Lectures MM231

ASSIGNMENT-1

Question 1: Below is Pb-Ag Phase Diagram. Describe the diagram in terms of points marked, Phase transformations, different regions and lines . Apply the Gibbs phase rule on regions ,curves and where ever possible. Mention the changeable parameters in terms of degree of freedom.

Solid lead+ Eutectic

Given here are the solidus and liquidus temperatures for copper-gold system. Construct the phase diagram for this system and label each region.

Composition wt% Au Solidus Temp(oC) Liquidus Temp (oC)

0 1085 1085

20 1019 1042

40 972 996

60 934 946

80 911 911

90 928 942

95 974 984

100 1064 1064

ASSIGNMENT-1

Question 2:

ASSIGNMENT-1

Question 1: Below is Pb-Ag Phase Diagram. Describe the diagram in terms of points marked, Phase transformations, different regions and lines . Apply the Gibbs phase rule on regions ,curves and where ever possible. Mention the changeable parameters in terms of degree of freedom.

Solid lead+ Eutectic

ASSIGNMENT-SOLUTION

D is the eutectic temperature of the system and the eutectic composition is given by B.

A and C are the freezing points of pure lead and silver respectively. Curve AB indicates the

temperatures at which lead begins to separate from various compositions of melt while BC

indicates initial separation of silver.

Curve ABC is the liquidus curve as it gives

the composition of the liquid phase that is in

equilibrium with the solid phase. ADBEC is

the solidus curve; AD represents solid lead,

DBE mixture of lead and Ag in equilibrium

with liquid phase of composition B and EC

solid silver. Solid lead+

Eutectic

A Freezing point of lead C=1, P=2, F=0 Fixed T

C Freezing point of silver C=1, P=2, F=0 Fixed T

B Eutectic point C=2, P=3, F=0 Fixed T and composition

AB Crystallization of lead

begins C=2, P=2, F=1 T or

composition

BC Crystallization of silver

begins C=2, P=2, F=1 T or

composition

Area above ABC Liquid phase C=2, P=1, F=2 T and

composition

Area below DBE Solid mixture C=2, P=2, F=1 T or

composition

Area ADBA

Solid lead in equilibrium with liquid having

composition given by the curve AB C=2, P=2, F=1

T or composition

Area CEBC

Solid silver in equilibrium with liquid having

composition given by the curve BC C=2, P=2, F=1

T or composition

DBE

Both lead and silver separate from liquid of

composition B C=2, P=3, F=0 Fixed T

Solid lead+

Eutectic

ASSIGNMENT-SOLUTION

Phase Diagram of Zn-Mg

Similarly, ED is the freezing point curve

of magnesium. Solid magnesium is in

equilibrium with liquid containing

magnesium and zinc, composition of

the liquid phase lying on the curve DE.

The melting points of pure Zn and pure Mg are represented by points A and E respectively.

AB is the freezing point curve of Zn. In the area ABFA, solid zinc is in equilibrium with

liquid containing zinc and magnesium, the composition of which is given by the curve AB.

This temperature, the congruent melting

point of the compound, remains constant

till the entire liquid phase freezes. On

further cooling, the temperature of the

solid decreases. Thus, the cooling pattern

of the liquid of composition c' is similar to

that of a pure component. The formula of

the compound formed is Mg (Zn)2 which

corresponds to the composition c'.

c’

If a liquid having the composition c' is cooled, the liquid merely cools till it reaches the point C. At the point C, a solid compound, having the same composition as the liquid starts separating.


c’

CB and CD give the freezing point curves of Mg (Zn)2. Addition of zinc depresses the freezing

point of Mg(Zn)2 and the temperatures at which the solid compound Mg (Zn)2 will begin to

freeze (separate) from various liquids, composition lying between B and G, fall on the curve

CB.

