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Submitted on 1 Jan 1977
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VII. - SPINODAL DECOMPOSITION AND
CRITICAL PHENOMENATHEORY OF SPINODAL
DECOMPOSITION
J. Langer
To cite this version:
V11
-
SPINODAL
DECOMPOSITION
A N D
CRITICAL
PHENOMENA.
THEORY OF SPINODAL DECOMPOSITION
J.
S.
LANGER
Carnegie-Mellon University, Pittsburgh,
PA
15213 U.S.A.
Rksurni.. - On dCcrit succinctement une theorie analytique de la dkcomposition spinodale, deji publike [l] et rCsumke par ailleurs [2], en insistant sur son domaine d'application. Cette thtorie conduit aux mdmes rtsultats quantitatifs que des simulations de separation de phases au centre de la lacune de miscibilitk B l'aide de la methode de Monte Carlo 131. Tout comme les simulations, la theorie
analytique ne montre aucune difference qualitative entre la dtcomposition spinodale et la decomposi- tion par germination et croissance au voisinage de la ligne spinodale classique. La theorie est utile surtout par rapport aux exptriences ou les proprietks d'tquilibre du systeme monophast pr&s de la lacune de miscibilitk coherente sont mesurtes en m&me temps que la diffusion aux petits angles, la rksistivite Clectrique, la susceptibilitt magnttique, etc. pendant la decomposition. Des mesures directes de la distance de.corrtlation atomique et du coefficient de diffusion sont particulitrement importantes. Les rksultats recents de Goldburg et al. [5] sur la dkcomposition spinodale d'un melange fluide, 2-6 lutidine et eau, illustrent bien l'utilisation de ce type de donnkes pour I'interprbtation des r6@tats: Ces rtsulhts montrent tgalement l'importance d'une trempe rapide sur un faible intervalle de temptrature pour observer effectivement la rtaction spinodale.
Abstract.
-
An analytic theory of spinodal decomposition, originally published in Reference [l]and reviewed in [2], is described briefly with emphasis on its limits of validity. This theory is quanti- tatively consistent with Monte-Carlo simulations [3] of phase separation in the center of the misci- bility gap and, like these simulations, exhibits no qualitative distinction between spinodal and nuclea- tion mechanisms in the neighbor-hood of the classical spinodal line. The theory is most useful in connection with experiments in which equilibrium properties of the one-phase system just outside the coherent miscibility gap are measured along with time-dependent small-angle scattering, resistivity, magnetic susceptibility, etc. [4] during decomposition. In particular, direct measurements of the correlation length and diffusion constant are specially valuable. The use of such information in the analysis of experimental data is illustrated by recent results of Goldburg et al. [S] on spinodal decomposition in a two-fluid mixture, 2-6 lutidine and water. These results also demonstrate the importance of a rapid, shallow quench for observation of the actual spinodal reaction.
References
[l] LANGER, J. S., BAR-ON, M. and MILLER, H. D., Phys. Rev. A [3] MARRO, J., BORTZ, A. B., KALOS, M. H. and LEBOWITZ, J. L., 11 (1975) 1417. See also LANGER, J. S., Acta Met. 21 Phys. Rev. B 12 (1975) 2000.
(1973) 1649. [4] See preceding paper by GRILH~, J. Also see contributions to [2] LANGER, J. S., c Spinodal Decomposition )>, in Fluctuations, this Symposium by DELAFOND, J. et al. and by GUYOT, P.
Instabilities, and Phase Transitions, T . Riste, ed. (Plenum and LASLAZ, G.
Publishing Corp., New York) 1975. [S] GOLDBERG, SHAW, HUANG and PILANT, to be published.
