phase diagrams theory and applications. some basic concepts u phase a homogeneous region with...
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PHASE DIAGRAMS
THEORY AND APPLICATIONS
Some basic concepts Phase
• A homogeneous region with distinct structure and physical properties
• In principle, can be isolated
• Can be solid, liquid or gas Phase Diagram
• Representation of phases present under a set of conditions (P, T, Composition etc.)
Concepts…...
Phase transformation
• Change from one phase to another
• E.g. L S, S S etc.
• Occurs because energy change is negative/goes from high to low energy state
Phase boundary
• Boundary between phases in a phase diagram
A simple phase diagram
Triple point(Invariant point)
Solid
Liquid
Vapor
Pressure
Temperature
Phase boundary
System: H2O
Gibb’s Phase Rule
P + F = C + 2
P=number of phasesC=number of componentsF=number of degrees of freedom (number of independent variables)
Modified Gibbs Phase Rule (for incompressible systems)
P + F = C + 1
Pressure is a constant variable
F = C - P + 2
F = C - P + 1
Application of the phase rule
At triple point, P=3, C=1, F=0i.e. this is an invariant point
At phase boundary, P=2, C=1, F=1
In each phase, P=1, C=1, F=2
Solidification(cooling) curves
L
S
L
S
Pure metal Alloy
Tm
L S L + S
Solidificationcomplete
Soldificationbegins
TL
TS
Construction of a simple phase diagram
Conduct an experiment Take 10 metal samples(pure Cu, Cu-
10%Ni, Cu-20%Ni, Cu-30%Ni………, pure Ni)
Melt each sample and then let it solidify Record the cooling curves Note temperatures at which phase
transformations occur
Results
L
S
L S
t
T
L
L + S
TL
TS S
L
L + S
TL
TS
Pure CuCu-10%Ni
Cu-20%Ni
LL S
Pure NiS
TNi
TCu
Binary isomorphous phase diagram
x x
x
x
x
x
xx
x
x x
x
x x x x
x x x x
L+S
L
S
Composition
Temp
TCu
TNi
10 60 70 80 9030 40 50200 100
Cu Ni%Ni
Cu
Ni
Microstructural changes during solidification
L
S
L S
T
t
Tm
L
S
Pure metal
S
Microstructural changes during solidification
L
S
Alloy
L + STL
TS
L
S
T
t
L
Binary isomorphous phase diagram
L+S
L
S
Composition
T
10 60 70 80 9030 40 50200 100
A B%B
L
L
S
T1
T2
T3
T4
CL C0 CS
Notes This is an equilibrium phase diagram (slow
cooling) The phase boundary which separates the L from
the L+S region is called LIQUIDUS The phase boundary which separates the S from
the L+S region is called SOLIDUS The horizontal (isothermal) line drawn at a
specific temperature is called the TIE LINE The tie line can be meaningfully drawn only in a
two-phase region The average composition of the alloy is CO
Notes….. The intersection of the tie line with the liquidus gives
the composition of the liquid, CL
The intersection of the tie line with the solidus gives the composition of the solid, CS
By simple mass balance,
CO = fS CS + fL CL
and fS + fL = 1
CO = fS CS + (1- fS) CL
Sf 0C
LCSC LCS
f OC LC
SC LC Lf SC
OCSC LC
LeverRule
Some calculations In our diagram at T3, CO= A-40%B,
CS=A-90%B and CL=A-11%B
Therefore, fS=29/79 or 37% and
fL=50/79 or 63%
If we take an initial amount of alloy =100 g,
amt. of solid=37 g (3.7 g of A and 33.4 g of B) and amt. of liquid=63 g (56.07 g of A and 6.93 g of B)
The Eutectic Phase Diagram
T
A BWt%B
L
+L+L
+
E
TE
CE
Liquidus
Solidus
Solvus
L + TE, CL=CE
T
A BWt%B
L
+L+L
+
E
TE
CE
Pure A or B
Other alloysbetween A and B
CE
L
S
L
+L
+
L
L
L+L +
+
T
A BWt%B
L
+L+L
+
E
TE
CE
Solidification for alloy of eutectic composition
L
S
+
+
Eutectic microstructureLamellar structure
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T
A BWt%B
L
+L+L
+
TE
CE
L
Proeutectic
+
+
L
T
A BWt%B
L
+L+L
+
TE
CE
L
particles
The Eutectoid Phase Diagram
T
A BWt%B
+ +
+
E
TE
CE
+ TE, C=CE
T
A BWt%B
+ +
+
E
TE
CE
Cooling of an alloy of eutectoid composition
S
+
+
T
A BWt%B
+ +
+
E
TE
Cooling of an alloy of hypoeutectoid composition
S
+
+
Pro-eutectiod
Pro-eutectiod
The Peritectic Phase Diagram
T
A BWt%B
L
+ L
+ L
+
PTP
CP
L at TP
NM
Note: and L will react only in a certain proportion= NP:PM
L
L
T
A BWt%B
L
+ L
+ L
+
PTP
CP
L at TP
NM
Note: and L will react only in a certain proportion= NP:PM
10 25 85
NP:PM=1:2
60
L
L
L
T
A BWt%B
L
+ L
+ L
+
PTP
CP
L at TP
NM
Note: and L will react only in a certain proportion= NP:PM
L
L
L
