Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth

Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth Noriko Akutsu, Yoshihiro Kangawa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3980836/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Kinetic roughening of the (001) singular surface for nucleation-limited steady crystal growth is studied on the basis of a lattice model using the Monte Carlo method. At a sufficiently low temperature, there are two kinetic roughening points as the driving force for crystal growth Δμ increases. At a low driving force ΔμKPZ(001), there is the Karder-Parisi-Zhang (KPZ) roughening transition point. On the KPZ rough surface, elementary steps around islands are well defined though the surface is thermodynamically rough, with a roughness exponent α of 0.3869. At a relatively large driving force, the Berezinskii-Kosteritz-Thouless (BKT)-type kinetically rough region was found for ΔμBKT(001) < Δμ. Around the middle driving force between the two kinetic roughening points, the crossover area that starts from the driving force ΔμKtoT(001) was found. For ΔμKtoT(001) < Δμ, the surface grows linearly as the driving force increases (adhesive growth). The points ΔμKPZ(001), ΔμKtoT(001), and ΔμBKT(001) decrease with increasing temperature because the step free energy decreases. Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Statistical physics Physical sciences/Materials science/Condensed matter physics/Surfaces interfaces and thin films Physical sciences/Nanoscience and technology/Other nanotechnology/Computational nanotechnology Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 08 May, 2024 Reviews received at journal 31 Mar, 2024 Reviews received at journal 24 Mar, 2024 Reviewers agreed at journal 20 Mar, 2024 Reviewers agreed at journal 12 Mar, 2024 Reviewers invited by journal 10 Mar, 2024 Editor assigned by journal 10 Mar, 2024 Editor invited by journal 06 Mar, 2024 Submission checks completed at journal 06 Mar, 2024 First submitted to journal 23 Feb, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3980836","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":276725550,"identity":"84c623f0-c33a-46ae-be12-312fa53543ae","order_by":0,"name":"Noriko Akutsu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYJCCgx8qGBKgbBjNg1/LYYkzpGph4G3D0IIHmLP3PjwgOe9OnsH5A4wPf9SkyfM3MD/8wCBzB6cWy57jBgcKtz0rNriRwGzMcyzHcMYBNmMJBp5nOLUY3EhjOCC57XDihhsMbNIMbBWMGxgYzIB+OYxfC+8coJbzB9gkf/yrsN/AwP6NCC0NQC0HEtgkeNtyEjcw8BCw5cwxYCAfe5Y480ZiszFvX1ryjMM8xRIJ+PxyvI3544eaO4l95w8ffPjjW7Jtf3v7xg8fe3CHGBQcYFA4wNgAYTMDcWLPAcJa5BtQBH4Q1DIKRsEoGAUjBwAAx2Bd81BtVRYAAAAASUVORK5CYII=","orcid":"","institution":"Osaka Electro-Communication University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Noriko","middleName":"","lastName":"Akutsu","suffix":""},{"id":276725551,"identity":"355b73d9-a72c-4517-99f0-04b676f2f5c2","order_by":1,"name":"Yoshihiro Kangawa","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yoshihiro","middleName":"","lastName":"Kangawa","suffix":""}],"badges":[],"createdAt":"2024-02-23 06:01:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3980836/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3980836/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-79380-5","type":"published","date":"2024-11-29T15:57:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":70389108,"identity":"e87272b3-5b39-4d8d-8ff1-98063b68b14a","added_by":"auto","created_at":"2024-12-02 17:28:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2362840,"visible":true,"origin":"","legend":"","description":"","filename":"TdependenceKPZBKTu8.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3980836/v1_covered_0926a7e4-a337-4b2d-b26a-8fd24916d13d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3980836/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3980836/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Kinetic roughening of the (001) singular surface for nucleation-limited steady crystal growth is studied on the basis of a lattice model using the Monte Carlo method. 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