Similarly CD gives the temperatures at which

the solid compound Mg(Zn)2 starts freezing

from liquids having their composition lying

between H and D. The curve CD gives the

depression in the freezing point of Mg (Zn)2

due to the addition of Mg. B is an eutectic

point at which solid zinc and solid Mg (Zn)2

are in equilibrium with liquid of composition

B. Similarly at D, another eutectic point,

solid magnesium and solid Mg(Zn)2 are in

equilibrium with liquid of composition D.


c’

This is because the compound formed is

usually not very stable and dissociates

partly. The dissociation products in the

liquid phase depress the actual melting of

the compound resulting in a rounded

melting point.

Theoretically, the curves BC and DC should meet to give a sharp point at C. But normally a

rounded maximum is observed as shown in the phase diagram.


Application of Gibbs Phase Rule on Zn-Mg System

c’

A Freezing point of Zn C=1, P=2, F=0 Fixed T

E Freezing point of Mg C=1, P=2, F=0 Fixed T

C Freezing point of Mg(Zn)2 C=2, P=2,F=0 Fixed T and composition

B

Eutectic point (Zn,Mg(Zn)2, liq. Of

composition B) C=2, P=3, F=0 Fixed T and composition

D

Eutectic point (Mg,Mg(Zn)2, liq of

composition D) C=2, P=3, F=0 Fixed T and composition

AB

Freezing point curve of Zn,

crystallization of Zn begins C=2, P=2, F=1 T or composition

BC and CD Crystallization of Mg(Zn)2 begins C=2, P=2, F=1 T or composition

ED Crystallization of Mg begins C=2, P=2, F=1 T or composition

Area ABFA Zn +liquid (composition given by AB) C=2, P=2, F=1 T or composition

Area CBGC

Mg(Zn)2 + liquid (composition given

by CB) C=2, P=2, F=1 T or composition

Area CHDC

Mg(Zn)2 + liquid

(composition given by CD) C=2, P=2, F=1 T or composition

Area EDIE

Mg + liquid

(composition given by ED) C=2, P=2, F=1 T or composition

Area below FBG

Solid mixtures of Zn and

Mg (Zn)2 C=2, P=2, F=1 T or composition

Area below HDI

Solid mixtures of Mg and

Mg (Zn)2 C=2, P=2, F=1 T or composition

Area above ABCDE

Liquid containing Zn and

Mg C=2, P=1, F=2 T and composition

Development of Microstructures in Binary Alloys

Development of Microstructures in Isomorphous Alloys


a

b

c

d

e

Equilibrium Cooling

An alloy of composition 35 wt% Ni–65 wt% Cu as it is cooled from 1300oC

Cooling of an alloy of the above composition corresponds to moving down the vertical dashed line.


a

b

At 1300oC point a, the alloy is completely liquid (of composition 35 wt% Ni–65 wt% Cu) and has the microstructure.

As cooling begins, no microstructural or compositional changes . until the liquidus line (point b, ~1260 )

At this point, the first solid α begins to form, which has a composition dictated by the tie line drawn at this temperature [i.e., 46 wt% Ni–54 wt% Cu, noted as (46 Ni)];the composition of liquid is still approximately 35 wt% Ni–65 wt% Cu [L(35 Ni)]


a

b

c

Note that the overall alloy composition (35 wt% Ni–65 wt% Cu) remains unchanged during cooling even though there is a redistribution of copper and nickel between the phases.

At (1250oC)point c , the compositions of the liquid and phases are 32 wt% Ni–68 wt% Cu [L(32 Ni)] and 43 wt% Ni–57 wt% Cu [ (43 Ni)],respectively.

The solidification process is virtually complete at (1220oC) about point d; the composition of the solid is approximately 35 wt% Ni–65 wt% Cu (the overall alloy composition) while that of the last remaining liquid is 24 wt% Ni–76 wt% Cu.

d


a

b

c

d

e

Upon crossing the solidus line, this remaining

liquid solidifies; the final product then is a

polycrystalline-phase solid solution that has a

uniform 35 wt% Ni–65 wt% Cu composition

(point e). Subsequent cooling will produce no

microstructural or compositional alterations.


