Topological and geometrical properties of crack patterns produced by the thermal shock in ceramics

We study the crack patterns produced by thermal shock in ceramic tableware. Cracks produced at sufficiently high-temperature gradients partition the surface plane of a ceramic material into cells forming a random two-dimensional space-filling cellular structure. The topological and geometrical properties of these structures are described and analyzed. The distribution of the number of cell sides, the topological correlations between adjoining cells, the probability distributions of a cell area and side length, the average area and perimeter of n-sided cells, and the distribution of vertex angles are determined. The results show that the studied cellular structures obey the Aboav-Weaire law [Metallography 3, 383 (1970); 7, 157 (1974)] and Desch's law [J. Inst. Metals 22, 241 (1919)]. The scaling behavior of cellular structures obtained at different temperature gradients of the thermal shock is also presented.