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

Abstract

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 BaF(2) lattice favored the formation of interstitial sites that were located close to the Ca atoms, whilst doping larger Ba species into the CaF(2) 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 CaF(2)-BaF(2) 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).

Mismatch in cation size causes rapid anion dynamics in solid electrolytes: the role of the Arrhenius pre-factor

“…On the other hand, the generation of Frenkel defects in Ba-doped CaF 2 is energetically disfavored by 0.14 eV. 26 In our case substitutional disorder is much larger than dopant concentrations and a direct comparison with results for extremely low levels of doping turns out to be difficult. At least we can say the following.…”

“…At very low levels of doping, the incorporation of Ca 2+ ions resulted in trapped F interstitial sites and mobile F vacancies as the opponent defect. 26 The formation of such interstitial site next to a Ca 2+ dopant in BaF 2 was promoted by 0.08 eV. On the other hand, the generation of Frenkel defects in Ba-doped CaF 2 is energetically disfavored by 0.14 eV.…”

“…24,25 Recently, it has also attracted groups from theory to model ion conductivities. 26,27 Nanocrystalline Ba 1−x Ca x F 2 (0 < x < 1) can easily be prepared by mechanochemical reaction at low temperatures from the binary fluorides BaF 2 and CaF 2 . 24,25 Joint milling the two fluorides forces the cations to mix at atomic scale while the symmetry of the educts remains the same; both BaF 2 and CaF 2 crystallize with antifluorite structure.…”

Doping Strategies in Inorganic and Organic Materials

“…[19] Even though only +2 cations are involved, it is the effect of different cation size that leads to elastic interactions such that e.g. in Ca 1-δ Ba δ F 2 fluoride vacancies are stabilized and in Ba 1-δ Ca δ F 2 interstitial defects (as shown in Figure 6 l.h.s.…”

Structure and ion dynamics of mechanosynthesized oxides and fluorides

“…The expected shift of the rate peaks towards lower T, for samples with x around 0.5, can only be explained by an enhanced pre-exponential factor of the underlying Arrhenius relation [49]. Further insight into this metastable solid solution is being gained by molecular dynamics simulations and X-ray absorption spectroscopy measurements [52,53].…”