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.

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)