ChEg_3161

Year III Taye Zewdu

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PHASE DIAGRAMS AND MICROSTRUCTURES

Lecture 9

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Focal points in this lecture:

(1) Terminology associated with phase diagrams and phase transformations;

(2)Pressure–temperature phase diagrams for pure materials;

(3)The interpretation of phase diagrams;

(4)Some of the common and relatively simple binary phase diagrams, including that for the iron–carbon system; and

(5)The development of equilibrium microstructures, upon cooling,

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Key Words

(1)Component: pure metal and/or compound of which an alloy

is composed

(2)System: a specific body of material under consideration or

series of possible alloys consisting of the same components

(3)Solubility limit: a maximum concentration of solute atoms

that may dissolve in the solvent to form a solid solution

(4)Phase: a homogeneous portion of a system that has uniform

physical and chemical characteristics

(5)Microstructure: Visible under optical or electron microscopes

(6)Equilibrium: When the free energy of a system is at a

minimum under some specified combination of temperature,

pressure, and composition.

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a (darker phase)

b (lighter

phase)

Pu

re

Su

ga

r

Te

mp

era

ture

(°C

)

0 20 40 60 80 100Co=Composition (wt% sugar)

L (liquid solution

i.e., syrup)

Solubility Limit L

(liquid)

+ S

(solid sugar)

65

20

40

60

80

100

Pu

re

Wa

ter

Water-Sugar System

Aluminum-Copper alloy

• Changing T can change # of phases: path A to B.

• Changing Co can change # of phases: path B to D. A

B D

Adapted from Callister6e.

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Phase Diagrams

Tell us about phases as function of T, Co, P.

Tools to determine: the number and types of phases, the wt% of each phase, and the composition of each phase

Independent variables: T and Co (P = 1atm is always used).

Unary, binary and ternary phase diagrams

The phases can be liquidus, solidus or the combination

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One-component (Or Unary) Phase Diagrams

Also called P-T diagrams The phase diagram is for a pure substance; this means that

pressure and temperature are the variables A good example is Pressure–temperature phase diagram for H2O

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Binary Phase Diagrams

Maps that represent the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy

Isomorphous systems refer to complete liquid and solid solubility of two components.

Cu-Ni system PD

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Understanding Phase Diagrams

Rule 1 Phases Present: If we know T and Co, then we know the # and types of phases present.

Cu-Niphase

diagram

Example

B(T, Co) has two phases: α+ L

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Rule 2 Determination of Phase Compositions: If we know T and Co, then we know the composition of each phase.

wt% Ni

20

1200

1300

T(°C)

L (liquid)

a

(solid)L + a

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L + a

433532CoCL Ca

At TA:

Only Liquid (L) CL = Co ( = 35wt% Ni)

At TB:

Both a and L CL = Cliquidus ( = 32wt% Ni here)

Ca = Csolidus ( = 43wt% Ni here)

At TD:

Only Solid (a)

Ca = Co ( = 35wt% Ni)

Co = 35wt%Ni

Example

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Rule 3 Determination of Phase Amounts: If we know T and Co, then we know the amount of each phase (weight fractions of phases, wt%).

wt% Ni

20

1200

1300

T(°C)

L (liquid)

a

(solid)L + a

liquidus

solidus

30 40 50

TAA

DTD

TBB

tie line

L + a

433532CoCL Ca

R S

At TB: Both a and L

At TA: Only Liquid (L)

WL = 100wt%, Wa = 0At TD: Only Solid (a)

WL = 0, Wa = 100wt%

Co = 35wt%Ni

WL S

R S

Wa R

R S

43 35

43 32 73wt %

= 27wt%

Example

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- Sum of weight fractions:

- Conservation of mass (Ni):

- Combine above equations:

Co WLCL WaCa

R

R S Wa

Co CL

Ca CL

S

R SWL

Ca Co

Ca CL

- A geometric interpretation:

Co

R S

WaWL

CL Camoment equilibrium:

1 Wa

solving gives Lever Rule

WLR WaS

Derivation of the Lever Rule

WL Wa 1

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Here you have a class exercise!

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Calculate the amount of each phase present in 1 kg of a 50 wt.% Ni-50 wt.% Cu alloy at

a) 1400°C, b) 1300°C and c) 1200°C.

Adapted from Fig. 9.3, Callister 8e.

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For an alloy consisting of α and β phases, the volume fraction of the α phase,Vα, is defined as:

However, the densities are computed from

For multiphase alloys, it is convenient to specify relative phase amount in terms of volume fraction rather than mass fraction.

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Microstructure in Isomorphous Alloys

Lecture 10

Eq

uilib

riu

m C

oo

lin

g

Case I- Solidification at very slow cooling

Phase equilibrium is continously maintained Compositions of the L and α phases follow the Liquidus and solidus lines.

Adapted from Fig. 9.4, Callister 8e.

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No

n-e

qu

ilib

riu

m C

oo

lin

g

Case II- Solidification at slow diffusion rates

Assume equilibrium in liquid phase Average composition Segregation Cored structures

Adapted from Fig. 9.5, Callister 8e.

