[영문 학부 고체물리 과제] potassium phonon dispersion relation 계산 (C++ 코드 첨부)
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- 2013.05.18
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- 2012.04
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목차
1. Introduction
2. Theory
3. Method
4. Results
5. Conclusion
본문내용
1. Introduction
At the temperature 9K, the phonon dispersion relation of Potassium K was measured by the inelastic neutron scattering, and the values of force constant between Potassium atoms were extracted [2]. In this paper, by using those force constants, we obtained the phonon dispersion relation of Potassium with considering the effects of the nearest-neighbor interactions and the second-neighbor interactions. We also compared the results with those experimental data measured by the inelastic neutron scattering [2].
2. Theory
For a monatomic crystal with the atom mass , the total potential energy , the -th component of the displacement vector of the -th atom , and the -th component of the equilibrium position vector of the -th atom , we can write the equation of motion for the zeroth atom as the following
<중 략>
We calculated the phonon dispersion along the major lines of the 1st Brillouin zone for Potassium. By using the force constants of the reference [2] and considering the nearest-neighbor interaction and second-nearest-neighbor interaction
참고 자료
A. D. B. Woods, B. N. Brockhouse, R. H. March, and A. T. Stewart, “Crystal Dynamics of Sodium at 90K,” Phys. Rev. 128, 1112 (1962).
R. A. Cowley, A. D. B. Woods, and G. Dolling, “Crystal Dynamics of Potassium. I. Pseudopotential Analysis of Phonon Dispersion Curves at 9K,” Phys. Rev. 150, 487 (1966).
The cubic formula: http://en.wikipedia.org/wiki/Cubic_function