

ORIGINAL ARTICLE 

Year : 2018  Volume
: 41
 Issue : 3  Page : 123127 


A study of energy absorption buildup factors of some steels
L Seenappa^{1}, HC Manjunatha^{2}, N Sowmya^{2}, KN Sridhar^{3}
^{1} Department of Physics, Government College for Women, Kolar, Karnataka; Research and Development Centre, Bharathiar University, Coimbatore, Tamil Nadu, India ^{2} Department of Physics, Government College for Women, Kolar, Karnataka, India ^{3} Department of Physics, Government First Grade College, Kolar, Karnataka, India
Date of Submission  20Jun2018 
Date of Decision  23Aug2018 
Date of Acceptance  28Aug2018 
Date of Web Publication  19Nov2018 
Correspondence Address: Dr. H C Manjunatha Department of Physics, Government College for Women, Kolar  563 101, Karnataka India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_52_18
We have studied the energy absorption buildup factors of some steels (316 LN, 317 L, 317 LM, 317 LMN, 317 LN, XM14, XM17, XM18, and Nitronic 60) for wide energy range (0.015–15 MeV) up to the penetration depth of 40 mfp using geometric progression fitting method. Buildup factors increase with the increase in the penetration depth. It is found that the shielding parameters such as mass attenuation coefficient, effective atomic number, and buildup factor values are larger for steel type 316 LN than the other studied steels. Hence, the steel type 316 LN is a good shielding material among the studied steels. The present study is useful in the field of radiation shielding.
Keywords: Buildup factor, penetration depth, shielding parameter
How to cite this article: Seenappa L, Manjunatha H C, Sowmya N, Sridhar K N. A study of energy absorption buildup factors of some steels. Radiat Prot Environ 2018;41:1237 
How to cite this URL: Seenappa L, Manjunatha H C, Sowmya N, Sridhar K N. A study of energy absorption buildup factors of some steels. Radiat Prot Environ [serial online] 2018 [cited 2021 Apr 13];41:1237. Available from: https://www.rpe.org.in/text.asp?2018/41/3/123/245801 
Introduction   
When gamma and Xrays enter the medium, they degrade their energy through scattering with the medium, giving rise to secondary radiation which can be estimated by a factor which is called the “buildup factor.” The energy absorption buildup factor is also defined as the buildup factor in which the quantity of interest is the absorbed or deposited energy in the interacting material and the detector response function is that of absorption in the interacting medium. Manjunatha and Rudraswamy^{[1]} studied energy absorption and exposure buildup factors in hydroxyapatite, and these are helpful in dosimetry and diagnostics. The same group^{[2],[3]} computed the buildup factors and photon relative dose distribution in different regions of teeth, which is useful in dental science. Previous researchers^{[4]} also employed computed buildup factors for the estimation of specific absorbed fractions of energy in the biological samples. Previous researchers used exposure buildup factors for the calculations of secondary radiation dose such as bremsstrahlung.^{[5],[6]} Steel is used for shielding of gamma radiation.
