On the basis of the photomicrograph (i.e., the relative amounts of the microconstituents)...

On the basis of the photomicrograph (i.e., the relative amounts of the microconstituents) for the lead–tin alloy shown in Figure 9.17 and the Pb–Sn phase diagram (Figure 9.8), estimate the composition of the alloy, and then compare this estimate with the composition given in the legend of Figure 9.17. Make the following assumptions: (1) The area fraction of each phase and microconstituent in the photomicrograph is equal to its volume fraction; (2) the densities of the α and β phases and the eutectic structure are 11.2, 7.3, and 8.7 g/cm3, respectively; and (3) this photomicrograph represents the equilibrium microstructure at 180°C (355°F).

Figure 9.17 Photomicrograph showing the microstructure of a lead–tin alloy of composition 50 wt% Sn–50 wt% Pb. This microstructure is composed of a primary lead-rich α phase (large dark regions) within a lamellar eutectic structure consisting of a tin-rich β phase (light layers) and a lead-rich α phase (dark layers). 400×.

(From Metals Handbook, Vol. 9, 9th edition, Metallography and Microstructures, 1985. Reproduced by permission of ASM International, Materials Park, OH.)

Figure 9.8 The lead–tin phase diagram.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]