凸形晶粒的各向异性三维von Neumann方程研究

王浩; 刘国权; 栾军华

doi:10.7498/aps.61.048102

摘要

三维晶粒长大规律是材料科学研究的核心问题之一, 本文通过考虑实际多晶组织中晶界能和晶界迁移率的不均匀性和各向异性因素对晶粒三晶棱处两面角大小的影响, 借助经典体视学中晶粒界面积分平均曲率与平均切直径的关系, 经推导得到了适合于凸形晶粒的一般性三维von Neumann方程, 结果表明实际凸形晶粒的准确长大速率可以表示为晶粒的平均切直径、三晶棱总长度和三晶棱处两面角的函数. 所得方程经过了Kelvin十四面体和5种规则多面体验证, 对于三维von Neumann方程(Nature, 2007, 446:1053)进一步推广并应用于实际金属和陶瓷材料具有重要的意义.

关键词:

Abstract

Understanding the laws of grain growth in three dimensions is one of the classic problems of materials science. By considering the anisotropy in real polycrystalline structure and the relationship between the integral of surface mean curvature and the mean caliper diameter of a convex individual grain, three-dimensional von Neumann equation for accurate grain growth rate is studied. The result shows that accurate grain growth rate of a convex grain is related to the grain mean caliper diameter, the sum of the length of grain edges and the corresponding dihedral exterior angles. This result is verified by Kelvin tetrakaidecahedron and the only five convex regular polyhedra.

Keywords:

作者及机构信息

1.
北京科技大学材料科学与工程学院, 北京 100083;

2.
北京科技大学新金属材料国家重点实验室, 北京 100083

基金项目: 国家自然科学基金(批准号: 50901008, 50871017), 中国博士后科学基金(批准号: 20090460209, 201003050), 高等学校博士学科点专项科研基金(批准号: 200800080003)和中央高校基本科研业务费专项资金资助的课题.

Authors and contacts

1.
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China;

2.
State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 50901008, 50871017), the China Postdoctoral Science Foundation (Grant Nos. 20090460209, 201003050), the Doctoral Program Foundation of Institute of Higher Education of China (Grant No. 200800080003), and the Fundamental Research Funds for the Central Universities.

参考文献

[1]	Kinderlehrer D 2007 Nature 446 995
[2]	MacPherson R D , Srolovitz D J 2007 Nature 446 1053
[3]	Barrales Mora L A, Gottstein G, Shvindlerman L S 2008 Acta Mater. 56 5915
[4]	Wang H , Liu G Q 2008 Appl. Phys. Lett. 93 131902
[5]	Glicksman M E, Rios P R, Lewis D J 2009 Int. J. Mat. Res. 100 536
[6]	Wang H, Liu G Q, Yue J C, Luan J H, Qin X G 2009 Acta Phys. Sin. 58 S137 (in Chinese) [王浩, 刘国权, 岳景朝, 栾军华, 秦湘阁 2009 58 S137]
[7]	Wang H , Liu G Q , Qin X G 2008 Acta Metall. Sin. 44 13 (in Chinese) [王浩, 刘国权, 秦湘阁 2008 金属学报 44 13]
[8]	Wang H, Liu G Q 2008 Acta Metall. Sin. 44 769 (in Chinese) [王浩, 刘国权 2008 金属学报 44 769 ]
[9]	Wang H , Liu GQ 2008 Acta Metall. Sin. 44 1332 (in Chinese) [王浩, 刘国权 2008 金属学报 44 1332]
[10]	Zhao D W, Li J F 2009 Acta Phys. Sin. 58 7094 (in Chinese) [赵达文, 李金富 2009 58 7094]
[11]	Wang Z J, Wang J C, Yang G C 2008 Acta Phys. Sin. 57 1246 (in Chinese) [王志军, 王锦程, 杨根仓 2008 57 1246]
[12]	Barrales Mora L A , Mohles V , Shvindlerman L S , Gottstein G 2008 Acta Mater. 56 1151
[13]	Gottstein G, Shvindlerman LS 2006 Scrip. Mater. 54 1065
[14]	Glicksman M E, Rios P R, Lewis D J 2007 Acta Mater. 55 4167
[15]	Hilliard J E 1967 Stereology (Elias H, ed. New York, Springer- Verlag) 221
[16]	Cahn J W 1967 Trans. TMS-AIME 239 610
[17]	DeHoff R T, Liu G Q 1985 Metall. Trans. 16A 2007
[18]	Wang H, Liu G Q, Luan J H, Yue J C, Qin X G 2009 Acta Phys. Sin. 58 S132 (in Chinese) [王浩, 刘国权, 栾军华, 岳景朝, 秦湘阁 2009 58 S132]
[19]	Hilgenfeldt S, Kraynik A M, Koehler S A, Stone H A 2001 Phys. Rev. Lett. 86 2685
[20]	Russ J C, DeHoff R T 1999 Practical Stereology (2nd edition) (New York: Plenum Press) p117
[21]	Thinh Le, Qiang Du 2009 Commun. Math. Sci. 7 551
[22]	Hillert M 1965 Acta Metall. 13 227