Calculations of the energy absorbed in a medium include not only the contribution of uncollided photons from the source but also the contributions from the collided and secondary photons. In practice, this is done by multiplying the contribution of uncollided photons with the energy absorption buildup factor.^{[7],[8]} The energy absorption buildup factor is the ratio of the total energy absorbed due to uncollided, collided, and secondary photons to the energy absorbed due to only uncollided photons. The buildup factor is an important parameter in the distribution of photon flux in every object. In brnchytherapy, radioactive seeds are implanted into the patient's body to destroy the cancerous tumor.^{[9],[10]} Thus, it is important to consider the photon buildup factor in the calculation of radiation dose received by the cancer cells. The buildup factor data were computed by different codes such as PALLASPL,^{[11]} RADHEATV4,^{[12]} ADJMOM1,^{[13]} and ASFIT.^{[14]} Several authors have provided different buildup factor data for extensive utilization of design in radiation shields and other purposes.^{[7],[15],[16],[17],[18],[19]} ANSI/ANS 6.4.3 used the geometric progression (GP) fitting method^{[20]} and provided buildup factor data for 23 elements, water, air, and concrete at 25 standard energies in the energy range 0.015–15 MeV with suitable interval up to the penetration depth of 40 mfp. Previous studies^{[21]} compared the computed buildup factors using the GP fitting method with the PALLAS code. Good agreement was observed for penetration depth up to 40 mfp. Shimizu et al.^{[22]} compared the buildup factors obtained by three different methods (GP fitting, invariant embedding, and Monte Carlo method), and only small discrepancies were observed for lowZ elements up to 10 mfp. Singh et al.^{[23]} studied the variation of energy absorption buildup factors with incident photon energy and penetration depth for some solvents. Sidhu et al.^{[24]} computed the exposure buildup factors in biological samples and studied the variation of exposure buildup factors with incident photon energy and effective atomic number. In the present study, we have studied the energy absorption buildup factors of some steels (316 LN, 317 L, 317 LM, 317 LMN, 317 LN, XM14, XM17, XM18, and Nitronic 60) for wide energy range (0.015–15 MeV) up to the penetration depth of 40 mfp using GP fitting method.
Materials and Methods   
The equivalent atomic number of a composite material that will produce the same effect as that of the single element when it interacts with photons is referred as effective atomic number (Z_{eff}). The effective atomic number is a convenient parameter for representing Xray and gamma interactions. The number of electrons per unit mass is referred as effective electron density (N_{e}).
For the computation of Z_{eff}, the values of mass attenuation coefficients were computed from WinX Com computer program.^{[25]} Z_{eff} and N_{e} can be computed from the following equations:
Where n_{i} is the number of atoms of i^{th} element in a given molecule, (μ/ρ)_{st} is the mass attenuation coefficient of steels, N is the Avogadro's number, A_{i} is the atomic weight of element i. (μ/ρ)_{st} was estimated based on the chemical composition shown in [Table 1] and f_{i} is the fractional abundance.  Table 1: Chemical composition of different steels used in the present study
Click here to view 
During the interaction of gamma/Xray with the medium, it degrades their energy and produces secondary radiations through the different interaction processes. The quantity of secondary radiations produced in the medium and energy deposited/absorbed in the medium is studied by calculating buildup factors. In the present study, we have estimated energy absorption buildup factors (B_{en}) using GP fitting method.^{[26],[27],[28],[29],[30],[31],[32]} We have evaluated the GP fitting parameters (b, c, a, X_{k}, and d) for different stent alloys using the following expression which is based on the Lagrange's interpolation technique:
Where lower case z is the atomic number of the element of known GP fitting parameter P_{z} adjacent to the effective atomic number (Z_{eff}) of the given material whose GP fitting parameter P_{Zeff} is desired and upper case Z are atomic numbers of other elements of known GP fitting parameter adjacent to Z_{eff}. GP fitting parameters (b, c, a, X_{k}, and d) for element adjacent to Z_{eff} are provided by the standard data available in the literature.^{[33]} The computed GP fitting parameters (b, c, a, X_{k}, and d) were then used to compute the EABF in the energy range of 0.015–15 MeV up to a penetration depth of 40 mfp with the help of GP fitting formula, as given by the following equations:^{[26],[27],[28],[29],[30],[31],[32]}
Where X is the sourcedetector distance for the medium in mean free paths and b is the value of buildup factor at 1 mfp. K(E, X) is the dose multiplication factor, and b, c, a, X_{k}, and d are computed GP fitting parameters that depend on attenuating medium and source energy.
