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Chapter 9

Phase Diagrams

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System • The universe or any part of it.

Phase • A region in the system that has a distinct structure and/or composition

Structure • How the atoms or molecules of the components are physically arranged in space

Composition • The relative amounts of different components

Components • Chemically distinct species, generally pure elements or compounds

Phase Diagram • A graphical representation of the influence of various factors, such as temperature, pressure, and composition on the phases that exist in a system.

Unary System • A system that has only one component

Binary System • A system that has two components – what this course primarily deals with

Ternary System • A system that has three components

Quaternary System • A system that has four components

A, B, C … • Generic names of components

L, α, β, … • Generic names of phases

Phase Diagram Vocabulary

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Unary Phase Diagrams – H2O

1 atmosphere

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Unary Phase Diagram – Pure Fe

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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

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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 nm rNi = 0.125 nm– Both have a face centered cubic (fcc) structure– Electronegativity Cu = 0.19; Ni = 0.18– Valance – Cu+ and Cu++; Ni++

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Cooling Curves during Solidification

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

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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

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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+ region– P=2, C=2– P+F=C+1– F=1– If we pick a temperature,

then compositions of L and are fixed

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

TL

TS

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Tie Line and Lever Rule

• At point B both liquid and are present

• WL×R = WS×S

SR

RW

SR

SW

S

L

WL WS

R S

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Equilibrium Cooling

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• Non-equilibrium cooling results in– Cored structure

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

– Solidification point is depressed

– Melting point on reheat is lowered

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

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Effect on Mechanical Properties

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

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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

Liquid α (solid solution) + β (solid solution)Eutectic temperature

Cooling

61.9% Sn 18.3% Sn 97.8% Sn183ºC

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Binary Eutectic System

• Apply Modified Gibbs Phase Rule– Phases present: L, and (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)

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Microstructures in the Eutectic System

Depending on the system, eutectic solidification can result in:

•Lamellar structure – alternating plates•Rod-like•Particulate

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Microstructures in the Eutectic System

Solvus Line

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Microstructures in the Eutectic System

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Amounts of Phases at different temperatures

QP

PW

QP

QW

L

• At Teutectic + T

• At Teutectic - T

RQP

PW

RQP

RQW total

QP

PW

QP

QW

L

cproeutecti

cproeutectitotaleutectic WWW

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Other Reactions in the Binary System

• Upon Cooling the following reactions are also possible– Peritectic L + – Monotectic L1 L2 +

– Eutectoid + – Peritectoid +

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Copper-Zinc System

• Terminal phases

• Intermediate phases

• Several peritectics

• Eutectoid

• Two phase regions between any two single phase regions

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Mg-Pb System

• Intermediate Compound Mg2Pb

• Congruently melting

Mg2Pb L heating

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Portion of the Ni-Ti System

• Congruently melting intermediate phase

L heating

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Iron-Carbon System

• Reactions on cooling

• Peritectic

L +

• Eutectic

L + Fe3C

• Eutectoid

Fe3C

Steel Cast Iron

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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 iron – bcc structure– Austenite – iron – fcc structure– High temperature iron – bcc structure– Cementite – Fe3C

• Steels have carbon contents <2%, usually <1.2%• Cast irons have carbon contents >2%

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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

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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

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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

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Phase Transformations in Steels

Hypoeutectoid Hypereutectoid

Proeutectoid ferrite

Pearlite Proeutectoid cementite

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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