####
J. Japan Inst. Metals, Vol. 73, No. 8 (2009),

pp. 566-570

##
First Principles Calculations of Vibrational Free Energy Estimated by the Quasi-Harmonic Approximation

**
Shigeto R. Nishitani**^{1}, Ryohei Takeda^{1}, Hideki Ishii^{1}, Yosuke Yamamoto^{1} and Tadaaki Kaneko^{2}

^{1}Department of Informatics, Kwansei Gakuin University, Sanda 669-1337

^{2}Department of Physics, Kwansei Gakuin University, Sanda 669-1337,

#### Abstract:

The quasi-harmonic approximation is a powerful tool for predicting the vibrational free energy using the first principles calculations. This method with the phonon density of states shows reliable estimation of the thermal expansion and the relative stabilities of SiC polytypes. For the binary systems, we derived a cancelling condition of the vibrational free energy change due to the phase separations within the first order approximation in terms of the nearest bond pair interaction.

(Received 2009/5/7)

#### Keywords:

Einstein lattice, phonon, thermal expansion, SiC, polytypes, binary

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