Non-Equilibrium Cooling

a‘

b'

Let us begin cooling from a temperature of

about 1300oC; a’ point liquid region. This liquid

has a composition of 35 wt% Ni–65 wt% Cu

,L(35 Ni) , and no changes occur while cooling

through the liquid phase region At point

b’(approximately ) 1260oC, α-phase particles

begin to form, which, from the tie line

constructed, have a composition of 46 wt% Ni–

54 wt% Cu [α(46 Ni)].

a‘

b'

c'

d'

e'


At point c’ (1240oC), the liquid composition is

29 wt% Ni–71 wt% Cu; at this temperature the

composition α phase that solidified is 40 wt%

Ni–60 wt% Cu, (40 Ni). Diffusion in the solid

phase is relatively slow, the α phase that

formed at point b has not changed

composition appreciably—that is, it is still

about 46 wt% Ni—and the composition of the

α grains has continuously changed with radial

position, from 46 wt% Ni at grain centers to 40

wt% Ni at the outer grain perimeters.


At point (d’,1220oC ) and for equilibrium cooling rates, solidification should be completed. However, for this non-equilibrium situation, there is still an appreciable proportion of liquid remaining, and the α phase that is forming has a composition of 35 wt% Ni [ (35 Ni)]; also the average -phase composition at this point is 38 wt% Ni [ (38 Ni)].

Non-equilibrium solidification finally reaches completion at point ( e’,1205oC). The composition of the last phase to solidify at this point is about 31 wt% Ni; the average composition of the α phase at complete solidification is 35 wt% Ni. The inset at point (f’) shows the microstructure of the totally solid material.

Coring the distribution of the two elements within the grains is non uniform, a phenomenon termed segregation; that is, concentration gradients are established across the grains.

The center of each grain, which is the first part to freeze, is rich in the high-melting element (e.g., nickel for this Cu–Ni system), whereas the concentration of the low-melting element increases with position from this region to the grain boundary. This is termed a cored structure, which gives rise to less than the optimal properties.

Coring may be eliminated by a homogenization heat treatment carried out at a temperature below the solidus point for the particular alloy composition. During this process, atomic diffusion occurs, which produces compositionally homogeneous grains.


Mechanical Properties in Isomorphous Alloys

For all temperatures and compositions

below the melting temperature of the

lowest-melting component, only a single

solid phase will exist. Therefore, each

component will experience solid-solution

strengthening or an increase in strength

and hardness by additions of the other

component.

Mechanical Properties in Isomorphous Alloys

Ductility(%EL)–composition behavior,

which is just the opposite of tensile

strength; that is, ductility decreases

with additions of the second

component, and the curve exhibits

a minimum.

Development of Microstructures in Eutectic Alloys

First case

For compositions

ranging between a pure

component and the

maximum solid solubility

for that component at

room temperature

( 20oC).

For the lead–tin system, this includes lead-rich alloys containing between 0 and about 2

wt% Sn (for the αphase solid solution), and also between approximately 99 wt% Sn and

pure tin (for the β phase).


For lead–tin system, this includes lead-rich

alloys containing between 0 and about 2 wt%

Sn (for the α phase solid solution), and also

between approximately 99 wt% Sn and pure

tin (for the β phase).

Alloy of composition C1 , slowly cooled from

a temperature within the liquid- phase

region, this corresponds to moving down the

dashed vertical line.

No subsequent changes will occur upon

cooling to room temperature.

At 330oC,α will begin to form

Second case

Compositions that range between the room

temperature solubility limit and the maximum

solid solubility at the eutectic temperature.

Compositions extend from about 2 wt% Sn to

18.3 wt% Sn (for lead-rich alloys) and from

97.8 wt% Sn to approx 99 wt% Sn (for tin-rich

alloys).

Composition ,cooled along the vertical line xx’


Upon crossing the solvus line, the α solid

solubility is exceeded, results in the formation

of small β-phase particles.

With continued cooling, these particles will

grow in size because the mass fraction of the

phase increases slightly with decreasing

temperature.


Third case Involves solidification of the eutectic composition, 61.9 wt% Sn(C3) . Alloy having this composition is cooled from a temperature within the liquid-phase region (e.g., 250C) down the vertical line yy’

No changes occur until reach the

(183oC) eutectic temperature.

