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Two problems related to the calculation of lattice vibration energy in a crystal of gaas using the debye model for acoustic phonons and the einstein model for optical phonons. The first problem asks to calculate the lattice vibration energy per cm³ at liquid n2 temperature (77 k). The second problem involves solving the phonon dispersion in a two atom basis with different force constants and finding the expression for the adjacent displacements.
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Consider a crystal of GaAs in which the sound velocity is 5.6 x 10^5 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 N 2 temperature. (77 K)
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 f 1 and f 2. Also find the expression which describes the adjacent displacements. (i.e. U 2 / U 1 =…).
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