{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T04:43:00Z","timestamp":1786164180131,"version":"build-2736575974"},"reference-count":50,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T00:00:00Z","timestamp":1785974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"crossref","award":["075-00269-25-00"],"award-info":[{"award-number":["075-00269-25-00"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This work is devoted to the description of the thermodynamics of the condensed states of the rare-earth metal europium under intense mechanical and thermal loading in shock waves. A new model of the equation of state for metallic materials is proposed based on the characteristic function of entropy with volume and internal energy (per unit mass) as variables. Within the framework of this model, calculations of the thermodynamic characteristics of europium at high pressures and specific entropies were carried out, the results of which are presented in comparison with the available data from shock-wave experiments. The developed equation of state for this material can be effectively applied to the modeling and simulation of various dynamic processes at high energy densities.<\/jats:p>","DOI":"10.3390\/ma19153351","type":"journal-article","created":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T13:03:27Z","timestamp":1786021407000},"page":"3351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equation of State for Europium at High Pressures and Entropies in Shock Waves"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6895-6362","authenticated-orcid":false,"given":"Konstantin V.","family":"Khishchenko","sequence":"first","affiliation":[{"name":"Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya 13 Bldg 2, Moscow 125412, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,6]]},"reference":[{"key":"ref_1","unstructured":"Zel\u2019dovich, Y.B., and Raizer, Y.P. 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