Upon crossing the eutectic isotherm, the liquid transforms to the two α and β phases.


L (61.9 wt% Sn) α (18.3 wt% Sn) + β(97.8 wt% Sn)

During this transformation, there

must necessarily be a redistribution

of the lead and tin components,

inasmuch as the α and β phases have

different compositions neither of

which is the same as that of the

liquid.

This redistribution is accomplished

by atomic diffusion.



The microstructure of the solid that results from this

transformation consists of alternating layers (sometimes

called lamellae) of the αand β phases that form

simultaneously during the transformation.

This is called Eutectic Structure

Photomicrograph showing the microstructure of a lead–tin alloy of eutectic composition.

This microstructure consists of

alternating layers of a lead rich α

-phase solid solution (dark

layers), and a tin-rich β -phase

solid solution (light layers).

Sn-50%In. Globules of tin rich intermetallic phase (light) in a matrix of dark indium –rich intermetallic phase

Al-13% Si. Acicular structure consisting of short ,angular particles of Si(dark) in a matrix of Aluminum.

Eutectic Microstructures in different Alloys

Al-33%Cu. Lamellar structure consisting of dark platelets of CuAl2 and light platelets of aluminum solid solution

Mg-37%Sn. Lamellar structure consisting of Mg2Sn “Chinese script”(dark) in am matrix of Mg Solid Solution.

Eutectic Microstructures in different Alloys


Fourth case:

system includes all compositions other

than the eutectic that, when cooled,

cross the eutectic isotherm.

Composition, which lies to the left of

the eutectic; as the temperature is

lowered, we move down the zz’ line

beginning at point j.

Photomicrograph showing the microstructure of a

lead–tin alloy of composition 50 wt% Sn–50 wt% Pb.


Hypereutectic Alloy

HYPOEUTECTIC & HYPEREUTECTIC

Physical/Mechanical Properties in Eutectic Alloys

Properties of Alloys depends on individual characteristics of phases and upon the mode of distribution of these phases in the microstructure.

If phase behave as solid solution whose properties very within the composition range covered in same manner as those in isomorphous solid solutions.

Properties changes with first addition of the solute to the solvent component.

Hardness and Tensile strength increases with alloying . Elongation and Electrical conductivity decreases.

When two phases occur together in a structure, the resulting properties of the mixture

resembles most nearly those of physically continuous phase.

The phase which forms matrix ,in which particles of the other phase are embedded. As the

quantity of embedded phase increases with composition, its properties are gradually

changes.

These changes are linear in most system, but in some cases these deviates widely.

These deviations are due to

1-Inhomogenity of individual phase

2-Peculiarties of particle shape that cause one of the phase to remain physically continue over

a disproportionately large range of composition.

3-Variation of particle size across the two phase zone.

Physical/Mechanical Properties in Eutectic Alloys

Eutectoid Reaction

Eutectoid Reaction in Binary Phase Diagrams

copper–zinc system

at 560oC and 74

wt% Zn–26 wt% Cu.

Upon cooling, a solid

phase δ transforms

into two other solid

phases (γ and ε)

according to the

reaction δ ε+γ

The reverse reaction

occurs upon heating. It

is called a eutectoid (or

eutectic-like) reaction,

and the invariant point

,E and the horizontal

tie line at 560oC are

termed the eutectoid

and eutectoid

isotherm, respectively.


Difference of “eutectoid”

from “eutectic” is that

one solid phase instead

of a liquid transforms into

two other solid phases at

a single temperature. A

eutectoid reaction is

found in the iron–carbon

system that is very

important in the heat

treating of steels.


Microstructures of Eutectoid Reaction

(A) Hypoeutectoid steel ,0.3%C,Light areas are proeutectoid ferrite(alpha)and dark areas

are pearlite.500X

(B) Eutectoid steel,0.8 % carbon, typically pearlite.500X

(C) Hypereutectoid steel ,1.2% carbon. Thin bands of proeutectoid Cementite, light gray

,outline the grains of pearlite. 500X

Lectures MM231

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