Abstract
We study electrostatic and phonon properties of Yukawa crystals. It is shown that in the harmonic approximation these systems which are used in the theory of dusty plasma can be described analytically by the model from the theory of neutron stars and white dwarfs. Using this approximation, we consider properties of body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and ${\mathrm{MgB}}_{2}$ lattices. Studies of ${\mathrm{MgB}}_{2}$ and hcp lattices in the context of Yukawa systems are lacking. It is shown that they never possess the smallest potential energy and the phase diagram of stable Yukawa crystals contains bcc and fcc lattices only. However, corrections to the charge density proportional to ${(\ensuremath{\kappa}a)}^{4}$ can noticeably change the structural diagram of Yukawa systems. The analytical model developed also allows us to describe low-temperature effects where numerical simulations are difficult.
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