Uniformly valid asymptotic solutions of rod eutectic growth in directional solidification for liquid-solid interface slopes of small order
Recently, uniformly valid asymptotic solutions of rod eutectic growth for liquid-solid interface slopes at triple phase junction being the normal order have been presented in reference (Li and Xu, 2017). In this work, analytical calculations of rod eutectic growth during directional solidification f...
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| Veröffentlicht in: | Journal of crystal growth 2019-02, Vol.507, p.453-458 |
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| creator | Li, Xiang-Ming Chen, Xiang-Kai Xu, Fei |
| description | Recently, uniformly valid asymptotic solutions of rod eutectic growth for liquid-solid interface slopes at triple phase junction being the normal order have been presented in reference (Li and Xu, 2017). In this work, analytical calculations of rod eutectic growth during directional solidification for liquid-solid interface of small order are performed. The purpose is to study the liquid-solid interfacial shape and average undercooling of rod eutectic growth. We give the mathematical formulation of rod eutectic growth for the general case. The steady solutions of rod eutectic growth are obtained by using asymptotic expansion method and matching method. The relationship of the overall average interfacial undercooling with the rod eutectic spacing is presented. The overall average interfacial undercooling always exists a minimum value at the minimum-undercooling spacing, and the minimum-undercooling spacing is slightly smaller than one given by Jackson and Hunt. We also analyze the effect of pulling speeds and thermal gradients on the interfacial shapes for the case of the minimum-undercooling spacing. |
| doi_str_mv | 10.1016/j.jcrysgro.2018.10.015 |
| format | Article |
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In this work, analytical calculations of rod eutectic growth during directional solidification for liquid-solid interface of small order are performed. The purpose is to study the liquid-solid interfacial shape and average undercooling of rod eutectic growth. We give the mathematical formulation of rod eutectic growth for the general case. The steady solutions of rod eutectic growth are obtained by using asymptotic expansion method and matching method. The relationship of the overall average interfacial undercooling with the rod eutectic spacing is presented. The overall average interfacial undercooling always exists a minimum value at the minimum-undercooling spacing, and the minimum-undercooling spacing is slightly smaller than one given by Jackson and Hunt. We also analyze the effect of pulling speeds and thermal gradients on the interfacial shapes for the case of the minimum-undercooling spacing.</description><identifier>ISSN: 0022-0248</identifier><identifier>EISSN: 1873-5002</identifier><identifier>DOI: 10.1016/j.jcrysgro.2018.10.015</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>A1. Asymptotic solution ; A1. Directional solidification ; A1. Eutectic growth ; A1. Interfacial shape ; A1. 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In this work, analytical calculations of rod eutectic growth during directional solidification for liquid-solid interface of small order are performed. The purpose is to study the liquid-solid interfacial shape and average undercooling of rod eutectic growth. We give the mathematical formulation of rod eutectic growth for the general case. The steady solutions of rod eutectic growth are obtained by using asymptotic expansion method and matching method. The relationship of the overall average interfacial undercooling with the rod eutectic spacing is presented. The overall average interfacial undercooling always exists a minimum value at the minimum-undercooling spacing, and the minimum-undercooling spacing is slightly smaller than one given by Jackson and Hunt. We also analyze the effect of pulling speeds and thermal gradients on the interfacial shapes for the case of the minimum-undercooling spacing.