{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T01:34:59Z","timestamp":1775007299256,"version":"3.50.1"},"reference-count":79,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,20]],"date-time":"2021-02-20T00:00:00Z","timestamp":1613779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["DE 598\/28-1"],"award-info":[{"award-number":["DE 598\/28-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Access Publishing Fund of Clausthal University of Technology","award":["-"],"award-info":[{"award-number":["-"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, methods of description of crystal nucleation by using the statistical approach are analyzed. Findings from classical nucleation theory (CNT) for the average time of formation of the first supercritical nucleus are linked with experimental data on nucleation in glass-forming liquids stemming from repetitive cooling protocols both under isothermal and isochronal conditions. It is shown that statistical methods of lifetime analysis, frequently used in medicine, public health, and social and behavioral sciences, are applicable to crystal nucleation problems in glass-forming liquids and are very useful tools for their exploration. Identifying lifetime with the time to nucleate as a random variable in homogeneous and non-homogeneous Poisson processes, solutions for the nucleation rate under steady-state conditions are presented using the hazard rate and related parameters. This approach supplies us with a more detailed description of nucleation going beyond CNT. In particular, we show that cumulative hazard estimation enables one to derive the plotting positions for visually examining distributional model assumptions. As the crystallization of glass-forming melts can involve more than one type of nucleation processes, linear dependencies of the cumulative hazard function are used to facilitate assignment of lifetimes to each nucleation mechanism.<\/jats:p>","DOI":"10.3390\/e23020246","type":"journal-article","created":{"date-parts":[[2021,2,21]],"date-time":"2021-02-21T21:15:01Z","timestamp":1613942101000},"page":"246","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Statistical Approach to Crystal Nucleation in Glass-Forming Liquids"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3474-7490","authenticated-orcid":false,"given":"Joachim","family":"Deubener","sequence":"first","affiliation":[{"name":"Institute of Non-Metallic Materials, Clausthal University of Technology, Zehntner Str. 2a, 38678 Clausthal-Zellerfeld, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5414-6860","authenticated-orcid":false,"given":"J\u00fcrn W. P.","family":"Schmelzer","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik der Universit\u00e4t Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,20]]},"reference":[{"key":"ref_1","unstructured":"Gibbs, J.W. (1928). The Collected Works. Thermodynamics, Longmans & Green."},{"key":"ref_2","unstructured":"Volmer, M. (1939). Kinetik der Phasenbildung (Engl.: Kinetics of Phase Formation), Th. Steinkopff."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ulbricht, H., Schmelzer, J.W.P., Mahnke, R., and Schweitzer, F. (1988). Thermodynamics of Finite Systems and the Kinetics of First-Order Phase Transitions, Teubner-Verlag. 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