculation by GP fitting method and fast neutron removal cross section is explained below.
2.1. Exposure Build-Up Factor
The EBF of the bricks and the GP fitting parameters are calculated by method of interpolation from the equivalent atomic number, , of the bricks. The computational work of these parameters is done in three steps as follows:(1)calculation of equivalent atomic number (Table 2),(2)calculation of GP fitting parameters (Tables 3, 4, 5, 6, and 7),(3)calculation of build-up factors. is a parameter which describes the material properties in terms of equivalent elements similar to atomic number for a single element. Since interaction processes of gamma-ray photon with matter, photo-electric absorption, Compton scattering, and pair-production are energy dependent, therefore for each interaction varies according to the photon energy. However the build-up of photons in the medium is mainly due to multiple scattering events by Compton scattering, so that is derived from the Compton scattering interaction process.
The , for individual brick, is estimated by the ratio of , at a specific energy with the correspondance of an element at the same energy. Thus first the Compton partial mass attenuation coefficient, , and the total mass attenuation coefficients, , are obtained for elements to 40 for the selected bricks in the energy region from 0.0015 to 15 MeV using WinXCom [29, 30].
The interpolation of is employed by the following formula [31, 32]: where and are the atomic numbers of the elements corresponding to the ratios and , respectively. is the ratio, , at specific energy and the ratio for lies between two successive ratios of the elements.
The GP fitting parameters are calculated in a similar fashion of interpolation procedure for . The GP fitting parameters for the elements were taken from the ANS-6.4.3 standard reference database which provides the GP fitting parameters for twenty three elements ( to 92) in the energy region from 0.015 to 15 MeV up to 40 mfp penetration depth. The GP fitting parameters for the bricks were interpolated using a similar formula: where and are the values of the GP fitting parameters corresponding to the atomic numbers of and , respectively, at a given energy.
The third and final step is build-up factors estimation by GP fitting parameters (, , , , and ) in the photon energy range of 0.015–15 MeV up to a 40 mfp by the following equations : where is the source-detector distance for the medium in terms of mfp and the value of the exposure build-up factor at 1 mfp, is the dose multiplicative factor, and , , , , and are computed GP fitting parameters which depend on the attenuating medium and source energy.
2.2. Fast Neutron Removal Cross Section
An approximate method for calculation of the attenuation of fast neutrons by use of an effective removal cross section has been developed to allow for scattering or build-up. The effective removal crosssection for compounds and homogenous mixtures may be calculated from the value of or for various elements in the compounds by mixture rule. Difference in application of mixture for neutron interaction differs as weight fraction is replaced by partial density and mass attenuation coefficient by neutron removal cross section: The values obtained for effective neutron removal cross section by the above equations are accurate within 10% of the experimental values investigated for aluminium, beryllium, graphite, hydrogen, iron, lead, oxygen, boron carbide, and so forth . The values of elements of the bricks have been taken from Kaplan and Chilton et al. [34, 35].
The uncertainties in the build-up factor estimated by GP fitting are comparable with ANS-6.4.3 standard and MCNP-5  for air and water. Figure 1 shows that the EBFs in water by GP fitting, ANS-6.4.3 standard, and MCNP-5 at different photon energies are comparable. The MCNP-5 results vary from those ANS-6.4.3 standards with greatest 13.83% due to difference in cross section libraries, method of solution for codes, calculation methods, standard deviation, and physics assumptions for bremsstrahlung and coherent scattering . It is found that the invariant embedding, GP fitting, and MCNP simulation are in good agreement with 18 low- materials with small discrepancies . This quantitative and comparative approach shows that our results for gamma-ray EBF will be of small uncertainties for easy establishment of the data and analysis by GP fitting methodology.
4. Result and Discussion
The photon energy dependency of the EBFs is shown in Figure 2 at various penetration depths (0.5, 5, 10, 20, 30, and 40 mfp) for each FAB, BOM, and COB. Variation of EBF with penetration depths is shown in Figure 3 at photon energies 0.015, 0.15, 1.5, and 15 MeV. The chemical compositions of the selected materials are investigated at penetration depths of 0.5, 5, 10, 20, 30, and 40 mfp and shown in Figure 4. The fast neutron removal cross sections of the studies bricks are given in Tables 8(a) and 8(b). The variation of EBF with photon energy, penetration depth, and chemical compositions is explained in next coming sections.