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.

Pattern formation in directional solidification under shear flow. I. Linear stability analysis and basic patterns.

An asymptotic interface equation for directional solidification near the absolute stability limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies which is described in the following paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.

Pattern formation in directional solidification under shear flow. II. Morphologies and their characterization.

In the preceding paper, we have established an interface equation for directional solidification under the influence of a shear flow parallel to the interface. This equation is asymptotically valid near the absolute stability limit. The flow, described by a nonlocal term, induces a lateral drift of the whole pattern due to its symmetry-breaking properties. We find that at not-too-large flow strengths, the transcritical nature of the transition to hexagonal patterns shows up via a hexagonal modulation of the stripe pattern even when the linear instability threshold of the flowless case has not yet been attained. When the flow term is large, the linear description of the drift velocity breaks down and transitions to flow-dominated morphologies take place. The competition between flow-induced and diffusion-induced patterns (controlled by the temperature gradient) leads to new phenomena such as the transition to a different lattice structure in an array of hexagonal cells. Several methods to characterize the morphologies and their transitions are investigated and compared. In particular, we consider two different ways of defining topological defects useful in the description of patterns and we discuss how they are related to each other.

Orbital frustration at the origin of the magnetic behavior in LiNiO2.

We report on the ESR, magnetization, and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T(of) approximately 400 K, an orbitally frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.