MSE 308: Thermodynamics of Materials
Department of Materials Science & Engineering
Boise State University
Spring 2005
Practice Final Exam 2
May, 2005
Problem
1.
2.
3.
4.
5.
6.
7.
8
Grand
Total:
Total Points
1
Points Obtained
Binary Equilibrium Phase Diagrams
1. Shown below is a temperature versus activity phase diagram for a two component (1 and
2) system. Draw the corresponding binary phase diagram (temperature versus
composition, X2). For BOTH DIAGRAMS, label all important aspects.
T(K)
L
α
β
χ
0
δ
X2
2
ε
1
2. Shown below is a temperature versus activity phase diagram for a two component (1 and
2) system. Draw the corresponding binary phase diagram (temperature versus
composition, X2). For BOTH DIAGRAMS, label all important aspects.
T(K)
L
α
φ
β
ρ
0
γ
X2
3
ε
1
Lever Rule
3. For the phase diagram below, at 210oC for the arrow pointing to point P for Plumber's
solder, calculate:
a. The composition at point P
b. The composition of the liquid phase
c. The composition of solid Pb phase
d. The fractional amount of liquid phase
e. The fractional amount of the solid Pb phase
P
4
4. For the Sn-Pb binary phase diagram above, draw a T -vs- a2 phase diagram and label all
significant aspects of the diagram.
5
Gibb’s Free Energy Composition and Phase Diagrams of Binary Systems
5. The Gibb's free energy of mixing for these phases may be modeled by the following
expressions (all in J/mol).
α
∆Gmix
{α ; β } = ∆Gα {α ;α } + X 2α ∆G2oβ →α
β
∆Gmix
{α ; β } = ∆G β {β ; β } + X 1β ∆G1oα → β
L
∆Gmix
{α ; β } = ∆G L {L; L} + X 1β ∆G1oα → β + X 2α ∆G2oβ →α
These expressions are plotted on the following pages for a range of temperatures. Use
these plots to construct a T-X2 diagram. A grid to construct the plot is also included in the
following pages.
1300K
1200K
Red Dash =Liq ; Blue =α; ThickGreen =β
Red Dash =Liq ; Blue =α; ThickGreen =β
6000
4000
4000
∆Gmix H J L
mol
∆Gmix H J L
mol
6000
2000
0
-2000
-4000
2000
0
-2000
-4000
-6000
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
XB
0.6
0.8
1
XB
1100K
1250K
Red Dash =Liq ; Blue =α; ThickGreen =β
Red Dash =Liq ; Blue =α; ThickGreen =β
4000
4000
∆Gmix H J L
mol
∆Gmix H J L
mol
6000
2000
0
-2000
-4000
-6000
2000
0
-2000
-4000
0
0.2
0.4
0.6
0.8
1
0
XB
0.2
0.4
0.6
XB
6
0.8
1
1065K
950K
Red Dash =Liq ; Blue =α; ThickGreen =β
Red Dash =Liq ; Blue =α; ThickGreen =β
4000
∆Gmix H J L
mol
∆Gmix H J L
mol
4000
2000
0
-2000
-4000
2000
0
-2000
-4000
0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
1000K
0.6
0.8
1
XB
XB
900K
Red Dash =Liq ; Blue =α; ThickGreen =β
Red Dash =Liq ; Blue =α; ThickGreen =β
4000
∆Gmix H J L
mol
∆Gmix H J L
mol
4000
2000
0
-2000
2000
0
-2000
-4000
0
0.2
0.4
0.6
0.8
1
0
XB
0.2
0.4
0.6
XB
7
0.8
1
6. Consider that the regular solution model applies for the two Gibb's Free Energy of
α
L
p
mixing: ∆Gmix
{α ;α } and ∆Gmix
{L; L} . Derive ∆Gmix
{?;?} for the phases α and L for the
p
reference states listed in parts a, b and c for components A and B. Then plot ∆Gmix
{?;?}
(at T=1000K) for the phases α and L for the following choices of reference states for
components A and B:
a. {L;L}
b. {L;α}
c. {α; α}
kJ
kJ
Parameters: aoα = 8.4
; a oL = 10.5
; TAα → L = 1500 K ; TBα → L = 850 K ;
mol
mol
J
J
; ∆S Bo ,α → L = 7
∆S Ao ,α → L = 9
mol ⋅ K
mol ⋅ K
8