Abstract
Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.
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References
H. Gleiter, Prog. Mater. Sci. 33, 233 (1989)
K. Lu, Mater. Sci. Eng., R Rep. 16, 1611 (1996)
J. Weissmüller, Nanostruct. Mater. 3, 261 (1993)
R. Kirchheim, Acta Mater. 50, 413 (2002)
F. Liu, R. Kirchheim, Scr. Mater. 51, 521 (2004)
F. Liu, R. Kirchheim, J. Cryst. Growth 264, 385 (2004)
Y.Z. Chen, G. Csiszár, J. Cizek, C. Borchers, T. Ungár, S. Goto, R. Kirchheim, Scr. Mater. 64, 390 (2011)
Y.Z. Chen, A. Herz, R. Kirchheim, Mater. Sci. Forum 667-669, 265 (2010)
Y. Estrin, G. Gottstein, L.S. Shvindlerman, Scr. Mater. 41, 385 (1999)
Y. Estrin, G. Gottstein, L.S. Shvindlerman, Acta Mater. 47, 3541 (1999)
Y. Estrin, G. Gottstein, E. Rabkin, L.S. Shvindlerman, Scr. Mater. 43, 141 (2000)
C.E. Krill III, L. Helfen, D. Michels, H. Natter, A. Fitch, O. Masson, R. Birringer, Phys. Rev. Lett. 86, 842 (2001)
Y. Kuru, M. Wohlschlögel, U. Welzel, E.J. Mittemeijer, Appl. Phys. Lett. 95, 163112 (2009)
L.S. Shvindlerman, G. Gottstein, V.A. Ivanov, D.A. Molodov, D. Kolesnikov, W. Lojkowsi, J. Mater. Sci. 41, 7725 (2006)
H.J. Leamy, G.E. Pike, C.H. Seager, Grain Boundaries in Semiconductors (North-Holland, Amsterdam, 1982)
R.C. Pond, V. Vitek, Proc. R. Soc. London, Ser. B 357, 453 (1977)
K.L. Merkle, D.J. Smith, Phys. Rev. Lett. 59, 2887 (1987)
J.R. Trelewicz, C.A. Schuh, Phys. Rev. B 79, 094112 (2009)
A. Kirchner, B. Kieback, Scr. Mater. 64, 406 (2011)
B. Färber, E. Cadel, A. Menand, G. Schmitz, R. Kirchheim, Acta Mater. 48, 789 (2000)
D.K. Shi, Fundamentals of Materials Science, 2nd edn. (China Machine Press, Beijing, 2003)
C.C. Koch, R.O. Scattergood, K.A. Darling, J.E. Semones, J. Mater. Sci. 43, 7264 (2008)
C.E. Krill, R. Klein, S. Janes, R. Birringer, Mater. Sci. Forum 179, 443 (1995)
K.A. Darling, R.N. Chan, P.Z. Wong, J.E. Semones, R.O. Scattergood, C.C. Koch, Scr. Mater. 59, 530 (2008)
F. Liu, Mater. Lett. 59, 1458 (2005)
J. Weissmüller, W. Krauss, T. Haubold, R. Birringer, H. Gleiter, Nanostruct. Mater. 1, 439 (1992)
C.E. Krill III, H. Ehrhardt, R. Birringer, Z. Metallkd. 96, 1134 (2005)
Z. Chen, F. Liu, K. Zhang Y.Z. Ma, G.C. Yang, Y.H. Zhou, J. Cryst. Growth 313, 81 (2010)
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Gong, M.M., Liu, F. & Zhang, K. Thermodynamic stability of binary nanocrystalline alloys: analysis of solute and excess vacancy. Appl. Phys. A 105, 927–934 (2011). https://doi.org/10.1007/s00339-011-6501-2
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DOI: https://doi.org/10.1007/s00339-011-6501-2