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*Materials Transactions*, Vol.51 No.09 (2010) pp.1521-1525

© 2010 The Japan Institute of Metals

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Theoretical Calculation of Activation Free Energy for Self-Diffusion in Prototype Crystal

K. Sato, S. Takizawa and T. Mohri

Division of Materials Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
We investigate temperature dependency of the activation free energy for the atomic diffusion in the fcc Lennrad-Jones system within the transition states theory based on the quasi-harmonic approximation. The activation free energy consists of the static activation energy and the vibrational free energy difference between the saddle point and the equilibrium state, and it is shown that both of them strongly depend on the system volume and the temperature. The temperature dependencies of both quantities exhibit opposite tendencies, i.e., the static activation energy decreases, while the free energy difference increases with increasing temperature. As a result, the activation free energy shows a weak temperature dependency. We discuss the effects of anharmonicity on the activation free energy by comparing the activation free energy obtained by the quasi-harmonic and harmonic approximations.

(Received 2010/4/26; Accepted 2010/5/20; Published 2010/7/7)

**Keywords:** atomic diffusion, transition state theory, quasi-harmonic approximation

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#### REFERENCES

- G. H. Vineyard: J. Phys. Chem. Solids
**3** (1957) 121.
- W. Franklin: J. Phys. Chem. Solids
**28** (1967) 829.
- G. De Lorenzi, G. Jacucci and C. P. Flynn: Phys. Rev. B
**36** (1987) 9461.
- W. Frank, U. Breier, C. Elsässer and M. Fähnle: Phys. Rev. Lett.
**77** (1996) 518.
- M. Mantina, Y. Wang, R. Arroyave, L. Q. Chen and Z. K. Liu: Phys. Rev. Lett.
**100** (2008) 215901.
- N. Sandberg, B. Magyari-Köpe and T. R. Mattsson: Phys. Rev. Lett.
**89** (2002) 065901.
- B. P. Uberuaga, S. M. Valone and M. I. Baskes: J. Alloy. Compd.
**444** (2007) 314.
- H. Yildirim, A. Kara, S. Durukanoglu and T. S. Rahman: Surf. Sci.
**600** (2006) 484.
- U. Kürpick: Phys. Rev. B
**64** (2001) 075418.
- L. Kong and L. J. Lewis: Phys. Rev. B
**77** (2008) 165422.
- A. van der Walle and G. Ceder: Rev. Mod. Phys.
**74** (2002) 11.
- C. Herzig, T. Przeorski and Y. Mishin: Intermetallics
**7** (1999) 389.
- J. M. Ziman:
*Principles of the theory of solids*, (Syndics of the Cambridge University Press, Cambridge, 1972).
- R. G. D. Valle and E. Venuti: Phys. Rev. B
**58** (1998) 206.

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