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The accurate quantitative relationship between the excess volume at the grain boundary and the nanograin size in nanocrystalline alloy is deduced. The fundamental thermodynamic function of nanocrystalline alloy is derived as a function of nanograin size and temperature. By taking the SmCo7 alloy for example, the thermal stability of the nanocrystalline alloy, as well as its evolution characteristics, is studied based on the calculated excess Gibbs free energy of nanograin boundary. The results show that the nanostructure with grain size below a critical value that corresponds to the maximum excess Gibbs free energy can have higher thermal stability than a coarser nanograin structure. Once the grain size is larger than the critical value, the nanostructure may lose its stability and undergo discontinuous grain growth. By combining the nanothermodynamic model with the cellular automaton algorithm, the quantitative and visual simulations of nanograin growth in nanocrystalline SmCo7 alloy are performed. The nanograin growth behavior described by the two approaches are consistent with each other, which validates the conclusion of the thermal stability of nanocrystalline alloy, drawn from the present thermodynamic study.
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Keywords:
- nanothermodynamics /
- nanocrystalline SmCo7 alloy /
- thermal stability /
- cellular automaton simulation
[1] Sun J B, Han D, Cui C X, Yang W, Li L, Yang F, Yang L G 2010 Intermetallics 18 599
[2] Li A H, Dong S Z, LiW2002 Acta Phys. Sin. 51 2320 (in Chinese) [李安华, 董生智, 李卫 2002 物理学报 51 2320]
[3] Gutfleisch O, Müller K H, Khlopkov K, Wolf M, Yan A, Schäfer R, Gemming T, Schultz L 2006 Acta Mater. 54 997
[4] Zhang C W, Li H, Dong J M, Wang Y J, Pan F C 2005 Acta Phys. Sin. 54 1814 (in Chinese) [张昌文, 李华, 董建敏, 王永娟, 潘凤春 2005 物理学报 54 1814]
[5] Sun J B, Han D, Cui C X, Yang W, Li L, Yang F 2009 Acta Mater. 57 2845
[6] Guo Y Q, Li W, Feng W C, Luo J, Liang J K, He Q J 2005 Appl. Phys. Lett. 86 192513
[7] Wang W Q, Wang J L, Tang N, Bao F Q, Wu G H, Yang F M, Jin H M 2001 Acta Phys. Sin. 50 752 (in Chinese) [王文全, 王建立, 唐宁, 包富泉, 吴光恒, 杨伏明, 金汉民 2001 物理学报 50 752]
[8] Song X Y, Zhang J X, Yue M, Li E D, Zeng H, Lu N D, Zhou M L, Zuo T Y 2006 Adv. Mater. 18 1210
[9] Song X Y, Liu X M, Zhang J X 2006 J. Am. Ceram. Soc. 89 494
[10] Zhang Z X, Song X Y, Xu W W 2010 Scr. Mater. 62 594
[11] Gleiter H 2000 Acta Mater. 48 1
[12] Feth H J 1990 Phys. Rev. Lett. 65 610
[13] Wagner M 1992 Phys. Rev. B 45 635
[14] Chattopadhyay P P, Nambissan P, Pabi S K, Manna I 2001 Phys. Rev. B 63 054107
[15] Song X Y, Zhang J X, Li L M, Yang K Y, Liu G Q 2006 Acta Mater. 54 5541
[16] XuWW, Song X Y, Lu N D, Huang C H 2010 Acta Mater. 58 396
[17] Rose J H, Smith J R, Ferrante J 1983 Phys. Rev. B 28 1835
[18] Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2936
[19] Vinet P, Smith J R, Ferrante J, Rose J H 1987 Phys. Rev. B 35 1945
