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Problem Set 13 for Physics 8510, Fall 2007: Calculating Lattice Vibration Energy in GaAs -, Assignments of Solid State Physics

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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Pre 2010

Uploaded on 08/31/2009

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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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Download Problem Set 13 for Physics 8510, Fall 2007: Calculating Lattice Vibration Energy in GaAs - and more Assignments Solid State Physics in PDF only on Docsity!

Physics 8510, Fall 2007

Problem Set 13

  1. 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)

  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 f 1 and f 2. Also find the expression which describes the adjacent displacements. (i.e. U 2 / U 1 =…).

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