From Composites to Solid Solutions: Modeling of Ionic Conductivity in the CaF2-BaF2 System

By using calcium fluorite and barium fluorite as test materials, we demonstrated that homovalent dopants can greatly affect ionic conductivity through locally changing the defect density. Whilst this doping is a state-of-the-art effect in the case of dopants that replace native ions of different charge (heterovalent dopants), it is a rather surprising effect at a first glance for substitutional dopants of the same charge; here, the phenomenon is not electrostatic, but elastic in nature. As a consequence of size mismatch, the smaller Ca atoms in the BaF2 lattice favored the formation of interstitial sites that were located close to the Ca atoms, whilst doping larger Ba species into the CaF2 phase favored vacancy formation. In terms of conductivity, and in agreement with the different mobilities, the first doping effect was favorable, whilst the other decreased conductivity. The concentration effects were formalized by a heterogeneous Frenkel reaction that was distinguished from the mean Frenkel reaction by additional (elastic) trapping that became more pronounced the lower the temperature. It was very revealing to relate this phenomenon to CaF2BaF2 multilayers and composites. In very general terms, these effects in the solid solutions were understood as being the atomistic limit of the interfacial charge-transfer that occurred at the hetero-interface of the crystallites or films, and reflected the transition from heterogeneous doping (higher-dimensional doping) to homogeneous doping (zero-dimensional doping).