# Itarare Group Sandstone as a Sustainable Alternative Material for Photon Radiation Shielding
## 2 Materials and Methods
### Radiation Shielding Parameters  
The radiation shielding parameters were theoretically simulated using Phy-X PSD, a free code developed by [PERSON] et al. [24], which allows for the calculation of radiation shielding parameters over a broad range of energies. The software is Photon Shielding and Dosimetry (PSD) software. To conduct measurements utilizing the software, we firstly selected the appropriate data input form. For our analysis, we utilized the chemical composition measured by weight. Next, we entered the density of each sample. We chose an energy range of 0.015 MeV to 15 MeV (the standard grid). This energy range allows us to evaluate how different interaction effects, such as photoelectric absorption, incoherent scattering, and pair production, impact the attenuation of photons. We then selected the shielding parameters relevant to our study, including MAC, LAC, HVL, TVL, MFP, EBF, and EABF. Each sandstone sample for every layer was analyzed in triplicate, and we simulated the parameters for each sample independently. The first parameter calculated was the mass attenuation coefficient using the mixture rule (Equation (3)):  
\[\mathrm{MAC}=\Sigma\mathrm{iw}_{\mathrm{i}}(\mathrm{MAC})_{\mathrm{i}}\, \tag{3}\]  
where \(\mathrm{w}_{\mathrm{i}}\) represents the weight fraction of the i-th constituent element of the absorber material and \(\mathrm{MAC}_{\mathrm{i}}\) represents the mass attenuation coefficient of each element of the absorber material. After determining the MAC, the linear attenuation coefficient (Equation (4)) was calculated by multiplying the MAC by the rock's density (\(\mathrm{p}_{\mathrm{s}}\)). The density of the rock was obtained using the volumetric flask method (Equation (2)) after macroating the rocks and passing them through a 45 \(\mathrm{\SIUnitSymbolMicro m}\) sieve. We also measured the particle density, which was later used to measure porosity. High-purity ethyl alcohol was used for the measurements. The average particle density (six samples) for the rock fragments was 2.53 \(\pm\) 0.01 g cm\({}^{-3}\). \[\mathrm{MAC}\times\mathrm{p}_{\mathrm{s}}=\mathrm{LAC}\quad, \tag{4}\]  
The mean free path (Equation (5)), which represents the average distance a photon travels inside of the material until it interacts with one of its components, the half-value layer (Equation (6)), which indicates the thickness of material needed to attenuate 50% of the photons, and the tenth-value layer (Equation (7)), which refers to the thickness of material that attenuates 90% of the photons, were calculated as  
\[\mathrm{MFP}=\frac{1}{\mathrm{LAC}}\quad, \tag{5}\]  
\[\mathrm{HVL}=\frac{\mathrm{ln}(2)}{\mathrm{LAC}}=\frac{0.693}{\mathrm{LAC}}\quad, \tag{6}\]  
\[\mathrm{TVL}=\frac{\mathrm{ln}(10)}{\mathrm{LAC}}=\frac{2.303}{\mathrm{LAC}}\quad, \tag{7}\]  
To obtain the EBF and the EABF, the first step was to calculate the ratio (R) (Equation (8)) between the partial MAC due to the Compton Effect (incoherent scattering) and the total MAC:  
\[\mathrm{R}=\frac{\mathrm{MAC}_{\mathrm{Compton}}}{\mathrm{MAC}_{\mathrm{Total }}}\quad, \tag{8}\]  
The second step was to calculate the equivalent atomic number (\(\mathrm{Z}_{\mathrm{eq}}\)) (Equation (9)) through interpolation using the following equation:  
\[\mathrm{Z}_{\mathrm{eq}}=\frac{\mathrm{Z}_{1}(\mathrm{logR}_{2}-\mathrm{logR })+\mathrm{Z}_{2}(\mathrm{logR}-\mathrm{logR}_{1})}{\mathrm{logR}_{2}-\mathrm{ logR}_{1}}\quad, \tag{9}\]where \(Z_{1}\) and \(Z_{2}\) represent the atomic numbers of the elements corresponding to the radii R\({}_{1}\) and R\({}_{2}\) that satisfy the inequality R\({}_{2}\) < R < R\({}_{1}\) for photons of a given energy.