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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.
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关键词:
- 三维晶粒长大 /
- 各向异性 /
- von Neumann方程 /
- 平均切直径
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:
- three-dimensional grain growth /
- anisotropy /
- von Neumann relation /
- mean caliper diameter
[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
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[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
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