Funct. Mater. 2023; 30 (2): 255-267.
Probability of forming a through conductive inclusion for the case of large-scale cylindrical inserts with their uniform distribution over the layer height and over the sample height
Institute for Single Crystals, National Academy of Science of Ukraine, 60 Nauky Ave., 61072 Kharkiv, Ukraine
For a special case of percolation, when the size of the inserts is comparable to the size of the system, the dependencies P(r) of probability of forming a through inclusion are obtained from the radius of inserts - cylinders of radius r and height h. This form allows one to find P(r) using the results obtained earlier for the layered case - the distribution of inserts over layers of height h in the sample from N layers with the number of inserts per layer n. The cases of homogeneous distribution of Nn inserts over height of sample of height Nh and a transitional case between given and layered are studied. For n = 1 the results were obtained analytically. For N = 2 and/or n = 2 results obtained analytically for r = R. For the general case, the results are obtained numerically. It is shown, that P(r) can be described by a small number of numerical parameters: the value P(R), percolation radius rc and an indicator of proximity to the threshold form tc. The dependences of the values of these parameters on N, n are obtained and analized.
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