Capillary-wave model for the solidification of dilute binary alloys

Korzhenevskii, Alexander L.; Bausch, Richard; Schmitz, Rudi

doi:10.1103/physreve.83.041609

Cited by 22 publications

(39 citation statements)

References 42 publications

(93 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[1]. For m = 0 the neutral stability curve F P (v P ) = 0 of the Cahn instability is attended by an oscillation of period Ω(v P ).…”

Section: Stationary Planar Growthmentioning

confidence: 96%

“…[1]. It determines all static properties of the system in thermal equilibrium at some fixed temperature T S < T M where T M denotes the melting temperature of the solvent, showing up in the temperature-concentration phase diagram, Fig.…”

Section: Capillary-wave Modelmentioning

confidence: 99%

“…[1] for the case of solidification by under-cooling the liquid phase from T S to T P . In particular, the result (14) is independent of the parameter m 2 , which only enters in discussing the stability of the planar morphology.…”

Section: Stationary Planar Growthmentioning

confidence: 99%

“…[1] and only differs by the additional term m 2 . Inspection of the low -q, ω behavior of the dispersion relation (18) leads to identify an eigenfrequency ω 1 (q), which captures the Mullins-Sekerka instability.…”

Section: Stationary Planar Growthmentioning

confidence: 99%

See 3 more Smart Citations

Capillary-wave description of rapid directional solidification

2012

Self Cite

View full text Add to dashboard Cite

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We, moreover, establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands, and, taking into account the Mullins-Sekerka instability, of banded structures.

show abstract

“…[1]. For m = 0 the neutral stability curve F P (v P ) = 0 of the Cahn instability is attended by an oscillation of period Ω(v P ).…”

Section: Stationary Planar Growthmentioning

confidence: 96%

Section: Capillary-wave Modelmentioning

confidence: 99%

Section: Stationary Planar Growthmentioning

confidence: 99%

Section: Stationary Planar Growthmentioning

confidence: 99%

See 2 more Smart Citations

Capillary-wave description of rapid directional solidification

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…Following Ref. [13], we then find the dispersion relation with λ ≡ −(v P /2) + (v P /2) 2 + ω + q 2 where the term m 2 is the only new element. The wave-number threshold q c for the Mullins-Sekerka instability [16] is determined by the relations ω 1 (q c ) = ω 1 (q c ) = 0.…”

Section: Rudi Schmitzmentioning

confidence: 99%

Diffusion-Induced Oscillations of Extended Defects

2012

Self Cite

View full text Add to dashboard Cite

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...

show abstract