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A larger barium cation expands the fluorite structure and can widen the constrictions through which fluoride ions move. A plausible explanation is therefore a smaller ionic migration barrier and greater fluoride mobility. In a simple dilute-carrier description, ${\sigma }_{\mathrm{ion}}=n|q|\mu$, or $n{q}^{2}D/(k_{B}T)$ when an uncorrelated Nernst-Einstein relation applies. fluoride vacancies and interstitial defects, including those generated as Frenkel pairs, provide possible carriers.

More open migration pathways can raise the conductivity, but ion size by itself is not a proof: defect formation free energies set $n$, migration free energies set mobility, and correlated hopping can alter the simple relation. A controlled comparison would use crystals with comparable impurity content, thermal history and electrode conditions, and measure conductivity over temperature to separate plausible activation behaviour from extrinsic defect effects.