Phonon density of states of the Einstein model

In the Einstein model, all of the modes have the same frequency ω0. The density of states is a delta function D(ω) = 3nδ(ω - ω0). Here n is the density of atoms.

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 delta function is approximated by a square pulse that is ω0/1000 wide.

[1015s/(rad m³)]

ω [1012 rad/s]

Frequency: ω0 =


Density of atoms: n =


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