phase diagrams of 2 component solid liquid systems handout
DESCRIPTION
Phase Diagrams of 2 Component Solid Liquid Systems HandoutTRANSCRIPT
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Phase Diagrams of 2Component SolidLiquid Systems
If only condensed phases are present,system is not sensitive to changes in pp can be held constant Phase diagram shows only changes in T
and ConcF = C P + 1
= 2 P + 1= 3 P
P = k
Temp
Composition
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1. No interaction occurs between pure components only pure components crystallize from solution
A B
P = K
TTA
TB
Consider systems where complete miscibility is observed in the liquid state
Composition, mole %
A B Composition, mole %
P = K
melt
A(s) + melt B(s) + melt
A + eutectic C B + eutectic C
TA
TB
TC
C
T
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Determine the variance in different parts of the diagram:
A C B Composition, mole %
P = K
melt
A(s) + melt B(s) + meltA + eutectic C
B + eutectic C
TA
TB
TC
F = 3 1 = 2
F = 3 2 = 1
F = 3 2 = 1
F = 3 3 = 0
T, C
T or Cmelt
(T)
Consider a mixture of composition m cooled to T
A m m C BComposition, mole %
P = K
melt
A(s) + melt B(s) + melt
A + eutectic C B + eutectic C
TA
TB
TC
T
Mixture obtained at m, T: A(s) + melt mwhere m = composition of the melt
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Material Balance
Lever rule: (force x distance)1 = (force x distance)2
If force no. of moles, nA x m = nmelt x (m m)nA/nmelt = (m m) / m
2. Components interact to form congruent melting compound, i.e. comp of solid = comp of melt
A B
Composition, mole %
P = K
TTA
TB
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Congruent melting: 3A2B(s) melt60% A 60 % A
A D 40 E BComposition, mole %
P = K
melt
TTA
TB
A(s) + melt
3A2B + melt
A + eut D
3A2B + eut D
3A2B + eut D
B(s) + melt
B + 3A2B
T 3A2B
TD
TE
3. Components interact to form incongruent melting compound, i.e. comp of solid comp of melt
A B
Composition, mole %
P = K
TTA
TB
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Incongruent melting: A2B(s) B(s) + melt
A 67 BComposition, mole %
P = K
TTA
TBmelt
A(s) + melt A2B(s)
+ melt
B(s) + melt
A + eut F
F
A2B(s) + eut F
B(s) + A2B(s)TF
TA2B
F = 3 3 = 0
4. Components are completely miscible in both liquid and solid statesa. melting points are between those of pure components
A B Composition, mole %
P = K
T
TA
TBmelt
Solid soln
Solid soln + melt
solidus
liquidus
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What will be observed if a melt of composition m is cooled from T1 to T2? T3? T4?
A B Composition, mole %
P = K
T
TA
TBmelt
Solid soln
Solid soln + melt solidus
liquidusT1
T2
T3T4
ml s2 s1ffff
If melt of composition m is cooled from T1 to: T2: Appearance of the first solid solution (s1) is
observed T3: mixture of solid solution (s2) and melt (l) is
obtainednsolid soln/nmelt = (m l) / (s2 m)
T4: Complete solidification is observedcomposition of solid solution = mcomposition of last drop of liquid = f
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b. Melting point curve exhibits a maximum
P = k
TA
T
A Composition B
TBliquidus
solidus
melt
Solid soln + melt
Solid soln
c. Melting point curve exhibits a minimum
P = k
TA
T
A Composition B
TB
liquidus
solidus
Solid soln + melt
melt
Solid soln
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Composite Diagrams
T
Composition, mole %
P = k
A 25 40 60 B
Composite Diagrams
T
Composition, mole %
P = k
A 25 40 60 B
melt
TA TB
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Composite Diagrams
T
Composition, mole %
P = k
A C 25 40 60 B
melt
TA TB
A(s) + melt 3AB(s) + melt
A+ eut C
3AB + eut C
C= A + 3AB
Composite Diagrams
T
Composition, mole %
P = k
A C 25 D 40 60 B
melt
TA TB
A(s) + melt
3AB(s) + melt
A +
eut C3AB + eut C
3A2B(s) + melt
3A2B +
eut D
3AB + eut D
C= A + 3AB D = 3AB + 3A2B
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Composite Diagrams
T
Composition, mole %
P = k
A C 25 D 40 60 B
melt
TA TB
A(s) + melt
3AB(s) + melt
A +
eut C3AB + eut C
3A2B(s) + melt
3A2B +
eut D
3AB + eut D
2A3B + melt
2A3B +
3A2B
C= A + 3AB D = 3AB + 3A2B
Composite Diagrams
T
Composition, mole %
P = k
A C 25 D 40 60 B
melt
TA TB
A(s) + melt
3AB(s) + melt
A +
eut C3AB + eut C
3A2B(s) + melt
3A2B +
eut D
3AB + eut D
2A3B + melt
2A3B +
3A2B Solid soln of B and 2A3B
Solid soln + melt
solidus
liquidus
C= A + 3AB D = 3AB + 3A2B