CHARACTERIZATION OF THE MICROSTRUCTURE OF YAG CERAMICS VIA STEREOLOGY-BASED IMAGE ANALYSIS

The microstructure of transparent YAG ceramics is investigated by stereology-based microscopic image analysis using SEM and FE-SEM micrographs. Interface densities, mean curvature integral densities and the related grain size measures (mean chord length and Jeffries size) have been determined with relative errors of 9-12 % for interface densities and mean curvature integral densities and 6-9 % for the corresponding grain size measures. A comparison of the two grain size measures confi rmed an excellent linear correlation between the Jeffries size and the mean chord length, with a mean-chordlength-to-Jeffries-size ratio of 0.928 +/- 0.086. The overall range of average grain sizes is approx. 11-34 μm. It has been found that the sintering time has a signifi cant influence on the grain size, especially for YAG ceramics without Yb doping. When the sintering time is increased by a factor 8 (from 2 h to 16 h) the grain size increases by more than 200 % in undoped YAG ceramics, whereas the grain growth is much weaker in Yb-doped YAG ceramics (grain growth only 50-70 % for YAG ceramics with 5-10 at.% Yb). Thus it can be concluded that the Yb dopant acts as a grain growth inhibitor in YAG ceramics, at least for suffi ciently long sintering times (8 h and more). The infl uence of the sintering additive (tetraethyl orthosilicate TEOS) content on the grain size is negligible in the concentration range tested (0.3-0.5 wt.%)

A GENERALIZED CLASS OF TRANSFORMATION MATRICES FOR THE RECONSTRUCTION OF SPHERE SIZE DISTRIBUTIONS FROM SECTION CIRCLE SIZE DISTRIBUTIONS

A generalized formulation of transformation matrices is given for the reconstruction of sphere diameter distributions from their section circle diameter distributions. This generalized formulation is based on a weight shift parameter that can be adjusted from 0 to 1. It includes the well-known Saltykov and Cruz-Orive transformations as special cases (for parameter values of 0 and 0.5, respectively). The physical meaning of this generalization is explained (showing, among others, that the Woodhead transformation should be bounded by the Saltykov transformation on the one side and by our transformation from the other) and its numerical performance is investigated. In particular, it is shown that our generalized transformation is numerically highly unstable, i.e. introduces numerical artefacts (oscillations or even unphysical negative sphere frequencies) into the reconstruction, and can lead to completely wrong results when a critical value of the parameter (usually in the range 0.7-0.9, depending on the type of distribution) is exceeded. It is shown that this numerical instability is an intrinsic feature of these transformations that depends not only on the weight shift parameter value and is affected both by the type and the position of the distribution. It occurs in a natural way also for the Cruz-Orive and other transformations with finite weight shift parameter values and is not just caused by inadequate input data (e.g. as a consequence of an insufficient number of objects counted), as commonly assumed. Finally it is shown that an even more general class of transformation matrices can be defined that includes, in addition to the aformentioned transformations, also the Wicksell transformation