Electrostatic structural transitions in a Yukawa‐Wigner solid

Abstract

A derivation is supplied for a functional relation between the Fuchs energy e and the Madelung energy S for a Yukawa‐Wigner solid (YWS) in which the usual uniform background of a Wigner solid (WS) is replaced by a periodic array of Yukawa charge distributions with variable ‘‘ripple’’ parameter λ allowing the WS and the empty lattice in the limits of small λ and large λ, respectively. It is the zeros of Δe, and not of ΔS, that are relevant for structural transitions between two lattices. It is knwon that 2eWS=SWS, and Medeiros and Mokross incorrectly assumed 2e=S for the YWS. Here it is first shown by elementary means that the relation between e and S varies with λ, and then the functional relation is supplied for all λ. When applied to the bcc‐fcc system, it is found that Δe has two zeros whereas ΔS has one not equal to either of those of Δe. Starting with small λ, the sequence of lowest energy structures is bcc, fcc, and bcc if these are the only two allowed to compete. The equations for the sc case have...