A 7H polytype of AgI (characterised by stacking fault arrangement) is detected at the interface of beta -AgI and gamma -Al2O3, which may even form the major (or even the only) AgI-constituent at pronounced Al2O3-contents. The driving force for the formation of the 7H phase is assumed to be the interaction of Ag+ with the basic alumina phase similar as in the AgCl and AgBr composites in which due to the relative stability of the rock salt structure only ideal semi-infinite space charge layers occur. Considering the 7H structure as a heterostructure of gamma- and beta -phase (beta/gamma/beta/gamma/...) leads to an explanation that is consistent with all the features observed: The extreme Ag+-conductivity (that can hardly be explained by semi-infinite space charges) and the peculiar phase transition behaviour on one hand, and the qualitative similarities with AgCl:Al2O3 and AgBr:Al2O3 on the other hand. Since the layer separation is in the sub-Debye length range we expect a mesoscopic effect on the ionic conductivity as predicted earlier. This is supported by conductivity anomalies in ply two phase mixtures. This mesoscopic heterolayer is discussed in the context of nano-ionics (ion conductivity in nanocrystalline materials and nano-composites) and nano-electronics (quantum wells, wires and dots).