Research Article, J Nucl Ene Sci Power Generat Technol Vol: 7 Issue: 2

Beta Induced Bremsstrahlung Shielding Parameters in Al-Based Glassy Alloys

Chandrika BM^1,2, Manjunatha HC^3*, Sridhar KN⁴, Seenappa L^2,3 and Hanumantharayappa C⁵

¹Department of Physics, Government First grade College, Bangarpet, India

²Researches and Development Centre, Bharathiar University, Coimbatore, India

³Department of Physics, Government College for women, Kolar, Karnataka, India

⁴Department of Physics, Government First grade College, Kolar, Karnataka, India

⁵Vivekananda Degree College, Bangalore, Karnataka, India

*Corresponding Author : Manjunatha
Department of Physics, Government College for women, Kolar, Karnataka, India
Tel: 09964624412
E-mail: manjunathhc@rediffmail.com

Received: December 26, 2017 Accepted: January 11, 2018 Published: January 19, 2018

Citation: Chandrika BM, Manjunatha HC, Sridhar KN, Seenappa L, Hanumantharayappa C, et al. (2018) Proton Irradiation Effects on the Physio-Mechanical Properties and Microstructure of Cold-Worked Molybdenum$. J Nucl Ene Sci Power Generat Technol 7:1. doi: 10.4172/2325-9809.1000181

Abstract

Keywords: Shielding laterials; Electromagnetic radiation; Nuclear reactor

Introduction

Bremsstrahlung is a nonstop electromagnetic radiation discharged when an electron or a beta molecule is deflected in the coulomb field of the core. Sommerfeld developed a theory for bremsstrahlung produced by a non-relativistic electron in the coulomb field of the nucleus of a thin target [1]. Bathe-Heitler Sauter and Racah obtained analytical expressions for the relativistic case by neglecting coulomb effects of the nucleus [2-4]. An accurate theory has been developed by Tseng–Pratt using the self-consistent coulomb field wave function [5]. Seltzer extends the Tseng–Pratt theory to the field of an atomic electron [6]. Theoretical methods for calculating thick targets have been formulated by many authors [2,7-10]. Manjunatha and Rudraswamy formulated a method to study the bremsstrahlung parameters in thick target compounds [11-27]. In a nuclear reactor, beta nuclides are discharged during nuclear reactions. These beta nuclides connect with shielding materials and produces bremsstrahlung. The Bremsstrahlung segment of beta producers has been customarily overlooked in shielding calculations. This might be because of an absence of accessible techniques for incorporating this segment in the counts or to the conviction that the commitment of this segment is irrelevant contrasted with that of different outflows. The phenomenon of Bremsstrahlung creation is most imperative at high energies and high medium nuclear numbers [28].

Radiation shielding in nuclear reactor are usually consist of barriers of lead, concrete and stainless steel. Lead has recently been recognised as a source of environmental pollution and produces more secondary radiation such as bremsstrahlung. Steel is found to be heavy, costly and corrosive material. For the purpose of the radiation shielding, there is a need to search the substitute for steel. The Aluminum is anticorrosive and cheaper than the stainless steel. Alloys with a shapeless structure have great potential for radiation shielding applications as a consequence of their interesting mechanical properties. Hence in the present study we have studied the bremsstrahlung shielding properties of Al-based glassy alloys such as Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5, Al₈₅Y₈Ni₅Co₁Fe_0.5Pd_0.5, Al₈₄Y₉Ni₄Co_1.5Fe_0.5Pd₁, Al₈₀Y₁₃Ni₅Co₁Fe_0.5Pd_0.5, Al₇₀Y₂₃Ni₅Co₁Fe_0.5Pd_0.5 and Al₆₀Y₃₃Ni₅Co₁Fe_0.5Pd_0.5. We have also compared the shielding properties among the studied different Albased glassy alloys and that of stainless steel.

