Respuesta :
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
A) The mass fractions of α and β phases are respectively; Wα = 0.8 and Wβ = 0.20
B) The mass fractions of primary α and eutectic microconstituents are respectively; Wα = 0.73 and W_e = 0.27
C) The mass fraction of eutectic α is; Wα = 0.07
What is the mass fraction?
(a) We are trying to find the mass fractions of α and β phases.
From the Cu - Ag phase diagram, we have;
Cα = 8.0 wt% Ag
Cβ = 91.2 wt% Ag
C₀ = 25 wt% Ag
Using the lever-rule, we have;
Total mass fraction of α is;
Wα = (Cβ - C₀)/(Cβ - Cα)
Wα = (91.2 - 25)/(91.2 - 8)
Wα = 0.8
Total mass fraction of β is;
Wβ = (C₀ - Cα)/(Cβ - Cα)
Wβ = (25 - 8)/(91.2 - 8)
Wβ = 0.20
(b) We want to find the mass fractions of primary α and eutectic microconstituents. We have;
C_eutetic = 71.9 wt.%Ag
Mass fraction of primary α is;
Wα = (C_eutetic - C₀) /(C_eutetic - Cα)
Wα = (71.9 - 25)/(71.9 - 8)
Wα = 0.73
Mass fraction of eutectic micro-constituents is;
W_e = (C₀ - Cα)/(C_eutetic - Cα)
W_e = (25 - 8)/(71.9 - 8)
W_e = 0.27
(c) Determine the mass fraction of eutectic α.
From the eutetic reaction;
Total α = Primary α + α in eutectic mixture
Thus:
mass fraction of eutectic α = Total α - Primary α
mass fraction of eutectic α = 0.8 - 0.73 = 0.07
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