The size-dependent structure of CdSe nanoparticles, with diameters ranging from 2 to 4 nm, has been studied using the atomic pair distribution function (PDF) method. The core structure of the measured CdSe nanoparticles can be described in terms of the wurtzite atomic structure with extensive stacking faults. The density of faults in the nanoparticles ∼ 50% . The diameter of the core region was extracted directly from the PDF data and is in good agreement with the diameter obtained from standard characterization methods suggesting that there is little surface amorphous region. A compressive strain was measured in the Cd-Se bond length that increases with decreasing particle size being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This study demonstrates the size-dependent quantitative structural information that can be obtained even from very small nanoparticles using the PDF approach.

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Variations in the structure of gamma-alumina (γ-Al 2 O 3 ), derived from well-crystalline boehmite, calcined at various temperatures in air were investigated. Consistent distribution of cation coordination, ∼69% octahedral and ∼31% tetrahedral, was observed for material calcined between 500 and 900 °C. Gamma alumina was found to be present between 450 and 750 °C. Its structure was tetragonally distorted but showed a reduced tetragonal distortion with increasing temperature. A cubic γ-Al 2 O 3 phase was never detected. Above 750 °C, δ-Al 2 O 3 was not observed, but instead a new phase was identified and designated gamma-prime-alumina (γ′-Al 2 O 3 ). Similarly to δ-Al 2 O 3 , γ′-Al 2 O 3 was determined to be a triple cell of γ-Al 2 O 3 and was described using the P4 hm2 space group. The cation ordering in this structure is more obvious than that for γ-Al 2 O 3 , with fewer site positions being occupied with increasing calcination temperature.

We have applied a local structural technique, atomic pair distribution function (PDF) analysis of powder diffraction data to γ-Al 2 O 3 , to obtain a quantitative structure. Refinements of the PDF support previous findings that nonspinel model representations are more suitable to describe the average structure of γ-Al 2 O 3 , as opposed to the spinel model. Surprisingly, also we find a previously unknown fine-scale nanostructure with a domain size ∼ 1 nm. Modeling suggests that within these nanodomains the oxygen sublattice is modified from the average structure and retains aspects of the boehmite precursor that reflects a stacking fault in the γ-Al 2 O 3 matrix. This results in a novel and unexpected view of the γ-Al 2 O 3 structure because earlier controversies about it centered on the arrangement of Al ions among different cation sites, whereas the oxygen sublattice arrangement was rarely questioned. This average oxygen sublattice structure is recovered in our models on longer length scales by introducing aperiodic arrays of stacking faults. The use of γ-Al 2 O 3 in catalysis depends sensitively on its nanoporosity and defect structure. Here we present a new view which may allow for additional understanding and optimization of its functional properties.