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 I 9] 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) 2S 7] 2−[Cu IS 4] 7− framework sub-structure. It is shown how the mutual incommensurability of the two component sub-structures 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 S 2−(Ag,Cu) 6 octahedral sites is shown to provide a mechanism for low temperature superstructure ordering.