513.001 Molecular and Solid State Physics
Below is the phonon dispersion relation for a crystal with an fcc structure. The lattice constant is a = 0.2 nm.
a) How many atoms are there in the primitive unit cell?
b) Choose a direction and a polarization (longitudinal or transverse) and estimate the speed of sound in this direction for long wavelength sound waves.
c) What is the shortest wavelength sound wave possible in this crystal?
d) Which of these phonon states would be occupied at room temperature?
Hint: Note that the dispersion plot uses ν in THz (instead of ω)