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Volume‐fraction dependence of the scaling function for phase‐separating systems
Author(s) -
Fratzl P.
Publication year - 1991
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889890012201
Subject(s) - scaling , volume fraction , spinodal decomposition , scattering , small angle scattering , function (biology) , volume (thermodynamics) , thermodynamics , phase (matter) , physics , work (physics) , materials science , miscibility , statistical physics , condensed matter physics , chemistry , optics , mathematics , polymer , nuclear magnetic resonance , geometry , quantum mechanics , evolutionary biology , biology
In the last decades, the kinetics of phase separation following a quench into the miscibility gap have been studied in a variety of systems by small‐angle scattering techniques. A scaling behavior in the late stages of coarsening, first observed in computer simulations, was found to be a `universal' feature of the small‐angle scattering intensity S ( k,t ) with S ( k,t ) = S [ k m ( t ), t ] F [ k / k m ( t )], where k m ( t ) is the value of the modulus k of the scattering vector at which S ( k,t ) has its maximum. Furthermore, it was observed recently that, for many systems ranging from liquid and polymer mixtures to solid alloys and computer simulation models, the scaling function F ( x ) does not change appreciably from one system to another when the volume fraction is kept constant. This paper first reviews work carried out jointly with J. L. Lebowitz and O. Penrose, discussing various features of the scaling function F leading to a simple analytical expression suitable to fit experimental data. New small‐angle X‐ray scattering results on the shape of the scaling function for dilute Al–Ag and Cu–Fe systems are then presented and compared with the predictions of the model.