First a to solidfy: 46wt%Ni

Uniform Ca:

35wt%Ni

Last a to solidfy: < 35wt%Ni

Ca changes as we solidify. Cu-Ni case:

Fast rate of cooling:

Cored structure Slow rate of cooling:

Equilibrium structure

First a to solidify has Ca = 46wt%Ni.Last a to solidify has Ca = 35wt%Ni.

Equilibrium Vs Non-equilibrium Cooling

Effect of solid solution strengthening on:

Tensile strength (TS) Ductility (%EL,%AR)

Peak as a function of Co Min. as a function of Co

Adapted from Fig. 9.6, Callister 8e.

MECHANICAL PROPERTIES: Cu-Ni System

Eutectic- has a special composition with a min. melting T.

• 3 single phase regions (L, a b)

• Limited solubility: a: mostly Cu

b: mostly Ni

• TE: No liquid below TE

• CE: Min. melting T

composition

Ex.: Cu-Ag system

Binary-eutectic Systems

Eutectic reaction

Pb-Sn EUTECTIC SYSTEM

• For a 40wt%Sn-60wt%Pb

alloy at 150C, find... the phases present: a + b the compositions of

the phases:Ca = 11wt%SnCb = 99wt%Sn

the relative amountsof each phase:

W a 59

88 67 wt %

W b 29

88 33 wt %

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Tin–bismuth (Sn-Bi) phase diagram.

Co < 2wt%Sn

Result:

polycrystal of a grains.

Adapted from Fig. 9.9, Callister 8e.

Microstructures in Eutectic Systems-I

Pb-Snsystem

2wt%Sn < Co < 18.3wt%Sn

Result:

a polycrystal with fine b crystals

Adapted from Fig. 9.10, Callister 68.

Microstructures in Eutectic Systems-II

Pb-Snsystem

160m

Micrograph of Pb-Sn eutectic microstructure

Co = CEResult: Eutectic microstructure

--alternating layers of a and b crystals.

Pb-Snsystem

Adapted from Fig. 9.11, Callister 8e.

Adapted from Fig. 9.12, Callister 6e.(Fig. 9.12 from Metals Handbook, Vol. 9, 9th ed., Metallography and Microstructures, American Society for Metals, Materials Park, OH, 1985.)

Microstructures in Eutectic Systems-III

18.3wt%Sn < Co < 61.9wt%Sn

Result: a crystals and a eutectic microstructure

• Just above TE:

WL = (1-Wa) =50wt%

Ca = 18.3wt%Sn

CL = 61.9wt%SnS

R + SWa = =50wt%

• Just below TE:

Ca = 18.3wt%Sn

Cb = 97.8wt%SnS

R + SWa = =73wt%

Wb = 27wt%

Adapted from Fig. 9.14, Callister 8e.

Microstructures in Eutectic Systems-IV

Pb-Snsystem

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H2O–NaCl phase diagram

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Primary and Eutectic fractions

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EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS

Terminal solid solutions, exist over composition ranges near the concentration extremities of the phase diagram.Eg. The eutectic copper–silver and lead–tin phase diagrams

Intermediate solid solutions (or intermediate phases) may be found at other than the two composition extremes.Eg. The copper–zinc system

-there are some invariant points and reactions-there are six different solid solutions—two terminal (α and η) and four intermediate (β, ϒ, δ, and ε)

The commercial brasses are copper-rich copper–zinc alloys; Eg. Cartridge brass :70 wt% Cu–30 wt% Zn and a microstructure consisting of a single α phase

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Intermetallic compounds

For some systems, discrete intermediate compounds rather than solid solutions may be found on the phase diagram, and these compounds have distinct chemical formulas; for metal–metal systems, they are called intermetallic compounds. For example, magnesium–lead system

The compound Mg2Pb exists by itself only at 19 wt% Mg–81 wt% Pb

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EUTECTOID AND PERITECTIC REACTIONS

Eutectic: liquid transforms to two solid phasesEutectoid: one solid phase to two other solid phasesPeritectic: liquid and one solid phase transform to a second

solid phaseIn all cases, three phases are at equilibrium.

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Eutectoid reaction

Peritectic reaction

Phase transformations for which there are no compositionalalterations are said to be congruent transformations.Eg. Allotropic transformations, pure substance transformations

Incongruent transformations, at least one of the phases will experience a change in composition. Eg. Isomorphous and eutectic transformations

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THE GIBBS PHASE RULE

This rule represents a criterion for the number of phases that will coexist within a system at equilibrium, and is expressed by the simple equation:

P+F=C+N

Where: P is the number of phasesF is the degree of freedom or the no. of externally

controlled variablesC is the number of components in the systemN is the number of non-compositional variables

F is the number of variables that can be changedindependently without altering the number of phases thatcoexist at equilibrium.

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Binary T-C PDs

P+F=2+1=3

Single phase fields

F=3-1=2

Two phase fields

F=3-2=1

Three phases at Eq.

F=3-3=0

The phase rule helps in analyzing for non-equilibrium conditions.

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The most important Phase Diagram