Model phase diagram

Ciferri, A., and K. J. Smith Phase changes in fibrous macromolecular systems and associated elasticity. Model phase diagrams. J. Polymer Sci. Pt. A-2, 731 (1964). 

Fig. 25 Ising model phase diagram. The reconstructed (1 x 2) and unreconstructed (1x1) regions are separated by Ising disordered phase (D).

Lattice model phase diagram for rigid, impenetrable rods of axial ratio ISO, indicating the three phases isotropic (I), liquid crystalline (LQ and the biphasic region (I + LC) (see [402-40S]). Rei oduced from Liquid Crystals and Ordered Fluids, Vol 2 [Ref. 405] the courtesy Plenum Publishing Corporation, New York... 

Figure 10.1. A model phase diagram of two compounds A and B that do not mix but dissolve somewhat in each other. The corresponding AG/x plots are given for six different temperatures. The three curves in each of these six plots correspond to the phases A, B, and the liquid phase.

For nonzero temperatures, the model phase diagram given in terms of the reduced chemical potential, Jl = p/e, versus reduced temperature, T = k T/e, is illustrated in Fig. 6. Data are from numerical simulations for y = —2e. As the temperature is increased the low- and high-density phases that may be identified as amorphous, due to a zero diffusion coefficient, smoothly turn into low- and high-density liquids, respectively, analogously to the two-dimensional case. 

Figure 10.S Model phase diagram I - virtual diffusion path between two single-phase alloys X and Y (pseudobinary approximation) II - complex diffusion path. PQ - precipitate zone LR - jump along the conode RS - nonplanar interphase boundary.

In the model phase diagram, the phase boundaries have the form of segments with conodes orthogonal to them. 

The thermodynamic driving force of the discontinuous precipitation, as for any process at constant temperature and pressure, is the decrease of the system s Gibbs potential, which is schematically illustrated in the model phase diagram (Figure 12.2). 

Figure 12.2 Model phase diagram and phase equilibria in the Pb-Sn system.

From Equations (25.17) and (25.18), you can compute the critical point Xc and Tc for the lattice model. Because Xc = Ci/Tc = 2, you have Tc = Cj/2, where ci is the quantity that describes the strengths of interactions between the A s and B s. If ci = 0, then the system is fully miscible at all temperatures, and there is no two-phase region at all. Figure 25.11 shows the lattice model phase diagram. 

Figure 25.11 The lattice model phase diagram for mixing.

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