Pure tysonite La1-xBaxF3-x solid solutions for x < 0.15 were prepared by solid state synthesis in a platinum tube under an azote atmosphere with subsequent quenching for 0.07 ≤x < 0.15. The solid solutions were studied by X-ray, electron and neutron diffractions and by (19)F NMR and impedance spectroscopy. The evolution of the cell parameters obeying Vegard's rule was determined for 0 < x≤ 0.15 and atomic position parameters were accurately refined for x = 0.03, 0.07 and 0.10. The chemical pressure induced by large Ba(2+) cations leads to an increase of the unit cell parameters. Fluorine environment and mobilities are discussed on the basis of the results of neutron diffraction and (19)F solid state NMR. The F1 subnetwork is lacunar; fluorine exchange occurs according to the order: F1-F1 and F1-F2,3. 2D EXSY NMR spectra of La0.97Ba0.03F2.97 reveal, for the first time, a chemical exchange between F2 and F3 sites that requires two successive jumps. The ionic conductivity was evaluated from sintered pellets and different shaping methods were compared. The only structural features which could explain the conductivity maximum are a crossover together with a smaller dispersion of F1-F1,2,3 distances at x = 0.05-0.07.