Directional solidification of aqueous solutions and slurries in a temperature gradient is widely used to produce cellular materials through a phase separation of solutes or suspended particles between growing ice lamellae. While this process has analogies to the directional solidification of metallurgical alloys, it forms very different hierarchical structures. The resulting honeycomb-like porosity of freeze-cast materials consists of regularly spaced, lamellar cell walls which frequently exhibit unilateral surface features of morphological complexity reminiscent of living forms, all of which are unknown in metallurgical structures. While the strong anisotropy of ice-crystal growth has been hypothesized to play a role in shaping those structures, the mechanism by which they form has remained elusive. By directionally freezing binary water mixtures containing small solutes obeying Fickian diffusion, and phase-field modeling of those experiments, we reveal how those structures form. We show that the flat side of lamellae forms because of slow faceted ice-crystal growth along the c-axis, while weakly anisotropic fast growth in other directions, including the basal plane, is responsible for the unilateral features. Diffusion-controlled morphological primary instabilities on the solid-liquid interface form a cellular structure on the atomically rough side of the lamellae, which template regularly spaced “ridges” while secondary instabilities of this structure are responsible for the more complex features. Collating the results, we obtain a scaling law for the lamellar spacing,
λ
∼
(
V
G
)
-
1
/
2
, where
V
and
G
are the local growth rate and temperature gradient, respectively.
To characterize the dynamical formation of three-dimensional (3D) arrays of cells and dendrites under diffusive growth conditions, in situ monitoring of a series of experiments on a transparent succinonitrile -0.24 wt% camphor model alloy was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. The continuous interface observation enables to construct space-time evolution maps of cell location and primary spacing. Both convergent and divergent sub-boundaries are identified and new insights on their effects on the spatiotemporal evolution of the pattern are thus evidenced. 3D phase-field simulations that reproduce the experimental sub-boundary configurations are performed to support the analyses. Even for the low angle sub-boundaries studied, the primary spacing increases or decreases in the vicinity of the boundary respectively for divergent and convergent sub-boundary. This effect may extend on a long distance within the different sub-grains and its magnitude depends on the average primary spacing and its positioning relative to the limits of the stability band. On the sample scale, the primary spacing profile is also influenced by the presence of sources and sinks at the crucible wall due to the pattern drift. Their type and distance from the sub-boundaries give rise to complex spatial distributions of primary spacing over the entire sample.
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