施引文献

[1]	Kinderlehrer D 2007 Nature 446 995
[2]	MacPherson R D , Srolovitz D J 2007 Nature 446 1053
[3]	Barrales Mora L A, Gottstein G, Shvindlerman L S 2008 Acta Mater. 56 5915
[4]	Wang H , Liu G Q 2008 Appl. Phys. Lett. 93 131902
[5]	Glicksman M E, Rios P R, Lewis D J 2009 Int. J. Mat. Res. 100 536
[6]	Wang H, Liu G Q, Yue J C, Luan J H, Qin X G 2009 Acta Phys. Sin. 58 S137 (in Chinese) [王浩, 刘国权, 岳景朝, 栾军华, 秦湘阁 2009 58 S137]
[7]	Wang H , Liu G Q , Qin X G 2008 Acta Metall. Sin. 44 13 (in Chinese) [王浩, 刘国权, 秦湘阁 2008 金属学报 44 13]
[8]	Wang H, Liu G Q 2008 Acta Metall. Sin. 44 769 (in Chinese) [王浩, 刘国权 2008 金属学报 44 769 ]
[9]	Wang H , Liu GQ 2008 Acta Metall. Sin. 44 1332 (in Chinese) [王浩, 刘国权 2008 金属学报 44 1332]
[10]	Zhao D W, Li J F 2009 Acta Phys. Sin. 58 7094 (in Chinese) [赵达文, 李金富 2009 58 7094]
[11]	Wang Z J, Wang J C, Yang G C 2008 Acta Phys. Sin. 57 1246 (in Chinese) [王志军, 王锦程, 杨根仓 2008 57 1246]
[12]	Barrales Mora L A , Mohles V , Shvindlerman L S , Gottstein G 2008 Acta Mater. 56 1151
[13]	Gottstein G, Shvindlerman LS 2006 Scrip. Mater. 54 1065
[14]	Glicksman M E, Rios P R, Lewis D J 2007 Acta Mater. 55 4167
[15]	Hilliard J E 1967 Stereology (Elias H, ed. New York, Springer- Verlag) 221
[16]	Cahn J W 1967 Trans. TMS-AIME 239 610
[17]	DeHoff R T, Liu G Q 1985 Metall. Trans. 16A 2007
[18]	Wang H, Liu G Q, Luan J H, Yue J C, Qin X G 2009 Acta Phys. Sin. 58 S132 (in Chinese) [王浩, 刘国权, 栾军华, 岳景朝, 秦湘阁 2009 58 S132]
[19]	Hilgenfeldt S, Kraynik A M, Koehler S A, Stone H A 2001 Phys. Rev. Lett. 86 2685
[20]	Russ J C, DeHoff R T 1999 Practical Stereology (2nd edition) (New York: Plenum Press) p117
[21]	Thinh Le, Qiang Du 2009 Commun. Math. Sci. 7 551
[22]	Hillert M 1965 Acta Metall. 13 227