</description><subject>A1. Asymptotic solution</subject><subject>A1. Directional solidification</subject><subject>A1. Eutectic growth</subject><subject>A1. Interfacial shape</subject><subject>A1. Undercooling</subject><subject>Asymptotic methods</subject><subject>Asymptotic series</subject><subject>Directional solidification</subject><subject>Liquid-solid interfaces</subject><subject>Slopes</subject><subject>Solids</subject><subject>Supercooling</subject><issn>0022-0248</issn><issn>1873-5002</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNqFkM1OwzAQhC0EEqXwCsgS5wQ7dpPmBqr4kypxoWfLsdfgyI1TOynqK_DUOBTOXGxpdmZW-yF0TUlOCS1v27xV4RDfg88LQpdJzAldnKAZXVYsWxBSnKJZeouMFHx5ji5ibAlJSUpm6GvTWePD1h3wXjqrsYyHbT_4wSocvRsH67uIvcHBawzjAGqapF2fwwe2HdY2TJLvpJv8VltjlZwEnGqxs7vR6uxnkuwDBCMV4Oh8Dz-1cSudwz5oCJfozEgX4er3n6PN48Pb6jlbvz69rO7XmWKcDFnNyhJKxmFBgVECDWjJa6hYQRrdcNPQsjKy1qypDTOKVgXndEmgLrgqpeFsjm6OvX3wuxHiIFo_hnRAFEVCVtOaVGVylUeXCj7GAEb0wW5lOAhKxMRdtOKPu5i4T3rinoJ3xyCkG_YWgojKQqfgiEpob_-r-AbQZJOx</recordid><startdate>20190201</startdate><enddate>20190201</enddate><creator>Li, Xiang-Ming</creator><creator>Chen, Xiang-Kai</creator><creator>Xu, Fei</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20190201</creationdate><title>Uniformly valid asymptotic solutions of rod eutectic growth in directional solidification for liquid-solid interface slopes of small order</title><author>Li, Xiang-Ming ; Chen, Xiang-Kai ; Xu, Fei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c340t-9366e634e51e310ebeda49e7320bdb4fb167fa9d3b9f3fc17244180e924c6af43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>A1. Asymptotic solution</topic><topic>A1. Directional solidification</topic><topic>A1. Eutectic growth</topic><topic>A1. Interfacial shape</topic><topic>A1. Undercooling</topic><topic>Asymptotic methods</topic><topic>Asymptotic series</topic><topic>Directional solidification</topic><topic>Liquid-solid interfaces</topic><topic>Slopes</topic><topic>Solids</topic><topic>Supercooling</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Xiang-Ming</creatorcontrib><creatorcontrib>Chen, Xiang-Kai</creatorcontrib><creatorcontrib>Xu, Fei</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of crystal growth</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Xiang-Ming</au><au>Chen, Xiang-Kai</au><au>Xu, Fei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniformly valid asymptotic solutions of rod eutectic growth in directional solidification for liquid-solid interface slopes of small order</atitle><jtitle>Journal of crystal growth</jtitle><date>2019-02-01</date><risdate>2019</risdate><volume>507</volume><spage>453</spage><epage>458</epage><pages>453-458</pages><issn>0022-0248</issn><eissn>1873-5002</eissn><abstract>Recently, uniformly valid asymptotic solutions of rod eutectic growth for liquid-solid interface slopes at triple phase junction being the normal order have been presented in reference (Li and Xu, 2017). In this work, analytical calculations of rod eutectic growth during directional solidification for liquid-solid interface of small order are performed. The purpose is to study the liquid-solid interfacial shape and average undercooling of rod eutectic growth. We give the mathematical formulation of rod eutectic growth for the general case. The steady solutions of rod eutectic growth are obtained by using asymptotic expansion method and matching method. The relationship of the overall average interfacial undercooling with the rod eutectic spacing is presented. The overall average interfacial undercooling always exists a minimum value at the minimum-undercooling spacing, and the minimum-undercooling spacing is slightly smaller than one given by Jackson and Hunt. We also analyze the effect of pulling speeds and thermal gradients on the interfacial shapes for the case of the minimum-undercooling spacing.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.jcrysgro.2018.10.015</doi><tpages>6</tpages></addata></record> |
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| ispartof | Journal of crystal growth, 2019-02, Vol.507, p.453-458 |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | A1. Asymptotic solution A1. Directional solidification A1. Eutectic growth A1. Interfacial shape A1. Undercooling Asymptotic methods Asymptotic series Directional solidification Liquid-solid interfaces Slopes Solids Supercooling |
| title | Uniformly valid asymptotic solutions of rod eutectic growth in directional solidification for liquid-solid interface slopes of small order |
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