Phonon density of states of the Debye model

In the Debye model, the dispersion relation is linear, ω = c|k|, and the density of states is quadratic as it is in the long wavelength limit.

Here c is the speed of sound. This holds up to a maximum frequency called the Debye frequency ω_D. In three dimensions there are 3 degrees of freedom per atom so the total number of phonon modes is 3n.

Here n is the atomic density. There are no phonon modes with a frequency above the Debye frequency.

The form below generates a table of where the first column is the angular frequency ω in rad/s and the second column is the density of states D(ω) in units of s/(rad m³).

The density of states can be used to calculate the temperature dependence of thermodynamic quantities.

• Energy spectral density u(ω)
• Internal energy density u(T)
• Specific heat c_v(T)
• Helmholtz free energy density f(T)
• Entropy density s(T)