This paper proposes the application of capillary and chain random models of pore space structure for determination of limit pore diameter distributions of porous materials, based on the mercury intrusion curves. Both distributions determine the range in which the pore diameter distribution of the investigated material occurs and defines the degree of inaccuracy of the method based on the mercury intrusion data caused by the indeterminacy of the sample shape and its pore space architecture. We derived equations describing the quasi-static process of mercury intrusion into the porous layer and porous ball with a random chain pore space structure and analysed the influence of the model parameters on the mercury intrusion curves. It was shown that the distribution of link length in the chain model of the pore space, random location of chain capillaries in the sample and the length distribution of the capillaries do not influence significantly the intrusion process. Therefore, a simple model of the mercury intrusion into the layer is proposed in which chain links of the pore space have random diameters and constant length. This model is used as a basic model of the intrusion process into a sample of any shape and size and with homogeneous and isotropic chain pore space architecture. The thickness of the layer then represents the mean length of chain capillaries in the sample. It was also proved that the capillary and chain models of pore space architecture are limit models of the network model identified in this paper with the pore architecture of the investigated sample. This justifies the application of both models for determination of limit cumulative distributions of pore diameters in porous materials based on the mercury intrusion data.

Ce³⁺ doped Al₂O₃-YAG eutectics were successfully grown by the horizontal directional crystallization method. The crystallization rate of eutectic growth was changed in the 1–7.5 mm/h range at a growth temperature of 1835 ℃. The microstructure of eutectic samples was investigated using scanning electron microscopy and X-ray microtomography. The intrinsic morphology of eutectic represents the stripe-like channel structure with a random distribution of the garnet Y₃Al₅O₁₂ (YAG) and Al₂O₃ (sapphire) phases. The content of these phases in the stripes changes in the 52.9–55.3% and 46.1–47.1% ratios, respectively, depending on the growth rate of the crystallization of the eutectic samples. The luminescent properties of the eutectic demonstrated the dominant Ce³⁺ luminescence in the garnet phase. The luminescence of the Ce³⁺ ions in Al₂O₃ has also been observed and the effective energy transfer processes between Ce³⁺ ions in the Al₂O₃ and YAG garnet phases were revealed under high-energy excitation and excitation in the UV Ce³⁺ absorption bands of sapphire. The phosphor conversion properties and the color characteristics (Al₂O₃-YAG):Ce eutectic with different thicknesses were investigated under excitation by a blue LED. We have also tested the prototypes of white LEDs, prepared using a blue 450 nm LED chip and (Al₂O₃-YAG):Ce eutectic photoconverters with 0.15 to 1 mm thicknesses. The results of the tests are promising and can be used for the creation of photoconverters for high-power white LEDs.

A one-dimensional problem of propagation of plane harmonic wave in macroscopically inhomogeneous materials is analyzed. A general description is proposed for the material of the equivalent fluid type characterized locally by two acoustical parameters: the wavenumber and the acoustical impedance. The coupled system of ordinary differential equations for amplitudes of forward and backward waves is derived. As an example the problem of wave interaction with a layer of inhomogeneous material placed between two homogeneous halfspaces is considered. The analytical solution and explicit expressions for reflection and transmission coefficients are obtained. It is shown that the presence of the inhomogeneous transition layer causes strong frequency dependence on both coefficients.