Phase diagram for

Figure 6-1. Calculated phase diagram for the acetone(I)-methanol(2) system.

Fig. XVII-17. Schematic phase diagram for O2 on graphite (see text). (From Ref 95. Reprinted with permission from American Chemical Society, copyright 1996.)...

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Figure A2.5.5. Phase diagrams for two-eomponent systems with deviations from ideal behaviour (temperature T versus mole fraetion v at eonstant pressure). Liquid-gas phase diagrams with maximum (a) and minimum (b) boiling mixtures (azeotropes), (e) Liquid-liquid phase separation, with a eoexistenee eurve and a eritieal point.

Figure A2.5.10. Phase diagram for the van der Waals fluid, shown as reduced temperature versus reduced density p. . The region under the smooth coexistence curve is a two-phase liquid-gas region as indicated by the horizontal tie-lines. The critical point at the top of the curve has the coordinates (1,1). The dashed line is the diameter, and the dotted curve is the spinodal curve.

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Figure A2.5.13. Global phase diagram for a van der Waals binary mixture for whieh The...

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 B3.3.9. Phase diagram for polydisperse hard spheres, in the volume fraction ((]))-polydispersity (s) plane. Some tie-lines are shown connecting coexistmg fluid and solid phases. Thanks are due to D A Kofke and P G Bolhuis for this figure. For frirther details see [181. 182].

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

The accompanying sketch qualitatively describes the phase diagram for the system nylon-6,6, water, phenol for T > 70°C.f In this figure the broken lines are the lines whose terminals indicate the concentrations of the three components in the two equilibrium phases. Consult a physical chemistry textbook for the information as to how such concentrations are read. In the two-phase region, both phases contain nylon, but the water-rich phase contains the nylon at a lower concentration. On this phase diagram or a facsimile, draw arrows which trace the following procedure ... 

Fig. 8. (a) Schematic for an FCC unit showing where the various fluidization regimes are found and (b) a corresponding phase diagram for Group A powder (FCC catalyst) where the numbers on the curves represent the superficial soHd velocity in m/s. A represents the bubbling regime B, the turbulent ... 

Even at the lowest temperatures, a substantial pressure is required to soHdify helium, and then the soHd formed is one of the softest, most compressible known. The fluid—soHd phase diagrams for both helium-3 and helium-4 are shown in Eigure 1 (53). Both isotopes have three allotropic soHd forms an fee stmeture at high pressures, an hep stmeture at medium and low pressures, and a bcc stmeture over a narrow, low pressure range for helium-4 and over a somewhat larger range for helium-3. The melting pressure of helium-4 has been measured up to 24°C, where it is 11.5 GPa (115 kbar) (54). 

Eig. 1. SoHd—Hquid phase diagram for ( ndashrule ) He and (—) He where bcc = body-centered cubic, fee = face-centered cubic, and hep = hexagonal close-packed (53). To convert MPa to psi, multiply by 145. 

Fig. 2. Phase diagram for helium-4 where CP is the critical poiat. To convert MPa to psi, multiply by 145.

Fig. 3. Phase diagram for helium-3 where A, B, and A1 represent the three superfluid phases and PCP is the polycritical poiat. The dashed lines iadicate the...

Fig. 4. Phase diagram for Hquid and soHd mixtures of He and He where CP is the critical point (—), Hquid ( ndashrule ), soHd.

Fig. 3. Vapor—liquid-phase diagram for the HCl—H2 O system (5) where (-) represents the demarcation between the two-phase region and the gas...

Heat Treatment of Steel. Steels are alloys having up to about 2% carbon in iron plus other alloying elements. The vast application of steels is mainly owing to their ability to be heat treated to produce a wide spectmm of properties. This occurs because of a crystallographic or aHotropic transformation which takes place upon quenching. This transformation and its role in heat treatment can be explained by the crystal stmcture of iron and by the appropriate phase diagram for steels (see Steel). 

Fig. 6. Phase diagram for three crystalline and two Hquid forms of phosphoms(V) oxide. To convert kPa to mm Hg, multiply by 7.5.

Fig. 1. Phase diagram for mixtures (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) (c) composition dependence of the free energy of the mixture (on an arbitrary scale) for temperatures above and below the critical value.

E. M. Levin, C. R. Robbins, and H. F. McMurdie, Phase Diagrams for Ceramists, The American Ceramic Society, Inc., Columbus, Ohio, 1964. 

Fig. 1. Binary soap—water phase diagram for sodium palmitate (4). Courtesy of Academic Press, Ltd.

Fig. 26. Ternary-phase diagram for the system styrene—PS—polybutadiene mbber.

Phase Behavior. One of the pioneering works detailing the phase behavior of ternary systems of carbon dioxide was presented ia the early 1950s (12) and consists of a compendium of the solubiHties of over 260 compounds ia Hquid (21—26°C) carbon dioxide. This work contains 268 phase diagrams for ternary systems. Although the data reported are for Hquid CO2 at its vapor pressure, they yield a first approximation to solubiHties that may be encountered ia the supercritical region. Various additional sources of data are also available (1,4,7,13). 

---