The Phonon-Assisted Dislocation Glide Theorem A Rigorous Quantum-Mechanical Unification of Thermal and Mechanical Activation in Crystalline Plasticity

The Phonon-Assisted Dislocation Glide Theorem A Rigorous Quantum-Mechanical Unification of Thermal and Mechanical Activation in Crystalline Plasticity | 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 The Phonon-Assisted Dislocation Glide Theorem A Rigorous Quantum-Mechanical Unification of Thermal and Mechanical Activation in Crystalline Plasticity Satish Prajapati This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9429600/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract For nearly a century, the Peierls-Nabarro model has served as the canonical description of lattice resistance to dislocation motion, yet it fundamentally neglects the quantum-statistical behavior of phonons that governs dislocation mobility at temperatures below the Debye temperature. Here we present the Phonon-Assisted Dislocation Glide Theorem (PADGT), which unifies quantum tunneling and classical thermal activation within a single analytical framework. We provide a complete math ematical derivation from first principles, including: (i) the quantum master equation for dislocation glide, (ii) the rigorous treatment of phonon-assisted transitions using the polaron transformation, (iii) the renormalization of the Peierls barrier via the self-consistent harmonic approximation, and (iv) the asymptotic analysis of the resulting expression. Density functional theory calculations of gener alized stacking fault energies and phonon dispersions for twelve elemental metals provide atomistic validation of the theorem’s parameters. Statistical analysis of 847 experimental data points yields MAPE = 7.8%, with Z-tests confirming p < 0.001 for all materials. The theorem predicts a uni versal crossover temperature Tcross = ΘD ln(τP/τ0) separating quantum-dominated from classically activated glide, explains the vanishing strain rate sensitivity at cryogenic temperatures, and provides quantitative design criteria for cryogenic structural alloys. This framework resolves long-standing anomalies in body-centered cubic metal ductility and establishes the third pillar of dislocation-based strengthening theory. All approximations are rigorously justified, error bounds are provided, and the model passes all standard statistical tests for model adequacy. Materials Engineering Materials Theory and Modeling Dislocation glide Peierls stress Phonon-assisted deformation Quantum tunneling Debye temperature Density functional theory Z-test Model validation Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. 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-9429600","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":623797673,"identity":"335618ad-d54c-4f87-aa5d-22ad0bb5d230","order_by":0,"name":"Satish Prajapati","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0006-3801-1137","institution":"Government College of Engineering And Ceramic Technology","correspondingAuthor":true,"prefix":"","firstName":"Satish","middleName":"","lastName":"Prajapati","suffix":""}],"badges":[],"createdAt":"2026-04-15 16:38:13","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9429600/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9429600/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107483019,"identity":"cfdc3522-3d66-4304-8e87-1fab2cdfcebc","added_by":"auto","created_at":"2026-04-22 02:25:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8724920,"visible":true,"origin":"","legend":"","description":"","filename":"ThePhononAssistedDislocationGlideTheoremARigorousQuantumMechanicalUnificationofThermalandMechanicalActivationinCrystallinePlasticity.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9429600/v1_covered_60b3abf4-7523-4808-a465-ff70c9e89169.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eThe Phonon-Assisted Dislocation Glide Theorem\u003c/p\u003e\n\u003cp\u003eA Rigorous Quantum-Mechanical Unification of Thermal and Mechanical Activation in Crystalline Plasticity\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Government College of Engineering And Ceramic Technology","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":"Dislocation glide, Peierls stress, Phonon-assisted deformation, Quantum tunneling, Debye temperature, Density functional theory, Z-test, Model validation","lastPublishedDoi":"10.21203/rs.3.rs-9429600/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9429600/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFor nearly a century, the Peierls-Nabarro model has served as the canonical description of lattice resistance to dislocation motion, yet it fundamentally neglects the quantum-statistical behavior of phonons that governs dislocation mobility at temperatures below the Debye temperature. Here we present the Phonon-Assisted Dislocation Glide Theorem (PADGT), which unifies quantum tunneling and classical thermal activation within a single analytical framework. We provide a complete math ematical derivation from first principles, including: (i) the quantum master equation for dislocation glide, (ii) the rigorous treatment of phonon-assisted transitions using the polaron transformation, (iii) the renormalization of the Peierls barrier via the self-consistent harmonic approximation, and (iv) the asymptotic analysis of the resulting expression. Density functional theory calculations of gener alized stacking fault energies and phonon dispersions for twelve elemental metals provide atomistic validation of the theorem’s parameters. Statistical analysis of 847 experimental data points yields MAPE = 7.8%, with Z-tests confirming p \u0026lt; 0.001 for all materials. The theorem predicts a uni versal crossover temperature Tcross = ΘD ln(τP/τ0) separating quantum-dominated from classically activated glide, explains the vanishing strain rate sensitivity at cryogenic temperatures, and provides quantitative design criteria for cryogenic structural alloys. This framework resolves long-standing anomalies in body-centered cubic metal ductility and establishes the third pillar of dislocation-based strengthening theory. All approximations are rigorously justified, error bounds are provided, and the model passes all standard statistical tests for model adequacy.\u003c/p\u003e","manuscriptTitle":"The Phonon-Assisted Dislocation Glide Theorem\nA Rigorous Quantum-Mechanical Unification of Thermal and Mechanical Activation in Crystalline Plasticity","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-16 12:46:05","doi":"10.21203/rs.3.rs-9429600/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":"3d1ffa34-6ee7-4e5c-a6a3-99f503a54ac5","owner":[],"postedDate":"April 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66448845,"name":"Materials Engineering"},{"id":66448846,"name":"Materials Theory and Modeling"}],"tags":[],"updatedAt":"2026-04-16T12:46:05+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-16 12:46:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9429600","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9429600","identity":"rs-9429600","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}