Simple phase diagrams

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

When the iateraction energy density is positive, equation 5 defines a critical temperature of the UCST type (Fig. la) that is a function of component molecular weights. The LCST-type phase diagram, quite common for polymer blends, is not predicted by this simple theory unless B is... 

Phase diagrams can be used to predict the reactions between refractories and various soHd, Hquid, and gaseous reactants. These diagrams are derived from phase equiHbria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equiHbria. Moreover, equiHbrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

FIG. 22-2 Simple eutectic-phase diagram at constant pressure. (Zief and Wilcox, Fractional Solidification, i>c/. 1, Marcel Dekker, New York, 1967, p. 24.)... 

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

Fig. 4.5. Schematic of top left corner of the "silicon-impurity" phase diagram. To make things simple, we assume that the liquidus and solidus lines ore straight. The impurity concentration in the solid is then always less than that in the liquid by the factor k (called the distribution coefficient).

Take the silica-alumina system as an example. It is convenient to treat the components as the two pure oxides SiOj and AI2O3 (instead of the three elements Si, A1 and O). Then the phase diagram is particularly simple, as shown in Fig. 16.6. There is a compound, mullite, with the composition (Si02)2 (Al203)3, which is slightly more stable than the simple solid solution, so the alloys break up into mixtures of mullite and alumina, or mullite and silica. The phase diagram has two eutectics, but is otherwise straightforward. 

Figure A1.27 shows the unusual silver-strontium phase diagram. It has four inter-metallic compounds. Note that it is just five simple phase diagrams, like the Pb-Sn diagram, stuck together. The first is the Ag-SrAgj diagram, the second is the SrAgj-Sr.Agj diagram, and so on. Each has a eutectic. You can always dissect complicated diagrams in this way.

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

The phase diagram of the MM model is quite simple for I"a< — 1/2 (7a > 7]a) the catalyst becomes poisoned by A (B) species, respectively. Thus one has a first-order IPT where 7ia = 1/2 is a trivial critical point given by the stoichiometry of the reaction. In contrast to the ZGB model. 

The curious phase relations between phosphorus, sulfur and their binai compounds are worth noting. Because both P4 and Sg are stable molecules the phase diagram, if studied below 100°, shows only solid solutions with a simple eutectic at 10° (75 atom % P). By contrast, when the mixtures are heated above 200° the elements react and an entirely different phase diagram is obtained however, as only the most stable compounds P4S3, P4S7 and P4S10... 

The Pd-Rh alloy system provides a convenient test case for application of the methodology because of its particularly simple phase diagram, which consists of only the liquid and a fee solid solution phases. 

To summarize we have reproduced the intricate structural properties of the Fe-Co, Fe-Ni and the Fe-Cu alloys by means of LMTO-ASA-CPA theory. We conclude that the phase diagram of especially the Fe-Ni alloys is heavily influenced by short range order effects. The general trend of a bcc-fcc phase transition at lower Fe concentrations is in accordance with simple band Ailing effects from canonical band theory. Due to this the structural stability of the Fe-Co alloys may be understood from VGA and canonical band calculations, since the common band model is appropriate below the Fermi energy for this system. However, for the Fe-Ni and the Fe-Cu system this simple picture breaks down. 

No chalcogenide halides of zinc and cadmium are known. The phase diagrams of CdS-CdCl (7, 198, 210), CdSe-CdCl (220, 314), CdTe-CdClj 368), CdTe-CdBr2 (368), and CdTe-Cdl (323) are of a simple, eutectic type. The system CdS-CdCl shows a range of solubility of CdS in solid CdClj that extends to 5% of CdS at room temperature, and increases to a maximum of 12.5% of CdS at 500°C (7,210). 

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