A 45 wt% Pb-55 wt% Mg alloy is rapidly quenched to room temperature from an elevated temperature in such a way that the high-temperature microstructure is preserved. This microstructure is found to consist of the \(\alpha\) phase and Mg\(_2\)Pb, having respective mass fractions of 0.65 and 0.35. Determine the approximate temperature from which the alloy was quenched.
\( C_0 \) = 45 wt% Pb-55 wt% Mg
rapidly quenched to room temp
\(C_{\alpha}\) = 0.65
\(C_{Mg_{2}Pb}\) = 0.35
T\(_{before quenching}\)
\( W_{\alpha}\) = \( {C_{Mg_{2}Pb} - C_0} \over {C_{Mg_{2}Pb} - C_{\alpha} } \)
\( C_{Mg_{2}Pb} \) = 81 wt% Pb-19 wt% Mg
Solve for \(C_{\alpha}\):
\(C_{\alpha}\) = \(C_{Mg_{2}Pb}\) - \(C_{Mg_{2}Pb} - C_0 \over W_{\alpha}\) = 81 - \(81 - 45 \over 0.65\)
\(C_{\alpha}\) = 25.6 wt% Pb-74.4 wt% Mg
Now, inspect the Mg-Pb phase diagram to determine at what temp the \(\alpha\) phase will have the composition of 25.6 wt% Pb-74.4 wt% Mg
T = 360\(^\circ\)C