 Phonon density of states

The number of lattice-vibration modes per unit angular frequency. For a three-dimensional isotropic monatomic crystal with three linear acoustic branches of a common speed $v_s$, wavevector-shell counting gives $g(\omega )=3V{\omega }^2/(2{\pi }^2{v}_s^3)$ below a suitable cutoff. Different branch speeds replace $3v_s^{-3}$ by $v_L^{-3}+2v_T^{-3}$.