Experimental characterization and theoretical analysis of cell tip oscillations in directional solidification.

Experiments performed in DECLIC-DSI on board the International Space Station evidenced oscillatory modes during the directional solidification of a bulk sample of succinonitrile-based transparent alloy. The interferometric data acquired during a reference experiment, V_{p}=1 µm/s and G=19 K/cm, allowed us to reconstruct the cell shape and thus measure the cell tip position, radius, and growth velocity evolution, in order to quantify the dynamics of the oscillating cells. This study completes our previous reports [Bergeon et al., Phys. Rev. Lett. 110, 226102 (2013)10.1103/PhysRevLett.110.226102; Tourret et al., Phys. Rev. E 92, 042401 (2015)10.1103/PhysRevE.92.042401; Pereda et al., Phys. Rev. E 95, 012803 (2017)10.1103/PhysRevE.95.012803] with, to our knowledge, the first complete monitoring of the geometric cell tip characteristics variations in bulk samples. The evolution of the shape, velocity, and position of the tip of the oscillating cells is associated with an evolution of the concentration field, inaccessible experimentally but mediating the diffusive interactions between the cells. The experimental results are supported by 3D phase-field simulations which evidence the existence of transversal solute fluxes between neighboring cells that play a fundamental role in the oscillation dynamics. The dynamics of oscillation of an individual cell is analyzed using a theoretical model based on classical equations of solidification through the calculation of the phase relationships between oscillation of the different tip characteristics.

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

We present a detailed analysis of oscillatory modes during three-dimensional cellular growth in a diffusive transport regime. We ground our analysis primarily on in situ observations of directional solidification experiments of a transparent succinonitrile 0.24wt% camphor alloy performed in microgravity conditions onboard the International Space Station. This study completes our previous reports [Bergeon et al., Phys. Rev. Lett. 110, 226102 (2013)10.1103/PhysRevLett.110.226102; Tourret et al., Phys. Rev. E 92, 042401 (2015)10.1103/PhysRevE.92.042401] from an experimental perspective, and results are supported by additional phase-field simulations. We analyze the influence of growth parameters, crystal orientation, and sample history on promoting oscillations, and on their spatiotemporal characteristics. Cellular patterns display a remarkably uniform oscillation period throughout the entire array, despite a high array disorder and a wide distribution of primary spacing. Oscillation inhibition may be associated to crystalline disorientation, which stems from polygonization and is manifested as pattern drifting. We determine a drifting velocity threshold above which oscillations are inhibited, thereby demonstrating that inhibition is due to cell drifting and not directly to disorientation, and also explaining the suppression of oscillations when the pulling velocity history favors drifting. Furthermore, we show that the array disorder prevents long-range coherence of oscillations, but not short-range coherence in localized ordered regions. For regions of a few cells exhibiting hexagonal (square) ordering, three (two) subarrays oscillate with a phase shift of approximately ±120^{∘} (180^{∘}), with square ordering occurring preferentially near subgrain boundaries.

Oscillatory cellular patterns in three-dimensional directional solidification.

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.

Spatiotemporal dynamics of oscillatory cellular patterns in three-dimensional directional solidification.

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.

Cellular pattern dynamics on a concave interface in three-dimensional alloy solidification.

Three-dimensional interface patterns are common in condensed matter, whose dynamical behavior is still deserving clarification. The dynamics of cellular patterns formed at the concave solid-liquid interface during directional solidification in a cylinder of a transparent alloy is studied by means of bright-field live imaging. For each pulling velocity, in situ observation shows that the asymptotic cellular pattern, which establishes with time, is characterized by the continuous birth of a large number of cells at a circular source of morphological instability on the periphery, the sustained collective gliding of the whole cellular array down the interface slope, and the elimination of coarse cells at the central sink. This very peculiar dynamics is the specific signature of the cell advection imposed by interface curvature for the concave situation in three-dimensional solidification. It follows from the comparison between experimental cell gliding and pure slope advection that an additional mechanism of pattern advection is active. It is attributed to fluid flow interaction, estimated on the basis of the Forth and Wheeler traveling wave equations.

In situ and real-time probing of quasicrystal solidification dynamics by synchrotron imaging.

Quasicrystal growth remains an unsolved problem in condensed matter. The dynamics of the process is studied by means of synchrotron live imaging all along the solidification of icosahedral AlPdMn quasicrystals. The lateral motion of ledges driving faceted growth at the solid-melt interface is conclusively shown. When the solidification rate is increased, nucleation and free growth of new faceted grains occur in the melt due to the significant interface recoil induced by slow attachment kinetics. The detailed analysis of the evolution of these grains reveals the crucial role of aluminum rejection, both in the poisoning of their growth and driving fluid flow.

Free growth and instability morphologies in directional melting of alloys.

The dynamics of melting morphologies, namely, liquid droplets in the bulk solid and liquid dendrites due to morphological instability of the phase boundary, is observed in situ and in real time during directional melting of transparent succinonitrile-acetone alloys in a cylinder. Specific patterns are associated to grain boundaries. A model based on free growth but with time-dependent superheating is proposed for the lateral growth of the liquid inclusions. Contrary to what is largely believed, it is shown that free melting is not the mere reversal of free crystal growth, basically because solute diffusion is much lower in the solid, which imposes a boundary layer approach.

Localized microstructures induced by fluid flow in directional solidification.

The dynamical process of microstructure localization by multiscale interaction between instabilities is uncovered in directional solidification of transparent alloy. As predicted by Chen and Davis, morphological instability of the interface is observed at inward flow-stagnation regions of the cellular convective field. Depending on the driving force of fluid flow, focus-type and honeycomb-type localized patterns form in the initial transient of solidification, that then evolves with time. In the case of solute-driven flow, the analysis of the onset of thermosolutal convection in initial transient of solidification enables a complete understanding of the dynamics and of the localization of morphological instability.

In situ observation and interferometric characterization of solid-liquid interface morphology in directionally growing transparent model systems.

The performance of a new directional solidification device dedicated to the characterization of solid-liquid interface morphology by means of optical methods is presented in this paper. In contradiction to usual solidification studies on transparent materials carried out on thin films, which eliminates the complex coupling between solidification and convection, this device enables in situ and real time studies on bulk transparent materials. The alloy is contained in a cylindrical crucible and observation is performed in two perpendicular directions: the growth one and the transverse one. In addition to direct observation by light transmission in those directions, an interferometer is also set up in the growth direction to provide information on the shape and the motion of the interface through an analysis of the interferometer fringes. The combined determination of solidification front characteristics by these three observation modes has already given critical information on interface dynamics: front recoil measurements during initial transient, formation of microstructure patterns, and influence of convection on the triggering of instabilities.