Calculation of Phonon dispersion relations:One dimensional Monatomic Lattice Chains

Calculation of Phonon dispersion relations:One dimensional Monatomic Lattice Chains

1Chain of interionic separation:a-
2Wave number:k=2π/λ. λ:Wavelength of Phonon.k≦|π/a|
3Mass of Atom:m-
4Spring constant:α-
5GraphPlot Input Data: , Figure:
You need to upgrade your Flash Player
:Export Graph Image.

Keyword・Reference・Remarks・History

LaTex


Markup:\omega^{2} =4\frac{\alpha }{m}\sin^{2}(\frac{ka}{2})

Keyword

Angular frequency of Phonon,Phonon dispersion relations,One dimensional Monatomic Lattice Chains,Chain of interionic separation,Wave number,Wavelength of Phonon,Mass of Atom,Spring constant.

Reference

[1]:Graham Woan著・堤正義訳:『ケンブリッジ物理公式ハンドブック』,共立出版,p.127,2007.
[2]:Gang Chen:『Nanoscale Energy Transport and Conversion: A Parallel Treatment of Elections, Molecules, Phonons, and Photons』,Oxford Univ Pr on Demand,pp.101.

Remarks

・Angular frequency of Phonon:ω
・Chain of interionic separation:a
・Wave number:k
・Mass of Atom:m
・Spring constant:α
・Input "k" must be under |π/a| in this page
・Making Equation Image is powered by CODECOGS

History

・2010/08/17:Upload

Copyright©Asset Management Consulting Corporation All Rights Reserved.