Results and Discussion   
The variation of mass attenuation coefficient as a function of energy is shown in [Figure 1]. The value of mass attenuation coefficient is large of low energies due to the dominance of photoelectric effect. The mass attenuation coefficient decreases progressively with the photon energy. We have calculated energy absorption buildup factors using GP fitting method. The calculated energy absorption buildup factors are graphically represented. The variation of energy absorption buildup factors with incident photon energy for steels is shown in [Figure 2]. From [Figure 1] and [Figure 2], it is observed that energy absorption increases up to the E_{pe} (0.1 MeV) and then decreases. Here, E_{pe} is the energy value at which the photoelectric interaction coefficients match with Compton interaction coefficients for a given value of effective atomic number (Z_{eff}). The variation of buildup factors with energy is due to the dominance of photoelectric absorption in the lower end and the dominance of pair production in the higher photon energy region. As the energy of incident photon increases, Compton scattering overtakes the photoelectric absorption. It results in multiple Compton scattering events, which increases the energy absorption buildup factor up to the E_{pe}, and it becomes maximum at E_{pe}. Thereafter (above E_{pe}), pair production starts dominating (absorption process) which reduces the energy absorption buildup factor to a minimum value. The variation of energy absorption buildup factors with the penetration depth at 0.1 MeV, 0.2 MeV, 0.5 MeV, 5 MeV, and 15 MeV is shown in [Figure 3]. The buildup factor increases with the penetration depth.  Figure 1: Variation of mass attenuation coefficient with energy for different types of steels
Click here to view 
 Figure 2: Variation of energy absorption buildup factor with photon energy for different types of steels
Click here to view 
 Figure 3: Variation of energy absorption buildup factor with free mean path for different types of steels
Click here to view 
We have compared the calculated mass attenuation coefficient among the studied different types of the steels; it is found that mass attenuation coefficient for steel type 316 LN is higher than that of other studied steels. If mass attenuation coefficient is large, penetration properties such as halfvalue layer, tenthvalue layer, and mean free path are small. We have also compared the calculated effective atomic number among the studied different types of the steels; it is found that the effective atomic number for steel type 316 LN is higher than that of other studied steels. The comparison of calculated energy absorption buildup factors among the studied different types of steels shows that build factors for steel type 316 LN is higher than that of other studied steels. This means Xray and gamma undergo more scattering and absorption in steel type 316 LN. Hence, the steel type 316 LN is a good shielding material for Xray and gamma among the studied steels.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Manjunatha HC, Rudraswamy B. Energy absorption and exposure buildup factors in hydroxyapatite. Radiat Meas 2012;47:364. 
2.  Manjunatha HC, Rudraswamy B. Computation of exposure buildup factors in teeth. Radiat Phy Chem 2011;80:14. 
3.  Manjunatha HC, Rudraswamy B. Energy absorption buildup factors in teeth J Radio Nucl Chem 2012;294:251. 
4.  Manjunatha HC, Rudraswamy B. A study of thickness and penetration depth dependence of specific absorbed fraction of energy in bone. Ann Nucl Energy 2011;38:2271. 
5.  Manjunatha HC. A dosimetric study of Beta induced bremsstrahlung in bone. Appl Radiat Isotopes 2014;94:28293. 
6.  Manjunatha HC, Rudraswamy B. Beta induced bremsstrahlung exposure in DNA and RNA. Phys Med 2011;27:188. 
7.  Harima Y. An approximation of gamma ray buildup factors by modified geometrical progression. Nucl Sci Eng 1983;83:299. 
8.  Shultis JK, Faw RE. Radiation shielding technology. Health Phys 2005;88:587612. 
9.  Chibani O. A subminute Monte Carlo dose calculation engine for prostate implants. Med Phys 2005;32:368898. 
10.  Tsiakalos MF. Monte Carlo dosimetric evaluation of high energy vs. low energy photon beams in low density tissues. Radio Ther Oncol 2006;79:1318. 
11.  Takeuchi K. PALLASPL, SPA Code Dimensional Transport Code. Japan: Paper 42, Ship Research Institute; 1973. 
12.  Yamano N, Minami K, Koyama K, Naito Y. RADHEAT V4 A Code System to Generate Multi Group Constants and Analyses Radiation Transport for Shielding Safety Evaluation. Atomic Energy Research Institute Report 1316. Japan; 1989. 
