Investigation of radiation shielding efficacy of vanadium–tellurite–antimonite semiconducting glasses

Effects of antimony trioxide (Sb 2 O 3 ) on neutron and gamma-radiation shielding parameters of tellurite vanadio-antimonite glasses with compositions 40TeO 2 -(60-x)V 2 O 5 -xSb 2 O 3 : 0 ≤ xSb 2 O 3 ≤ 10 mol% coded as (TVS0-TVS10) were investigated. The mass attenuation coefficients (MAC) were evaluated using the Monte Carlo simulation code (MCNP-5) and WinXcom program for photon energies in the range of 15 keV to 15 MeV. The SRIM program was used to compute the stopping power and projected range of the charged particles, such as proton and alpha particles, on the investigated glass samples. Based on the theoretically evaluated MAC, some shielding parameters were computed, such as linear attenuation coefficient, electric cross-section, atomic cross-section, effective atomic number, half-value thickness (HVT), and the mean free path. The EXABCal program was applied to the level of the photons accumulation in the investigated glass samples (buildup factors). The effective cross-section for fast neutrons was computed theoretically on the fast neutron effective removal cross-section (Σ R ) for the constituting components. Results revealed that the maximum values of in the range between 28.9-31.3 cm 2 /g with increasing the Sb 2 O 3 substitution ratio between 0-10 mol %, respectively. In contrast, the HVT values decrease with an increase in the increment of Sb 2 O 3 rate. The maximum (Σ R ) was obtained for glass coded TVS0 among the investigated glasses. Results concluded that the higher Sb 2 O 3 concentration in TVS glasses leads to an increase in their capability to apply in several radiation shielding applications.

Recently, glass materials in their different structures have an essential role in most modern applications such as laser medium, optical switching instruments, optoelectronic materials, and space technology [13][14][15]. Besides, glasses can be applied in medical applications in CT scans, windows, and doors in nuclear medicine. For the characteristics mentioned above, glasses got more attention to be utilized as an alternative radiation protection materials instead of rocks, bricks, concrete, alloys, and polymers materials [9][10][11][12][16][17][18].
From our best acquaintance that tellurite, phosphate, borate, and silicate-based glass networks are the best glass candidates due to their excellent characteristics, for example (low cost and ease molding, low melting points, high transparency, and good thermal stability) [8][9][10]. Moreover, TeO2 based glasses have gained more focusing from many researchers and investigators due to their unique features such as high linear and nonlinear refractive indices and good shield for radiations [11,15,[19][20][21][22]. Therefore, glasses with TeO2 as a former have many beneficial uses in the solid-state lasers applications, memory switching instruments, and solar cells [23][24][25].
Commonly, vanadium oxide (V2O5) is also an excellent glass former and enhances the magnetic, electric properties of the synthesized glasses [1,3]. Furthermore, modification of the TeO2 glass with V2O5 produces the n-type semiconducting glass samples, which contain V +4 /V +5 valance states [1,3,9].
In this study, neutron and gamma radiation shielding competences, mass stopping power, and projectile range for proton and alpha particles were evaluated for the TeO2-V2O5-Sb2O3 (TVS) glass samples to be used in nuclear protection applications.
The principle information, such as the density, molecular weight, molar volume, and chemical concentration of the investigated glass samples was listed in Table 1.

Linear and mass attenuation coefficient (LAC and MAC)
The interaction of photons with an absorbing medium, as it propagates in the medium, can be quantified in several parameters. Generally, the transmission of photons of particular energy is governed by the modified Beer-Lambert equation: X is the ratio of a measured photon quantity/quality parameters (such as dose, intensity, energy, and or number flux) of interest at a particular point with an absorber of thickness t to the same parameter without the absorber. The parameters B and μ are called the photon buildup factor and linear attenuation coefficient (LAC) of the absorber. B represents the number of photons scattering and buildup within the material, while μ is the ability of the material to resist the passing of photons through the studied material. Generally, LAC depends on absorber thickness, photon-energy, and the chemical nature of the glass network.
The mass attenuation coefficient (MAC) defined as: With ρ being the mass density of the absorbing medium. However, μm does not depend on thickness but on the nature of absorbing material and photon energy only. In equation (1) There is an obvious increase in the MAC values of the glass samples as their density increased in the lower photon energies (less than 1.5 MeV) compared to the energy region above 1.5 MeV.
This implies that an increase in Sb content in the investigated TVS glass samples improves the shielding capacity of the glass samples more in the low energy region compared to at energies above 1.5 MeV.
The simulated MAC was compared to the MAC obtained using the WinXCOM computer program, as illustrated in table 2. The difference between the simulated and computed MAC was calculated and also presented in Table 2. The results showed that the difference was ranged between 0.5-10 %.
The variation of the linear attenuation coefficients (LAC) versus the incident photon energy for the glassTVS samples is illustrated in

