{"id":"https://openalex.org/W2991090889","doi":"https://doi.org/10.3390/e21121147","title":"Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results","display_name":"Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results","publication_year":2019,"publication_date":"2019-11-25","ids":{"openalex":"https://openalex.org/W2991090889","doi":"https://doi.org/10.3390/e21121147","mag":"2991090889"},"language":"en","primary_location":{"id":"doi:10.3390/e21121147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21121147","pdf_url":"https://www.mdpi.com/1099-4300/21/12/1147/pdf?version=1574671574","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/12/1147/pdf?version=1574671574","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047421458","display_name":"J\u00fcrn W. P. Schmelzer","orcid":"https://orcid.org/0000-0002-5414-6860"},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00fcrn W. P. Schmelzer","raw_affiliation_strings":["Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5414-6860","affiliations":[{"raw_affiliation_string":"Institute of Physics, University of Rostock, Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany","institution_ids":["https://openalex.org/I4665924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047421458"],"corresponding_institution_ids":["https://openalex.org/I4665924"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":1298,"currency":"EUR","value_usd":1399},"fwci":0.7486,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72419699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"12","first_page":"1147","last_page":"1147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10474","display_name":"Material Dynamics and Properties","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nucleation","display_name":"Nucleation","score":0.8816691637039185},{"id":"https://openalex.org/keywords/crystallization","display_name":"Crystallization","score":0.6569274067878723},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.5854379534721375},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5761412382125854},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.549440860748291},{"id":"https://openalex.org/keywords/crystal","display_name":"Crystal (programming language)","score":0.529589831829071},{"id":"https://openalex.org/keywords/classical-nucleation-theory","display_name":"Classical nucleation theory","score":0.4930121600627899},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4583974778652191},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.45632317662239075},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4489891529083252},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4481920599937439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42694658041000366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3023953139781952},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12383091449737549},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1172914206981659},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11671936511993408}],"concepts":[{"id":"https://openalex.org/C61048295","wikidata":"https://www.wikidata.org/wiki/Q909022","display_name":"Nucleation","level":2,"score":0.8816691637039185},{"id":"https://openalex.org/C203036418","wikidata":"https://www.wikidata.org/wiki/Q284256","display_name":"Crystallization","level":2,"score":0.6569274067878723},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.5854379534721375},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5761412382125854},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.549440860748291},{"id":"https://openalex.org/C2781285689","wikidata":"https://www.wikidata.org/wiki/Q21921428","display_name":"Crystal (programming language)","level":2,"score":0.529589831829071},{"id":"https://openalex.org/C2780393986","wikidata":"https://www.wikidata.org/wiki/Q19892223","display_name":"Classical nucleation theory","level":3,"score":0.4930121600627899},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4583974778652191},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.45632317662239075},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4489891529083252},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4481920599937439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42694658041000366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3023953139781952},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12383091449737549},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1172914206981659},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11671936511993408},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e21121147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21121147","pdf_url":"https://www.mdpi.com/1099-4300/21/12/1147/pdf?version=1574671574","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/12/1147/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21121147","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514492","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514492","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21121147","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21121147","pdf_url":"https://www.mdpi.com/1099-4300/21/12/1147/pdf?version=1574671574","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2991090889.pdf","grobid_xml":"https://content.openalex.org/works/W2991090889.grobid-xml"},"referenced_works_count":88,"referenced_works":["https://openalex.org/W10684602","https://openalex.org/W29051238","https://openalex.org/W109108658","https://openalex.org/W288366531","https://openalex.org/W592615579","https://openalex.org/W853327289","https://openalex.org/W1272747048","https://openalex.org/W1480586711","https://openalex.org/W1513206095","https://openalex.org/W1540588250","https://openalex.org/W1969641936","https://openalex.org/W1970033288","https://openalex.org/W1972303335","https://openalex.org/W1973542361","https://openalex.org/W1974006140","https://openalex.org/W1974159665","https://openalex.org/W1976428766","https://