{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T10:49:30Z","timestamp":1777546170689,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["RNF 18-12-00438"],"award-info":[{"award-number":["RNF 18-12-00438"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The effect of planar interfaces on nucleation (namely, on the work of critical cluster formation and their shape) is studied both for crystallization and melting. Advancing an approach formulated about 150 years ago by J. W. Gibbs for liquid phase formation at planar liquid\u2013liquid interfaces, we show that nucleation of liquids in the crystal at crystal\u2013vapor planar interfaces proceeds as a rule with a much higher rate compared to nucleation in the bulk of the crystal. Provided the surface tensions crystal\u2013liquid (\u03c3cl), liquid\u2013vapor (\u03c3lv), and crystal\u2013vapor (\u03c3cv) obey the condition \u03c3cv=\u03c3cl+\u03c3lv, the work of critical cluster formation tends to zero; in the range \u03c3cv&lt;\u03c3cl+\u03c3lv, it is less than one half of the work of critical cluster formation for bulk nucleation. The existence of a liquid\u2013vapor planar interface modifies the work of critical cluster formation in crystal nucleation in liquids to a much less significant degree. The work of critical crystal cluster formation is larger than one half of the bulk value of the work of critical cluster formation, reaching this limit at \u03c3cv=\u03c3cl+\u03c3lv. The shape of the critical clusters can be described in both cases by spherical caps with a radius, R, and a width parameter, h. This parameter, h, is the distance from the cutting plane (coinciding with the crystal\u2013vapor and liquid\u2013vapor planar interface, respectively) to the top of the spherical cap. It varies for nucleation of a liquid in a crystal in the range (h\/R)\u22641 and for crystal nucleation in a liquid in the range 2\u2265(h\/R)\u22651. At \u03c3cv=\u03c3cl+\u03c3lv, the ratio (h\/R) of the critical cluster for nucleation in melting tends to zero ((h\/R)\u21920). At the same condition, the critical crystallite has the shape of a sphere located tangentially to the liquid\u2013vapor interface inside the liquid ((h\/R)\u22452). We present experimental data which confirm the results of the theoretical analysis, and potential further developments of the theoretical approach developed here are anticipated.<\/jats:p>","DOI":"10.3390\/e24081029","type":"journal-article","created":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T22:03:42Z","timestamp":1658873022000},"page":"1029","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Effect of Planar Interfaces on Nucleation in Melting and Crystallization"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5414-6860","authenticated-orcid":false,"given":"J\u00fcrn W. P.","family":"Schmelzer","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Physik, Universit\u00e4t Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany"},{"name":"Competence Centre CALOR, Faculty of Interdisciplinary Research, University of Rostock, Albert-Einstein-Str. 25, 18051 Rostock, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6939-7339","authenticated-orcid":false,"given":"Azat O.","family":"Tipeev","sequence":"additional","affiliation":[{"name":"Institute of Metallurgy, Ural Branch of the Russian Academy of Sciences, 620016 Ekaterinburg, Russia"},{"name":"Institute for High Pressure Physics, Russian Academy of Sciences, 108840 Troitsk, Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,26]]},"reference":[{"key":"ref_1","unstructured":"Volmer, M. (1939). Kinetik der Phasenbildung (Engl.: Kinetics of Phase Formation), Theodor Steinkopff."},{"key":"ref_2","unstructured":"Skripov, V.P., and Koverda, V.P. (1984). 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