The lattice dynamics of beryllium, a metal with hexagonal close-packed structure and two atoms per unit cell, is investigated within the framework of Harrison's first-principles pseudopotential theory, using (i) the Slater approximation for the conduction-band-core exchange, and (ii) a modified dielectric-screening function employing the Kohn-Sham approximation for exchange among the conduction electrons. The energy-wave-number characteristic $F\left(q\right)\mathrm{}$ is constructed from the Hartree-Fock-Slater (HFS) wave function for ${\mathrm{Be}}^{++}$; this is used to calculate the phonon dispersion relations in the [0001], [$01\overline{1}0$], and [$11\overline{2}0$] directions. Good agreement is obtained with neutron diffraction experiments. The three independent elastic shear constants are also calculated from $F\left(q\right)\mathrm{}$; good agreement with experiment is obtained for $C$ and $C^{\prime }$, but only fair results obtain for $c_{44}$.

• Received 15 April 1970

DOI:https://doi.org/10.1103/PhysRevB.2.1733