The need for high efficiency energy production, conversion, storage and transport is serving as a robust guide for the development of new materials. Materials with physical-chemical properties matching specific functions in devices are produced by suitably tuning the crystallographic- defect- and micro-structure of the involved phases. In this review, we discuss the case of Rare Earth doped Ceria. Due to their high oxygen diffusion coefficient at temperatures higher than ~500°C, they are very promising materials for several applications such as electrolytes for Solid Oxide Fuel and Electrolytic Cells (SOFC and SOEC, respectively). Defects are integral part of the conduction process, hence of the final application. As the fluorite structure of ceria is capable of accommodating a high concentration of lattice defects, the characterization and comprehension of such complex and highly defective materials involve expertise spanning from computational chemistry, physical chemistry, catalysis, electrochemistry, microscopy, spectroscopy, and crystallography. Results coming from different experimental and computational techniques will be reviewed, showing that structure determination (at different scale length) plays a pivotal role bridging theoretical calculation and physical properties of these complex materials.

Up to now, the crystallographic structure of the magnetoelectric perovskite EuTiO3 has been considered to remain cubic down to low temperature. Here we present high-resolution synchrotron x-ray powder-diffraction data showing the existence of a structural phase transition, from cubic Pm-3m to tetragonal I4/mcm, involving TiO6 octahedra tilting, in analogy to the case of SrTiO3. The temperature evolution of the tilting angle and of the full width at half maximum of the (200) cubic reflection family indicate a critical temperature Tc = 235 K. This critical temperature is well below the recent anomaly reported by specific-heat measurement at TA $\sim${} 282 K. By performing atomic pair distribution function analysis on diffraction data, we provide evidence of a mismatch between the local (short-range) and the average crystallographic structures in this material. Below the estimated Tc, the average model symmetry is fully compatible with the local environment distortion, but the former is characterized by a reduced value of the tilting angle compared to the latter. At T = 240 K, data show the presence of local octahedra tilting identical to the low-temperature one, while the average crystallographic structure remains cubic. On this basis, we propose that intrinsic lattice disorder is of fundamental importance in the understanding of EuTiO3 properties.