[20] Vinet P, Ferrante J, Smith J R, Rose J H 1986 J. Phys. C 19 L467
[21] Kittel C 1996 Introduction to Solid State Physics (New York: John Wiley & Sons)
[22] XuWW, Song X Y, Li E D,Wei J, Zhang J X 2009 J. Appl. Phys. 105 104310
[23] Song X Y, Gao J P, Zhang J X 2005 Acta Phys. Sin. 54 1313 (in Chinese) [宋晓艳, 高金萍, 张久兴 2005 物理学报 54 1313]
[24] XuWW, Song X Y, Zhang Z X 2010 Appl. Phys. Lett. 97 181911
[25] Song X Y, Liu G Q, He Y Z 1998 Prog. Nat. Sci. 8 92
[26] Song X Y, Liu G Q 1998 Scr. Mater. 38 1691
[27] Song X Y, Liu G Q 1999 J. Mater. Sci. 34 2433
[28] Xu W W, Song X Y, Li E D, Wei J, Li L M 2009 Acta Phys. Sin. 58 3280 (in Chinese) [徐文武, 宋晓艳, 李尔东, 魏君, 李凌梅 2009 物理学报 58 3280]
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[1] Sun J B, Han D, Cui C X, Yang W, Li L, Yang F, Yang L G 2010 Intermetallics 18 599
[2] Li A H, Dong S Z, LiW2002 Acta Phys. Sin. 51 2320 (in Chinese) [李安华, 董生智, 李卫 2002 物理学报 51 2320]
[3] Gutfleisch O, Müller K H, Khlopkov K, Wolf M, Yan A, Schäfer R, Gemming T, Schultz L 2006 Acta Mater. 54 997
[4] Zhang C W, Li H, Dong J M, Wang Y J, Pan F C 2005 Acta Phys. Sin. 54 1814 (in Chinese) [张昌文, 李华, 董建敏, 王永娟, 潘凤春 2005 物理学报 54 1814]
[5] Sun J B, Han D, Cui C X, Yang W, Li L, Yang F 2009 Acta Mater. 57 2845
[6] Guo Y Q, Li W, Feng W C, Luo J, Liang J K, He Q J 2005 Appl. Phys. Lett. 86 192513
[7] Wang W Q, Wang J L, Tang N, Bao F Q, Wu G H, Yang F M, Jin H M 2001 Acta Phys. Sin. 50 752 (in Chinese) [王文全, 王建立, 唐宁, 包富泉, 吴光恒, 杨伏明, 金汉民 2001 物理学报 50 752]
[8] Song X Y, Zhang J X, Yue M, Li E D, Zeng H, Lu N D, Zhou M L, Zuo T Y 2006 Adv. Mater. 18 1210
[9] Song X Y, Liu X M, Zhang J X 2006 J. Am. Ceram. Soc. 89 494
[10] Zhang Z X, Song X Y, Xu W W 2010 Scr. Mater. 62 594
[11] Gleiter H 2000 Acta Mater. 48 1
[12] Feth H J 1990 Phys. Rev. Lett. 65 610
[13] Wagner M 1992 Phys. Rev. B 45 635
[14] Chattopadhyay P P, Nambissan P, Pabi S K, Manna I 2001 Phys. Rev. B 63 054107
[15] Song X Y, Zhang J X, Li L M, Yang K Y, Liu G Q 2006 Acta Mater. 54 5541
[16] XuWW, Song X Y, Lu N D, Huang C H 2010 Acta Mater. 58 396
[17] Rose J H, Smith J R, Ferrante J 1983 Phys. Rev. B 28 1835
[18] Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2936
[19] Vinet P, Smith J R, Ferrante J, Rose J H 1987 Phys. Rev. B 35 1945
[20] Vinet P, Ferrante J, Smith J R, Rose J H 1986 J. Phys. C 19 L467
[21] Kittel C 1996 Introduction to Solid State Physics (New York: John Wiley & Sons)
[22] XuWW, Song X Y, Li E D,Wei J, Zhang J X 2009 J. Appl. Phys. 105 104310
[23] Song X Y, Gao J P, Zhang J X 2005 Acta Phys. Sin. 54 1313 (in Chinese) [宋晓艳, 高金萍, 张久兴 2005 物理学报 54 1313]
[24] XuWW, Song X Y, Zhang Z X 2010 Appl. Phys. Lett. 97 181911
[25] Song X Y, Liu G Q, He Y Z 1998 Prog. Nat. Sci. 8 92
[26] Song X Y, Liu G Q 1998 Scr. Mater. 38 1691
[27] Song X Y, Liu G Q 1999 J. Mater. Sci. 34 2433
[28] Xu W W, Song X Y, Li E D, Wei J, Li L M 2009 Acta Phys. Sin. 58 3280 (in Chinese) [徐文武, 宋晓艳, 李尔东, 魏君, 李凌梅 2009 物理学报 58 3280]
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