Oscillatory morphological instabilities due to non-equilibrium segregation

Coriell, S. R.; Sekerka, Robert F.

doi:10.1016/0022-0248(83)90179-3

Cited by 171 publications

(50 citation statements)

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“…By considering both the velocity dependent solute partition model and the limitation of atomic kinetic attachment, the interface stability analysis has found the time-dependent oscillatory instability of planar interface with the velocities near the absolute stability limit velocity of a planar interface [77,78]. In this stability analysis, it also has been shown that the oscillatory instability is controlled by the non-equilibrium solidification effects, i.e.…”

Section: Chapter 1 Introductionmentioning

confidence: 92%

“…Merchant-Davis [78] modified the analysis of Coriell-Sekerka [77]. Using Aziz's solute trapping model for dilute solutions [2] and incorporating the kinetic undercooling at the interface, the Merchant-Davis's model allows velocity-dependent k V and T* in a thermodynamically consistent way.…”

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

“…The modified linear absolute stability analysis accounting for local non-equilibrium effect, such as solute trapping [77,78], may be related with the band structure formation. The result of the modified linear absolute stability analysis for planar interface showed that the velocity of absolute stability limit, V AS , is higher than that from the classical Mullins-Sekerka's stability analysis, and at velocities slightly less than V AS , there is an oscillatory instability with time for rather long wavelengths.…”

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

“…Coriell-Sekerka [77] modified the classical Mullins-Sekerka's linear stability theory [10] by considering the velocity-dependent chemical partition coefficient for the first time. In the result of this analysis, it was shown that at high velocities there exists oscillatory instability Figure 2.28 Experimentally determined microstructure selection map for Ag-Cu alloys by electron beam solidification [66] for relatively long wavelength perturbations, in addition to the instability predicted by MullinsSekerka's theory.…”

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

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Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

Choi

2011

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Section: Chapter 1 Introductionmentioning

confidence: 92%

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

Section: Interface Stability Analysis For Banded Structure Formationmentioning

confidence: 99%

See 2 more Smart Citations

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

Choi

2011

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“…A major advantage of our approach is that it allows a transparent and, to a large extend, analytical evaluation. This includes a readjustment of the stability analysis by Merchant and Davis [11] who discovered an oscillatory instability, similar to that, discussed earlier by Coriell and Sekerka [12]. Also included is a clarifying analysis of the so far barely understood low-velocity sections of the cyclic trajectories, identified by Carrard et al [1], and by Karma and Sarkissian [9].…”

mentioning

confidence: 99%

Diffusion-Induced Oscillations of Extended Defects

2012

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From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures. The interaction of propagating extended defects with a diffusion field frequently leads to oscillations or jerky motions of the defects. A prime example of such an effect is the oscillation of a solidification front, induced by the diffusion of the solute component in a dilute binary alloy, which is growing in the setup of directional solidification. In a large number of metallic materials this leads to the formation of banded structures [1], reflecting a periodic array of layers with high and low solute concentrations where the former ones show a dendritic microstructure. The appearance of similar banding effects has recently been discussed [2] in rapid solidification of colloids.Layered structures are also generated by the oscillatory nucleation of a solid phase under the action of a diffusion field [3]. A related phenomenon is the oscillatory zoning, observed in solid solutions [4] and in natural minerals [5]. Another notable scenario is that of diffusion-controlled jerky motions of a driven grain boundary [6]. A similar behavior of dislocations in metallic alloys leads to the Portevin-Le Chatelier effect [7], denoting the appearance of jerky plastic deformations. We, finally, mention the oscillatory motion of a crack tip, which is coated by the nucleus of a new phase [8], replacing the attached cloud of a diffusion field.Theoretical discussions of such effects either are of a phenomenological type, like those in Ref. [7], and partly in Refs.[1] and [2], or they rely on a Fokker-Planck [6], or a diffusion equation with non-equilibrium boundary conditions [9]. In all approaches the source of oscillatory defect motions is identified as an unstable regime where a reduction of the driving force leads to an increase of the defect velocity. Additional information is provided by simulations, based on phase-field models for directional solidification [10] and for nucleation [3] processes.In the present Letter we introduce an extremely simple but powerful model for the diffusion-induced oscillatory motion of a planar interface, using the language adapted to the directional solidification of a dilute binary alloy. A major advantage of our approach is that it allows a transparent and, to a large extend, analytical evaluation. This includes a readjustment of the stability analysis by Merchant and Davis [11] who discovered an oscillatory instability, similar to that, discussed earlier by Coriell and Sekerka [12]. Also included is a clarifying analysis of the so far barely understood low-velo...

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Solidification

Müller‐Krumbhaar

Kurz

Brener

2013

Materials Science and Technology

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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

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Oscillatory morphological instabilities due to non-equilibrium segregation

Cited by 171 publications

References 5 publications

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

Diffusion-Induced Oscillations of Extended Defects

Solidification

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