Electrostatic properties and stability of Coulomb crystals

We calculate the electrostatic properties of more than 20 different Coulomb crystals and study their resistance to small oscillations of the ions around their equilibrium positions (phonon oscillations). We discuss the stability of multicomponent crystals against separation into set of one-component lattices and for some cases, the influence of energy of the zero-point vibrations. It is confirmed that the body-centred cubic (bcc) lattice possesses the lowest electrostatic energy among all one-component (one type of ion in the elementary cell) crystals. For systems composed of two types of ions (their charge and density numbers are Z(1), n(1) and Z(2), n(2), respectively) and for n(1) = n(2), it is found that the formation of a binary bcc lattice is possible at 1/2.4229 < alpha < 2.4229, where alpha equivalent to Z(2)/Z(1). Under the same conditions, the NaCl lattice forms at alpha > 5.197 and alpha < 0.192. While for n(2) = 2n(1), the MgB2 lattice is found be stable at 0.1 < alpha < 0.32. For multicomponent lattices with hexagonal structure (binary hexagonal close-packed, MgB2 and some others lattices), it is shown that their properties depend on the distance between hexagonal layers and this distance changes with alpha.