The evolution and morphological stability of a spherical crystal

作     者：CHEN MingWen1,2, WANG ZiDong2 & XU JianJun3,4 1 School of Applied Sciences, University of Science and Technology Beijing, Beijing 100083, China 2 School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China 3 School of Mathematical Sciences, Nankai University, Tianjin 300071, China 4 Department of Mathematics and Statistics, McGill University, Montreal H3A 2K6, Canada 

作者机构：School of Applied Sciences University of Science and Technology Beijing Beijing China School of Materials Science and Engineering University of Science and Technology Beijing Beijing China School of Mathematical Sciences Nankai University Tianjin China Department of Mathematics and Statistics McGill University Montreal Canada 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2008年第51卷第3期

页      面：225-243页

核心收录：

学科分类：0810[工学-信息与通信工程] 07[理学] 070205[理学-凝聚态物理] 08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0703[理学-化学] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by the National Basic Research Program of China (Grant No. 2006CB605205) the National Natural Science Foundation of China (Grant Nos. 10672019 and 10572062) the Science and Technology Foundation of Shanghai (Grant No. 055207081) 

主　　题：solid-liquid interface spherical crystal convective flow crystal growth morphological stability 

摘      要：The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.