= Solution
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, $\sigma_{\rm ion}=n|q|\mu$, or $nq^2D/(k_BT)$ when an uncorrelated <Nernst-Einstein relation> applies. <fluoride> <vacancies> and <interstitial defects>, including those generated as <Frenkel pairs>, provide possible carriers.
\b[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.
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