·1318· 工程科学学报，第37卷，第10期 effect of anisotropic surface tension and interface kinetics on pat- 由枝晶生长.物理学报，2009,58(10)：7094) tern formation during the growth of two-dimensional crystals.J 9]Coriell S R,Parker R L.Stability of the shape of a solid eylinder Cryst Growth,1992,125(34):389 growing in a diffusion field.J Appl Phys,1965,36(2):632 [5]Voorhees P W,Coriell S R,Sekerka R F.The effect of anisotrop- [10]Chen Y J,Chen Q,Wang Z D,et al.Growth mechanism of col- ic crystal-melt surface tension on grain boundary groove morpholo- umn crystals in direction solidification.JTsinghua Unie Sci .JCryst Growth,1984,67(3):425 Technol,.2004,44(11):1464. Eggleston J J,MeFadden G B,Voorhees P W.A phase-field (陈亚军，陈琦，王自东，等.定向凝固过程中柱状品的生长 model for highly anisotropic interface energy.Phys D,2001,150 机制.清华大学学报：自然科学版，2004,44(11)：1464) (12):91 [11]Chen M W,Wang Z D,Xu JJ.The effect of anisotropic surface Zhao D W.Li Q S,Hao W X.Phase-field method simulation of tension on the interface evolution of a particle in the undercooled the crystal growth with strongly surface tension anisotropy.Found- melt.J Cryst Grouth,2014,385:115 ry Technol,2011,32(3):318 [12]Chen M W,Wang Z D,Xu JJ.Dynamical mechanism of forma- (赵达文，李秋书，郝维新。相场模型模拟强界面能各向异性 tion of Fe nanoparticles in Tin bronze alloys//Proceeding of the 作用下品体生长.铸造技术，2011,32(3)：318) 13th IEEE International Conference on Nanotechnology.Beijing, [8]Zhao D W,Li J F.Phase-field modeling of the effect of liquid-sol- 2013:590 id interface anisotropies on free dendritic growth.Acta Phys Sin, [13]Debroy PP,Sekerka R F.Weakly nonlinear morphological insta- 2009,58(10):7094 bility of a cylindrical crystal growing from a pure undercooled (赵达文，李金富.相场模型模拟液固界面各向异性作用下自 met.Phys Rev E,1996,53(6):6244工程科学学报，第 37 卷，第 10 期 effect of anisotropic surface tension and interface kinetics on pat￾tern formation during the growth of two-dimensional crystals． J Cryst Growth，1992，125( 3-4) : 389 ［5］ Voorhees P W，Coriell S Ｒ，Sekerka Ｒ F． The effect of anisotrop￾ic crystal-melt surface tension on grain boundary groove morpholo￾gy． J Cryst Growth，1984，67( 3) : 425 ［6］ Eggleston J J，McFadden G B，Voorhees P W． A phase-field model for highly anisotropic interface energy． Phys D，2001，150 ( 1-2) : 91 ［7］ Zhao D W，Li Q S，Hao W X． Phase-field method simulation of the crystal growth with strongly surface tension anisotropy． Found￾ry Technol，2011，32( 3) : 318 ( 赵达文，李秋书，郝维新． 相场模型模拟强界面能各向异性 作用下晶体生长． 铸造技术，2011，32( 3) : 318) ［8］ Zhao D W，Li J F． Phase-field modeling of the effect of liquid-sol￾id interface anisotropies on free dendritic growth． Acta Phys Sin， 2009，58( 10) : 7094 ( 赵达文，李金富． 相场模型模拟液固界面各向异性作用下自 由枝晶生长． 物理学报，2009，58( 10) : 7094) ［9］ Coriell S Ｒ，Parker Ｒ L． Stability of the shape of a solid cylinder growing in a diffusion field． J Appl Phys，1965，36( 2) : 632 ［10］ Chen Y J，Chen Q，Wang Z D，et al． Growth mechanism of col￾umn crystals in direction solidification． J Tsinghua Univ Sci Technol，2004，44( 11) : 1464 ( 陈亚军，陈琦，王自东，等． 定向凝固过程中柱状晶的生长 机制． 清华大学学报: 自然科学版，2004，44( 11) : 1464) ［11］ Chen M W，Wang Z D，Xu J J． The effect of anisotropic surface tension on the interface evolution of a particle in the undercooled melt． J Cryst Growth，2014，385: 115 ［12］ Chen M W，Wang Z D，Xu J J． Dynamical mechanism of forma￾tion of Fe nanoparticles in Tin bronze alloys / / Proceeding of the 13th IEEE International Conference on Nanotechnology． Beijing， 2013: 590 ［13］ Debroy P P，Sekerka Ｒ F． Weakly nonlinear morphological insta￾bility of a cylindrical crystal growing from a pure undercooled melt． Phys Ｒev E，1996，53( 6) : 6244 ·1318·