Nanoscale order in the frustrated mixed conductor La$_{5.4}WO$_{12-delta}$

We report a comprehensive investigation of the average and local structure of La$_{5.4}$WO$_{12-delta}$, which has excellent mixed proton, electron and oxide ion conduction suitable for device applications. Synchrotron X-ray and neutron powder diffraction show that a cubic fluorite supercell describes the average structure, with highly disordered lanthanum and oxide positions. On average the tungsten sites are six-fold coordinated, and we detect a trace (4.4(2) %) of anti-site disorder. In addition to sharp Bragg reflections, strong diffuse neutron scattering is observed, which hints at short-range order. We consider plausible local configurations, and show that the defect chemistry implies a simple chemical exchange interaction that favours ordered WO6 octahedra. Our local model is confirmed by synchrotron x-ray pair distribution function analysis and EXAFS experiments performed at the La K and W L3-edges. We show that ordered domains of around ca. 3.5 nm are found, implying that mixed conduction in La$_{5.4}$WO$_{12-delta}$? is associated with a defective glassy-like anion sublattice. The origins of this ground state are proposed to lie in the non-bipartite nature of the fcc lattice and the pairwise interactions which link the orientation of neighbouring octahedral WO6 sites. This function through frustration could provide a means of designing new mixed conductors.