Physical mechanisms of the oscillatory 2λ -O mode in directional solidification

Abstract

The 2λ−O oscillatory mode of cellular solidification patterns is studied in thin samples of a succinonitrile-acrylonitrile transparent alloy. The origin and the nature of oscillations are revisited and discussed by combining experiment with 3D phase-field numerical simulations. The existence domain of 2λ−O oscillations and the evolution of their period with growth velocity are determined and compared. Simulations evidence transversal solute fluxes between neighbor cells as an essential feature of cell dynamics. A solute balance model in which transversal fluxes are crucial for oscillations recovers the emergence of a 2λ−O mode and its period-velocity relationship. It thus confirms the fundamental role of transversal fluxes and provides a complete coherent description of the physical mechanisms of 2λ−O oscillations. Parametric excitations are finally used to force 2λ−O oscillations beyond their stability domain and highlight the nature of the underlying oscillator, especially its non-linearity responsible for intermittent oscillations and complex behavior in the resonance band.

Oscillatory-nonoscillatory transitions for inclined cellular patterns in three-dimensional directional solidification

“…The present phase-field approach readily combines two numerical codes used in recent studies that considered crystal misorientation and oscillatory states separately. In both cases, solidification of a succinonitrile-acrylonitrile alloy was simulated in a thin sample and the simulation results were compared with experimental data [5,15]. On the one hand, regarding the effects of the crystal misorientation, the numerical results [15] confirmed the orientational response law found experimentally [16,17].…”

“…Comparable oscillatory patterns were also observed in directional solidification of succinonitrile-based diluted binary alloys [4][5][6][7][8]. In thin samples, the existence of a generic 2λ − O mode was reported and characterized by a large set of experimental and numerical data [4,5]. More recently, it was shown that these oscillations result from a coherent interaction between the solute diffusion fields that surrounds two neighboring cell tips (firstneighbor correlations) [5].…”

“…In the recent decades, a number of solidification experiments led to spectacular oscillatory growth modes for both liquid crystals [1] and eutectic alloys [2,3]. Comparable oscillatory patterns were also observed in directional solidification of succinonitrile-based diluted binary alloys [4][5][6][7][8]. In thin samples, the existence of a generic 2λ − O mode was reported and characterized by a large set of experimental and numerical data [4,5].…”

“…For thin samples, a first study using the one-sided phase field * Corresponding author: fatima.lisboa-mota@im2np.fr model reported the onset of an oscillatory single structure 51 in an intermediate domain of spacings [10]. Subsequently, a 52 similar model was used in a dedicated study of 2λ − O mode 53 that gave rather quantitative agreement with the oscillations 54 existence domain and proposed a complete description of 55 the physical underlying mechanisms [5]. For bulk samples, 56 numerical studies first relied on amplitude equations [11][12][13], 57 later on the two-sided version of the phase-field formalism 58 applied to a model system [14], and even more recently on 59 the one-sided phase-field model parametrized with the actual 60 physical parameters of microgravity experiments [6][7][8].…”

“…In thin samples, the existence of a generic 2λ − O mode was reported and characterized by a large set of experimental and numerical data [4,5]. More recently, it was shown that these oscillations result from a coherent interaction between the solute diffusion fields that surrounds two neighboring cell tips (firstneighbor correlations) [5]. In bulk samples, oscillating growth modes are more difficult to observe experimentally and their existence was not mentioned until recent experiments were performed under microgravity conditions in the DECLIC-DSI device.…”