Interpolation insights: Accurate mass attenuation coefficient and effective atomic number estimation in PbO and BaO doped borosilicate glasses

Interpolation techniques such as Piecewise Cubic Hermite Interpolating Polynomials (PCHIP) and Cubic Splines (CS) were used to estimate the mass attenuation coefficient values (MAC) and the effective atomic number values (Zeff) of borosilicate glasses doped with PbO and BaO. The mathematical models were used to obtain a function between the parameters and the energy of the incoming photons, to provide a better understanding of the glass system. The glasses had a composition of 10Na2O–15PbO-(65-x)B2O3–10SiO2-xBaO, where x = 5, 10, 15, 20, and 25 mol%. The derived values were compared against theoretical data obtained from Phy-X, to determine the accuracy of the mathematical models. The results demonstrate that both the CS and PCHIP methods are useful tools that can accurately be used to determine the MAC and Zeff values of the investigated samples. For instance, at certain energies such as 0.103 MeV, the relative difference between the MAC values obtained through PCHIP and through Phy-X is as low as 0.07, demonstrating the effectiveness of the PCHIP model at these energies. The same is true for the Zeff values, where the same relative difference at 0.384 MeV is as low as 0.0002. Therefore, both the mathematical models demonstrate an effective ability at interpolating the MAC and Zeff values of the investigated glass system. •PCHIP and Cubic Splines (CS) were used to estimate the MAC for borosilicate glasses.•CS and PCHIP methods are in good agreement with Phy-X data.•CS and PCHIP can be used as well to derive the Zeff for the glasses.•At 0.103 MeV, the MAC values obtained using PCHIP and Phy-X differ by 0.07.•At 0.384 MeV, the Zeff values obtained using PCHIP and Phy-X differ by 0.0002.