Affinities for topological arrangements in grain structures

Boundaries between neighboring grains with different numbers of faces exhibit a wide range of tendencies to occur in a structure, from high preference to high avoidance. These tendencies are described here in terms their contact affinity, which describes the extent to which an i-j faced grain pair actually occurs in the structure relative to that expected from statistically random contact. An affinity of unity indicates random occurrence and values above or below unity indicate the corresponding factor above or below random with which a particular pairing occurs. Grain contact affinities determined for both 3-D Monte Carlo grain growth simulations and experimental serial sectioned grains show similar trends of high affinity for contact between few- and many-faced grains, avoidance of contact between grains in similar face classes, and random contact between grains of intermediate face classes and all other classes. Contact affinities have been modeled in terms of the relative face curvatures, with high curvatures of opposite sign exhibiting the highest contact affinities, like signs the lowest, and relatively flat-faced grains showing near-random contact with all other classes. The measure of affinity is thus interpreted as the degree of stability or instability of boundaries against rapid face loss from topological events. The affinity approach overcomes a significant bias of the Aboav-Weaire analysis, which describes the average neighbors of face classes but is insensitive to the actual preference or avoidance for boundaries with other classes. The contact affinity term quantifies these tendencies.