# Gamma Ray Shielding Properties of Yb\({}^{3+}\)-Doped Calcium Borotellurite Glasses
## 2 Materials and Methods  
Gamma rays have been, to a large degree, utilized in several areas, and for that reason, gamma ray attenuation parameters--including the dose rate of photons, the radiation protection percentage of the sample, the tenth value thickness, the photon interaction cross sections and some other shielding factors--have gained great importance due to their applications in nuclear shielding and health physics [29; 30; 31]. It is necessary to report the aforementioned quantities for several glass systems in order to obtain the suitable glass that can supply a convenient safe shielding from the ionizing radiation. In our work, the photon attenuation factors of CaF\({}_{2}\)-CaO-B\({}_{2}\)O\({}_{3}\)-TeO\({}_{2}\)-Yb\({}_{2}\)O\({}_{3}\) glass systems (for simplicity, we will use TeBYbX to denote the glass samples) were theoretically studied by the Phy-X/PSD program [28], and the influence of varying the amount of TeO\({}_{2}\) from 10 to 54 mol\(\%\) on the attenuation effectiveness of these systems was examined. Previously, [PERSON] et al. fabricated the chosen glasses. The full glass fabrication details, the optical and the spectroscopic features of the glasses are reported in [25]. The chosen glasses are coded as:  
10 TeO\({}_{2}\)-54B\({}_{2}\)O\({}_{3}\)-25.5 CaO-10 CaF\({}_{2}\)-0.5 Yb\({}_{2}\)O\({}_{3}\) (TeBYb1), the density is 3.08 g/cm\({}^{3}\)  
16 TeO\({}_{2}\)-50.4B\({}_{2}\)O\({}_{3}\)-23.1 CaO-10 CaF\({}_{2}\)-0.5 Yb\({}_{2}\)O\({}_{3}\) (TeBYb2), the density is 3.25 g/cm\({}^{3}\)  
22 TeO\({}_{2}\)-46.8B\({}_{2}\)O\({}_{3}\)-20.7 CaO-10 CaF\({}_{2}\)-0.5 Yb\({}_{2}\)O\({}_{3}\) (TeBYb3), the density is 3.43 g/cm\({}^{3}\)  
31 TeO\({}_{2}\)-41.4B\({}_{2}\)O\({}_{3}\)-17.1 CaO-10 CaF\({}_{2}\)-0.5 Yb\({}_{2}\)O\({}_{3}\) (TeBYb4), the density is 3.71 g/cm\({}^{3}\)  
54 TeO\({}_{2}\)-27.6B\({}_{2}\)O\({}_{3}\)-7.9 CaO-10 CaF\({}_{2}\)-0.5 Yb\({}_{2}\)O\({}_{3}\) (TeBYb5), the density is 4.46 g/cm\({}^{3}\)  
For the above glasses, Phy-X/PSD was applied to generate the mass attenuation coefficient (\(\mu/\varrho\)) values, and we examined the influence of increasing the concentration of 10 to 54 mol\(\%\) on the \(\mu/\varrho\) values of the glasses under study. In addition, we used the obtained \(\mu/\varrho\) values to determine the linear attenuation coefficient (\(\mu\)), and from this parameter we can check the enhancement of the radiation shielding ability of the samples when the density increases from 3.08 g/cm\({}^{3}\) (for TeBYb1) to 4.46 g/cm\({}^{3}\) (for TeBYb5). Two other important factors that can be generated from \(\mu\) are the transmission factor (\(TF\)) and the radiation protection percentage (\(RPP\)). The \(TF\) and \(RPP\) can be calculated via the following relations:  
\[TF=e^{-u\times t} \tag{1}\]  
\[RPP=\left(1-\frac{I}{I_{0}}\right)\times 100\% \tag{2}\]  
In Equation (1), \(t\) represents the thickness of the sample, while \(I\) and \(I_{0}\) in Equation (2) are the attenuated and incident intensities of the photons. Moreover, the half value thick ness (_HVL_) represents the width of glass that able to shield half of the initial radiation [32]. The smaller the sample thickness that is able to provide adequate radiation protection, the better it will be used in practical applications. The _HVL_ for the chosen CaF\({}_{2}\)-CaO-B\({}_{2}\)O\({}_{3}\)-TeO\({}_{2}\)-Yb\({}_{2}\)O\({}_{3}\) glass systems can be obtained from the next formula:  
\[HVL=\frac{Ln2}{\mu} \tag{3}\]  
Additionally, the Phy-X/PSD program which was used in this study to calculate some of the shielding parameters is an accurate and quick tool for radiation shielding calculations. In this program, the users must first define the material by inputting the composition with the density of the material. Then, the users need to select the investigated energy value/range and select the parameter that they wish to calculate (\(\mu/\varrho\), HVL, etc.). Then, they can obtain the results as an MS Excel file.