Q.4 For a diatomic linear chain, the phonon dispersion relation o(k) has two branches, according to the+ and - sign in the equation below: 0² 1 1 (+) M₁ M₂ =C 1 + M₁ M₂. 2 1/2 ka 쌀² 4 M₁M₂ 2 sin ² There are two atoms in the unit cell with masses M₁ and M₂, and the force constant of the nearest-neighbor interaction is given by c. Show that for M₁ = M2, the result is equivalent to the dispersion curve of the single-atom chain.
Q.4 For a diatomic linear chain, the phonon dispersion relation o(k) has two branches, according to the+ and - sign in the equation below: 0² 1 1 (+) M₁ M₂ =C 1 + M₁ M₂. 2 1/2 ka 쌀² 4 M₁M₂ 2 sin ² There are two atoms in the unit cell with masses M₁ and M₂, and the force constant of the nearest-neighbor interaction is given by c. Show that for M₁ = M2, the result is equivalent to the dispersion curve of the single-atom chain.
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Transcribed Image Text:Q.4 For a diatomic linear chain, the phonon dispersion relation o(k) has two branches,
according to the+ and - sign in the equation below:
0²
1 1
(+)
M₁ M₂
=C
1
+
M₁ M₂.
2
1/2
ka
쌀²
4
M₁M₂ 2
sin ²
There are two atoms in the unit cell with masses M₁ and M₂, and the force constant of the
nearest-neighbor interaction is given by c.
Show that for M₁ = M2, the result is equivalent to the dispersion curve of the single-atom
chain.
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