Willi Pabst

A note on particle size analyses of kaolins and clays

Abstract Based on paradigmatic experimental results for one selected type of kaolin the systematic differences in the measurement of particle size distributions of kaolins and clays by the sedimentation method and by the low angle laser light scattering (LALLS) method are studied. A theoretically sound shape transformation procedure for sedimentation results is proposed, based on a physically justified modification of the Stokes law, which takes into account the oblate (plate-like) shape of kaolin and clay particles. It is found that, with realistic estimates of the shape factor (aspect ratio), the corrected sedimentation data come very close to the light scattering data. This indicates at the same time a way to extract shape information from the comparison of two independent size measurements. Scanning electron microscopy of the 2-μm-undersize sedimentation fraction shows kaolin particles with a disc diameter of 3–5 μm and is thus in full agreement with the interpretation of the size measure as an “equivalent disc diameter”.

Porous alumina and zirconia ceramics with tailored thermal conductivity

The thermal conductivity of porous ceramics can be tailored by slip casting and uniaxial dry pressing, using either fugitive pore formers (saccharides) or partial sintering. Porous alumina and zirconia ceramics have been prepared using appropriate powder types (ungranulated for casting, granulated for pressing) and identical firing regimes (but different maximum temperatures in the case of partial sintering). Thermal diffusivities have been measured by the laser- and xenon-flash method and transformed into relative thermal conductivities, which enable a temperature-independent comparison between different materials. While the porosity can be controlled in a similar way for both materials when using pore formers, partial sintering exhibits characteristic differences between alumina and zirconia (for alumina porosities below 45 %, full density above 1600 °C, for zirconia porosities below 60 %, full density above 1300 °C). The different compaction behavior of alumina and zirconia (porosity after pressing 0.465 and 0.597, respectively) is reflected in the fact that for alumina the relative conductivity data of partially sintered materials are below the exponential prediction, while for zirconia they coincide with the latter. Notwithstanding these characteristic differences, for both alumina and zirconia it is possible to tailor the thermal conductivity from 100 % down to approx. 15 % of the solid phase value.

Sea Urchin Spines as a Model-System for Permeable, Light-Weight Ceramics with Graceful Failure Behavior. Part II. Mechanical Behavior of Sea Urchin Spine Inspired Porous Aluminum Oxide Ceramics under Compression

Sea urchin spines were chosen as a model system for biomimetic ceramics obtained using starch-blended slip casting. Porous alumina ceramics with cap-shaped layers with different alternating porosities were found to have superior fracture behavior under bulk compression compared to ceramics with uniform porosity. They fail in a cascading manner, absorbing high amounts of energy during extended compression paths. The porosity variation in an otherwise single phase material mimicks the architectural microstructure design of sea urchin spines of Heterocentrotus mammillatus, which are promising model materials for impact protection.

Phase Mixture Models for the Thermal Conductivity of Nanofluids and Nanocrystalline Solids

Nanofluids exhibit enhanced thermal conductivity with decreasing particle size, while nanocrystalline solids show a thermal conductivity reduction with decreasing grain size. Both phenomena can be modeled as being due to a boundary phase acting as a thermal bridge or barrier, respectively. In this paper a new phase mixture model is presented, based on a “mixed average” of the upper and lower Wiener bounds. It is shown that in the case of alumina‐water nanofluids our model is able to describe very well the experimentally measured data for nanofluids with 38, 25 and 13 nm alumina particles, when the solid‐like boundary phase is assumed to possess ice‐like thermal conductivity (2 W/mK) and a thickness of 1–5 nm. For nanocrystalline alumina (assuming a grain boundary with thickness 1 nm and a glass‐like conductivity value of 1.1 W/mK), it is shown that significant grain size effects cannot be expected for grain sizes above 100 nm and a more than 10% conductivity reduction requires grain sizes below 50 nm.

Cross-Property Relations between Elastic and Thermal Properties of Porous Ceramics

The cross-property relations between the elastic moduli and the thermal conductivity of porous ceramics are reviewed from the viewpoint of micromechanics (composite theory). Consequences of the rigorous Milton-Torquato and Gibiansky-Torquato relations (in the form of bounds, i.e. inequalities derived between bulk or shear moduli on the one hand and thermal conductivity on the other) are compared to various approximate relations (equalities) recently proposed between the tensile modulus (Young’s modulus) and thermal conductivity, among them the two new cross-property relations proposed by the authors. The relations are critically discussed and applied to the case of porous alumina, zirconia and alumina-zirconia composite ceramics.

Particle Size and Shape Characterization of Kaolins-Comparison of Settling Methods and Laser Diffraction

It is well known that grain size distributions of clayey raw materials determined by sedimentation methods differ significantly from grain size distributions measured with laser diffractometers due to the anisometric shapes of the particles. Investigation on commercial Czech kaolins by XRD and SEM revealed that the differences of the grain size distributions can be attributed to different mineral contents of the fractions and varying habiti of the kaolinite. It is shown that a numerical analysis of the development of shape with grain size (“SSD-curve”) can translate between the grain size determination methods. The shape of those SSD-curves is regular and offers the possibility to evaluate the phase content of the kaolins.

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.

Rheology of Ceramic Suspensions with Biopolymeric Gelling Additives

An overview is given of the rheological behavior of biopolymers in aqueous suspensions and of their role in new ceramic shaping processes (starch consolidation casting and carrageenan gel casting). In particular, we give a state-of-the-art account of the viscometric behavior, measured via rotational viscometry (apparent viscosity, including its shear-rate and concentration dependence), and the viscoelastic properties characterized via oscillatory shear rheometry (storage modulus, loss modulus and phase angle, including their temperature dependence), of starch-water systems, starchcontaining alumina suspensions, carrageenan-water systems and carrageenan-containing zirconia suspensions.

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.

High-Temperature Elastic Properties of Ceramics in the System MgO-Al2O3-SiO2 Measured by Impulse Excitation

Youngs moduli of talc-based ceramics from the system MgO-Al2O3-SiO2 are measured for temperatures up to 1000 °C via impulse excitation. It is shown that, after pressing at 50 MPa and firing at 1280 °C, MgO-rich compositions exhibit higher porosity and lower Youngs moduli (approximately 2030 % lower than predicted via micromechanical relations). The Young moduli of materials with less MgO decrease with temperature, but those of MgO-rich ceramics increase with temperature and exhibit a large hysteresis between heating and cooling. Lower absolute values are mainly due to increased porosity, but the reason for the modulus increase with temperature and the hysteresis is the higher enstatite content in the MgO-rich compositions. For a special composition the Youngs moduli are more or less temperature-independent and without significant hysteresis effects, probably due to the low content of enstatite and the high content of sapphirine.