Determination of solvus curves parametric method

Whichever technique is used to detect the second phase, the accuracy of the disappearing-phase method increases as the width of the two-phase region decreases. If the (a + P) region is only a few jjercent wide, then the relative amounts of a and P will vary rapidly with slight changes in the total composition of the alloy, and this rapid variation of WJW will enable the phase boundary to be fixed quite precisely. This is true, for the x-ray method, even if the atomic numbers of A and B are widely different, because, if the (a + P) region is narrow, the compositions of a and P do not differ very much and neither do their x-ray scattering powers. 

As we have just seen, the disappearing-phase method of locating the boundary of the a field is based on a determination of the composition at which the P phase just disappears from a series of (a -f- P) alloys. The parametric method, on the other hand, is based on observations of the a solid solution itself. This method depends on the fact, previously mentioned, that the lattice parameter of a solid solution generally changes with composition up to the saturation limit, and then remains constant beyond that point. 

Suppose the exact location of the solvus curve shown in Fig. 12-8(a) is to be determined. A series of alloys, 1 to 7, is brought to equilibrium at temperature Tj, where the a field is thought to have almost its maximum width, and quenched to room temperature. The lattice parameter of a is measured for each alloy and plotted against alloy composition, resulting in a curve such as that shown in Fig. 12-8(b). 

This curve has two branches an inclined branch be, which shows how the parameter of a varies with the composition of a, and a horizontal branch de, which shows that the a phase in alloys 6 and 7 is saturated, because its lattice parameter does not change with change in alloy composition. In fact, alloys 6 and 7 are in a two-phase region at temperature T, and the only difference between them is in the amounts of saturated a they contain. The limit of the a field at temperature Tj is therefore given by the intersection of the two branches of the parameter curve. In this way, we have located one point on the solvus curve, namely x percent B at Tj. 

Other points could be found in a similar manner. For example, if the same series of alloys were equilibrated at temperature T2, a parameter curve similar to Fig. 12-8(b) would be obtained, but its inclined branch would be shorter and its horizontal branch lower. But heat treatments and parameter measurements on all these alloys are unnecessary, once the parameter-composition curve of the solid solution has been established. Only one two-phase alloy is needed to determine the rest of the solvus. Thus, if alloy 6 is equilibrated at Tj and then quenched, it will contain a saturated at that temperature. Suppose the measured parameter of a in this alloy is a,. Then, from the parameter-composition curve, we find that a of parameter contains y percent B. This fixes a point on the solvus at temperature T2. Points on the solvus at other temperatures may be found by equilibrating the same alloy, alloy 6, at various temperatures, quenching, and measuring the lattice parameter of the contained a. 

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