Spatiotemporal Dynamics of Oscillatory Cellular Patterns in Three-Dimensional Directional Solidification

Abstract

We report results of directional solidification experiments conducted on board the International Space Station and quantitative phase-field modeling of those experiments. The experiments image for the first time in situ the spatially extended dynamics of three-dimensional cellular array patterns formed under microgravity conditions where fluid flow is suppressed. Experiments and phase-field simulations reveal the existence of oscillatory breathing modes with time periods of several 10's of minutes. Oscillating cells are usually noncoherent due to array disorder, with the exception of small areas where the array structure is regular and stable.

Experimental observation of oscillatory cellular patterns in three-dimensional directional solidification

“…8(b) where the surface area of one cell of each group is represented as a function of time. In spite of its local character, this configuration is similar to the synchronization observed in the numerical simulations starting from a perfect hexagonal array, thus confirming that coherence directly results from the hexagonal ordering [26,36]. A qualitatively similar hexagonal mode was found in earlier numerical studies, albeit in the high velocity limit or with a two-sided phase field model [34].…”

“…This lack of coherence is related to the intrinsic lack of order of the extended patterns comparable to liquid structures with numerous topological defects. Phase-field simulations have shown that, if no specific order is imposed, the pattern displays the same spatial disorder and lack of oscillation coherence as in experiments, whereas long-range coherence sustained for long duration over the entire array may be obtained when starting from a perfect hexagonal arrangement, or enforcing a perfect hexagonal pattern [26,36].…”

“…A diversity of secondary instabilities can be found in spatially modulated interface patterns [24,25], but a number of them occur in a narrow range of growth conditions so that their observation is not straightforward. In a recent letter [26], we reported the unprecedented observation of an oscillatory instability in spatially extended 2D cellular patterns. This type of secondary instability, often termed "vacillating-breathing mode" has been experimentally and theoretically studied in thin samples for both cellular [27][28][29] and two-phase eutectic interfaces [30][31][32] and theoretically predicted for 3D cellular growth [33,34].…”

Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification

“…8, 2015 DOI: 10.1007/s11837-015-1444-2 Ó 2015 The Minerals, Metals & Materials Society (outside the U.S.) advanced numerical methods, such as adaptative remeshing 23 and massive parallelization, 24,25 have allowed PF simulations up to the scale of threedimensional arrays of cells 26 or dendrites. 25 Phase-field simulations are thus capable of predicting stable dendritic spacing ranges in the steady state, 14,[26][27][28] as well as the dynamical selection of spacings by elimination during the transient stage of solidification. [28][29][30] Recent PF studies have also shown that, in polycrystalline columnar growth, the dynamical evolution of dendritic spacing at converging grain boundaries is closely linked to the unusual overgrowth mechanism of a favorably oriented grain.…”

Convection Effects During Bulk Transparent Alloy Solidification in DECLIC-DSI and Phase-Field Simulations in Diffusive Conditions

“…[44][45][46][47][48] In the 534 specific case of the current DECLIC-DSI experi-535 ments, previous 3D PF simulations based on the 536 FTA had so far fallen short of accurately predicting 537 primary spacing. [8][9][10] The region between the upper 538 and lower bars in Fig. 6 shows the stable spacing 539 ranges predicted by PF simulations using a similar 540 procedure as in previous studies 9,10,49 Stable spacing 541 ranges are determined by the FTA as the steady-542 state thermal gradient is only weakly affected by 543 the different thermal representations.…”