# Chapter 9 - PowerPoint PPT Presentation

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Chapter 9. Phase Diagrams. Phase Diagram Vocabulary. Unary Phase Diagrams – H 2 O. 1 atmosphere. Unary Phase Diagram – Pure Fe. Gibbs Phase Rule (Section 9.17). Tells us how many phases can exist under a given set of circumstances. P+F=C+2 P = number of phases

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Chapter 9

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## Chapter 9

Phase Diagrams

1 atmosphere

### Gibbs Phase Rule (Section 9.17)

• Tells us how many phases can exist under a given set of circumstances.

P+F=C+2

• P = number of phases

• F = number of degrees of freedom – number of variables that can be changed independently of all other variables in the system

• C=number of components

• The number two indicates the ability to change temperature and pressure; these are non-compositional variables that affect the phases.

• Modified Gibbs phase rule

• Most engineering systems function at a pressure of 1 atmosphere, i.e. we have picked the pressure as one of our degrees of freedom. Therefore,

P+F = C+1

• ### Binary Isomorphous System

• Two components are completely soluble in each other in both solid and liquid phases

• Hume-Rothery’s Rules (Section 4.3 text 7th edition)

• Atomic size difference not greater than 15%

• Crystal structure is the same for both components

• Similar electronegativity (i.e. no ionic bonding)

• Elements have a similar valance

• Example: Cu-Ni System

• rCu = 0.128 nmrNi = 0.125 nm

• Both have a face centered cubic (fcc) structure

• Electronegativity Cu = 0.19; Ni = 0.18

• Valance – Cu+ and Cu++; Ni++

### Cooling Curves during Solidification

Solidification occurs at constant temperature while latent heat of fusion is released

### Cooling curves for a binary isomorphous alloy

• Features:

• Solidus – locus of temperatures below which all compositions are solid

• Start of solidification during cooling

• Liquidus – locus of temperatures above which all compositions are liquid

• Start of melting during heating

### Modified Gibbs Phase Rule

• In the liquid or solid phase:

• P=1, C=2

• P+F=C+1

• F=2

• Both composition and temperature can be varied while remaining in the liquid or solid phase

• In the L+a region

• P=2, C=2

• P+F=C+1

• F=1

• If we pick a temperature, then compositions of L and a are fixed

• If we pick a composition, liquidus and solidus temperatures are fixed

TL

TS

### Tie Line and Lever Rule

• At point B both liquid and a are present

• WL×R = WS×S

WL

WS

R

S

Equilibrium Cooling

• Non-equilibrium cooling results in

• Cored structure

• Composition variations in the solid phase as layers of decreasing Ni concentration are deposited on previously formed a phase

• Solidification point is depressed

• Melting point on reheat is lowered

• Homogenization or reheating for extended times at temperature below e’

### Effect on Mechanical Properties

Due to solid solution strengthening, alloys tend to be stronger and less ductile than the pure components.

Eutectic temperature

α (solid solution) + β (solid solution)

Liquid

Cooling

61.9% Sn

183ºC

18.3% Sn

97.8% Sn

### Binary Eutectic System

• The two components have limited solid solubility in each other

• Solubility varies with temperature

• For an alloy with the Eutectic composition the liquid solidifies into two solid phases

### Binary Eutectic System

• Apply Modified Gibbs Phase Rule

• Phases present: L, a and b (P=3)

• Components: Pb and Sn (C=2)

• P+F=C+1

• F=0  no degrees of freedom

• Therefore, three phases can coexist in a binary system only at a unique temperature and for unique compositions of the three phases

• Upon cooling, there is a temperature arrest during the solidification process (eutectic reaction)

### Microstructures in the Eutectic System

• Depending on the system, eutectic solidification can result in:

• Lamellar structure – alternating plates

• Rod-like

• Particulate

Solvus Line

### Amounts of Phases at different temperatures

• At Teutectic + DT

• At Teutectic - DT

### Other Reactions in the Binary System

• Upon Cooling the following reactions are also possible

• Peritectic L + a b

• Monotectic L1 L2 + a

• Eutectoid a b + g

• Peritectoid a + b g

### Copper-Zinc System

• Terminal phases

• Intermediate phases

• Several peritectics

• Eutectoid

• Two phase regions between any two single phase regions

### Mg-Pb System

• Intermediate Compound Mg2Pb

• Congruently melting

Mg2Pb  L

heating

### Portion of the Ni-Ti System

• Congruently melting intermediate phase g

g  L

heating

### Iron-Carbon System

• Reactions on cooling

• Peritectic

L + d  g

• Eutectic

L  g + Fe3C

• Eutectoid

g  a + Fe3C

Cast Iron

Steel

### Iron-Carbon or Iron-Fe3C

• In principle, the components of the phase diagram should be iron (Fe) and carbon/graphite (C).

• Fe and C form an intermediate compound Fe3C, which is very stable

• There isn’t anything of interest at carbon contents greater than 25 at.% or 6.7 wt.% C.

• Fe3C is considered to be a component, and the binary phase diagram is drawn using Fe and Fe3C.

• Names of phases:

• Ferrite - a iron – bcc structure

• Austenite – g iron – fcc structure

• High temperature d iron – bcc structure

• Cementite – Fe3C

• Steels have carbon contents <2%, usually <1.2%

• Cast irons have carbon contents >2%

### Phase Transformations in Steels

Eutectoid Composition – 0.76wt% C

Pearlite

Alternating plates (lamellae) of Fe and Fe3C

Austenite  Ferrite + Cementite (at 727ºC upon cooling)

0.76wt.%C 0.022wt.%C 6.7wt.% C

### Phase Transformations in Steels

• Hypoeutectoid composition <0.76 wt% C

• Proeutectoid ferrite nucleates and spreads along austenite grain boundaries at T>727ºC

• Remaining austenite converts to pearlite during eutectoid transformation

### Phase Transformations in Steels

• Hypereutectoid composition >0.76 wt% C

• Proeutectoid cementite nucleates and spreads along austenite grain boundaries at T>727ºC

• Remaining austenite converts to pearlite during eutectoid transformation

### Phase Transformations in Steels

Hypereutectoid

Hypoeutectoid

Proeutectoid ferrite

Pearlite

Proeutectoid cementite

### Effect of Alloying Elements

• Addition of an alloying element increases the number of components in Gibbs Phase Rule.

• The additional degree of freedom allows changes in the eutectoid temperature or eutectoid Carbon concentration