Evolution and Selection During Growth of Semicellular and Eutectic Patterns

Brener, Efim A.; Geǐlikman, M. B.; Temkin, E. D.

doi:10.1007/978-1-4615-3662-8_1

Cited by 11 publications

(29 citation statements)

References 8 publications

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“…Our conwidth, this means that finite Péclet number correcclusions appear to be in line with those of Brener tions to the shape will become more and more et a!. [33]. These authors studied crystal growth in important as~1/2.…”

Section: 00supporting

confidence: 79%

“…The decrease of V with increasing undercoolAlthough the results of the simulations of Hunt ing is, of course, counter-intuitive, and both ana- [75] give some support for this scenario, we em-phasize that the analysis of Brener et al [33] is velocities at small than the ST branch. For fixed non-rigorous in that it is based on a physically wavelength A, (9.Ib) shows that this conjectured motivated but ad-hoc ansatz for the finite Péclet branch is likely to have small groove width and number corrections to the zero surface tension small a -precisely the characteristics that disshape.…”

Section: 00mentioning

confidence: 66%

“…These authors studied crystal growth in important as~1/2. Motivated by this observaa channel, which corresponds to the 1T -s~limit tion, Brener et al [33] argue that in the absence of of DS. Not surprisingly, for small p, there is again surface tension anisotropy [76], the ST branch a branch of Saffman-Taylor-like solutions.…”

Section: 00mentioning

confidence: 99%

“…These finite amplitude solutions have wavelength branches of steady state solutions are believed to lying outside the planar instability band and evolve exist [33], a Saffman-Taylor like branch and a from the (infinitesimal amplitude) neutrally stable different one that for wide channels reduces to free modes forming the short wavelength side of the planar instability band (i.e. the left hand solid makes systematic many of the earlier approaches curve in fig.…”

Section: Or Fig Criterion As the Lcs Criterion Equations Similar Tomentioning

confidence: 99%

“…This will be discussed in ap-(6) The analysis of Brener et a]. [33] for crystal pendices B and C. growth in a channel, as well as arguments by…”

Section: Or Fig Criterion As the Lcs Criterion Equations Similar Tomentioning

confidence: 99%

See 4 more Smart Citations

Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Weeks

Saarloos

Grant

1991

Journal of Crystal Growth

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Ideas based on constitutional supercooling suggest that the periodic steady state cellular patterns seen in the directional solidification of systems with small partition coefficient may be unstable if the impurity concentration in the melt just in front of the tips falls into the two phase (miscibility gap) region of the phase diagram. This gives a simple stability criterion relating the position of the tips of the cells to the pulling velocity that is in good qualitative agreement with the limited experimental data available in the cellular regime. Implications of this criterion for a particular class of steady state solutions derived using asymptotic matching methods are explored. These solutions arise from a generalization to finite Péclet number for systems with small partition coefficient of the ideas of Dombre and Hakim relating directional solidification patterns to viscous (Saffman-Taylor) fingers. Families of steady state solutions yielding both small amplitude interface patterns as well as fingerlike solutions with narrow deep grooves are accurately described by the methods discussed herein. A systematic expansion method provides corrections to the classical Scheil shapes for the grooves. However, the stability criterion, as well as other considerations, suggest that the entire class of narrow grooved solutions found by the matching methods may be unstable. Comparison with other numerical work suggests that other branches of narrow grooved solutions exist and are relevant to experiments. Several experimental and numerical tests of these ideas are proposed.

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Section: 00supporting

confidence: 79%

Section: 00mentioning

confidence: 66%

Section: 00mentioning

confidence: 99%

Section: Or Fig Criterion As the Lcs Criterion Equations Similar Tomentioning

confidence: 99%

“…This will be discussed in ap-(6) The analysis of Brener et a]. [33] for crystal pendices B and C. growth in a channel, as well as arguments by…”

Section: Or Fig Criterion As the Lcs Criterion Equations Similar Tomentioning

confidence: 99%

See 3 more Smart Citations

Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Weeks

Saarloos

Grant

1991

Journal of Crystal Growth

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Phase-field modeling of the discontinuous precipitation reaction

Amirouche

Plapp

2009

Acta Materialia

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A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that the structure and steady-state growth velocity of spatially periodic precipitation fronts strongly depend on the relative magnitudes of the diffusion coefficients. Steady-state solutions always exist for a range of interlamellar spacings that is limited by a fold singularity for low spacings, and by the onset of tip-splitting or oscillatory instabilities for large spacings. A detailed analysis of the simulation data reveals that the hypothesis of local equilibrium at interfaces, used in previous theories, is not valid for the typical conditions of discontinuous precipitation.

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The stability of cells in directional solidification

Rappel

Brener

1992

J. Phys. I France

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The stability of numerically obtained cells in the one sided model of directional solidification is investigated, using a numerical approach. In particular, the shapes of the cells corresponding to the Saffman-Taylor branch are discussed. The possibility for an oscillatory instability is investigated and the results are compared with a recent approximate analytical stability calculation. For large thermal length we find an instability which is oscillatory for some parametervalues. The results agree partially with the analytical stability calculation. The possible limit cycle arising from this instability is discussed

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Evolution and Selection During Growth of Semicellular and Eutectic Patterns

Cited by 11 publications

References 8 publications

Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Stability and shapes of cellular profiles in directional solidification: expansion and matching methods

Phase-field modeling of the discontinuous precipitation reaction

The stability of cells in directional solidification

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