Authors - Rahul Basu Abstract - Spinodal decomposition in binary alloys produces complex, interconnected microstructures with fractal-like characteristicsduring early and intermediate stages of phase separation. This paper presents a computational framework for simulating three-dimensional (3D) spinodal decomposition using the Cahn–Hilliard phase-field model, with emphasis on fractal dimensionanalysis of the evolving microstructures. The model incorporates CALPHAD-consistent free-energy descriptions (via commontangent interpolation for miscibility gaps) for benchmark alloys such as Cu–Ni and Fe–Cr. Simulations in 3D revealinterconnected networks with fractal dimensions typically in the range 2.4–2.8 during coarsening (deviation <5\% RMSE fromFe–Cr APT data), consistent with experimental observations. Fractal analysis via box-counting ($\log(1/r)=0$–$1.2$) andcorrelation functions ($r=5$–$20$ dx) quantifies morphological complexity, providing insights into scaling behavior and self-similarity. The approach leverages efficient FFT-based solvers for large-scale 3D computations (up to 256$^3$), aligning withuseful descriptors for data-driven materials design, microstructure prediction, and alloy performance optimization. Resultshighlight the transition from early-stage fractal-like patterns to late-stage Ostwald ripening (with LS recovery on larger grids),offering quantitative metrics for alloy engineering.
Open Zoom