Calculation of Phonon dispersion relations:One dimensional Diatomic Lattice Chains

Calculation of Phonon dispersion relations:One dimensional Diatomic Lattice Chains

1Chain of interionic separation:a-
2Wave number:k=2π/λ. λ:Wavelength of Phonon.k≦|π/(2a)|
3Mass of Atom:m1m2>m1
4Mass of Atom:m2m2>m1
5Spring constant:α-
6GraphPlot Input Data: , Figure:
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Keyword・Reference・Remarks・History

LaTex


Markup:\omega^{2} =\frac{\alpha }{\mu }\pm \alpha \left [ \frac{1}{\mu ^{2}}-\frac{4}{m_{1}m_{2}}\sin^{2}(ka) \right ]^{1/2}

Keyword

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

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
・Reduced mass:μ=(m1*m2)/(m1+m2)
・Input "k" must be under |π/(2*a)| in this page
・Making Equation Image is powered by CODECOGS

History

・2010/08/17:Upload

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