Slope-dependent Kinetic-roughening diagram between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless rough surfaces for steady crystal growth

Slope-dependent Kinetic-roughening diagram between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless rough surfaces for 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 Slope-dependent Kinetic-roughening diagram between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless rough surfaces for steady crystal growth Noriko Akutsu, Yoshihiro Kangawa This is a preprint; it has not been peer reviewed by a journal.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-6675137/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract Surface roughness at the nanometer scale influences the morphology of crystallites at the micrometer scale, the structure factor in X-ray scattering, and backscattering in lidar for passive remote sensing of ice clouds. In this study, the surface roughness and its roughness exponent are calculated for nano-scale two-dimensional surfaces in three dimensions during the steady growth of crystals using the Monte Carlo method on a lattice model. By monitoring the roughness exponent, slope-dependent kinetic roughening diagrams are constructed for universality classes. The diagrams provide insight into the intricate relationship between the roughness exponent and surface slope, as well as the driving force for crystal growth. The resulting diagrams reveal that at low temperatures, two Kardar-Parisi-Zhang (KPZ) kinetic roughening regions, KPZ-1 and KPZ-2, are separated by a region of Berezinskii-Kosterlitz-Thouless (BKT) roughening. At high temperatures close to but below the thermal roughening transition temperature of the (001) surface, another KPZ region, KPZ-3, emerges for large driving forces for crystal growth. The terrace width histogram and surface height difference distribution function were also calculated using the Monte Carlo method and provide insight into how the surface crosses over to other classes or subclasses. Physical sciences/Physics/Condensed matter physics/Surfaces interfaces and thin films Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics Physical sciences/Mathematics and computing/Computational science Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 03 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 10 Jul, 2025 Reviews received at journal 12 Jun, 2025 Reviewers agreed at journal 02 Jun, 2025 Reviewers agreed at journal 02 Jun, 2025 Reviewers invited by journal 02 Jun, 2025 Editor assigned by journal 02 Jun, 2025 Editor invited by journal 29 May, 2025 Submission checks completed at journal 29 May, 2025 First submitted to journal 15 May, 2025 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. We do this by developing innovative software and high quality services for the global research community. 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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-6675137","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":465698090,"identity":"376fc6b3-fd45-47a0-88b7-213abe4c92fa","order_by":0,"name":"Noriko Akutsu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIiWNgGAWjYDACHjBpw8AGJBkbgIQBTAbMw64FJJVGupbDCEUGOBTCAX/PGfOHP9vO5/Oxn05gnNl22N5cIoFNgqHGjoF5NnZrJM72GDbztt22bOPJ3cC4se1w4s4ZIC3HkhkY5xzAbs15HsNmxrbbBmwMQC0P2w4nGNzI/ybBwHaAgXFGAlYd8kAtjT/bzhmw8b8Fa7E3uAGy5R9uLQZAhzXwth0wYJOAOIxxA0gLYxtuLYZnjhXO5jmXDNTydsPBGefSEzececBskdiXzIPLL3Jnkjd8/FFmZyDfn7vxYU+Ztb3B8QTGGx++2ckZ4ggxFHCAkQ3KAjqJx3AGYR1A8AeJLS9BlJZRMApGwSgY/gAA+rFgAwLQqmcAAAAASUVORK5CYII=","orcid":"","institution":"Kyushu University","correspondingAuthor":true,"prefix":"","firstName":"Noriko","middleName":"","lastName":"Akutsu","suffix":""},{"id":465698091,"identity":"ef052af9-2f5a-45cb-bb4b-3de9ed883e1f","order_by":1,"name":"Yoshihiro Kangawa","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Yoshihiro","middleName":"","lastName":"Kangawa","suffix":""}],"badges":[],"createdAt":"2025-05-15 18:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6675137/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6675137/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-18250-0","type":"published","date":"2025-10-03T15:57:17+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92883917,"identity":"f42538cc-3b3d-4ab4-b8cd-e5aeda89bc49","added_by":"auto","created_at":"2025-10-06 16:10:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1456008,"visible":true,"origin":"","legend":"","description":"","filename":"KRdiagramSRp8.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6675137/v1_covered_70fb835a-4866-4f41-98c3-11a5a8cfcd05.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Slope-dependent Kinetic-roughening diagram between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless rough surfaces for 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-6675137/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6675137/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Surface roughness at the nanometer scale influences the morphology of crystallites at the micrometer scale, the structure factor in X-ray scattering, and backscattering in lidar for passive remote sensing of ice clouds. 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