Question 1.20: THE 60% Pb–40% Sn ALLOY Consider the solidification of the 6...
THE 60% Pb–40% Sn ALLOY Consider the solidification of the 60% Pb–40% Sn alloy. What are the phases, compositions, and weight fractions of various phases existing in the alloy at 250, 210, 183.5 (just above 183 °C), and 182.5 °C (just below 183 °C)?
We again refer to the phase diagram in Figure 1.72 to identify which phases exist at what temperatures. At 250 °C, we only have the liquid phase. At 210 °C, point N, the liquid and the α-phase are in equilibrium. The composition of the α-phase is given by the solidus line; at 210 °C, C_{\alpha} = 18% Sn. The composition of the liquid is given by the liquidus line; at 210 °C, C_{L} = 50% Sn. To find the weight fraction of α in the alloy, we use the lever rule,
W_{\alpha}=\frac{C_{L}-C_{O}}{C_{L}-C_{\alpha}}=\frac{50-40}{50-18}=0.313
From W_{\alpha} + W_{L} = 1, we obtain the weight fraction of the liquid phase, W_{L} = 1 − 0.313 = 0.687.
At 183.5 °C, point O, the composition of the α-phase is 19.2% Sn corresponding to C and that of the liquid is 61.9% Sn corresponding to E. The liquid therefore has the eutectic composition. The weight fractions are
\begin{array}{l} W_{\alpha}=\frac{C_{L}-C_{O}}{C_{L}-C_{\alpha}}=\frac{61.9-40}{61.9-19.2}=0.513 \\ W_{L}=1-0.513=0.487 \end{array}
As expected, the amount of α-phase increases during solidification; at the same time, its composition changes along the solidus curve. Just above 183 °C, about half the alloy is the solid α-phase and the other half is liquid with the eutectic composition. Thus, on solidification, the liquid undergoes the eutectic transformation and forms the eutectic solid. Just below 183 °C, therefore, the microstructure is the primary α-phase and the eutectic solid. Stated differently, below 183 °C, the α and β phases coexist, and β is in the eutectic structure. The weight fraction of the eutectic phase is the same as that of the liquid just above 183 °C, from which it was formed. The weight fractions of α and β in the whole alloy are given by the lever rule applied at point P, or
\begin{array}{l} W_{\alpha}=\frac{C_{\beta}-C_{O}}{C_{\beta}-C_{\alpha}}=\frac{97.5-40}{97.5-19.2}=0.734 \\ W_{\beta}=\frac{C_{O}-C_{\alpha}}{C_{\beta}-C_{\alpha}}=\frac{40-19.2}{97.5-19.2}=0.266 \end{array}
The microstructure at room temperature will be much like that just below 183 °C, at which the alloy is a two phase solid because atomic diffusions in the solid will not be sufficiently fast to allow the compositions to change. Table 1.7 summarizes the phases that exist in this alloy at various temperatures.
| Table 1.7 The 60% Pb–40% Sn alloy | ||||
| Temperature (°C) | Phases | Composition | Mass (g) | Microstructure and Comment |
| 250 | L | 40% Sn | 100 | |
| 235 | L \alpha |
40% Sn 15% Sn |
100 0 |
The first solid (\alpha-phase) nucleates in the liquid. |
| 210 | L \alpha |
50% Sn 18% Sn |
68.7 31.3 |
Mixture of liquid and \alpha phases. More solid forms. Compositions change. |
| 183.5 | L \alpha |
61.9% Sn 19.2% Sn |
48.7 51.3 |
Liquid has the eutectic composition. |
| 182.5 | \alpha \\ \beta | 19.2% Sn 97.5% Sn |
73.4 26.6 |
Eutectic (\alpha and \beta phases) and primary α-phase. |
