Debye wavevector
= Debye wavevector
{c}
{title2=$q_D$}
The spherical cutoff in the three-dimensional <Debye model> preserves three vibrational modes per atom. For atom density $n_a$, $q_D=(6\pi^2n_a)^{1/3}$ and $\omega_D=c_s q_D$ in a single-speed approximation. A monovalent free-electron metal has $k_F=(3\pi^2n_a)^{1/3}$, giving $q_D=2^{1/3}k_F$. This cutoff is a mode-counting approximation, not an exact spherical boundary of the crystal's <Brillouin zone>.