CuO-doping effect on the optical properties (linear/linear terrace) and mechanical and acoustic features of lead borate glasses

In this study, we investigate the optical (linear/nonlinear) properties, mechanical characteristics, and acoustical behavior of lead borate glasses with a composition of 10ZnO–40 B2O3–(50-x) Pb3O4–xCuO, where x represents the varying concentrations of CuO (x = 0, 1, 2, 3, 5). The refractive index values, denoted as n, ranged from 2.533 for the ZBPC0 sample to 2.895 for the ZBPC4 sample. Estimations were conducted to determine the molar refraction, molar polarizability, reflection loss, and optical transmission of the samples. In the investigated glasses, both Rm (ranging from 41.855 to 43.657 cm3/mol) and αm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }_{m}$$\end{document} (ranging from 1.659×10-23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-23}$$\end{document} to 1.730 ×10-23\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-23}$$\end{document}cm3) exhibit similar behavior. The metallization (M) varied from 0.356 to 0.288, while the transmission coefficient (T) decreased from 0.683 to 0.618. The dielectric constant (ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document}) changed from 6.418 to 8.381, while optical electronegativity (χ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{*}$$\end{document}) decreased from 0.682 to 0448, and linear dielectric susceptibility (χ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{1}$$\end{document}) varied from 0.431 to 0.587. The nonlinear optical susceptibility (χ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{3}$$\end{document}) changed from 0.587 ×10-11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-11}$$\end{document} to 2.024 ×10-11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-11}$$\end{document} esu, while the nonlinear refraction index varied from 0.874 ×10-10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-10}$$\end{document} to 2.636 ×10-10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-10}$$\end{document} esu. The decrease in the values of M indicates that the glass samples are suitable for use in nonlinear applications, and they exhibit insulating properties. Additionally, a proportional relationship between χ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }^{3}$$\end{document} and n2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n}_{2}$$\end{document} in glass samples was observed in the glass samples. Also, the elastic moduli values, including Young’s modulus and Bulk modulus, ranged from 322.84 to 337.12 (GPa), 293.76 to 304.96 (GPa), respectively. These results suggest that ZBPC glasses possess favorable properties for optical applications. Lastly, this study provides valuable insights into the structural characteristics of the glass samples.