title: Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands.
abstract: Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.
authors.affiliation: Materials Chemistry Department, V. N. Karazin Kharkov National University, Kharkov 61077, Ukraine. alexander.i.korobov@univer.kharkov.ua
authors.forename: A
authors.initials: A
authors.lastname: Korobov