Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach *

Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach * | 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 Research Article Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach * Artur Benisek, Edgar Dachs, Gregor Zickler, Rainer Abart This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8258445/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract The Gibbs energy due to coherency strain associated with lamellar phase decomposition, including vibrational components, was investigated, using a microscopic perspective combining atomistic calculations based on density functional theory and calorimetric measurements. The model was applied to the lamellar decomposition of alkali feldspar, revealing that the coherency strain energy coefficient does not only depend on temperature and starting composition, as is the case within the macroscopic, i.e., continuum-mechanical approach, but it also depends on the chemical gradient at the lamellar interfaces and on the lamellar thickness. This difference to the macroscopic approach is caused by a realistic relaxation of the structure in the interior of the lamellae. The coherency strain energy coefficient decreases with decreasing chemical gradient. However, the lowering of the chemical gradient causes the unmixing process to be incomplete increasing the Gibbs energy of mixing, which destabilises lamellae with small chemical gradients. This incompleteness of the unmixing process was quantified in a correction procedure, which was then used to calculate the correct Gibbs energy of mixing. A minimisation procedure of the Gibbs energy that contains components from both mixing and coherency strain resulted in the determination of the equilibrium chemical gradient at lamellar interfaces and its dependence on temperature and lamellar thickness. Although the coherency strain energy coefficient depends on lamellar thickness and chemical gradient, the Gibbs energy minimisation results in a single coherent solvus, which is independent of these properties and is found to agree well with experimental data. The new method can be adapted for coherent lamellar decomposition in other binary solid solutions and alloys. Thermodynamics Precipitation Exsolution DFT Calorimetry Coherency strain energy Feldspar Full Text Additional Declarations The authors declare no competing interests. Supplementary Files SupplementaryMaterial.pdf ciffiles.zip Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8258445","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":561379417,"identity":"a181675b-1e79-4084-b251-6b3a55094034","order_by":0,"name":"Artur Benisek","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIie2RsUoDMRjH/+EgtwS7Gir1FVIOlFvaV7nSlzhQbIrQ6R5AofQZ2qVzINAuh7eeeEuWc9Wt4mIOW3WJ11EwvyUh+X7f/wsBPJ4/CP1cFBAARKY4a1U6Tem3koMdbk5dCpcHxUKmsyMU8VRsuimq3mUYGnO/qJgoFHnZYXDjVB7GlOeoo/iWRf3VumaiTAKeYexOyQPKJfRoqRnlZq2tAnTt05zKcK9Mljp8fjNz3QwWvAOT1pREaFyQlbSKSqhN0b8pUSxF3beDRfxuUzNejmZxJra2kUsh5lGm1bkotuY1u656J4XW5S696rhS9uLXTqH50Z8nrajjSz0ej+ff8AEuRVZRWP2yGwAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Artur","middleName":"","lastName":"Benisek","suffix":""},{"id":561379418,"identity":"0173aff5-c7d5-4971-ab14-7e5da778f311","order_by":1,"name":"Edgar Dachs","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Edgar","middleName":"","lastName":"Dachs","suffix":""},{"id":561379419,"identity":"67a84265-46e2-48a7-aa68-dc1082848f07","order_by":2,"name":"Gregor Zickler","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Gregor","middleName":"","lastName":"Zickler","suffix":""},{"id":561379420,"identity":"77339dd6-7cd2-4304-b91b-de08f4fa4366","order_by":3,"name":"Rainer Abart","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Rainer","middleName":"","lastName":"Abart","suffix":""}],"badges":[],"createdAt":"2025-12-02 09:09:00","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8258445/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-8258445/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98539769,"identity":"7842fccc-ada8-4c0e-9509-017e1d8db61c","added_by":"auto","created_at":"2025-12-18 17:11:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1039191,"visible":true,"origin":"","legend":"","description":"","filename":"Coherentdecompositionfeldspar.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8258445/v2_covered_2d91af1e-0802-4c40-b547-5ed92a547ca0.pdf"},{"id":98539731,"identity":"402c659f-d640-4131-8ff7-c8cfd0b28edf","added_by":"auto","created_at":"2025-12-18 17:11:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":817054,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SupplementaryMaterial.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8258445/v2/79990b93e4517ca662699377.pdf"},{"id":98539729,"identity":"45757a0a-1606-4ad2-b31c-05f289916e0a","added_by":"auto","created_at":"2025-12-18 17:11:39","extension":"zip","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":22250,"visible":true,"origin":"","legend":"","description":"","filename":"ciffiles.zip","url":"https://assets-eu.researchsquare.com/files/rs-8258445/v2/2416c885a4dd12cce5359a1b.zip"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach *","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Salzburg","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Thermodynamics, Precipitation, Exsolution, DFT, Calorimetry, Coherency strain energy, Feldspar","lastPublishedDoi":"10.21203/rs.3.rs-8258445/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8258445/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Gibbs energy due to coherency strain associated with lamellar phase decomposition, including vibrational components, was investigated, using a microscopic perspective combining atomistic calculations based on density functional theory and calorimetric measurements. The model was applied to the lamellar decomposition of alkali feldspar, revealing that the coherency strain energy coefficient does not only depend on temperature and starting composition, as is the case within the macroscopic, i.e., continuum-mechanical approach, but it also depends on the chemical gradient at the lamellar interfaces and on the lamellar thickness. This difference to the macroscopic approach is caused by a realistic relaxation of the structure in the interior of the lamellae. The coherency strain energy coefficient decreases with decreasing chemical gradient. However, the lowering of the chemical gradient causes the unmixing process to be incomplete increasing the Gibbs energy of mixing, which destabilises lamellae with small chemical gradients. This incompleteness of the unmixing process was quantified in a correction procedure, which was then used to calculate the correct Gibbs energy of mixing. A minimisation procedure of the Gibbs energy that contains components from both mixing and coherency strain resulted in the determination of the equilibrium chemical gradient at lamellar interfaces and its dependence on temperature and lamellar thickness. Although the coherency strain energy coefficient depends on lamellar thickness and chemical gradient, the Gibbs energy minimisation results in a single coherent solvus, which is independent of these properties and is found to agree well with experimental data. The new method can be adapted for coherent lamellar decomposition in other binary solid solutions and alloys.\u003c/p\u003e","manuscriptTitle":"Coherent lamellar phase decomposition of alkali feldspar studied by a microscopic approach *","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-12-18 17:10:07","doi":"10.21203/rs.3.rs-8258445/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":1,"date":"2025-12-03 03:52:41","doi":"10.21203/rs.3.rs-8258445/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9dfeab46-19f3-438e-b2a0-0f9cdcf50c70","owner":[],"postedDate":"December 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-03T03:52:41+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-18 17:10:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-8258445","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8258445","identity":"rs-8258445","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}