Simplify the 1D phonon-dispersion relation such that it is in terms of the mass ratio ?=?2/?1.

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Simplify the 1D phonon-dispersion relation such that it is in terms of the mass ratio ?=?2/?1.

Below is the phonon-dispersion relation for a 1D diatomic harmonic crystal:
M₁ + M₂)
M₁M₂
12) ₁
w² = c(
1 + 1
2M₁M₂
(M₁ + M₂)²
(1 - cos ka)
Transcribed Image Text:Below is the phonon-dispersion relation for a 1D diatomic harmonic crystal: M₁ + M₂) M₁M₂ 12) ₁ w² = c( 1 + 1 2M₁M₂ (M₁ + M₂)² (1 - cos ka)
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