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dc.contributor.authorMechighel, Fariden_US
dc.contributor.authorArmour, Neilen_US
dc.contributor.authorDost, Sadıken_US
dc.contributor.authorKadja, Mahfouden_US
dc.date.accessioned2020-09-18T13:29:39Z
dc.date.available2020-09-18T13:29:39Z
dc.date.issued2011-10-16
dc.identifier.citationMechighel, F., Armour, N., Dost, S. & Kadja, M. (2011). Mathematical modeling of the dissolution process of silicon into germanium melt. TWMS Journal of Applied and Engineering Mathematics, 1(2), 127-149.en_US
dc.identifier.issn2146-1147
dc.identifier.issn2587-1013
dc.identifier.urihttps://hdl.handle.net/11729/2424
dc.identifier.urihttp://jaem.isikun.edu.tr/web/index.php/archive/86-vol1no2/155
dc.description.abstractNumerical simulations were carried out to study the thermosolutal and flow structures observed in the dissolution experiments of silicon into a germanium melt. The dissolution experiments utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) crystal growth systems. In the present model, the computational domain was assumed axisymmetric. Governing equations of the liquid phase (Si-Ge mixture), namely the equations of conservation of mass, momentum balance, energy balance, and solute (species) transport balance were solved using the Stabilized Finite Element Methods (ST-GLS for fluid flow, SUPG for heat and solute transport). Measured concentration profiles and dissolution height from the samples processed with and without the application of magnetic field show that the amount of silicon transported into the melt is slightly higher in the samples processed under magnetic field, and there is a difference in dissolution interface shape indicating a change in the flow structure during the dissolution process. The present mathematical model predicts this difference in the flow structure. In the absence of magnetic field, a flat stable interface is observed. In the presence of an applied field, however, the dissolution interface remains flat in the center but curves back into the source material near the edge of the wall. This indicates a far higher dissolution rate at the edge of the silicon source.en_US
dc.description.sponsorshipWe gratefully acknowledge the financial support provided by the Canadian Space Agency (CSA), Canada Research Chairs (CRC) Program, and the Natural Sciences and Engineering Research Council (NSERC) of Canada.en_US
dc.language.isoengen_US
dc.publisherIşık University Pressen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectDissolutionen_US
dc.subjectConvectionen_US
dc.subjectDiffusionen_US
dc.subjectNumerical simulationen_US
dc.subjectStabilized finite element techniquesen_US
dc.titleMathematical modeling of the dissolution process of silicon into germanium melten_US
dc.typearticleen_US
dc.description.versionPublisher's Versionen_US
dc.relation.journalTWMS Journal of Applied and Engineering Mathematicsen_US
dc.identifier.volume1
dc.identifier.issue2
dc.identifier.startpage127
dc.identifier.endpage149
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıen_US


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