The stability of cells in directional solidification

Rappel, Wouter‐Jan; Brener, Efim A.

doi:10.1051/jp1:1992244

Cited by 3 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, to our knowledge, no theoretical modeling of the instability mechanism of the 2λ−O mode has been proposed so far. This contrasts with the case of oscillations of individual cells, i.e., with the 1λ−O mode, where various theoretical [40] or analytical and numerical results [42,43] have been obtained, with controversial conclusions however. In comparison, the major difference that will be brought about by the 2λ−O mode here will be the coupling between neighbor cells.…”

Section: Emergence Of Oscillationsmentioning

confidence: 85%

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

et al. 2018

View full text Add to dashboard Cite

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.

show abstract

Section: Emergence Of Oscillationsmentioning

confidence: 85%

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

et al. 2018

View full text Add to dashboard Cite

show abstract

Solidification

Müller‐Krumbhaar

Kurz

Brener

2013

Materials Science and Technology

View full text Add to dashboard Cite

The sections in this article are Introduction Basic Concepts in First‐Order Phase Transitions Nucleation Interface Propagation Growth of Simple Crystal Forms Mullins–Sekerka Instability Basic Experimental Techniques Free Growth Directional Growth Free Dendritic Growth The Needle Crystal Solution Side‐Branching Dendrites Experimental Results on Free Dendritic Growth Directional Solidification Thermodynamics of Two‐Component Systems Scaled Model Equations Cellular Growth Directional Dendritic Growth The Selection Problem of Primary Cell Spacing Experimental Results on Directional Dendritic Growth Extensions Eutectic Growth Basic Concepts Experimental Results on Eutectic Growth Other Topics Summary and Outlook

show abstract

Critical Role of Crystalline Anisotropy in the Stability of Cellular Array Structures in Directional Solidification

1996

Self Cite

View full text Add to dashboard Cite

We calculate numerically the full Floquet-Bloch stability spectrum of cellular array structures in a symmetric model of directional solidification. Our results demonstrate that crystalline anisotropy critically influences the stability of these structures. Without anisotropy, the stability balloon of cells in the plane of wave number and velocity closes near the onset of morphological instability. With a finite, but even small, amount of anisotropy this balloon remains open and a band of stable solutions persists for higher velocities into a deep cell regime. The width of the balloon depends critically on the anisotropy strength. [S0031-9007(96)01426-3] PACS numbers: 81.10.Aj, 05.70.Ln, 81.30.FbDirectional solidification has been an important focus of research in the pattern formation and materials science communities for many years [1]. In a generic experiment, a binary liquid mixture contained between two narrowly spaced glass plates is pulled at constant velocity through an externally imposed temperature gradient. The morphology of the solid-liquid interface depends sensitively on the pulling velocity. Below a critical velocity the planar interface is stable, and above this critical velocity it undergoes the well-known Mullins-Sekerka (MS) instability [2] which gives rise to cellular array structures that can exist for a range of spacings.Close to the onset of instability, cells are typically of small amplitude, while in an intermediate range of higher velocities, they develop a larger amplitude. The latter structures are marked by deep liquid grooves that determine the scale of the final microsegregation profile inside the solidified alloy, and hence its physical properties. Therefore much effort has been devoted to the search for the instabilities which limit the range of possible stable spacings. However, despite more than three decades since the MS analysis, there is still no coherent picture of cell stability in the low velocity regime of directional solidification that has been traditionally studied experimentally. In addition, it is not known how stability is influenced by crystalline anisotropy that is known to play a crucial role in interfacial pattern formation [3].This lack of understanding is largely due to the technical difficulty of calculating the stability of nonlinear structures in nonlocal models of diffusion controlled growth, and to the fact that spatially extended arrays can be subject to a broad range of instabilities. These can be either oscillatory or nonoscillatory (steady) and can range in wavelength from the cell spacing l to very long wavelengths. For these reasons, studies to date have been restricted to analyzing specific secondary instabilities [4-10], or to analyzing all possible instabilities but in a high velocity regime where the diffusive growth problem reduces to local equations [11].A host of instabilities have so far been identified. These include, in a low-velocity regime, the classic long wavelength Eckhaus instability [4,5], which is generically present in one-dimensio...

show abstract

The stability of cells in directional solidification

Cited by 3 publications

References 9 publications

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

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

Solidification

Critical Role of Crystalline Anisotropy in the Stability of Cellular Array Structures in Directional Solidification

Contact Info

Product

Resources

About