{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T10:32:59Z","timestamp":1786357979218,"version":"build-2736575974"},"reference-count":42,"publisher":"AIP Publishing","issue":"6","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12135019"],"award-info":[{"award-number":["12135019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12074028"],"award-info":[{"award-number":["12074028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004775","name":"Natural Science Foundation of Gansu Province","doi-asserted-by":"publisher","award":["25JRRA227"],"award-info":[{"award-number":["25JRRA227"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,8,14]]},"abstract":"<jats:p>BeF2 is a key component of fluoride coolants in molten salt reactors. The structural phase transition between its \u03b1- and \u03b2-quartz phases at high temperatures directly affects the mechanical and thermal properties. In this work, by combining first-principles calculations and machine learning molecular dynamics simulations, we systematically investigate the structural stability, elastic properties, and anharmonic lattice dynamics of BeF2 at finite temperatures. A displacive second-order phase transition from the \u03b1 to the \u03b2 phase driven by anharmonic effects is revealed. At low temperatures, F atoms are confined in a multi-well potential landscape, and their off-center displacements induce a multi-peak distribution of Be atoms through the Be\u2013F network coupling. As the temperature increases, enhanced anharmonic atomic motion and dynamic averaging gradually smear out the multi-well energy barriers, releasing F atoms from their local confinement and weakening the Be\u2013F vibrational coupling, which ultimately stabilizes the high-symmetry \u03b2 phase. The high temperature \u03b2 phase exhibits higher bulk and Young\u2019s moduli, indicating enhanced resistance to compression. The imaginary phonon modes present in the harmonic phonon spectrum disappear at high temperatures due to anharmonic renormalization, confirming the dynamical stability of the \u03b2 phase at elevated temperatures. The temperature evolution of the phonon density of states further shows that the Be\u2013F vibrational coupling weakens with increasing temperature, and the Be-related modes in the high-frequency region undergo red shifts and broadening, consistent with the enhanced anharmonicity and increased local disorder. This study provides a systematic theoretical basis for understanding the microscopic mechanism of the quartz-type phase transition in BeF2 and offers guidance for optimizing the high-temperature service performance of fluoride materials in molten salt reactors.<\/jats:p>","DOI":"10.1063\/5.0344119","type":"journal-article","created":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T10:04:15Z","timestamp":1786356255000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["The structural and dynamical stability of BeF2 at finite temperatures studied by machine learning molecular dynamics"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7610-5353","authenticated-orcid":false,"given":"Meng-yao","family":"Gou","sequence":"first","affiliation":[{"name":"College of Mathematics and Physics, Beijing University of Chemical Technology 1 , Beijing 100029,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-4889-0880","authenticated-orcid":false,"given":"Wen-qian","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Beijing University of Chemical Technology 1 , Beijing 100029,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"Basic Subjects Department, Lanzhou Institute of Technology 2 , Lanzhou 730050,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4572-8161","authenticated-orcid":false,"given":"Hong-zhou","family":"Song","sequence":"additional","affiliation":[{"name":"Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics 3 , Beijing 100094,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5501-7211","authenticated-orcid":false,"given":"Yong","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Physics, Beijing University of Chemical Technology 1 , Beijing 100029,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,8,10]]},"reference":[{"key":"2026081006040966100_c1","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1016\/j.enpol.2013.06.101","article-title":"Generation IV nuclear reactors: Current status and future prospects","volume":"61","year":"2013","journal-title":"Energy Policy"},{"key":"2026081006040966100_c2","doi-asserted-by":"publisher","first-page":"112345","DOI":"10.1016\/j.rser.2022.112345","article-title":"Fluoride-salt-cooled high-temperature reactors: Review of historical milestones, research status, challenges, and outlook","volume":"161","year":"2022","journal-title":"Renewable Sustainable Energy Rev."},{"key":"2026081006040966100_c3","doi-asserted-by":"publisher","first-page":"1778","DOI":"10.1080\/00295450.2019.1691400","article-title":"Fusion blankets and fluoride-salt-cooled high-temperature reactors with FLiBe salt coolant: Common challenges, tritium control, and opportunities for synergistic development strategies between fission, fusion, and solar salt technologies","volume":"206","year":"2019","journal-title":"Nucl. 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