Answer:
a)
mass fraction of α = 0.796
mass fraction of β = 0.204
b)
mass fraction of primary α (Wα) = 0.734
mass fraction of eutectic micro-constituents (We) = 0.266
c)
α in eutectic mixture = 0.062
Explanation:
Assumptions:
(i) the system is in thermal equilibrium with its surroundings
(ii) There are no impurities or other alloying elements present
(a) Determine the mass fractions of α and β phases
From the Cu - Ag phase diagram, Cα = 8.0 wt% Ag, Cβ = 91.2 wt% Ag, and C0 = 25 wt% Ag .Using the lever-rule:
Total mass fraction of α = (Cβ - C0) / (Cβ - Cα) = (91.2 - 25) / (91.2 - 8) = 0.796
Total mass fraction of β = (C0 - Cα) / (Cβ - Cα) = (25 - 8) / (91.2 - 8) = 0.204
(b) Determine the mass fractions of primary α and eutectic microconstituents
Ceutetic = 71.9 wt.%Ag
mass fraction of primary α (Wα) = (Ceutetic - C0) / (Ceutetic - Cα) = (71.9 - 25) / (71.9 - 8) = 0.734
mass fraction of eutectic micro-constituents (We) = (C0 - Cα) / (Ceutetic - Cα) = (25 - 8) / (71.9 - 8) = 0.266
(c) Determine the mass fraction of eutectic α.
From the eutetic reaction, L ↔ α + β
Total α = Primary α + α in eutectic mixture
Therefore: α in eutectic mixture = Total α - Primary α = 0.796 - 0.734 = 0.062
