A careful electron diffraction investigation of pearceite-Tac and polybasite-Tac samples in the Ag+ fast ion conducting state reveals that the average hexagonal [Ag-9(I)]9(+) sub-structure in these mineral solid electrolyte systems is mutually incommensurable with respect to the remaining [(Ag-I,Cu-I)(6)(As-III,Sb-III)(2)S-7](2-)[(CuS4)-S-I](7-) framework sub-structure. It is shown how the mutual incommensurability of the two component substructures can be compatible with crystal chemical commonsense, with previously reported average structure refinements of these phases as well as providing an insight into their Ag+ fast ion conductivity at such low temperatures. In addition, Ag+/Cu+ ion ordering (and associated displacive shifts of the centreing S-2-ions) in the S2-(Ag,Cu)(6) octahedral sites is shown to provide a mechanism for low temperature superstructure ordering. (C) 2008 Elsevier B.V. All rights reserved.