Stereology

The first detailed book to describe the practice and theory of stereology was assembled by two Americans, DeHoff and Rhines (1968) both these men were famous practitioners in their day. There has been a steady stream of books since then a fine, concise and very clear overview is that by Exner (1996). In the last few years, a specialised form of microstructural analysis, entirely dependent on computerised image analysis, has emerged - fractal analysis, a form of measurement of roughness in two or three dimensions. Most of the voluminous literature of fractals, initiated by a mathematician, Benoit Mandelbrot at IBM, is irrelevant to materials science, but there is a sub-parepisteme of fractal analysis which relates the fractal dimension to fracture toughness one example of this has been analysed, together with an explanation of the meaning of fractal dimension , by Cahn (1989). 

This whole field is an excellent illustration of the deep change in metallurgy and its inheritor, materials science, wrought by the quantitative revolution of mid-century. 

Reciprocal square root of grain size and particle spacing. mm 

Microscopy can provide visual details of the membrane surface and cross-section morphology. Image analysis of micrographs can give quantitative data from these direct observations. 

Atomic force and scanning tunnelling microscopies have recently revolutionised 

Several other techniques referred to as microscopy and based on several different phenomena can be found in the literature. These include acoustic microscopy based on the interactions of acoustic waves with materials [28] the projection microscopy which is still under development and gives a hologram image of the sample illuminated by a beam of low energy electrons [29]. For membrane applications a scarming electrochemical microscope has been developed based on the measurement of the local flux of electroactive ions across the membrane. The ability to detect 1 pm radius pores separated by 50-100 pm has been demonstrated with mica membranes [30]. 

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Whereas at the lower end of its range mercury porosimetry overlaps with the gas adsorption method, at its upper end it overlaps with photomicrography. An instructive example is provided by the work of Dullien and his associates on samples of sandstone. By stereological measurements they were able to arrive at a curve of pore size distribution, which was extremely broad and extended to very coarse macropores the size distribution from mercury porosimetry on the other hand was quite narrow and showed a sharp peak at a much lower figure, 10nm (Fig. 3.31). The apparent contradiction is readily explained in terms of wide cavities which are revealed by photomicrography, and are entered through narrower constrictions which are shown up by mercury porosimetry. 

DeHoff, R.T. (1986) Stereology in Encyclopedia of Materials Science and Engineering vol. 6, ed. Bever, M.B. (Pergamon Press, Oxford) p. 4633. 

The characterisation of materials is a central necessity of modern materials science. Effectively, it signifies making precise distinctions between different specimens of what is nominally the same material. The concept covers qualitative and quantitative analysis of chemical composition and its variation between phases the examination of the spatial distribution of grains, phases and of minor constituents the crystal structures present and the extent, nature and distribution of structural imperfections (including the stereological analysis outlined in Chapter 5). 

Guiot, P., Baudhuin, P., and Gotfredsen, C. (1980). Morphological characterization of liposome suspensions by stereological analysis of freeze fracture replicas from spray frozen samples, J. Microsc., 120, 159-174. 

Bierman, E.P.B, Brouwer, D.H., and van Hemmen, J.J. (1997) Measuring crop density comparison of volumetry and stereological methods, Bull. Environ. Contam. Tox., 58 1006-1013. 

Sherle, W. (1970) A simple method for volumetry of organs in quantitative stereology, Microscopy, 20 57-60. 

The computer age has brought about considerable innovation in the operation of laboratory instrumentation. One consequence of this is the wider acceptance and utilization of the optical microscope as a quantitative analytical instrument. A brief literature survey illustrates the diversity of disciplines and optical methods associated with the development of computer interfaced optical microscopy. This is followed by a description of how our methods of fluorescence, interferometry and stereology, nsed for characterizing polymeric foams, have incorporated computers. 

Stereological methods have often been used without the advantage of a computer or video screen. Such an approach superimposes a grid of dots, lines or areas on the specimen image and counts the inclusions and intersections this grid format shows with the feature of interest within the specimen field. Such a procedure, without automation, is most laborious requiring much effort to establish statistical validity for the measurements. 

Figure 2. An example of typical computer print out showing (a) the histogram of pixel frequency versus intensity with values of maximum and minimum intensity (b) adjusted raw data image (c) binary image and (d) calculated stereological parameters.

Underwood, E.E. Quantitative Stereology, Addison-Wesley, Reading, MA 1970. 

J. C. Russ, Practical Stereology, Plenum Press, New York, 1986, Chapter 4. 

Lehre, K. P. and Danbolt, N. C. The number of glutamate transporter subtype molecules at glutamatergic synapses chemical and stereological quantification in young adult rat brain. /. Neurosci. 18 8751-8757,1998. 

Sorensen, E.M.B., R.R. Mitchell, A. Pradzynski, T.L. Bayer, and L.L. Wenz. 1985. Stereological analyses of hepatocyte changes parallel arsenic accumulation in the livers of green sunfish. Jour. Environ. Pathol. Toxicol. Oncol. 6 195-210. 

Sahagian D.L. and Proussevitch A.A. (1998) 3D particle size distributions from 2D observations stereology for natural applications. /. Volcanol. Geotherm. Res. 84, 173-196. 

The sampling methods illustrated in Fig. 7 are the basis of all operations in stereology and are referred to as point counting (Fig. 7A, 7B), areal analysis... 

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