Physical Features of Binary Coulomb Crystals: Madelung Energy, Collective Modes and Phonon Heat Capacity

Electrostatic energy, collective modes, and thermodynamic functions of a Coulomb crystal with equal number of ions of two different types and uniform charge-compensating electron background are studied using harmonic lattice model. Simple cubic and hexagonal lattices with two different ions in the elementary cell (we denote these lattices sc2 and h2, respectively) are considered. The static sc2 lattice is more tightly bound than the h2 one at any charge ratio of the constituent ions. The phonon spectra depend on the ion charge and mass ratio. An analysis shows that these binary Coulomb crystals are stable, if the charge ratio is not too different from 1 (about 3.6 for sc2 and 1.3 for h2 lattices) regardless of the mass ratio. Heat capacity of the sc2 lattice is obtained by numerical integration over the first Brillouin zone as a function of temperature and charge and mass ratios. Well known classic and quantum asymptotes of the heat capacity are reproduced, and the dependence of the coefficient in the Debye T3 law on charge and mass ratios is presented ((c) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)