Question

For a copper-silver alloy of composition 25 wt% Ag-75 wt% Cu and at 775C (1425F) do the following: (a) Determine the mass fractions of α and β phases. (b) Determine the mass fractions of primary α and eutectic microconstituents. (c) Determine the mass fraction of eutectic α.

Answer 1

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

Answer 2

Answer:

a.)The mass fraction for α = 0.797

The mass fraction for β = 0.205

b.)

The mass fraction for primary α (Wα) = 0.733

mass fraction of eutectic micro-constituents (We) = 0.267

c.)

α in eutectic mixture = 0.063

Explanation:

ASSUMPTIONS MADE

1.) Let assume thermal equilibrium exist between the system and its surroundings

2.) let assume impurities elements doesn't available.

(a) To determine the mass fractions of α and β phases

This values for Cα,Cβ and C0 can be deducted from the Cu - Ag phase diagram by the use of lever-rule

Cα = 8.0 wt% Ag,

Cβ = 91.2 wt% Ag, and

C0 = 25 wt% Ag .Using the lever-rule:

mass fraction of α in total = (Cβ - C0) / (Cβ - Cα)

= (91.2 - 25) / (91.2 - 8) = 0.797

mass fraction of β in total = (C0 - Cα) / (Cβ - Cα)

= (25 - 8) / (91.2 - 8) = 0.205

(b) To determine the mass fractions of primary α and eutectic microconstituents

Ceutetic = 71.9 wt.%Ag

mass fraction of primary α (Wα) = (71.9 - 25) / (71.9 - 8) = 0.735

mass fraction of eutectic micro-constituents (We) = (C0 - Cα) / (Ceutetic - Cα) = (25 - 8) / (71.9 - 8) = 0.267

(c) To determine the mass fraction of eutectic α.

Total α = Primary α + α

α in eutectic mixture = Total α - Primary α =( 0.796 - 0.734) = 0.062