Measurement and Prediction of Local Structure

Complex perovskite-structured metal oxides form the backbone of advanced electroceramics. In many of these systems, competing interatomic interactions generate local deviations from average periodicity which modify, often critically, a material’s response to an external stimulus (e.g. electric field). Because of their relative subtlety and complexity, the exact nature of these average-structure perturbations remains uncertain even for classical and extensively studied compounds.  Relaxor ferroelectrics represent a prominent example of technologically useful materials whose structure remains elusive despite many decades of intense research.   As a result, the origin of the relaxor behavior is still not fully understood.  Recently, we have been able to elucidate the much-debated nanoscale structure of a classical relaxor ferroelectric PbMg_1/3Nb_2/3O₃ (PMN) by combining neutron and X-ray total scattering measured on powder samples with a 3D distribution of the X-ray diffuse-scattering intensity obtained for a single crystal.  This work capitalized on our recent major development of the computer software for atomistic structure refinements, which enabled a consistent description of the atomic arrangements over a broad range of length-scales in a single model, permitting the use of structural models sufficiently large to represent systems, like PMN.   Our results clarified several contentious hypotheses regarding the chemical and polar ordering in PMN and revealed a hitherto unsuspected hierarchical nature of polar nanoregions that are key to the relaxor properties.

Nanoparticles are another example of technological systems where traditional methods of structure determination which rely on Bragg diffraction peaks become ineffective.  Titania nanoparticles attract interest for their potentially useful photocatalytic properties.  In bulk titania crystals under ambient conditions, rutile is the thermodynamically stable phase, whereas in nanoparticles, anatase and brookite become preferred.  Commercial adaptation of TiO₂ in photocatalysts is hindered by its wider-than-optimal band gap and fast electron-hole recombination after absorption of light.  These issues can be mitigated by engineering nanoparticles with specific shapes, dimensions, and defect populations.  Indeed, promising photocatalytic properties have been reported for nanoparticles of all three polymorphs and mixtures thereof.   However, the exact mechanism of the improved performance in each case remains uncertain.  In nanoparticles, the already distinct electronic structures of bulk polymorphs are modified because of structural relaxations induced by particle-size and surface effects.  The effects of structural distortions, which can vary between the particle’s interior and surface, on electronic properties relevant to photocatalytic performance are uncertain, in part because such distortions themselves have not yet been characterized in detail.  We demonstrated structural refinements of whole-nanoparticle atomistic models for TiO₂ brookite nanorods, which exhibit enhanced photocatalytic properties.  Our results revealed that the atomic positions in the nanorods differ from the bulk structure by static atomic displacements that increase progressively from the nanorod axis toward its side surfaces.  A pattern of structural relaxations exhibited symmetry consistent with that imposed by the nanorod habits.  Density-functional-theory calculations were in qualitative agreement with the experimental observations and additionally revealed a strong dependence of the structural relaxations, including lattice-volume changes, on sorbate coverage.  The experimental and computed magnitudes of these relaxations appeared to be significantly larger than those predicted by a simple surface-stress model, with the difference attributed to electrostatic interactions.   This study demonstrated the potential of using atomistic structure refinements to obtain a detailed picture of atomic order in nanoparticles, and highlighted complex, spatially variable distortions that need to be considered while interpreting the electronic properties of these materials.