Phase diagrams projection

The authors (Pribylskii et al. 1983b) have studied the T-X phase diagram projection of the Tb2Se3-Cu2Se (fig. 2). The Cu3TbSe3 phase melts congruently... 

A convenient way of representing the T—x y phase diagram (Eig. 14b) is by projection onto the composition triangle at the base of the figure. It is understood that the temperature varies from point to point on the projected vapor line and on the projected boiling envelope. The latter looks like an isothermal Hquid—Hquid binodal envelope, but is not. Each tie line across the boiling envelope is associated with a different boiling temperature (Eig. 15). 

Figure 2-78. Typical phase diagram for a pure substance showing P-V-T surface and its projections [60],...

Rapidly solidified in-situ metal matrix composites. A design project for alloys based on the Fe-Cr-Mo-Ni-B system, and produced by rapid solidification, was undertaken by Pan (1992). During processing a mixture of borides is formed inside a ductile Fe-based matrix which makes the alloys extremely hard with high moduli. These alloys provide a good example of how phase-diagram calculations were able to provide predictions which firstly helped to identify unexpected boride formation (Saunders et al. 1992) and were ultimately used in the optimisation of the modulus of a shaft material for gas turbines (Pan 1992). 

Fig. 3. Phase diagram of a portion of ihe Sitb-AbO% system, showing regions of phase separation of undercooled melts. The projected composition of Class-F fly ash glasses lies in the range of 10-4051 mol /t AI,Ot. Adapted from Roth et al. (1987).

Often the essentials of phase diagrams in P,7,x-space are represented in a P,7-projection. In this type of diagrams only non-variant (F=0) and monovariant (F=l) equilibria can be represented. Since pressure and temperature of phases in equilibrium are equal, a four-phase equilibrium is now represented by one point and a three-phase equilibrium with one curve. Also the critical curve and the azeotropic curve are projected as a curve on the P, 7-plane. A four-phase point is the point of intersection of four three-phase curves. The point of intersection of a three-phase curve and a critical curve is a so-called critical endpoint. In this intersection point both the three-phase curve and the critical curve terminate. 

Fig. 9.10. Isolines of modulus of elasticity ( ) projected on the basal plane of the three-dimensional phase diagram of grinding tools. (After Decneut, 1967).

Consider first the Al-Fe-Ni system. Generally, the equilibrium phase diagram is known to be helpful in analysing the process of intermetallic layer formation. Projection of the liquidus surface on the concentration triangle and distribution of the phase fields in the solid state for Al-rich Al-Fe-Ni alloys are shown in Fig. 5.15. 

At this temperature the X-phase shows its maximum solid solution towards the Cu-rich portion of the system which diminishes above. However, with still increasing temperature, the X-phase solid solution width extends towards the Mo—S side, in particular towards MoS2 or sulfur, respectively. Figure 19 shows a schematic ternary T-X block diagram. To simplify the perspective drawing only a few isotherms are indicated. The extension of the whole solid solution width of the X-phase is projected on the base. Thus, the variation and the shifting of the temperature-dependent... 

As demonstrated in the previous section, it is advantageous to obtain a deeper understanding of how to perform projections and cuts for multicomponent reactive systems. A single projection or cut captures only part of the system under consideration. However, the user can form a mental picture of the phase diagram in its entirety by making a sequence of such projections and cuts [6],... 

Figure 11.6 shows an example of the phase diagram for a reactive system, in which a compound C is formed from components A and B. An isothermal cut and the polythermal projection are also shown. Such a phase diagram can be obtained via a reaction invariant projection of a higher-dimensional simple eutectic phase diagram. AS and BS are binary nonreactive eutectics, since their presence is not affected by the reaction, while ACSb and BCSa are ternary reactive eutectics. Similar... 

Fig. 11.8. Isobaric isothermal phase diagram for a six-salt simple ionic system (a) 3-D diagram (b) 2-D projection.

Figure 3. Al-Cu-Zn phase diagram, liquidus projection (Ref. 14) (+) alloys investigated by Friedrich et al. [26] ( ) alloys investigated by Bridgewater et al. [27].

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