Institute for Materials Science. Universitaet des Saarlandes

Prof. Mucklich
PF 151150, D-66041 Saarbruecken, Germany

3D-Characterization of grain size and shape distribution in silicon nitride and CIMC materials by means of statistical analysis for non textured as well as textured grain structure


The group is well experienced in the quantitative characterization of grain size and shape in silicon nitride microstructures by means of a new statistical approach, developed by us. It is based on the detection of all section profiles of the grains, which are assumed to have an average shape of hexagonal prisms. The solution of the stereological problem results in the unambiguous bivariate size-shape distribution of about 10,000 grains, which supplies good statistical relevance for microstructural correlation to the crack resistance due to the in-situ reinforcement of the ceramic by the elongated grains. Other relations to processing parameters have also been investigated.


Currently, the method is restricted only to non-textured ceramics, which usually do not hold in the outer regions of a sintered component. This can be overcome, if the orientation of each grain section can be measured. This would bring another advantage even for the non-textured case, since the grain sections could be contrasted clearly by their individual orientation instead of their grain boundaries, which often are not visible due to the very thin intergranular films. The microscopic orientation measurement will be made in the project by means of Electron Backscattered Diffraction (EBSD).

THE THEORETICAL PROBLEM consists of the solution of the stereological problem (discretization of integral equation and solution of the equation system) with the additional introduction of the three Euler angles, which will be available for each grain section. Thus: (1) non-textured samples could be investigated using a much lower number of grain sections to reach the same accuracy and reliability and (2) also textured microstructures could be investigated for the first time.

THE EXPERIMENTAL PROBLEM consists of the reliable detection of the orientations for the often fine grained structure which needs a high resolution Scanning Electron Microscope equipped with a powerful EBSD-system. The very low conductivity of the silicon nitride surface could not be improved by coating as usual, since the penetration depth of the backscattered electrons is only a few nanometers.

THE 3D GRAIN CHARACTERIZATION could be achieved for the different materials in the project and correlations could be quantitatively investigated which may have physical relevance towards the mechanical properties (crack propagation) as well as towards the sintering procedure (grain growth description).


The facilities (high resolution SEM and EBSD-equipment) are completely available and brandnew. The costs are calculated for a project time of 3 years:

PERSONAL: 1 PhD student for the theoretical work (see above) for 3 years = 98,000 US $ 1 PhD student for the experimental work (see above) for 3 years = 98,000 US $

TRAVELLING COSTS to the project partners

rough estimation: 16,000 US $


rough estimation: 34,000 US $

(this sum contains the costs of preparation of the samples which has to be done very careful in order to have electron backscattering in the undisturbed lattice of silicon nitride crystallites. It contains also a contribution to a little coating facility for very thin but homogeneous conductivity (mono-)layers as well as an amount for the rather long measuring time for EBSD at the SEM).