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.

中文翻译：

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库仑晶体的静电性能和稳定性

我们计算了20多种不同的库仑晶体的静电性质，并研究了它们对离子在其平衡位置附近的小振动（声子振动）的抵抗力。我们讨论了多组分晶体对单组分晶格分离的稳定性，以及在某些情况下零点振动能量的影响。可以确认，以体心立方（bcc）的晶格在所有单成分（基本单元中的一种离子）晶体中具有最低的静电能。对于由两种类型的离子组成的系统（其电荷数和密度数分别为Z ₁，n ₁和Z ₂，n ₂），对于Ñ ₁  =  Ñ ₂，可以发现，二进制BCC晶格的形成可以在1 / 2.4229 <  α  <2.4229，其中，α  ＆equiv;  ž ₂ / ž ₁。在相同条件下，NaCl晶格在α  > 5.197和α  <0.192时形成。当n ₂  = 2 n _1时，发现MgB ₂晶格稳定在0.1 <  α  <0.32。对于具有六边形结构的多晶格（二元六方密堆积，MgB ₂以及其他一些晶格），表明它们的性质取决于六角形层之间的距离，并且该距离随α变化。