Electronic and spectral properties of small TiO2 particles have been studied in order to gain more knowledge on their dependence on the crystal- and particle-size distributions. Our goal is to extend the recently developed light scattering based method for determining submicrometer size particles to nanoparticles. For that, we need to know how the refractive index function depends on the cluster size. As a first step, we have used time-dependent density functional theory (TDDFT) calculations having a focus on the shape changes of the calculated spectra, which can be related to changes in the refractive index function. Starting from the structure of TiO2 molecule for the two smallest particles and truncated bulk anatase structure for larger particles, the structures for (TiO2) n clusters, n = {1, 2, 8, 18, 28, 38}, have been modeled. After the structure optimization using standard density functional theory (DFT) approach, the photoabsorption spectra for the optimized particle structures have been calculated by using TDDFT calculations. The results show slight evidence of the band gap broadening in the case of three out of the smallest particles and strong structural dependence of electronic and spectral properties, which can partly be related to the transformation of the electron structure, and breaking of the crystal symmetry as the size of the particle becomes smaller. These findings indicate that in the case of small particles their refractive index function can differ from the bulk values, and this has to be taken into account in the interpretation of light-scattering measurements.

We present measurements of the complete scattering matrix as a function of the scattering angle of randomly oriented irregular hematite and rutile particles. The measurements were made at a wavelength of 632.8 nm in the scattering angle range from 5-174 degrees. Apart from their astronomical interest, these two samples are extremely interesting from a theoretical point of view, because they both have high real parts of the refractive index (about 3.0 for the hematite and 2.73 for the rutile). In addition, the hematite sample has a high imaginary part of the refractive index k, with values between 10 −1 and 10 −2 , whereas rutile is a non-absorbing material (k ≈ 0) at the studied wavelength. The scattering patterns of these mineral particles are quite similar to each other but show remarkable differences when compared to the results obtained for irregular mineral particles with moderate real parts of the refractive index. The measured results for both samples were compared with results of Mie calculations for projected surface equivalent spheres and T-matrix calculations for various spheroidal and cylindrical shapes. Both the experimental and theoretical results presented in this work seem to indicate that the scattering behavior of irregular mineral particles that have a high real part of the refractive index is not very dependent on the shape of the particles. In this case, Mie theory may give reasonable results despite the irregular shapes of the particles.

The mechanisms of formation and structure of precipitates hydrolyzed from aqueous solutions of titanium tetrachloride and titanium sulfate were studied by small-angle X-ray scattering (SAXS). SAXS was found a powerful method for that purpose. The small colloidal primary particles that were present in the solutions at room temperature started to aggregate when thermal precipitation started. The aggregated particles coalesced until their radius was approximately 1 nm depending of the precipitation conditions to some extent. After that, the aggregation continued producing either mass fractal or surface fractal structures. The structure was mass fractal when primary particle concentration was high enough and surface fractal when concentrations were closer to the equilibrium state. With a delay ionic titanium started to precipitate. Because of its rather slow precipitation rate in the conditions of this study, only surface fractal aggregates were formed. The mass fractal structure was found X-ray amorphous and the surface fractal aggregates nano crystalline. The mass and surface fractal dimensions of these aggregates were 2.2 (1 s ( 0.1) and 2.7 (1 s ( 0.2), respectively. The "titanic acids" were found to be aggregates of small titanium dioxide particles that have mass fractal structure in ortotitanic acid and surface fractal structure in metatitanic acid. The loose structure of the mass fractal aggregates causes the relatively easy solubility and the X-ray amorphous state found in ortotitanic acid. On the contrary, the more compact structure of metatitanic acid explains its nano crystallinity and insolubility. The changing of ortotitanic acid to metatitanic acid upon aging is obviously a consequence of the restructuring of the primary titanium dioxide particles toward the close-packed porous structure.

We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm ͑in air͒. These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length͞width ratio than measured.