P-T-x phase diagrams

Fig. 55. P-T cross section of the pseudo-binary P-T-x phase diagram of 123-Oj. The stability field of the 123 phase is smaller than shown. Slow decomposition kinetics do not allow the exact determination of the phase boundary with the 124 phase. After Karpinsid et al. (1991).

Fig. 6.4. Schematic 3-dimensional p — T — x phase diagram for a binary fluid-fluid system of the first kind. The curves terminating in (1) and (2) represent the vapor pressure curves of the less volatile (1) and more volatile (2) components. The dashed curve cl is the critical line extending from the critical point of component (1).

Fig. 6.4 Schematic 3-dimensional p-T-x phase diagram for a binary fluid-fluid system of the first kind. 203...

Figure 6. The suinmarized P T X-phase diagram of the tetraalkyl ammonium iodide -- water system.

At a given temperature and pressure eqs. (4.7) and (4.8) must be solved simultaneously to determine the compositions of the two phases a and P that correspond to coexistence. At isobaric conditions, a plot of the composition of the two phases in equilibrium versus temperature yields a part of the equilibrium T, x-phase diagram. 

Figure 1.3 Proposed CH4-H2O T-x phase diagram with the solid solution range (P 5 MPa). Regions expanded for ease of viewing. (Reproduced from Huo, Z., Hester, K.E., Sloan, E.D., Miller, K.T., AlChE. /., 49, 1300 (2003). With permission.)...

Because of the close relationship between the MNM transition and the vapor-liquid transition, it is to be expected that immiscibility in the mercury-helium system reaches up to the critical point, or even into the supercritical region. This expectation is confirmed by measurements of the phase diagram at very low helium concentrations and at pressures close to the critical pressure of pure mercury. The experiments extend up to 1610 °C and to pressures up to 3325 bar (Marceca et al., 1996). The p — T — X phase equilibrium surface obtained is qualitatively like the one shown schematically in Fig. 6.4 for a binary fiuid-fluid system of the first kind. The critical line starts at the critical point of pure mercury (Tc(l) = 1478 °C, Pc(l) = 1673 bar) and runs to higher temperatures and pressures as the helium composition X2 increases. 

The occurrence of solid clathrate solutions is clearly seen in Fig. 4, which gives a cross section of the P-T-x diagram at 60°C according to recent results.28 The two two-phase equilibria clath-rate-gas and clathrate-hydroquinone are separated by a one-phase... 

The composition of the hydrates varies with temperature along the three-phase lines H ice G and HL2G in a way similar to that described for the system hydroquinone-argon. But as already noted in Section II.D this variation is smaller than for the hydroquinone clathrates. Accordingly, a cross section through the P-T-x diagram at constant temperature below 0°C would reveal a two-phase area G+H in which the composition of the latter is less sensitive to pressure than found in the corresponding case for the hydroquinone clathrates (cf. Fig. 4). 

Let us call the melt phase a and the solid phase with complete immiscibility of components y. P is constant and fluids are absent. The Gibbs free energy relationships at the various T for the two phases at equilibrium are those shown in figure 7.2, with T decreasing downward from Ty to Tg. The G-X relationships observed at the various T are then translated into a T-X stability diagram in the lower part of the figure. 

Because there is an added term, the composition, binary systems are inherently more complex than unary systems. In order to completely represent the phase diagram of a binary system a three dimensional pressure-temperature-composition (P-T-x) diagram can be constructed. However, it is a more common... 

The occurrence of irreversible fatigue phenomena and grain-size effects indicates that important features of the SMA phenomenon lie outside the domain of equilibrium thermodynamics. Nevertheless, details of the SMA T-x (and T-P-x) phase diagram are clearly important for the understanding and engineering of this curious thermal effect. 

As the pressure is further increased at this fixed overall composition, the amount of the liquid phase increases while the amount of the vapor phase shrinks until only a small bubble of vapor remains. If the pressure is still further increased, the bubble of vapor finally disappears, then a single liquid phase exists. The locus of points that separates the two-phase vapor-liquid region from the one-phase liquid region is called the bubble point curve. This vapor-liquid envelope can now be inserted into the three-dimensional P-T-x diagram in figure 3.2a. 

Type-I phase behavior is probably the type of behavior most familiar to chemical engineers, since the description of this phase behavior can be found in many undergraduate thermodynamic textbooks. Rowlinson and Swinton (1982) present compilations of type-I mixtures as well as other types of mixtures. Hicks and Young (1975) also present an extensive compilation of P-T-x information on a wide variety of solvent-solute pairs from which the specific type of each system can easily be determined. Two examples of type-I P-x diagrams are shown in figure 3.3 (Li, Dillard, and Robinson, 1981 Ng and Robinson, 1978). For these two examples, the P-T traee of the critieal mixture curve exhibits a maximum in pressure. 

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