An analysis is presented to assess the relationships between particles distributed throughout a medium. The adopted approach is to compare the observed data-with the expected associations between particles calculated on the basis of random positioning. Since bulk structures are often examined by using a sectioning technique, the paper includes a method to transform two-dimensional observations into three-dimensional associations. This is achieved by assuming that the most complex association observed is the most complex association in the bulk material; the contributions to lower-order associations from this association are calculated and subtracted from the observed frequencies. The process is repeated, making the same assumptions about the next most complex association, and so on until a corrected matrix of associations has been compiled.The analysis is applied to a partially recrystallised iron-0.4 wt ~ carbon alloy to give a complete description of the associations between carbide particles and recrystallised grains. In particular, it is shown that carbide particles are exclusive nucleation sites for recrystallisation.
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