Solubility alloys with limited

Interpreting the Phases and Compositions in a Binary Phase Diagram as Described by the Lever Rule Alloy Compositions in a Solid Solution with Limited Solubility Determine the composition, relative amonnts, and phases present at point B on Figure 23.7. Alloy Compositions in a Solid Solution with Limited Solubility Determine the composition, relative amonnts, and phases present at point C on Figure 23.7. 

In the preceding chapter we have been considering the equilibrium of two phases of the same substance. Some of the most important cases of equilibrium come, however, in binary systems, systems of two components, and we shall take them up in this chapter. Wo can best understand what is meant by this by some examples. The two components mean simply two substances, which may be atomic or molecular and which may mix with each other. For instance, they may be substances like sugar and wrater, one of which is soluble in the other. Then the study of phase equilibrium becomes the study of solubility, the limits of solubility, the effect of the solute on the vapor pressure, boiling point, melting point, etc., of the solvent. Or the components may be metals, like copper and zinc, for instance. Then we meet the study of alloys and the whole field of metallurgy. Of course, in metallurgy one often has to deal with alloys with more than two components—ternary alloys, for instance, with three components—but they arc considerably more complicated, and we shall not deal with them. 

The atomic radius of silver (144 pm) is within about 15% of many elements, permitting solid solutions with Al, Au, Be, Bi, Cu, Cd, Ge, In, Mn, Pb, Pd, Pt, Sb, Sn, Th, and Zn. These metals form usefid brazing, jewelry, and soldering alloys. Copper is the only metal with which silver forms a simple eutectic between two solid solutions (Fig. 3). Silver has extremely limited solubility in B, C, Co, Cr, Fe, Ge, Ir, Ni, Mg, Mo, Se, Si, Te, Ti, and W. Thus these metals may be brazed by silver alloys without serious erosion during welding (qv). 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

It has been proposed by others that this B segregation produces disorder at grain boundaries, thus facilitating slip transmission across them. This view is supported by a Hall-Petch type analysis of flow stress data as a function of the grain size. There are observations on disordered grain boundary layers which indicate the formation of the y-Ni-Al phase at the grain boundaries. This is not improbable since the A1 content of Al-deficient NijAl is near the solubility limit, and in the case of the LI 2 phase CU3 Au it has been found (Tichelaar et al., 1992) that the order-disorder transition is preceded by the formation of disordered layers at the interfaces. However, such disordered layers have also been found in NijAI without B, and have not been found in many ductile NijAl alloys with B (see also Lin et al., 1993 Sun and Lin, 1993). 

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