Investigating the morphological properties of some spinodal network topologies constructed by the Gaussian random field

During the early stages of the phase separation process, the separated phases are spatially arranged in a stochastic bi-continuous topology whose evolution is governed by the Cahn-Hilliard equation. It has been shown that the phase-field at each point in space can be described by a Gaussian random field (GRF) - a superposition of some standing waves with fixed wavelength but random wave numbers and phase shift. Based on the GRF approach, in this paper three-dimensional topologies are constructed by computing the level sets or isosurfaces of the phase field. This is done to generate both the solid and shell topologies. The level set constant for solid topology is chosen based on its relationship to morphological properties which can be derived based on the statistical characteristics of the GRF. For the shell network topology, the level set constant is also affected by the shell thickness. After smoothing the data, the triangulation method of Delaunay has been utilized to represent the complex morphology of the solid topology. The relative density changes as a tool for measuring the porosity of the structure, in different directions have been discussed. It is found out that the relative density fluctuations around a mean value are different along the various base directions in Cartesian coordinate and the relationship between the standard deviation of the relative density along these directions and the threshold of the level set method is noted. The relationship between the norm of the relative density gradient versus the level set threshold is also investigated.