Phase separation of binary systems |
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Authors: | Tian Ma |
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Affiliation: | a Department of Mathematics, Sichuan University, Chengdu, PR China b Department of Mathematics, Indiana University, Bloomington, IN 47405, United States |
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Abstract: | In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions. |
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Keywords: | 05.70.Fh 64.60.Ht |
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