Periodic potential phonon dispersion

Phonon Dispersion in the Absence of a Periodic Electric Potential.140... 

PHONON DISPERSION IN THE ABSENCE OF A PERIODIC ELECTRIC POTENTIAL... 

The thermal energy in an insulating crystal takes the form of vibrations of the atoms about their equilibrium positions. The atoms do not vibrate independently, however, since the movements of one atom directly modulate the potential wells occupied by its neighbors. The result is coupled modes of vibration of the crystal as a whole, known as phonons. The phonon dispersion curve for an idealized one-dimensional lattice is sketched in Fig. 4. It is periodic, and it may be seen that there is a definite maximum phonon frequency, known as the Debye cut-... 

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