Materials and Methods

Bremsstrahlung efficiency

The bremsstrahlung production efficiency for a given beta/ electron kinetic energy and target material is defined as the ratio of total bremsstrahlung power radiated when an electron is incident on a target to the total power in the incident electron (ε =Ï�?/E ). φ Is energy loss by electron/beta during bremsstrahlung production and E is energy of incident electron. The bremsstrahlung efficiency also gives the total fraction of a beta/electron energy that will appear as bremsstrahlung radiation (it is also called as yield) and it can be expresses as

(1)

Where E is the maximum (not average) electron/beta energy (in MeV), Z is the atomic number of the target in which the interactions occur. The relation for the efficiency is derived by assuming that the total electron per unit path length can be expressed as

(2)

Where ρ and A are the density and atomic weight of the target material respectively. The first term is the collission loss and second term is the radiation loss. The distance (x₀) travelled by an electron in losing all of its energy is given by

(3)

The bremsstrahlung efficiency or bremsstrahlung yield for thick targets

(4)

For a compound target, Z is replaced by modified atomic number (Z_mod) [29] in the above equation. For a beta induced bremsstrahlung energy E=E_max (maximum energy of beta in MeV)

(5)

The above equation is used to estimate the bremsstrahlung efficiency/yield and it useful to estimate the bressstrahlung hazard. The fraction appearing as bremsstrahlung radiation is linearly related to the modified atomic number of the medium.

Bremsstrahlung dose rate

The rate of energy emission in the form of bremsstrahlung photons is therefore

(6)

We next compute the exposure rate from unshielded bremsstrahlung, treated as coming from a point source at a distance r in cm. The intensity at a distance r is given by

(7)

The bremsstrahlung dose rate is

(8)

Converting units and remembering that 1R=0.0088Gy in air

(9)

Above equation (9) is used to evaluate the bremsstrahlung dose rate by various beta nuclides.

Probability of energy loss by beta during Bremsstrahlung emission

The beta transmitting nuclides connects with shielding material and produces Bremsstrahlung radiation. The beta nuclides lose their energy amid this connection. The likelihood of a Radiative energy loss during Bremsstrahlung cooperation by each β-molecule is given by

(10)

Where [(E_max)_β]_i is the maximum kinetic energy of β-particle i in MeV; [(P_Br) _β]_i equals the probability of a radiative energy loss by β-particle i; Z_eff equals the effective atomic number of the stopping material. Markowicz et al. proposed an accurate expression of the modified atomic number (Z_mod ) for compound targets for the prediction of the Bremsstrahlung intensity to take into account the self-absorption and electron back scattering [30]. Here, W_i , A_i and Z_i are atomic weight, weight fraction and atomic number of i^th element respectively. Z_mod is defined for Bremsstrahlung interaction and hence Z_eff is replaced by Z_mod in equation (10).

(12)

The probability of radiative energy loss (radiative energy loss) by beta particle i during Bremsstrahlung emission [(P_Br)_β]_i depends on modified atomic number (Z_mod) of target material (tissue) and maximum initial kinetic energy of beta particle i that is [(E_max)_β]_i.

Specific Bremsstrahlung constant of the beta radionuclide (�?_Br)

The particular Bremsstrahlung steady is an amount practically equivalent to particular gamma beam consistent for a radioisotope. The particular gamma beam consistent is the introduction rate per unit movement at a specific separation from a source (radioisotope). Similarly, the specific Bremsstrahlung constant is the Bremsstrahlung exposure rate (in C/Kg/h) at a distance of 1cm from a 1-MBq beta source. It is given by Zanzonico et al. [30]

(13)

Where (f_β)_i is frequency of emission (i.e., the number per nuclear transformation) of β-ray i. is the mean energy of Bremsstrahlung for β-ray i emitted by a radznuclide. The mean energy of Bremsstrahlung for i^th beta particle is given by

