Phase diagrams unstable phases

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.

Tables 1 and 2, respectively, Hst the properties of manganese and its aHotropic forms. The a- and P-forms are brittle. The ductile y-form is unstable and quickly reverses to the a-form unless it is kept at low temperature. This form when quenched shows tensile strength 500 MPa (72,500 psi), yield strength 250 MPa (34,800 psi), elongation 40%, hardness 35 Rockwell C (see Hardness). The y-phase may be stabilized usiag small amounts of copper and nickel. Additional compilations of properties and phase diagrams are given ia References 1 and 2.

Many stainless steels, however, are austenitic (f.c.c.) at room temperature. The most common austenitic stainless, "18/8", has a composition Fe-0.1% C, 1% Mn, 18% Cr, 8% Ni. The chromium is added, as before, to give corrosion resistance. But nickel is added as well because it stabilises austenite. The Fe-Ni phase diagram (Fig. 12.8) shows why. Adding nickel lowers the temperature of the f.c.c.-b.c.c. transformation from 914°C for pure iron to 720°C for Fe-8% Ni. In addition, the Mn, Cr and Ni slow the diffusive f.c.c.-b.c.c. transformation down by orders of magnitude. 18/8 stainless steel can therefore be cooled in air from 800°C to room temperature without transforming to b.c.c. The austenite is, of course, unstable at room temperature. Flowever, diffusion is far too slow for the metastable austenite to transform to ferrite by a diffusive mechanism. It is, of course, possible for the austenite to transform displacively to give... 

From 160°C to room temperature. The lead-rich phase becomes unstable when the phase boundary at 160°C is crossed. It breaks down into two solid phases, with compositions given by the ends of the tie line through point 4. On further cooling the composition of the two solid phases changes as shown by the arrows each dissolves less of the other. A phase reaction takes place. The proportion of each phase is given by the lever rule. The compositions of each are read directly from the diagram (the ends of the tie lines). 

FIG. 4 Qualitative phase diagram close to a first-order irreversible phase transition. The solid line shows the dependence of the coverage of A species ( a) on the partial pressure (Ta). Just at the critical point F2a one has a discontinuity in (dashed line) which indicates coexistence between a reactive state with no large A clusters and an A rich phase (hkely a large A cluster). The dotted fine shows a metastability loop where Fas and F s are the upper and lower spinodal points, respectively. Between F2A and Fas the reactive state is unstable and is displaced by the A rich phase. In contrast, between F s and F2A the reactive state displaces the A rich phase. 

A similar treatment applies for the unstable regime of the phase diagram (v / < v /sp), where the mixture decays via spinodal decomposition.For the linearized theory of spinodal decomposition to hold, we must require that the mean square amplitude of the growing concentration waves is small in comparison with the distance from the spinodal curve. 

A number of publications have appeared recently on super-lattice complexes which have enhanced conductivity, eg. "nazirpsio NaaPOif 2Zr02 2Si02 whose conductivity at room temperature is of the same order as that of an aqueous salt solution. Most of the super-lattices are unstable thermodynamically, and can be expected to collapse under chemical attack by the anodic and cathodic reactants. However, there may exist some thermodynamically stable structures, and the search should concentrate on the complicated phase-diagram studies of selected quatemarys. 

Curve defining the region of composition and temperature in a phase diagram for a binary mixture across which a transition occurs from miscibility of the components to conditions where single-phase mixtures are metastable or unstable (see Note 4 in Definition 1.2). 

There are, obviously, no compounds to illustrate lattice-induced strains with GII 3> 0.2 vu. Such structures are unstable and cannot exist, but if it is possible to model structures of any arbitrary composition using the methods described in Chapter 11, it is possible to determine which compositions give rise to stable structures and which ones do not. A systematic exploration of different compositions occurring between a group of elements would then lead to an understanding of the phase diagram. For example, on the basis of a few simple rules, Skowron and Brown (1994) were able to predict most of the structures in the Pb-Sb-S phase diagram and their relative stabilities (Section 11.2.2.2). 

Figure 11-12. a) Gibbs phase diagram for a ternary system with a miscibility gap. Tie lines and reaction path between (A,B) and C are indicated, b) Possible reaction paths near and across the miscibility gap. Starting compositions of the reaction couple are indicated (o) in Figure a. (Stable and unstable morphologies see text.)... 

FIGURE 9 Phase portraits for the system when -yi = 0.001 and -y2 = 0.002. (a) Phase diagram at an apparent triple point (labelled P in Figure 8 a, = 0.025, a2 = 0.026) where only the value of 6t is identical for the three steady-states, (b) Limit cycle surrounding an unstable focus corresponding to the point labelled Q in Figures I and 8 (a, = 0.017, a2 = 0.028). 

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