Evaluating the effect of standing waves on morphological properties of spinodal topologies

During the spinodal decomposition process, a solid solution will be decomposed to its’ constituent phases due tothermodynamical instability. It has been shown that the phase-field in this chemical process can be described by asuperposition of some standing waves with fixed wave numbers but uniformly distributed waves’ directions on the surfaceof the unique sphere and waves’ phases uniformly distributed between ۰ and ۲π. It has been shown that if the number ofthe standing waves is large enough, the phase-field will tend to be a Gaussian Random Field (GRF) with specificmorphological properties. However, the relationships between the number of standing waves and morphologicalproperties have not been investigated yet. In this work, we shall examine this issue. In the first stage, by superposingvarious numbers of standing waves, the phase-field in a specific two-dimensional Representative Volume Element (RVE)is computed. In the next step, the level set method has been applied to construct spinodal topologies. For each topology,morphological properties like Betti numbers and relative density are computed, and the relationships between thenumber of standing waves and morphological properties are investigated. In order to consider the randomness ofstructures, the computations have been repeated fifteen times, and the mean value and variance of the morphologicalproperties for a fixed level set threshold have been computed.