THE NORMALIZED NUMBERS OF GRAIN-BOUNDARIES, TRIPLE POINTS AND GROWTH FRONTS IN A CIRCULAR GROWING 2-DIMENSIONAL VORONOI TESSELLATION WITH POISSON-DISTRIBUTED NUCLEI
Gew. Schulze et Lo. Schwan, THE NORMALIZED NUMBERS OF GRAIN-BOUNDARIES, TRIPLE POINTS AND GROWTH FRONTS IN A CIRCULAR GROWING 2-DIMENSIONAL VORONOI TESSELLATION WITH POISSON-DISTRIBUTED NUCLEI, Journal of Materials Science, 28(10), 1993, pp. 2706-2714
The topological properties of a set of nuclei undergoing a phase trans
formation were investigated. The nuclei were spread out in a plane acc
ording to a Poisson distribution. All centres started to grow at the s
ame moment and with the same constant rate. They grew circularly and f
ree of shrinking. The mean numbers per nucleus of grain boundaries, tr
iple points and growth fronts were calculated as functions of the degr
ee of transformation, F (0 less-than-or-equal-to F less-than-or-equal-
to 1). For these relationships we deduce plain and exact expressions.