Half-value layer (HVL) and mean free path (MFP)
The HVL is the thickness of the absorber required to decrease the photon intensity to half its initial value. From equation (1), for good geometry, at HVL value, one can write: In radiation protection analysis, the HVL is an important parameter when considering the choice of material in radiation shielding application. It is a quantity that can be used to relatively compare the photon shielding capacity of different materials when faced with different choices. (steel magnetite) concrete [32] at the same energy. This is an interesting result since the density of the heavy concrete of 5.11 g/cm 3 is higher than those of the glass samples. Using the HVL data, the photon shielding efficacy of TVS10 was almost twice that of heavy concrete despite being more than 20 % less dense.
The mfp of photons of specific energy, as defined in equation (4), is another quantity that compares the shielding effectiveness of materials.

Effective Atomic Number (Zeff)
Many

Fast neutron effective removal cross-section (FNRCS)
The probability that a fast neutron will undergo its first collision with the nucleus of an interactive medium, which could lead to its slowing down and subsequent removal from uncolliding ones, may be referred to as fast neutron effective removal cross-section (FNRCS)-ΣR. ΣR has been developed to accommodate neutron scattering and buildup. For the glass samples, ΣR was estimated via the next equation (6)

Buildup factors
The

The charged particles stopping power and projected range
In the present study, the SRIM program was utilized to predict stopping power (ᴪ) and projected range (Φ) for some charged ions, such as ( 2 4 ) Alpha particle and ( ) 1 proton in the energy range between 0.01-10 MeV [39,40]. The stopping power is used to describe the amount of energy lost by the charged particles (alpha and proton ) along their path length in the studied glasses. This loss in energy is due to the collision of the incident charged particles with the electrons and atoms constituting the glass network. The projected range is a term used to show the distance in which the charged particle lost all of its energy and transferred to a rest state. The predicted results were presented in Figs 13 and 14. The mentioned figures showed that both ᴪ and Φ are affected by the same parameters chemical composition and the kinetic energy of the incident particle. Fig 13a and   14a showed that the ᴪ of proton and alpha particles have the same variation with the kinetic energy of the incident charged particle where the ᴪ for proton and alpha particles began small at low kinetic energy and increased gradually with increase the kinetic energy of the incident particle.
The mass stopping power for protons reaches maximum values at kinetic energy around 0.1 MeV, while for alpha particle, it reaches maximum values at higher energy around 0.8 MeV. This can be related to the mass and speed of particles where the mass of alpha particles is high, so it creeps and lost a high amount of energy in a small path distance. In contrast, protons have a small mass and high speed. Thus, the mass storing power of the alpha particle is higher than that of the proton. Figures 13b and 14b showed that the Φ of protons and alpha particles increases with an increase in the incident kinetic energy of the incident particle. The Φ of protons is several hundred m while the Φ of alpha is lower and in the range of several m only. This high gape between the Φ of proton and alpha particles related to their speed. The alpha particles have a slow speed, so it loses a considerable amount of energy in a small range along its path length. In contrast, protons have a high speed to travel a longe distance associated with losing a small part of their energies.
The Φ of protons and alpha particles was also affected by the Sb2O3 substitution ratio, where the Φ decreased with increasing the Sb2O3 insertion ratio for both proton and alpha particles.

5-
The range (R) of p + in all the glasses were all greater than those of αparticles for all energies.
Results concluded that the higher Sb2O3 concentration in TVS glasses leads to an increase in their capability to apply in several radiation shielding applications.