Spherical and platy kaolinite crystals were prepared under several hydrothermal conditions. Spherical kaolinite was produced mainly at high solid/water ratio (1/4) and at low temperatures (150°-200°C). Platy kaolinite predominated in products from experiments with intermediate solid/water ratios (1/256-1/16) and at high temperatures. Boehmite predominated at low solid/water ratios (1/4096) at all experimental temperatures (180°-220°C). The results indicate that the growth of the spherical kaolinite was favored at high degrees of supersaturation, whereas the growth of the platy kaolinite was favored at relatively low degrees of supersaturation.

Scanning electron microscopy has revealed the presence of spherical, lath and platy kaolinite in gels with Si/Al atomic ratio ranging from 1.84 to 0.76 that are hydrothermally treated under different temperature and time conditions. Hemispherical structures and excavated zones, at different stages of evolution, have been observed on the surface of the gel grains, indicating that spherical particles do not precipitate from the solution but are generated from the gels. The quantity of spherical particles depends on temperature, time and the chemical composition of the starting gel. Products from starting material with Si/Al ≈ 1 yield the highest quantity of these particles. Being metastable, sphere dissolution controls the chemistry of the solution and consequently the morphology of the precipitating crystals thus producing more elongated, curved and irregular outlines when gels with Si/Al ≈ 1 are hydrothermally treated.

We consider the linearized elasticity system in a multidomain of ${\bf R}^3$ . This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius $r^{\varepsilon}$ . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^{\varepsilon}$ tend to zero simultaneously, with $r^{\varepsilon}\gg\varepsilon^2$ , we identify the limit problem. This limit problem involves six junction conditions.

In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate.We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in the energy norm for the degree $p={\cal O}(\left|{\log \varepsilon}\right|)$ and with ${\cal O}({p^4})$ degrees of freedom.