Superlattice ordering in digenite,Cu2−xS

We report a new sequence of superlattice ordering transitions in digenite-type crystals of ${\mathrm{Cu}}_{2\mathrm{-}\mathrm{x}}$S. A long-period arrangement of the copper ions is found to undergo a spatial period doubling followed by a transition to an incommensurate phase at low temperatures. The results are discussed in terms of a mass-density-wave model describing the ordering of copper vacancies in the nearly stoichiometric case. A direct relationship between composition x and the superlattice period is predicted, leading to discrete equilibrium structures (x=0.11 and 0.16), rather than continuous solid solutions.