Spinodal field

Because there is no energy barrier opposed to compositional fluctuations for compositions within the spinodal field, the decomposition mechanism is entirely a diffusional process. Unmixing effectively begins with a minimal compositional fluctuation that extends over the entire volume of the system. 

In pyroxenes, exsolutive processes proceed either by nucleation and growth or by spinodal decomposition (see sections 3.11, 3.12, and 3.13). Figure 5.30B shows the spinodal field calculated by Saxena (1983) for Cag sMgo sSiOj (diop-side) and MgSi03 (chnoenstatite) in a binary mixture, by application of the subregular Margules model of Lindsley et al. (1981) ... 

Figure 5JO (A) Simplified Gibbs free energy curves for various polymorphs along enstatite-diopside join at T = 1300 °C. (B) Resulting solvus, spinodal field, and miscibility gap compared with experimental data of McCallister and Yund (1977) on pyroxene unmixing kinetics (part B from Ganguly and Saxena (1992). Reprinted with permission of Springer-Verlag, New York).

The spinodal field, calculated at P = 1 bar on the basis of equations 3.201 and 3.202 (section 3.11) conforms quite well to the experimental observations of... 

When the partial derivative reaches zero, the two potentials coincide and component i is present unmixed as a pure term. If unmixing takes place in solvus conditions, the thermodynamic activity of component i remains constant for the entire solvus field. However, in the case of spinodal decomposition, the activity of i within the spinodal field plots within a maximum and minimum (cf sections 3.11 and 3.12). 

Figure A3.3.2 A schematic phase diagram for a typical binary mixture showmg stable, unstable and metastable regions according to a van der Waals mean field description. The coexistence curve (outer curve) and the spinodal curve (iimer curve) meet at the (upper) critical pomt. A critical quench corresponds to a sudden decrease in temperature along a constant order parameter (concentration) path passing through the critical point. Other constant order parameter paths ending within tire coexistence curve are called off-critical quenches.

Figure A3.3.5 Tliemiodynamic force as a fiuictioii of the order parameter. Three equilibrium isodiemis (fiill curves) are shown according to a mean field description. For T < J., the isothemi has a van der Waals loop, from which the use of the Maxwell equal area constmction leads to the horizontal dashed line for the equilibrium isothemi. Associated coexistence curve (dotted curve) and spinodal curve (dashed line) are also shown. The spinodal curve is the locus of extrema of the various van der Waals loops for T < T. The states within the spinodal curve are themiodynaniically unstable, and those between the spinodal and coexistence...

FIG. 2 Growth rates as a function of the driving force A//. Comparison of theory and computer simulation for different values of the diffusion length and at temperatures above and below the roughening temperature. The spinodal value corresponds to the metastability limit A//, of the mean-field theory [49]. The Wilson-Frenkel rate WF is the upper limit of the growth rate. 

Fig. 1. Equilibrium phase diagram T, c)=iT/Tc,c) for the alloy model used in Ref.. Solid lines boundaries of the disordered (a) and homogeneously ordered (6) fields areas c, d and e corre.spond to the two-phase region. Dashed line i.s the ordering spinodal separating the metastable disordered area c from the. spinodal decompo.sition area d. Dot-dashed line is the conditional spinodal that separate.s the area d from the ordered metastable area e.

Direct evidence of nucleation during the induction period will also solve a recent argument within the field of polymer science as to whether the mechanism of the induction of polymers is related to the nucleation process or to the phase separation process (including spinodal decomposition). The latter was proposed by Imai et al. based on SAXS observation of so-called cold crystallization from the quenched glass (amorphous state) of polyethylene terephthalate) (PET) [19]. They supposed that the latter mechanism could be expanded to the usual melt crystallization, but there is no experimental support for the supposition. Our results will confirm that the nucleation mechanism is correct, in the case of melt crystallization. 

Fig. 8 Phase diagram for PI-fc-PEO system. Only equilibrium phases are shown, which are obtained on cooling from high temperatures. ODT and OOT temperatures were identified by SAXS and rheology. Values of /AT were obtained using /AT = 65/T + 0.125. Dashed line spinodal line in mean-field prediction. Note the pronounced asymmetry of phase diagram with ordered phases shifted parallel to composition axis. Asymmetric appearance can be accounted for by conformational asymmetry of segments. Adopted from [53]...

Figure 5.5 Ball in a gravitational field illustration of (a) stable, (b) unstable, (c) spinodal and (d) metastable equilibria.

Figure 3,10 Solvus and spinodal decomposition fields in regular (B) and subregular (D) mixtures. Gibbs free energy of mixing curves are plotted at various T conditions in upper part of figure (A and C, respectively). The critical temperature of unmixing (or consolute temperature ) is the highest T at which unmixing takes place and, in a regular mixture (B), is reached at the point of symmetry.

Figure 3.10 also shows the fields of spinodal decomposition defined by the loci of the points of inflection in the Gibbs free energy of mixing curves. These points obey the following general conditions ... 

The energy of elastic strain modifies the Gibbs free energy curve of the mixture, and the general result is that, in the presence of elastic strain, both solvus and spinodal decomposition fields are translated, pressure and composition being equal, to a lower temperature, as shown in figure 3.16. 

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