Alloys, equilibrium curves

Fig. 15,—Equilibrium Curves of Alloys prepared by melting together the two metals of Potassium and Sodium. under rock oil. In some cases sodium displaces...

CE is the equilibrium curve for the compound A,fiy— in the example under consideration x = and y = 1—with the submerged maximum at D. The point D is not realised in practice because the compound decomposes completely at E into sohd picric acid and liquid benzene. The point E is spoken of as the incongruent melting point of the compound (since the composition of the liquid is not the same as that of the original compound) or as the transition point. The ctuve EB represents the equilibrium between solid B and the liquid. This system is rarely encountered among compounds, but other examples are acetamide - salicylic acid and di-methylpyrone - acetic acid it is, however, comparatively common in alloy systems e.g., gold - antimony, AuSbj). 

A carefully studied example is the transition which takes place in liquidheliumat about 2.2 K. Theheat capacity and density of liquid helium as functions of the temperature are shown in Fig. 22. In this instance at least it is known that the two phases are able to co-exist, not merely at a particular temperature and pressure, but along a p-T equilibrium curve, as in the ordinary phase transitions already discussed. Similar effects are known to occur in many solids, notably in alloys, in the crystalline ammonium salts, in polymers and in solidified methane and hydrogen halides. For example, in ammonium chloride there is a sharp break in the heat capacity curve at —30.4 GL Now in any given example, if it were knotm with certainty that the latent heat and volume change were vanishingly small, the entropy... 

The sequence just outlined provides a salutary lesson in the nature of explanation in materials science. At first the process was a pure mystery. Then the relationship to the shape of the solid-solubility curve was uncovered that was a partial explanation. Next it was found that the microstructural process that leads to age-hardening involves a succession of intermediate phases, none of them in equilibrium (a very common situation in materials science as we now know). An understanding of how these intermediate phases interact with dislocations was a further stage in explanation. Then came an nnderstanding of the shape of the GP zones (planar in some alloys, globniar in others). Next, the kinetics of the hardening needed to be... 

Another kinetic jjhenomenon where Calm s critical waves can possibly be visualized and studied is the replication of interphase boundaries (IPB) illustrated in Figs. 8-10. Similarly to the replication of APBs. it can arise after a two-step quench of an initially uniform disordered alloy. First the alloy is quenched and annealed at temperature T in some two-phase state that can be either metastable or spinodally unstable with respect to phase separation. Varying the annealing time one can grow here precipitates ("droplets ) of a suitable size /. For sufficiently large /, the concentration c(r) within A-riched droplets is close to the equilibrium binodal value C(,(T ) (thin curve in Fig. 9). 

For a cubic site, relations between the cumulants and the coefficients of the OPP model have been derived by Kontio and Stevens (1982), and applied to the Al(4) atom in the alloy VA110 4.2 The coordination of Al(4) is illustrated in Fig. 2.4(a), while the potential along [111], derived from the thermal parameter refinement, is shown in Fig. 2.4(b). It is clear from these figures that higher than third-order terms contribute to the potential, because the deviation from the harmonic curve is not exactly antisymmetric with respect to the equilibrium configuration. The potential appears steeper at the higher temperature, which is opposite to what is expected on the basis of the thermal expansion of the solid. 

Fig. 7.14 The binding energy curves for the elemental A and transition metals and the binary AB alloy. The heat of formation is given by AH = UAB—2(i/A + UB), where the binding energies are evaluated at the appropriate equilibrium positions as shown.

Figure 8. Temperature dependence of the equilibrium constant, Kp = p(HtO)/ p(Ht) for the reduction of several metal oxides often present in Tokamak walls. The Kp values are calculated from thermochemical data listed in Ref. 51. The reduction curve for NiO, the most prevalent metal oxide on Inconel alloys, lies above the FeO curve, and thus is more easily reduced in hydrogen than the oxides shown. (Reproduced, with permission, from Ref. 37. Copyright 1980, North-...

P—x isotherms for the FeTiH alloy. The upper curve corresponds to the equilibrium pressure as hydrogen is added stepwise to the alloy the lower curve corresponds to the equilibrium pressure as hydrogen is removed stepwise from the hydride. 

Function (1) appears enough good for reproduction of features of a characteristic curve in engineering calculations. With the help of this equation begins possible to project future intermetallic alloy by selection of necessary quantity of the alloying additive changing equilibrium pressure in hydride. 

In this equation, Qm is the molar surface area, m i is a structural parameter defined in Section 1.1 (see Figure 1.3) and A is the regular solution parameter of Ni-Si alloy defined by equation (4.3). From the slope of the osL(XNi) curve for XNi— 0, the adsorption energy is found to be E i,(f ) = —8.2 kJ/mole. Thus, in equations (1.2), all the quantities are known (or can be easily estimated), except W and Wf 1 which represent respectively the work of adhesion and the work of immersion of pure liquid Ni in metastable equilibrium with SiC (i.e., for a supposed non-reactive pure Ni/SiC system). The values deduced from equation (1.2) are Wj4 = 3.17 J/m2 and W = —1.35 J/m2 for pure Ni. They are reported in Figure 7.6 along with the corresponding value of contact angle. 

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