Mg-Pb Phase diagram Composition (at% Pb) 5 10 20 1 L 0 30 40 70 100 700 L 1200 600 + a +L Mg,Pb M 1000 500 800 400 B Temperature (°C) L + Temperature (°F) L Mg2Pb 300 600 200 B 400 a + Mg Pb 100 B + Mg Pb 200 Mg Pb 20 40 60 80 100 (Mg) Composition (wt% Pb) (Pb) 19. Utilize the previously given sheet of the Mg-Pb phase diagram, and for the alloy with composition (60 wt.%Pb-40 wt.% Mg), at temperature 300 oC, write down the weight percentage of the alpha phase. (2 points) Enter your answer
Utilize the previously given sheet of the Mg-Pb phase diagram, and for the alloy with composition (60 wt.%Pb-40 wt.% Mg), at temperature 300 oC, write down the weight percentage of the alpha phase.
The Correct Answer and Explanation is :
o determine the weight percentage of the alpha (α) phase in a 60 wt.% Pb–40 wt.% Mg alloy at 300°C, we can utilize the lever rule, a fundamental principle in phase diagram analysis.
Understanding the Phase Diagram:
he Mg-Pb phase diagram illustrates the equilibrium phases present at various compositions and temperatures.t 300°C, the diagram indicates that the α phase (a solid solution of Pb in Mg) and the liquid phase coexist for compositions between approximately 20 wt.% Pb and 80 wt.% Pb.or a 60 wt.% Pb alloy at 300°C, both α and liquid phases are present.
Applying the Lever Rule:
he lever rule allows us to calculate the mass fraction of each phase in a two-phase region.t is expressed as:
[ W_{\alpha} = \frac{C_{\text{L}} – C_0}{C_{\text{L}} – C_{\alpha}} ]
here:
( W_{\alpha} ) = mass fraction of the α phase- ( C_{\text{L}} ) = composition of the liquid phase- ( C_{\alpha} ) = composition of the α phase- ( C_0 ) = overall composition of the alloy
Determining Phase Compositions at 300°C:
rom the phase diagram at 300°C:
The liquid phase composition (( C_{\text{L}} )) is approximately 70 wt.% Pb. The α phase composition (( C_{\alpha} )) is approximately 10 wt.% Pb.
Calculating the Mass Fraction of the α Phase:
ubstituting the known values into the lever rule equation:
[ W_{\alpha} = \frac{70\% – 60\%}{70\% – 10\%} = \frac{10\%}{60\%} = 0.1667 ]
herefore, the mass fraction of the α phase is approximately 16.67%.
Calculating the Weight Percentage of the α Phase:
o find the weight percentage of the α phase, multiply the mass fraction by 100:
[ \text{Weight \% of α phase} = 0.1667 \times 100 = 16.67\% ]
Conclusion:
t 300°C, a 60 wt.% Pb–40 wt.% Mg alloy consists of approximately 16.67% α phase and 83.33% liquid phase by weight.
For a visual explanation of identifying intermediate compounds in a phase diagram, you might find the following video helpful:
videoIdentifying intermediate compounds in a phase diagramturn0search4