Tereza Uhlířová

Application of Stereological Relations for the Characterization of Porous Materials via Microscopic Image Analysis

In this work we demonstrate the application of stereology-based image analysis for the characterization of highly porous cellular ceramics (alumina foams) prepared by biological foaming with yeast and subsequent drying (80-105 °C) and firing (1570 °C). It is shown that the ceramics prepared usually have total porosities in the range 78-84 % and that the porosities made up by large pores (volume fraction of foam bubbles) are usually in the range 58-75 %. Further it is shown that the mean chord length and the Jeffries size, i.e. pore size measures related to the interface density and the mean curvature integral density, respectively, are relatively close to each other (usually 0.8-1.4 and 0.8-1.2 mm) with a ratio close to unity (0.9-1.3) and that the mean surface-to-surface distance of pores gives a realistic picture of the average pore wall thickness (usually 0.46-0.69 mm). Using a special processing variant (excess ethanol addition) it is possible to obtain microstructures with lower porosity (total porosity 68-70 %, foam bubble volume fractions 50-56 %) and smaller pore size (approx. 0.5 mm). Absolute errors are calculated using normalized deviations corresponding to 95 % reliability in the Student distribution and the standard errors for the quantities in question (both observed and estimated). Relative errors are found to be below 12 % when the number of measurements is of order 400-1000.

Quantitative microstructural characterization of transparent YAG ceramics via microscopic image analysis using stereological relations

The microstructure of transparent yttrium-aluminum garnet (YAG) ceramics is characterized using different microstructural descriptors, with special focus on grain size numbers. Both linear and planar grain size numbers are used to describe the dependence of the average grain size on Yb dopant content (0-10 at.%), sintering additive (tetraethyl orthosilicate, TEOS) content (0.3-0.5 wt.%) and firing time. Although the two grain size numbers are very close for the materials studied (with ratios very close to unity, around 0.987 ± 0.109), these two numbers are principally independent and provide complementary microstructural information. Their relations to other microstructural descriptors (interface density, mean curvature integral density, mean chord length, Jeffries size) are discussed throughout the text. It is found that Yb doping of more than 3 at.% has a grain-growth-inhibiting effect (after sufficiently long firing times), but differences in the TEOS content between 0.3 and 0.5 wt.% do not have any sensible effect. The largest effect on the microstructure is exerted by the firing time (with prolonged firing times leading to grain growth), but with higher Yb doping the effect of firing time on the grain size becomes less pronounced: for YAG samples without Yb doping, increasing the firing time by a factor of 8 (from 2 h to 16 h), deceases the grain size number by 33.2-35.0 %, whereas with a Yb dopant content of 10 at.%, the corresponding decrease in the grain size number is only 8.7-10.0 %. These findings are fully corroborated using the other microstructural descriptors.

Elastic Properties of Porous Alumina, Zirconia and Composite Ceramics

Micromechanical calculations and elasticity standard relations are used to predict the elastic properties of porous alumina, zirconia and kaolin-based ceramics, as well as the high-temperature Young moduli of alumina-zirconia and alumina-mullite composites. The predictions are compared with experimental results obtained via impulse excitation. It is found that the Young moduli of highly porous (cellular) alumina ceramics can be predicted via the Gibson-Ashby power-law relation, whereas for partially sintered kaolin-based ceramics our exponential relation, albeit better than the Gibson-Ashby relation, does not give a satisfactory prediction. However, once the Young moduli are known, the shear and bulk moduli can be reliably predicted in both cases, based on rough information on the Poisson ratio. The temperature dependence of the Youngs moduli of two-phase composites can be quite precisely predicted as soon as the master curves of the constituent phases and the type of porosity (convex, concave, or saddle-point) are known.