Self-similarity during growth of the Au/TiO2(110) model catalyst as seen by the scattering of x-rays at grazing-angle incidence

The growth of gold nanoparticles on TiO2(110) was investigated in situ by grazing incidence x-ray scattering techniques. The in-plane diffraction showed complex epitaxial relationships with a preferential alignment of dense gold direction along the bridging oxygen rows of TiO2(110) ([1 (1) over bar0](Au)parallel to[001](TiO2)) with a low lattice mismatch. Whatever the growth temperature (T=300,600 K), two nearly equiproportional epitaxial planes, i.e., (111)(Au)parallel to(110)(TiO2) and (11 (2) over bar)(Au)parallel to(110)(TiO2), were observed. The small angle scattering from the nanoparticles was analyzed using a truncated sphere shape with models [R. Lazzari, F. Leroy, and G. Renaud, Phys. Rev. B 76, 125411 (2007)] that account for (i) multiple scattering effects due to the graded profile of refraction index in the normal direction and (ii) the correlation between the particle spacing and sizes. At the beginning of the growth, gold particles are pinned on defects and grow through a diffusion-limited mechanism. However, coalescence does not occur via a static mechanism. It rather involves surface diffusion of clusters. It proceeds through a self-similar mechanism, not only on the size distribution but also on the spatial ordering. Particle locations, which are no longer controlled by the randomness of nucleation centers, become dominated by the correlation between the particle size and its influence area. A strong link between island height and radius indicates that particles are close to equilibrium. Indeed, the value derived for contact angle (adhesion energy) compares well with tabulated data. In addition, the cluster size before the onset of coalescence compares with that of the gold particles at the maximum of catalytic activity for the oxidation of CO.