openalex.org/W1977480358","https://openalex.org/W1981720584","https://openalex.org/W1981869633","https://openalex.org/W1984971272","https://openalex.org/W1985753636","https://openalex.org/W1985860357","https://openalex.org/W1987723981","https://openalex.org/W1988086771","https://openalex.org/W2004758392","https://openalex.org/W2010163409","https://openalex.org/W2014699027","https://openalex.org/W2027497593","https://openalex.org/W2030444456","https://openalex.org/W2034852583","https://openalex.org/W2036384007","https://openalex.org/W2045658724","https://openalex.org/W2046229659","https://openalex.org/W2046528357","https://openalex.org/W2047137396","https://openalex.org/W2049565132","https://openalex.org/W2052355932","https://openalex.org/W2057658953","https://openalex.org/W2058585715","https://openalex.org/W2061002423","https://openalex.org/W2061150119","https://openalex.org/W2063595534","https://openalex.org/W2063778738","https://openalex.org/W2064984128","https://openalex.org/W2074439496","https://openalex.org/W2081149893","https://openalex.org/W2083750851","https://openalex.org/W2088156633","https://openalex.org/W2088558421","https://openalex.org/W2092619424","https://openalex.org/W2093747401","https://openalex.org/W2095567101","https://openalex.org/W2123073876","https://openalex.org/W2130668410","https://openalex.org/W2132142633","https://openalex.org/W2239098806","https://openalex.org/W2399411120","https://openalex.org/W2472122678","https://openalex.org/W2473637508","https://openalex.org/W2484771791","https://openalex.org/W2486637755","https://openalex.org/W2489928500","https://openalex.org/W2491945782","https://openalex.org/W2508970202","https://openalex.org/W2514256124","https://openalex.org/W2549805809","https://openalex.org/W2603082871","https://openalex.org/W2610541749","https://openalex.org/W2611901592","https://openalex.org/W2772029758","https://openalex.org/W2893817715","https://openalex.org/W2947492734","https://openalex.org/W2961688522","https://openalex.org/W2968352359","https://openalex.org/W2973296545","https://openalex.org/W2981942189","https://openalex.org/W2988477182","https://openalex.org/W2997932550","https://openalex.org/W3101841585","https://openalex.org/W4230873885","https://openalex.org/W4231839311","https://openalex.org/W4252073945","https://openalex.org/W4256655203","https://openalex.org/W4285719527","https://openalex.org/W6635248728","https://openalex.org/W6679338983","https://openalex.org/W6720680801"],"related_works":["https://openalex.org/W86446358","https://openalex.org/W2904897503","https://openalex.org/W1521492379","https://openalex.org/W4402416100","https://openalex.org/W2371714203","https://openalex.org/W2980651902","https://openalex.org/W2373012553","https://openalex.org/W2884898669","https://openalex.org/W4388927674","https://openalex.org/W2430274953"],"abstract_inverted_index":{"Different":[0],"aspects":[1],"in":[2,26,71,126,222,310],"applying":[3],"the":[4,8,22,27,37,79,83,90,93,102,105,122,127,142,152,156,165,168,180,195,199,232,240,243,253,257,260,265,268,271,278,283,297,316,320,324],"nucleation":[5,38,63,106,143,216,298,305],"theorem":[6,39,107,144,163],"to":[7,73,89],"description":[9,29,128,255],"of":[10,12,30,36,61,82,92,104,129,141,158,161,176,179,198,214,231,242,259,267,270,273,280,282,296,315,319,326],"crystallization":[11],"liquids":[13],"are":[14,86,209],"analyzed.":[15],"It":[16,98],"is":[17,44,65,76,99,148,172,290,330],"shown":[18,100],"that,":[19],"by":[20,110,146,174,192,256],"employing":[21],"classical":[23,62,124,215,304],"Gibbs\u2019":[24],"approach":[25,125,263],"thermodynamic":[28],"heterogeneous":[31],"systems,":[32],"a":[33,293,313],"general":[34,139],"form":[35,140],"can":[40,249],"be":[41,250],"formulated":[42],"that":[43,78,101,167,292],"valid":[45],"not":[46,224],"only":[47],"for":[48,52,133,155,164,194,264],"one-component":[49],"but":[50],"generally":[51],"multi-component":[53,134],"systems.":[54],"In":[55,67,186],"this":[56,162,187,287],"analysis,":[57],"one":[58],"basic":[59,212],"assumption":[60,213],"theory":[64,217],"utilized.":[66],"addition,":[68],"commonly":[69],"employed":[70],"application":[72,258],"crystallization,":[74],"it":[75,289],"supposed":[77],"bulk":[80,227],"properties":[81,91,230,241,272],"critical":[84,233,274,321],"clusters":[85,235,276,322],"widely":[87,120],"identical":[88],"newly":[94],"evolving":[95,244],"crystal":[96,130,234,275],"phase.":[97,285],"formulation":[103,295],"as":[108,136,151,300],"proposed":[109],"Kashchiev":[111],"[J.":[112],"Chem.":[113],"Phys.":[114],"76,":[115],"5098-5102":[116],"(1982)],":[117],"also":[118,309],"relying":[119],"on":[121,205,277,303,323],"standard":[123],"nucleation,":[131],"holds":[132,307],"systems":[135],"well.":[137],"The":[138,211,226],"derived":[145,301],"us":[147,193],"taken":[149],"then":[150],"starting":[153],"point":[154],"derivation":[157],"particular":[159],"forms":[160],"cases":[166,311],"deviation":[169,327],"from":[170,239,328],"equilibrium":[171,329],"caused":[173],"variations":[175],"either":[177],"composition":[178],"liquid":[181,284],"phase,":[182],"temperature,":[183],"or":[184],"pressure.":[185],"procedure,":[188],"expressions":[189],"recently":[190],"developed":[191],"curvature":[196],"dependence":[197,204,269,314],"surface":[200,229],"tension,":[201],"respectively,":[202],"its":[203],"pressure":[206],"and/or":[207],"temperature":[208],"employed.":[210],"mentioned":[218],"above":[219],"is,":[220],"however,":[221],"general,":[223],"true.":[225],"and":[228],"may":[236],"differ":[237],"considerably":[238],"macroscopic":[245],"phases.":[246],"Such":[247],"effects":[248],"incorporated":[251],"into":[252],"theoretical":[254],"generalized":[261],"Gibbs":[262],"specification":[266],"degree":[279,325],"metastability":[281],"Applying":[286],"method,":[288],"demonstrated":[291],"similar":[294],"theorem,":[299],"based":[302],"theory,":[306],"true":[308],"when":[312],"state":[317],"parameters":[318],"appropriately":[331],"accounted":[332],"for.":[333]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}