Ion conductor heterostructures of BaF2 and CaF2 with various spacings have been prepared by molecular beam epitaxy (MBE) technique as reported previously by Sata et al. [Nature 408 (2000) 946]. In this paper, we are especially interested in the effects of orientation and substrate on the conductivity. Four kinds of substrates have been investigated (Al2O3(0 1 2), Al2O3(0 0 6), MgO(1 1 1), and MgO(1 1 0)), generating [1 1 1] and [1 0 0] oriented heterostructures with smooth surfaces. The samples have been investigated by ac impedance, dc polarization techniques, X-ray diffraction (XRD) and atomic force microscopy (AFM). The polarization measurements confirm that electronic effects are minor and the conductivity is ionic. The substrate itself causes a space charge effect which adds to the overall conductance as a constant contribution and is of the order of the effect of a single CaF2/BaF2 interface (or less), and hence totally negligible if the number of CaF2/BaF2 interfaces is high. Variation of the substrate's surface chemistry leads to a conductivity variation that is exactly opposite to the case of cation adsorption, and thus suggests F- adsorption as defect inducing mechanism at the Al2O3/BaF2 interface. The dominating contribution of the CaF2/BaF2 interfaces is approximately independent of the orientation, hence, favoring a fluoride ion transfer from one to the other phase rather than a charge accumulation at the interfacial core, in full agreement with the conclusions of Sata et al. [Nature 408 (2000) 946]. (C) 2003 Elsevier Ltd. All rights reserved.