DISORDER AT THE NANOSCALE IN PEROVSKITE TITANATES AND DOPED CERIA: MULTIPLE APPROACHES TO MODELLING TOTAL SCATTERING DATA

Crystal structures can take a number of forms and their relationship with the physics of a solid lends itself to an even greater number of interpretations. Ferroelectricity, for example, can be predicted to occur in certain symmetries, but sometimes it can be hidden in the response to an electric field, in a peculiar electron- or nuclear-spin resonance, in the unfolding of a phase transition, or else. In any of these cases, the emergence of ferroelectricity is intimately related to subtle changes in the atomic positions with respect to a high-symmetry parent structure. As is the case with many other physical properties, this often implies that the crystal structure is disordered locally (as opposed to on average or long-range), but the magnitude and the time- and length-scales of disorder can vary dramatically between different materials. This work combines multiple X-ray and neutron powder diffraction techniques to try to capture the most of the structural complexity hidden in the bulk of materials. First, reciprocal-space analysis by the Rietveld method allowed drawing the crystallographic phase diagram of a novel perovskite solid solution, praseodymium-doped strontium titanate (SPTO). SPTO is a perovskite that combines a centrosymmetric antiferrodistortive (AFD) structure and a large, diffuse dielectric response at room temperature, prompting the question of whether AFD and ferroelectric (FE) distortions coexist in the material. Subsequently, the Pair Distribution Function (PDF) of SPTO, representing the instantaneous spatial arrangement of the atoms in the material, was analysed using multiple approaches. X-ray PDF was fitted with structural models obtained by evaluating possible polar and rotational distortions of the cubic perovskite phase. The most accurate, a tetragonal structure derived from the long-range phase, showed a huge AFD distortion that could also be consistent with a local FE mode. To get a better insight into the local structure, neutron PDF data were collected and modelled by i) fitting the distorted tetragonal model over successive ranges in real space (`box-car� refinements) and ii) atomistic simulations using the Reverse Monte Carlo (RMC) method. This led to a model in which FE distortion caused by Pr-doping at the perovskite A-site spreads to the AFD framework of octahedra, resulting in distorted coordination of both A and B cations. Neutron PDF data of undoped strontium titanate was also used in the development of another approach to PDF modelling, in which structural models representing a unique soft-mode distortion are evaluated statistically against the experimental neutron PDF. This symmetry-adapted approach evidenced that four soft modes among those suggested by theoretical phonon dispersion are active distortions in SrTiO3, and have signatures in the local structure determined experimentally. This approach is aimed at obtaining an unbiased local structural model of strontium titanate, in that symmetry lowerings are inferred directly from the amplitudes of the individual soft modes refined against the PDF instead of assessing the goodness of fit of an arbitrarily chosen model. Whereas all these methods focused on a length scale of 10 �(1 nm), the last approach to PDF modelling presented in this work studies the coherence length of lower-symmetry nanometric domains in a solid solution by evaluating structural parameters up to 600 �(60 nm). Instead of titanates, though, this study involved yttrium-doped ceria: thanks to the extremely high structural coherence of crystalline ceria and owing to the high angular resolution of the instrument used, the data collected lend themselves very well to analysing the PDF well beyond the short range. The aim of this approach is to obtain a structural model for every slice of real space analysed, in order to describe in terms of order parameters how the local structure coalesces into the average crystallographic phase.