[1]	钱黎明, 孙梦然, 郑改革. α相三氧化钼中各向异性双曲声子极化激元的耦合性质. , 2023, 72(7): 077101. doi: 10.7498/aps.72.20222144
[2]	丁燕, 钟粤华, 郭俊青, 卢毅, 罗昊宇, 沈云, 邓晓华. 黑磷各向异性拉曼光谱表征及电学特性. , 2021, 70(3): 037801. doi: 10.7498/aps.70.20201271
[3]	蔡成欣, 陈韶赓, 王学梅, 梁俊燕, 王兆宏. 各向异性三维非对称双锥五模超材料的能带结构及品质因数. , 2020, 69(13): 134302. doi: 10.7498/aps.69.20200364
[4]	卢敏, 黄惠莲, 余冬海, 刘维清, 魏望和. 不同晶面银纳米晶高温熔化的各向异性. , 2015, 64(10): 106101. doi: 10.7498/aps.64.106101
[5]	周建美, 张烨, 汪宏年, 杨守文, 殷长春. 耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应. , 2014, 63(15): 159101. doi: 10.7498/aps.63.159101
[6]	凌瑞良, 冯进, 冯金福. 三维各向异性耦合谐振子体系的量子化能谱与精确波函数. , 2010, 59(12): 8348-8358. doi: 10.7498/aps.59.8348
[7]	万勇, 韩文娟, 刘均海, 夏临华, Xavier Mateos, Valentin Petrov, 张怀金, 王继扬. 单斜结构的Yb:KLu(WO4)2晶体光谱和激光性质的各向异性. , 2009, 58(1): 278-284. doi: 10.7498/aps.58.278.1
[8]	王浩, 刘国权, 岳景朝, 栾军华, 秦湘阁. MacPherson-Srolovitz晶粒长大速率方程的仿真验证. , 2009, 58(13): 137-S140. doi: 10.7498/aps.58.137
[9]	陈桂波, 汪宏年, 姚敬金, 韩子夜. 各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟. , 2009, 58(6): 3848-3857. doi: 10.7498/aps.58.3848
[10]	孟繁义, 吴群, 傅佳辉, 杨国辉. 各向异性超常媒质矩形波导的导波特性研究. , 2008, 57(9): 5476-5484. doi: 10.7498/aps.57.5476
[11]	王志军, 王锦程, 杨根仓. 各向异性作用下合金定向凝固界面稳定性的渐近分析. , 2008, 57(2): 1246-1253. doi: 10.7498/aps.57.1246
[12]	周建华, 刘虹遥, 罗海陆, 文双春. 各向异性超常材料中倒退波的传播研究. , 2008, 57(12): 7729-7736. doi: 10.7498/aps.57.7729
[13]	蔡力, 韩小云, 温熙森. 长波条件下二维声子晶体中的弹性波传播及各向异性. , 2008, 57(3): 1746-1752. doi: 10.7498/aps.57.1746
[14]	孟繁义, 吴群, 傅佳辉, 顾学迈, 李乐伟. 三维各向异性超常媒质交错结构的亚波长谐振特性研究. , 2008, 57(10): 6213-6220. doi: 10.7498/aps.57.6213
[15]	杨宏伟, 袁洪, 陈如山, 杨阳. 各向异性磁化等离子体的SO-FDTD算法. , 2007, 56(3): 1443-1446. doi: 10.7498/aps.56.1443
[16]	翁紫梅, 陈浩. 单离子各向异性影响下的一维铁磁链中的孤子. , 2007, 56(4): 1911-1918. doi: 10.7498/aps.56.1911
[17]	穆全全, 刘永军, 胡立发, 李大禹, 曹召良, 宣丽. 光谱型椭偏仪对各向异性液晶层的测量. , 2006, 55(3): 1055-1060. doi: 10.7498/aps.55.1055
[18]	刘少斌, 莫锦军, 袁乃昌. 各向异性磁等离子体的辅助方程FDTD算法. , 2004, 53(7): 2233-2236. doi: 10.7498/aps.53.2233
[19]	庄飞, 肖三水, 何江平, 何赛灵. 二维正方各向异性碲圆柱光子晶体完全禁带中缺陷模的FDTD计算分析和设计. , 2002, 51(9): 2167-2172. doi: 10.7498/aps.51.2167
[20]	庄飞, 何赛灵, 何江平, 冯尚申. 大带隙的二维各向异性椭圆介质柱光子晶体. , 2002, 51(2): 355-361. doi: 10.7498/aps.51.355

计量

文章访问数: 7271
PDF下载量: 508
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板