The significance of multipole interactions for the stability of regular structures composed from charged particles

Identifying the forces responsible for stabilising binary particle lattices is key to the controlled fabrication of many new materials. Experiments have shown that the presence of charge can be integral to the formation of ordered arrays; however, a complete analysis of the forces responsible has not included many of the significant lattice types that may form during fabrication. A theory of many-body electrostatic interactions has been applied to six lattice stoichiometries, AB, AB₂, AB₃, AB₄, AB₅ and AB₆, to show that induced multipole interactions can make a very significant (>80 %) contribution to the total lattice energy of arrays of charged particles. Particle radii ratios which favour global minima in electrostatic energy are found to be the same or a close match to those observed by experiment. Although certain lattice types exhibit local energy minima, the calculations show that many-body rather than two-body interactions are ultimately responsible for the structures observed by experiment. For a lattice isostructural with CFe₄, a particle size ratio not previously observed is found to be particularly stable due to many-body effects.