Electrostatic properties and stability of Coulomb crystals

Abstract

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 Z1, n1 and Z2, n2, respectively) and for n1 = n2, it is found that the formation of a binary bcc lattice is possible at 1/2.4229 < α < 2.4229, where α ≡ Z2/Z1. Under the same conditions, the NaCl lattice forms at α > 5.197 and α < 0.192. While for n2 = 2n1, the MgB2 lattice is found be stable at 0.1 < α < 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 α.

Electrostatic energy of Coulomb crystals with polarized electron background

“…Based on the results of Ref. [15], we chose four lattices with the lowest Madelung constant (bcc, fcc, hcp and MgB 2 ) and investigated polarization effects for them. Since the MgB 2 lattice never has the lowest energy the formation of other lattices, which were not considered in the present work, is very unlikely.…”

“…where ζ is called a Madelung constant, and N is the total number of ions. Accurate values of the Madelung constant for four lattices with the lowest U M are quoted in Table I from the previous works (see the recent review [15] and references therein).…”

“…The question, which type of crystal lattice forms in such stars, is not solved completely. For crystals with the same ion charge number Z it was discussed in [9,[13][14][15]. More complex systems with two or three different charged ions were studied in [14][15][16][17].…”

“…Madelung constant ζ in Eq. (9) and coefficient ηTF of the quadratic approximation(15) for the bcc, fcc, hcp, and MgB2 lattice types.…”

“…For crystals with the same ion charge number Z it was discussed in [9,[13][14][15]. More complex systems with two or three different charged ions were studied in [14][15][16][17]. In all of the papers cited above, the uniform electron background was considered.…”