{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T01:09:49Z","timestamp":1777338589156,"version":"3.51.4"},"reference-count":131,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>GeTe-based and PbSe-based high-entropy compounds have outstanding thermoelectric (TE) performance and crucial applications in mid and high temperatures. Recently, the optimization of TE performance of high-entropy compounds has been focused on reducing thermal conductivity by strengthening the phonon scattering process to improve TE performance. We report a first-principles investigation on nine GeTe-based high-entropy chalcogenide solid solutions constituted of eight metallic elements (Ag, Pb, Sb, Bi, Cu, Cd, Mn, and Sn) and 13 PbSe-based high-entropy chalcogenide solid solutions: Pb<jats:sub>0.99-y<\/jats:sub>Sb<jats:sub>0.012<\/jats:sub>Sn<jats:sub>y<\/jats:sub>Se<jats:sub>1-2x<\/jats:sub>Te<jats:sub>x<\/jats:sub>S<jats:sub>x<\/jats:sub> (x\u2009=\u20090.1, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and y\u2009=\u20090) and Pb<jats:sub>0.99-y<\/jats:sub>Sb<jats:sub>0.012<\/jats:sub>Sn<jats:sub>y<\/jats:sub>Se<jats:sub>1-2x<\/jats:sub>Te<jats:sub>x<\/jats:sub>S<jats:sub>x<\/jats:sub> (y\u2009=\u20090.05, 0.1, 0.15, 0.2, 0.25 and x\u2009=\u20090.25). We have investigated the mechanical properties focusing on Debye temperature (<jats:italic>\u0398<\/jats:italic><jats:sub>D<\/jats:sub>), thermal conductivity (<jats:italic>\u03ba<\/jats:italic>), Gr\u00fcneisen parameter <jats:italic>(\u03b3<\/jats:italic><jats:sub>\u03b1<\/jats:sub><jats:italic>)<\/jats:italic>, dominant phonon wavelength (<jats:italic>\u03bb<\/jats:italic><jats:sub>dom<\/jats:sub>), and melting temperature (<jats:italic>T<\/jats:italic><jats:sub>m<\/jats:sub>). We find that the lattice thermal conductivity is significantly reduced when GeTe is alloyed into the following compositions: Ge<jats:sub>0.75<\/jats:sub>Sb<jats:sub>0.13<\/jats:sub>Pb<jats:sub>0.12<\/jats:sub>Te, Ge<jats:sub>0.61<\/jats:sub>Ag<jats:sub>0.11<\/jats:sub>Sb<jats:sub>0.13<\/jats:sub>Pb<jats:sub>0.12<\/jats:sub>Bi<jats:sub>0.01<\/jats:sub>Te, and Ge<jats:sub>0.61<\/jats:sub>Ag<jats:sub>0.11<\/jats:sub>Sb<jats:sub>0.13<\/jats:sub>Pb<jats:sub>0.12<\/jats:sub>Mn<jats:sub>0.05<\/jats:sub>Bi<jats:sub>0.01<\/jats:sub>Te. This reduction is due to the mass increase and strain fluctuations. The results also show that Ge<jats:sub>0.61<\/jats:sub>Ag<jats:sub>0.11<\/jats:sub>Sb<jats:sub>0.13<\/jats:sub>Pb<jats:sub>0.12<\/jats:sub>Bi<jats:sub>0.01<\/jats:sub>Te solid solution has the lowest Young\u2019s modulus (30.362 GPa), bulk and shear moduli (18.626 and 12.359 GPa), average sound velocity (1653.128\u00a0m\/sec), Debye temperature (151.689\u00a0K), lattice thermal conductivity (0.574 W.m<jats:sup>\u20131<\/jats:sup>.K<jats:sup>\u20131<\/jats:sup>), dominant phonon wavelength (0.692\u00a0\u00c5), and melting temperature (535.91\u00a0K). Moreover, Ge<jats:sub>0.61<\/jats:sub>Ag<jats:sub>0.11<\/jats:sub>Sb<jats:sub>0.13<\/jats:sub>Pb<jats:sub>0.12<\/jats:sub>Bi<jats:sub>0.01<\/jats:sub>Te has the highest Gr\u00fcneisen parameter with a reduced and temperature-independent lattice thermal conductivity. The positive correlation between <jats:italic>\u0398<\/jats:italic><jats:sub>D<\/jats:sub> and <jats:italic>\u03ba<\/jats:italic> is revealed. Alloying of PbSe-based high-entropy by Sb, Sn, Te, and S atoms at the Se and Pb sites resulted in much higher shear strains resulted in the reduction of phonon velocity, a reduced <jats:italic>\u0398<\/jats:italic><jats:sub>D<\/jats:sub>, and a lower lattice thermal conductivity.<\/jats:p>","DOI":"10.1038\/s41598-023-42101-5","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T11:02:24Z","timestamp":1695812544000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Ab initio study of mechanical and thermal properties of GeTe-based and PbSe-based high-entropy chalcogenides"],"prefix":"10.1038","volume":"13","author":[{"given":"Sahib","family":"Hasan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Puja","family":"Adhikari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saro","family":"San","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wai-Yim","family":"Ching","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,27]]},"reference":[{"key":"42101_CR1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/adem.200300567","volume":"6","author":"JW Yeh","year":"2004","unstructured":"Yeh, J. 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