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Volume-fraction expressions are obtained for the systems of an infinitenumber of parallel planes arranged both regularly and randomly. As a specialcase of random arrangement, a non-Poissonian point process (the second-orderErlang process) of arrangement of planes is considered for the first time. Theexact volume-fraction expression obtained for this case shows that it cannot bederived by the Cahn method, i. e. the extended-volume approach is applicableonly to Poisson processes. The volume fraction equations for regular planes areused to study cubic grain structures, both regular and random. It is shown thatthe Cahn equation underestimates the transformation kinetics in both regularand random structures with four different size distributions of cubes; thedegree of underestimation depends on the size distribution, being the largestin the regular structure. The paradox of packing is described: the structurescomposed of the same elements (random parallelepipeds) transforming in the sameway, but packed differently, give different transformation rates.

Kinetics of grain-boundary nucleated transformations in rectangular geometries and one paradox relating to Cahn's model