Analysis of diffusive cellular patterns in directional solidification of bulk samples

The onset and evolution of cellular patterns at the solid-liquid interface were investigated in directional solidification. A bulk sample of the diluted transparent alloy succinonitrile-acetone was used and the experiments were carried out under diffusive conditions onboard a Space Shuttle mission. The experimental parameters and material properties were selected to cause a supercritical planar-to-cellular transition to small-amplitude cells. Distributions of cell spacings and cell neighbors were determined from CCD images as a function of time. In the steady-state regime, a hexagonal arrangement on the interface with approximately 50 pct defects was found. The average cell spacing of 210 µm was compared to different models, of which the Lu/Hunt model concurred best. A minimal-spanning-tree analysis was carried out to examine the disorder of the cellular patterns as a function of time. The resulting order parameters were compared to those of reference patterns generated from Monte-Carlo simulations. In these simulations cellular organization is often modeled by planar lattices disturbed with Gaussian noise. We have extended this model by the constraint of a minimum distance between the lattice points in analogue to the experimentally found distinct minimum spacings. With this new inhibition model, enhanced quantitative agreement with the experimental cellular patterns was found. [PUBLICATION ABSTRACT]