We present a phase-field study of oscillatory breathing modes observed during the solidification of three-dimensional cellular arrays in microgravity. Directional solidification experiments conducted onboard the International Space Station have allowed us to observe spatially extended homogeneous arrays of cells and dendrites while minimizing the amount of gravity-induced convection in the liquid. In situ observations of transparent alloys have revealed the existence, over a narrow range of control parameters, of oscillations in cellular arrays with a period ranging from about 25 to 125 min. Cellular patterns are spatially disordered, and the oscillations of individual cells are spatiotemporally uncorrelated at long distance. However, in regions displaying short-range spatial ordering, groups of cells can synchronize into oscillatory breathing modes. Quantitative phase-field simulations show that the oscillatory behavior of cells in this regime is linked to a stability limit of the spacing in hexagonal cellular array structures. For relatively high cellular front undercooling (i.e., low growth velocity or high thermal gradient), a gap appears in the otherwise continuous range of stable array spacings. Close to this gap, a sustained oscillatory regime appears with a period that compares quantitatively well with experiment. For control parameters where this gap exists, oscillations typically occur for spacings at the edge of the gap. However, after a change of growth conditions, oscillations can also occur for nearby values of control parameters where this gap just closes and a continuous range of spacings exists. In addition, sustained oscillations at to the opening of this stable gap exhibit a slow periodic modulation of the phase-shift among cells with a slower period of several hours. While long-range coherence of breathing modes can be achieved in simulations for a perfect spatial arrangement of cells as initial condition, global disorder is observed in both three-dimensional experiments and simulations from realistic noisy initial conditions. In the latter case, erratic tip-splitting events promoted by large-amplitude oscillations contribute to maintaining the long-range array disorder, unlike in thin-sample experiments where long-range coherence of oscillations is experimentally observable.

We present the results of a comprehensive phase-field study of columnar grain growth competition in bicrystalline samples in two dimensions (2D) and in three dimensions (3D) for small sample thicknesses allowing a single row of dendrites to form. We focus on the selection of grain boundary (GB) orientation during directional solidification in the steady-state dendritic regime, and study its dependence upon the orientation of two competing grains. In 2D, we map the entire orientation range for both grains, performing several simulations for each configuration to account for the stochasticity of GB orientation selection and to assess the average GB behavior. We find that GB orientation selection depends strongly on whether the primary dendrite growth directions have lateral components (i.e. components perpendicular to the axis of the temperature gradient) that point in the same or opposite directions in the two grains. We identify a range of grain orientations in which grain selection follows the classical description of Walton and Chalmers. We also identify conditions that favor unusual overgrowth of favorably-oriented dendrites at a converging GB. We propose a simple analytical description that reproduces the average GB orientation selection from 2D simulations within statistical fluctuations of a few degrees. In 3D, we find a similar GB orientation selection as in 2D when secondary branches grow in planes parallel and perpendicular to the sample walls. Remarkably, quasi-2D behavior is also observed even when those perpendicular sidebranching planes are rotated by a finite azimuthal angle about the primary dendrite growth axis as long as the absolute values of those azimuthal angles are equal in both grains. In contrast, when the absolute values of those azimuthal angles differ markedly, we find that unusual overgrowth events at a converging GB are promoted by a high azimuthal angle in the least-favorably-oriented grain. We also find that diverging GBs can be strongly affected by those azimuthal angles, while converging GBs exhibit a weak dependence on those angles. For diverging GBs, GB orientation is also strongly affected by the relative signs of the lateral components of the primary dendrite growth directions in both grains.

We study microstructure selection during during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing ⇤ and tip radius ⇢. While ⇢ shows a good agreement between experimental measurements and dendrite growth theory, with ⇢ ⇠ V 1/2 , ⇤ is observed to increase with V (@⇤/@V > 0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that @⇤/@V < 0. We show through simulations that this trend inversion for ⇤(V ) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical di↵usion boundary-layer approximation to semi-quantitatively incorporate the e↵ect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely di↵usive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V . We explain the observed inversion of @⇤/@V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.

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We carry out three-dimensional phase-field simulations to model unique experimental observations of cellular and dendritic solidification structures formed under diffusive growth conditions in the DSI (Directional Solidification Insert) of the DECLIC (DEvice for the study of Critical LIquids and Crystallization) aboard the International Space Station. We had previously shown experimentally that complex thermal conditions affect the stationary position of the solid-liquid interface, as well as its dynamics of relaxation towards this stationary position over a finite time after the onset of sample pulling. Here, we discuss the effects of thermal diffusion within the adiabatic zone of the directional solidification setup and of latent heat release at the solid-liquid interface by means of quantitative phase-field simulations. Simulations and experiments characterize the entire evolution of the primary spacing of cellular/dendritic array structures from the onset of morphological instability to the establishment of the final steady-state spacing, including the transient coarsening regime associated with a sharp increase of spacing. Accounting for these thermal effects leads to a major improvement in the agreement between simulations and microgravity measurements for both the time of occurrence of morphological instability after the start of the experiment and the subsequent spacing evolution, which are not accurately predicted using the standard frozen temperature approximation.