Interface dynamics, instabilities, and solute bands in rapid directional solidification

Conti, M.

doi:10.1103/physreve.58.2071

Cited by 27 publications

(31 citation statements)

References 33 publications

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“…2, which in part are remarkably close to the findings by Conti in Ref. [10], one concludes that the high-and low-concentration layers are connected by large-acceleration segments, explaining the sharpness of the interfaces between these layers. In order to explore the possible formation of dendritic ripples, one has to consider perturbations of the form h(x, t) =ĥ(q, ω) exp (iq · x + ωt) in a three-dimensional version of the model (1).…”

Section: Rudi Schmitzsupporting

confidence: 88%

“…Adopting from Ref. [10] typical values for S, T M , ξ, the parameter m 2 is of order 10 −5 . An independent second quantity is the velocity v P , applied in pulling the growing crystal in opposite direction to the temperature gradient.…”

Section: Rudi Schmitzmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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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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Section: Rudi Schmitzsupporting

confidence: 88%

Section: Rudi Schmitzmentioning

confidence: 99%

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confidence: 99%

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Diffusion-Induced Oscillations of Extended Defects

2012

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“…Conti demonstrated the time-periodic interface dynamics of planar direction growth [94], but the calculated dynamics was deviated from those in the previous phenomenological model and the sharp-interface numerical model. This might be caused by the failure to retain the numerical stability by allowing a sufficiently small grid spacing to resolve the dynamically changing length scales of physical properties around the solid-liquid interface.…”

Section: Chapter 1 Introductionmentioning

confidence: 55%

“…The continuous oscillation dynamics of planar front growth under fixed temperature gradients was calculated by Conti [94] in a one-dimensional system. Although the calculation successfully shows oscillating interface dynamics, the calculated cycle of the interface dynamics in T-V space showed some deviation from the model suggested by Carrard et al [54] and the calculation by Karma et al [80,81].…”

Section: Phase-field Simulation Of Rapid Solidificationmentioning

confidence: 99%