(14)

is specific Bremsstrahlung constant (in C/ kg-cm²/MBq-h) of β-ray yielding Bremsstrahlung of mean energy An estimation of the specific Bremsstrahlung constant is based on the Bremsstrahlung mean energy rather the actual Bremsstrahlung spectrum, is a gross approximation. The energy dependent corresponds to the conventional energy dependent specific gamma ray constant. Specific gamma ray constant (Ð�?) is an exposure rate( in R/h) due to gamma at a distance of one meter from a source with an activity of 1Ci

(15)

(16)

Specific bremsstrahlung constant in various aluminium based glassy alloys is estimated using the above formalism.

Results and Discussion

The variation of computed bremsstrahlung efficiency as a function of maximum energy of beta is as shown in Figure 1. Bremsstrahlung efficiency increases with increase in the maximum energy of the beta particle. The comparisons of bremsstrahlung efficiency at different energies (0.5, 1, 2, 3, 5 and 6 MeV) for various Al-glassy alloys (A--Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5, B--Al₈₅Y₈Ni₅Co₁Fe_0.5Pd_0.5 , C--Al₈₄Y₉Ni₄Co_1.5Fe_0.5Pd₁, D--Al₈₀Y₁₃Ni₅Co₁Fe_0.5Pd_0.5, E-- Al₇₀Y₂₃Ni₅Co₁Fe_0.5Pd_0.5 and F--Al₆₀Y₃₃Ni₅Co₁Fe_0.5Pd_0.5, G-Stainless steel) are also shown in (Figure 1). From this comparison, it is clear that aluminium based glassy alloy Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5 is having smaller bremsstrahlung efficiency than other alloys. The variation of computed bremsstrahlung dose rate as a function of maximum energy of beta is as shown in Figure 2. Bremsstrahlung dose rate increases exponentially with maximum energy of the beta. The comparisons of bremsstrahlung dose rate at different energies (0.5, 1, 2, 3, 5 and 6 MeV) for various Al-glassy alloys are also shown in Figure 2. The variation probability of energy loss by beta during bremsstrahlung emission with maximum energy of the beta is as shown in Figure 3. This energy loss of beta increments with increment in the most extreme energy of the beta molecule. The examinations of likelihood of energy misfortune by beta amid bremsstrahlung emanation at various energies for different Al-glassy alloys are also shown in Figure 3. From this comparison, it is clear that the energy lost by beta is small in Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5 than other alloys. The variation of specific bremsstrahlung constant with maximum energy of beta is as shown in Figure 4. The evaluated specific bremsstrahlung constant is also tabulated in the Table 1. The specific bremsstrahlung constant increases exponentially with the maximum energy of the beta. The comparisons of specific bremsstrahlung constant at different energies (0.5, 1, 2, 3, 5 and 6 MeV) for various Al-glassy alloys are also shown in Figure 3. From this comparison, it is clear that the specific bremsstrahlung constant values are smaller for Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5 than other alloys. The variation of bremsstrahlung dose rate and specific bremsstrahlung constant with modified atomic number is also shown in Figure 5. Bremsstrahlung dose rate and specific bremsstrahlung constant increases with increase in the modified atomic number of alloys. The contemplated bremsstrahlung shielding parameters , for example, bremsstrahlung productivity, probability of energy loss by beta during bremsstrahlung emission and specific bremsstrahlung constant values are littler in the Al-based lustrous alloys Al86Y7Ni5Co1Fe0.5Pd0.5 than alternate combinations. It means bremsstrahlung production is less in Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5 than other studied steels. Hence it is better to use the Al-glassy alloy Al₈₆Y₇Ni₅Co₁Fe_0.5Pd_0.5 in the nuclear power plants than that of the stainless steels and other steels to avoid the secondary radiation such as bremsstrahlung.

Table 1: Evaluated specific bremsstrahlung constant for various Al-glassy alloys (in ΓBr(R-cm²/mCi-h).

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