Stereology science

The goal of mixing measurement techniques is the acquisition and statistical analysis of data collected from samples in order to evaluate the quality of the process and the final product. These techniques are usually time consuming and laborious. One common problem in measurement techniques that examine a planar section of the product is that two-dimensional information should be transformed into three-dimensional information. This is done with the help of stereology science (Underwood, 1977). 

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

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). 

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). 

Warburton P.M., 1980. A stereological interpretation of joint trace data. International Journal of Rock Mechanics and Mining Sciences, 17, 181-190. 

It is sometimes necessary to extract quantitative data on three-dimensional features from two-dimensional sections or surface micrographs taken by OM, SEM, or TEM. Such data extraction requires a careful consideration of how the two-dimensional representation samples the true three-dimensional objects. This branch of metrology, or measurement science, is known as stereology. Detailed techniques for the... 

The science of studying two-dimensional sections using statistical search methods, with consequent description of three dimensional properties of the system, is known as quantitative microscopy or quantitative stereology. Comprehensive texts on these two subjects are available in R. T. DeHoff and F. N. Rhines, Quantitative Microscopy, McGraw-Hill, New York, 1968, and E. E. Underwood, Quantitative Stereology, Addison Wesley, Reading, MA 1970. 

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