Types of Binary Phase Diagrams

Given below are some other types of binary phase diagrams... 

Only Eu and Yb, among the rare earths, form immiscibility gaps with Sc in the liquid and solid. The difference in valence of these two rare earths and Sc is, perhaps, the main reason of this difference of interaction. The divalent state is more typical for Eu and Yb, whereas the other rare earths are usually trivalent. The same divalent state is characteristic for aUcaline earths which are immiscible with Sc in the liquid and solid too. Therefore, it is possible to predict the same type of binary phase diagrams of Sc with alkaline metals. These elements are even more different from Sc in the valence state and other characteristics (melting temperature, electronegativity, etc.) than are the alkaline-earth metals. 

Figure 1.8 in combination with Table 1.3 shows basic types of binary phase diagrams being responsible for the mentioned growth processes. Some material systems will be selected and discussed in more detail. 

Two other common types of binary-phase diagrams are shown in Figures 8.4 and 8.5. In Figure 8.4, temperature is plotted vs. liquid and vapor mole fraction to construct a Txy phase diagram for the water—methanol system. This type of phase diagram is similar to the Pxy diagram discussed above however, instead of holding T constant, pressure is held constant, in this case at 1 atm. Could you construct such a plot What data would you need ... 

Figure 2.13. Building blocks of binary phase diagrams examples of three-phase (invariant) reactions. In the upper part the general appearance, inside a phase diagram, of the two types of invariant equilibria is presented, that is, the so-called 1 st class (or eutectic type) and the 2nd class (or peritectic type) equilibria. In the lower part the various invariant equilibria formed by selected binary alloys for well-defined values of temperature and composition are listed. In the Hf-Ru diagram, for instance, three 1 st class equilibria may be observed, 1 (pHf) — (aHf) + HfRu (eutectoid, three solid phases involved), 2 L — (3Hf + HfRu (eutectic), 3 L —> HfRu + (Ru) (eutectic).

Three types of binary phase equilibrium curves are shown in Fig. 13-18. The y-x diagram is almost always plotted for the component that is the more volatife (denoted by the subscript 1) in the region where distillation is to take place. Curve A shows the common case in which component 1 remains more volatile over the entire composition range. Curve B is typical of many systems (e.g., ethanol-water) in which the... 

Binary solutions that deviate significantly from ideal behavior (as exemplified in their temperature-composition phase diagrams) have important consequences for fractional distillation processes. Figure 9.16 shows two types of such phase diagrams for... 

In Figures 1.22a,b the T-x projections of binary phase diagrams of type Id with the low-temperature parts of critical curves Li = L2 are shown for the water-salt systems H2O - Na2B407, H2O - NaHP04, H2O - UO2SO4 and H2O -K2CO3. However, the studied range of temperatures is far apart from critical temperatures of nonvolatile components... 

Figure 1.35 Main types of fluid phase diagrams (T-X projections) for ternary mixtures with one volatile component (A) and immiscibility phenomena of types b, c and d in binary subsystems A-B and A-C (Reproduced by permission of the PCCP Owner Societies).

The lanthanides with valences other than three produce differences from trivalent lanthanides in the systematic studies of binary phase diagrams. The effect is most noticeable in compound formation. The same crystal structure can exist, but the cell dimensions are usually not in the correct proportion relative to those of the neighboring lanthanides. Furthermore, compounds present in the trivalent systems may either be of different structure types or may not exist at all for the other valence states. Physical properties such as magnetic susceptibility, electrical conductivity, specific heat, heat of formation, etc., also show remarkable changes. Therefore, the valency changes can be detected by studying both crystallographic and other physical properties of these compounds. 

A method based on thermodynamic perturbation theory is described which allows strong directional Intermolecular forces to be taken into account when calculating thermodynamic properties. This is applied to the prediction of phase equilibrium and critical loci for mixtures containing polar or quadrupolar constituents. Two applications of the theory are then considered. In the first, the relation between intermolecular forces and the type of phase behavior is explored for binary mixtures in which one component is either polar or quadrupolar. Such systems are shown to give rise to five of the six classes of binary phase diagrams found in nature. The second application Involves comr-parison of theory and experiment for binary and ternary mixtures. 

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

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].

Binary Alloys. Aluminum-rich binary phase diagrams show tliree types of reaction between liquid alloy, aluminum solid solution, and otlier phases eutectic, peritectic, and monotectic. Table 16 gives representative data for reactions in tlie systems Al—Al. Diagrams are shown in Figures 10—19. Compilations of phase diagrams may be found in reference 41. 

In conclusion, we have presented a new formulation of the CVM which allows continuous atomic displacement from lattice point and applied the scheme to the calculations of the phase diagrams of binary alloy systems. For treating 3D systems, the memory space can be reduced by storing only point distribution function f(r), but not the pair distribution function g(r,r ). Therefore, continuous CVM scheme can be applicable for the calculations of phase diagrams of 3D alloy systems [6,7], with the use of the standard type of computers. 

It is known that in five of the six principal types of binary fluid phase equilibrium diagrams, data other than VLE may also be available for a particular binary (van Konynenburg and Scott, 1980). Thus, the entire database may also contain VL2E, VL E, VL]L2E, and L,L2E data. In this section, a systematic approach to utilize the entire phase equilibrium database is presented. The material is based on the work of Englezos et al. (1990b 1998)... 

Data for the hydrogen sulfide-water and the methane-n-hexane binary systems were considered. The first is a type III system in the binary phase diagram classification scheme of van Konynenburg and Scott. Experimental data from Selleck et al. (1952) were used. Carroll and Mather (1989a b) presented a new interpretation of these data and also new three phase data. In this work, only those VLE data from Selleck et al. (1952) that are consistent with the new data were used. Data for the methane-n-hexane system are available from Poston and McKetta (1966) and Lin et al. (1977). This is a type V system. 

Figure 2.9. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the liquid state and, at high temperature only, in the solid state. By lowering the temperature, however, the continuous solid solution decomposes into two phases. In (d) a schematic representation of NiAu or PtAu type diagrams is shown as formed by two generic components A and B.

Figure 4.17. The binary phase diagrams of the magnesium alloy systems with the divalent metals ytterbium and calcium (Ca is a typical alkaline earth metal and Yb one of the divalent lanthanides). Notice, for this pair of metals, the close similarity of their alloy systems with Mg. The compounds YbMg2 and CaMg2 are isostructural, hexagonal hP12-MgZn2 type.

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