Physics 8510, Fall 2007
Problem Set 13
1) Consider a crystal of GaAs in which the sound velocity is 5.6 x 105 cm/s and the
optical phonon energy is 36 meV. Using the Debye model for the acoustic phonon energy
and Einstein model for optical phonons, calculate the lattice vibration energy per cm³ at
liquid N2 temperature. (77 K)
2) We solved the problem of phonon dispersion in a two atom basis which has the same
force constants between atoms. This is true only for longitudinal modes but not for
transverse modes. Do the calculation again for two different force constants f1 and f2. Also
find the expression which describes the adjacent displacements. (i.e. U2 / U1 =…).
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