M. M. Abd El Raheem, M. M. Wakkad, H. A. Mohamed, N. A. Hamed, H. F. Mohamed
{"title":"Impact of lead concentration on linear and nonlinear optical parameters of amorphous chalcogenide Sn-Ge-Se system","authors":"M. M. Abd El Raheem, M. M. Wakkad, H. A. Mohamed, N. A. Hamed, H. F. Mohamed","doi":"10.1186/s40712-025-00314-8","DOIUrl":null,"url":null,"abstract":"<div><p>Some physical properties of Sn<sub>5</sub>Ge<sub>10</sub>Se<sub>85-x</sub>Pb<sub>x</sub>; (<i>x</i> = 2.5, 5, 10, 15 17.5 and 20 at. %) chalcogenide glasses, namely average coordination number (CN), deviation of stoichiometry (r), floppy modes (f), cross-linking density (X), average number of constraints (Ncon), lone pair electrons (Lp), overall mean bond energy ( < E˃), and average heat of atomization (Hs), are depicted. The experimental and theoretical values of the optical band gap <i>E</i><sub>op</sub> for different contents of Pb were found to be very close to each other. The dispersion properties, such as complex dielectric function <span>\\(\\widetilde{\\varepsilon }\\)</span>, optical conductivity <span>\\({\\sigma }_{op}\\)</span>, single oscillator <i>E</i><sub>o</sub>, and dispersion energies <i>E</i><sub>d</sub>, are investigated. On the other hand, electrical conductivity is studied. Our results are based on the Tauc equation, Wemple and Di-Domenico (WDD) model, Pankove method, Tichy and Ticha relationship, and Miller’s rule. The values of the first-order <i>χ</i><sup>(1)</sup> and third-order <i>χ</i><sup>(3)</sup> of optical susceptibility and the nonlinear refractive index (<i>n</i><sub>2</sub>) were found to increase with the increase of Pb content, which has a maximum value, hence decreasing thereafter with the increase of the latter.</p></div>","PeriodicalId":592,"journal":{"name":"International Journal of Mechanical and Materials Engineering","volume":"20 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://jmsg.springeropen.com/counter/pdf/10.1186/s40712-025-00314-8","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanical and Materials Engineering","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1186/s40712-025-00314-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Some physical properties of Sn5Ge10Se85-xPbx; (x = 2.5, 5, 10, 15 17.5 and 20 at. %) chalcogenide glasses, namely average coordination number (CN), deviation of stoichiometry (r), floppy modes (f), cross-linking density (X), average number of constraints (Ncon), lone pair electrons (Lp), overall mean bond energy ( < E˃), and average heat of atomization (Hs), are depicted. The experimental and theoretical values of the optical band gap Eop for different contents of Pb were found to be very close to each other. The dispersion properties, such as complex dielectric function \(\widetilde{\varepsilon }\), optical conductivity \({\sigma }_{op}\), single oscillator Eo, and dispersion energies Ed, are investigated. On the other hand, electrical conductivity is studied. Our results are based on the Tauc equation, Wemple and Di-Domenico (WDD) model, Pankove method, Tichy and Ticha relationship, and Miller’s rule. The values of the first-order χ(1) and third-order χ(3) of optical susceptibility and the nonlinear refractive index (n2) were found to increase with the increase of Pb content, which has a maximum value, hence decreasing thereafter with the increase of the latter.
Sn5Ge10Se85-xPbx的一些物理特性(x = 2.5, 5, 10, 15, 17.5, 20 at。 %) chalcogenide glasses, namely average coordination number (CN), deviation of stoichiometry (r), floppy modes (f), cross-linking density (X), average number of constraints (Ncon), lone pair electrons (Lp), overall mean bond energy ( < E˃), and average heat of atomization (Hs), are depicted. The experimental and theoretical values of the optical band gap Eop for different contents of Pb were found to be very close to each other. The dispersion properties, such as complex dielectric function \(\widetilde{\varepsilon }\), optical conductivity \({\sigma }_{op}\), single oscillator Eo, and dispersion energies Ed, are investigated. On the other hand, electrical conductivity is studied. Our results are based on the Tauc equation, Wemple and Di-Domenico (WDD) model, Pankove method, Tichy and Ticha relationship, and Miller’s rule. The values of the first-order χ(1) and third-order χ(3) of optical susceptibility and the nonlinear refractive index (n2) were found to increase with the increase of Pb content, which has a maximum value, hence decreasing thereafter with the increase of the latter.