Find the optical and acoustical branches of the dispersion relation for a diatomic linear lattice, solids, physics Question 1:Find the optical and acoustical branches of the dispersionrelation for a diatomic linear lattice,

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Find the optical and acoustical branches of the dispersion relation for a diatomic linear lattice,

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Question

Find the optical and acoustical branches of the dispersion relation for a diatomic linear lattice,

solids, physics

Expert Solution

Introduction:

We study the vibrations in 1D a monoatomic and diatomic lattices and obtain the dispersion relation.

The dispersion relation of vibrations in 1D diatomic lattice is given by

${ω_{\pm}}^{2} = c (\frac{1}{m_{1}} + \frac{1}{m_{2}}) \pm c \sqrt{{(\frac{1}{m_{1}} + \frac{1}{m_{2}})}^{2} - \frac{4 \sin^{2} (\frac{k a}{2})}{m_{1} m_{2}}}$

Here $m_{1}, m_{2}$ are the masses of 2 atoms.

In this , $ω_{+}$ represents the optical branch.

$ω_{-}$ represents the acoustical branch.

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