Phase Diagrams: Theory And Applications

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 System: H2O Liquid Phase boundary Pressure Solid Vapor

Temperature

Triple point (Invariant point)

Gibb’s Phase Rule P+F=C+ 2 F=C-P+2

P=number of phases C=number of components F=number of degrees of freedom (number of independent variables)

Modified Gibbs Phase Rule (for incompressible systems)

P+F=C+1 F=C-P+1

Pressure is a constant variable

Application of the phase rule At triple point, P=3, C=1, F=0 i.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 Pure metal

Alloy L

L TL Tm

L

S TS S

Soldification begins L+S

Solidification complete

S

Construction of a simple phase diagram ◆

Conduct an experiment ◆ Take 10 metal samples(pure Cu, Cu10%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

T

L L

S

L L

L

TL

TL

L+S L

L+S

S

Pure Ni

TS TCu

TNi

S TS

S

S Cu-20%Ni

Pure Cu Cu-10%Ni

t

Binary isomorphous phase diagram L

Temp

TCu x

x

x

x

x

x x

x x L+S x x x x

x

x

x x

x

x

x TNi

Cu

S

Ni

0

100 10

Cu

20

30

40

50

60

%Ni Composition

70

80

90

Ni

Microstructural changes during solidification Pure metal L

T L

S L

S

Tm S S t

Microstructural changes during solidification Alloy L

T L TL

L+S

TS S

S t

Binary isomorphous phase diagram T

L

L

L

T1 T2

L+S

T3

T4

L S

S CL

C0

CS

0

100 10

A

20

30

40

50

60

%B Composition

70

80

90

B

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

f

fS + fL = 1

CO = fS CS + (1fS) CL − − − CO C C C C C 0 L O L S Lever f S= − f L = = S CS C L Rule CS − CL CS − C L

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 α + β (TE, CL=CE)

L

Liquidus Solidus Solvus

T L

α

α +L

TE

β +L

β

E CE A

α +β

Wt%B

B

Pure A or B L

T

L S

L

α

α +L

TE

β +L

CE

L

β

L

α +β α +β

E CE

Other alloys between A and B

α +β

L

A

Wt%B

B

L+α L α +β α +β

Solidification for alloy of eutectic composition T L

L

α

α +L

TE

β +L

β

E CE A

α +β

α +β

Wt%B

S B α +β

Eutectic microstructure Lamellar structure QuickTime™ and a Photo - JPEG decompressor are needed to see this picture.

QuickTime™ and a Photo - JPEG decompressor are needed to see this picture.

L

T L

α

β +L

α +L

TE

CE A

β

Proeutectic α

α +β α +β

Wt%B

B α +β

T L L

α

β +L

α +L

TE

CE A

β L

α +β

Wt%B

α B β particles

The Eutectoid Phase Diagram α + β (TE, Cγ =CE)

γ T

γ

α

α +γ

TE

β +γ

β

E CE A

α +β

Wt%B

B

Cooling of an alloy of eutectoid composition T γ

γ

α

α +γ

TE

β +γ

β

γ

E CE A

α +β

α +β

Wt%B

S B α +β

Cooling of an alloy of hypoeutectoid composition γ

T γ

α

α +γ

TE

β +γ

γ β

Pro-eutectiod α

E

γ

α +β A

Wt%B

Pro-eutectiod α

B

α +β

S α +β