Accurate determination of oxide nanoparticle size and shape based on X-ray powder pattern simulation:: Application to boehmite AlOOH

The control of oxide nanoparticle size and shape is of great importance to tune their physical and chemical properties. As a consequence, routine methods are required to determine the nanoparticle morphology. Since diffraction patterns strongly depend on both size and shape, X-ray powder diffraction (XRD) is widely used to determine the particle morphology. Herein, an accurate approach is proposed based on the simulation of morphology-dependent diffraction patterns using the Debye formula and on the comparison of these calculated patterns to the experimental ones. The most representative particle morphology is also obtained. This methodology has been first validated on a simple model system of MgO cubic and octahedral nanoparticles. It has been then applied to three different morphologies of boehmite AlOOH samples, obtained by varying the synthesis pH value. The method is characterized in terms of sensitivity, and extensive comparisons with transmission electron microscopy (TEM) results are also performed: the results appear as consistent. The XRD method is especially efficient for the smallest nanoparticles (about 3-7 nm), since the XRD approach leads to a full and accurate determination of the particle morphology, whereas the TEM observations only provide average diameters of the particles. Moreover, oriented aggregation is observed for all the samples. The developed method can be easily extended to a wide range of nanomaterials.