Stereological principles

The stereological principles are fulfilled for the quantitative characterization of the microporosity (eiA,macro)> the primary particle sizes (t/particie)> and the interparticle distance (Dnn-surt) because of the statistically cut primary particles. eiA,macro is calculated following (11.5) from the void area Amicro.void within the granule shell and the total shell area zlsheii. 

Dullien et. al. [55-57] examined salt particles embedded in a matrix of Wood s metal using the principles of quantitative stereology. They then leached out the salt particles and examined the matrix using mercury porisimetry. Poor agreement was obtained and this they attribute to the mercury porosimetry being controlled by neck diameter. Nicholson... 

H. Digabel, Principles of Stereology in Bone Studies. In Proc. First Workshop on Bone Morphometry, Ed., Z.F.G. Jaworski, Univ. Ottawa Press, pp. 16-23, 1976. 

Presents an excellent treatment (p. 129ff) of the structure-function relationships for trabecular bone using the principles of continuum mechanics and quantitative stereology. 

The mathematical task of reconstructing the material s three-dimensional structure parameters from measured data obtained on a section of the material is called stereology. Different principles are used for areal, linear, and point analyses. The problem of scale is solved with a fractal approach, making the length of a curve a function of the size of the measuring device (22). 

All micromechanical relations presented in this chapter are based on the volume fraetions of the constituent phases (i.e. one-point correlation fimctions and a special part of the two-point correlation functions) as the only input information. If complete two-point and three-point information would be available (e.g. from stereological analysis or 3D tomography), the Hashin-Shtrikman bounds (i.e. the two-point bounds) could be improved in principle, whieh leads to the three-point bounds due to [Beran Molyneux 1966] and [Milton Phan-Thien 1982], cf. also [Jeulin 2001, 2002, Markov 2000, Milton 2002, Sobczyk Kirkner 2001, Torquato 2000, 2002]. Of course, in the case of dense alumina-zirconia composites it is quite... 

Mouton PR (2002) Principles and practices of unbiased stereology an introduction for bioscientists. Johns Hopkins University Press, Baltimore... 

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