Phase diagram quasi-binary

Figure 9-14. a) Possible reaction path during interdiffusion m the quasi-binary AO-BO system, plotted into a phase diagram of the second kind. The initial couple is (A,B)0 and (A,B)0". b) Real-space presentation of the processes occurring at different times during interdiffusion. 

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

In addition, several other models have been used with method I to calculate binary or ternary phase diagrams (183, 188-201). Among these models are the quasi chemical equilibrium model (188,190), truncated Mar-gules expansions (183,191, 192), Gaussian formalism (193), orthogonal series... 

Fig. 5. Temperature-concentration section (isopleth) through the Si-N-0 phase diagram from Si02 to Si3N4 [69]. Below 2114 K it is a quasi-binary system. G = gas phase LS = oxide nitride liquid LM = metallic liquid...

Figure 4.22 Phase diagram of the quasi-binary system Ca0-P205-H20 at a water partial pressure of 65.5 kPa. (After Riboud (1973).) Note that incongruent melting of hydroxyapatite (HAp) occurs at 1570°C under formation of a -C3P (a -TCP) and C4P (TTCP).

One can see the very complicated behavior of quasi-binary solutions where the phase boundary is given by a cloud-point curve and where an infinite number of coexistence curves exists (one pair for each starting concentration, i.e., each cloud-point). The cloud-point is a point in the T-W2- or the P-W2-diagram where a homogeneous solution of concentration Wq2 begins to demix (where the firsf droplet of the second phase occurs, T(2) in Figure 4.4.19). If W02 is smaller than the critical concentration, the cloud-point belongs to the sol-phase, otherwise to the gel-phase. 

In this way we have limited ourselves to a quasi-binary system. Unless interrupted externally, the reaction will continue until at least one of the two reactants is completely consumed (Gibbs phase rule). If the reaction is interrupted at a time when both reactants are still present, then the reaction product will consist of a sequence of all those phases which occur in the phase diagram as compounds between the reactants A and B in the quasi-binary system, as long as local equilibrium is maintained. It can be seen that we have here a convenient method for investigating quasi-binary lines in ternary phase diagrams. 

If several compounds occur in the phase diagram between the quasi-binary reactants (for example, between the oxides AO and B2O3), then a multiphase product layer will be formed during the solid state reaction. This situation is shown in Fig. 6-7 where the activity of one component is plotted. 

Once again, it should be mentioned that the reaction products and the reactants together comprise a quasi-binary system which can be read from the phase diagram for the case where local thermodynamic equilibrium is maintained at the phase boundaries. If local equilibrium at all the phase boundaries is not established, then it is possible that certain product phases do not form, even though they are present in the equilibrium phase diagram. The probability that local equilibrium at the phase boundaries will, in fact, occur becomes better and better as the product layer grows. Reactions as discussed here are most easily studied experimentally today by means of the electron probe (electron beam microanalysis). 

Majewski, P., Epple, L., Rozumek, M., Schluckwerder, H., and Aldinger, E. (2000). Phase diagram studies in the quasi binary systems LaMnOt-SrMnOt and LaMnOs-CaMnOt. /. Mater. Res. 15 1161-1166. 

Fig. 4.3-76 Quasi-binary phase diagram Ba0-Fe203. p 02) = 1 atm X = BaO FeO 7Fe203 W — BaO 2FeO-8Fe203-vawi/oojfc 1964 [3.10,59]...

S. J. Mumby, C. Qian, and B. E. Eichinger, Phase diagrams of quasi-binary polymer systems with LCST/UCST spinodals and hourglass cloud-point curves. Polymer, 33,23, 5105-5105,1992. 

Representation of three-component systems as a set of quasi-binary cross-sections is not quite rigorous for the most real ternary mixtures because a ratio of second and third components in equibbrium phases is not usually constant. However, if we intend to study the phase behavior from the point of view of topological schemes, the sequence of binary phase diagrams of quasi-binary sections (including the sections through the ternary nonvariant points) give an exhaustive description of possible phase equilibria and phase transformations in ternary systems. 

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