13.  Simmons GL. An Adjoint GammaRay Moments Computer Code ADJMOM 1. National Bureau of Standards Technical Note; 1973. p. 748. 
14.  Gopinath DV, Samthanam K. Radiation transport in onedimensional finite systems part I. Development in the anisotropic sourceflux technique. Nucl Sci Eng 1971;43:186. 
15.  Hubbell JH. A power series buildup factor formulation. Application to rectangular and offaxis disk source problems. J Res 1963;67C: 2918. 
16.  Chilton AB, Eisenhauer CM, Simmons GL. Photon point source buildup factors for air, water and iron. Nucl Sci Eng 1980;73:97. 
17.  Sakamoto Y, Tanaka S, Harima Y. Interpolation of gamma ray buildup factors for point isotropic source with respect to atomic number. Nucl Sci Eng 1988;100:33. 
18.  Brar GS, Sandhu AK, Makhan S, Mudahar GS. Exposure buildup factors for bakelite, Perspex and magnox – A12 upto 40 mfp using the interpolation method. Radiat Phys Chem 1994;44:45965. 
19.  Brar GS, Mudahar GS. Energy and effective atomic number dependence of the exposure buildup factor in soils – A study. Nucl Geophys 1995;9:47180. 
20.  American National Standard (ANS). GammaRay Attenuation Coefficients and Buildup Factor for Engineering Materials. American National Standard; 1991. 
21.  Harima Y, Sakamoto Y, Tanaka S, Kawai M. Validity of the geometric progression formula in approximating the gamma ray buildup factors. Nucl Sci Eng 1986;94:2430. 
22.  Shimizu A, Onda T, Sakamoto Y. Calculations of gammaray buildup factor up to depths of 100 mfp by the method of invariant embedding, (III) generation of an improved data set. J Nucl Sci Technol 2004;41:4138. 
23.  Singh PS, Tejbir S, Paramajeet K. Variation of energy absorption buildup factors with incident photon energy and penetration depth for some commonly used solvents. Ann Nucl Energy 2008;35:10937. 
24.  Sidhu GS, Singh PS, Mudahar GS. A study of energy and effective atomic number dependence of the exposure buildup factors in biological samples. J Radiol Prot 2000;20:5368. 
25.  Gerward Leif, Guilbert N, Jensen K. B, Leving, H. WinXCom – A program for calculating xray attenuation coefficients. Rad Phy Chem 2004;71:6534. 
26.  Manjunatha HC, Rudraswamy B. Energy absorption and exposure buildup factors in hydroxyapatite. Radiat Meas 2012;47:36470. 
27.  Manjunatha HC, Rudraswamy B. Computation of exposure buildup factors in teeth. Radiat Phys Chem 2011;80:1421. 
28.  Manjunatha HC, Rudraswamy B. Energy absorption buildup factors in teeth. J Radio Nucl Chem 2012;294:25160. 
29.  Manjunatha HC, Rudraswamy B. Study of effective atomic number and electron density for tissues from human organs in the energy range of 1 keV100 GeV. Health Phys 2013;104:15862. 
30.  Suresh KC, Manjunatha HC, Rudraswamy B. Study of Z eff for DNA, RNA and RETINA by numerical methods. Radiat Prot Dosimetry 2007;128:2948. 
31.  Manjunatha HC, Rudraswamy B. Computation of CTnumber and Zeff in Teeth. Health Phys 2011;100:S929. 
32.  Manjunatha HC. A study of photon interaction parameters in lung tissue substitutes. J Med Phys 2014;39:112. [ PUBMED] [Full text] 
33.  American National Standard. ANSI/ANS 6.4.3. Oak Ridge, TN 378316362; 1991. 
[Figure 1], [Figure 2], [Figure 3]
[Table 1]
