Consider a diatomic lattice containing two identical atoms (i.e., mi = m2) with an interatomic distance of 2.5x10-10 m. Calculate the values of angular frequency (in rad/sec) of acoustic and optical phonons of wave length 109 m in the first Brillouin zone. Given (i) the velocity of sound in a solid is 3×10³ m/s (ii) the dispersion relations of a diatomic crystal in the first Brillouin zone for the two phonon branches to be (i) 1 1 2K w? = 2K and (ii) @² = M' M2 (M, + M,)"“
Consider a diatomic lattice containing two identical atoms (i.e., mi = m2) with an interatomic distance of 2.5x10-10 m. Calculate the values of angular frequency (in rad/sec) of acoustic and optical phonons of wave length 109 m in the first Brillouin zone. Given (i) the velocity of sound in a solid is 3×10³ m/s (ii) the dispersion relations of a diatomic crystal in the first Brillouin zone for the two phonon branches to be (i) 1 1 2K w? = 2K and (ii) @² = M' M2 (M, + M,)"“
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Transcribed Image Text:Consider a diatomic lattice containing two identical atoms (i.e., mi = m2) with an
interatomic distance of 2.5x10-10 m. Calculate the values of angular frequency (in
rad/sec) of acoustic and optical phonons of wave length 10- m in the first Brillouin zone.
Given (i) the velocity of sound in a solid is 3×10° m/s (ii) the dispersion relations of a
diatomic crystal in the first Brillouin zone for the two phonon branches to be (i)
1
1
2K
-k’a².
(М,+M,)
w = 2K
and (ii) @?
+
M1
M,
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