Solidificatio n

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SOLIDIFICATION OF METALS

(To be completed)Prof. H. K. Khaira

Professor, Deptt. of MSME

M.A.N.I.T., Bhopal


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Contents

Solidification of Metals

Cooling Curves


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Solidification of a pure metal.


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1. During solidification, the liquid changes in to solid during cooling.

2. The energy of liquid is less than that of the solid above the melting point. Hence

liquid is stable above the melting point.

3. Below the melting point, the energy of liquid becomes more than that of the solid.

4. Hence below the melting point, the solid becomes more stable than the liquid.

5. Therefore at the melting point, liquid gets converted in to solid during cooling.6. This transformation of liquid into solid below melting point is known as

solidification.


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Cooling curve for a pure metal showing

possible undercooling. The transformation

temperature, as shown on theequilibrium diagram,represents the point at whichthe free energy of the solid

phase is equal to that of theliquid phase.

Thus, we may consider thetransition, as given in a phasediagram, to occur when thefree energy change, GV, is

infinitesimally small andnegative, i.e. when a small butpositive driving force existsdue to undercooling.


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Nucleation and Growth of Crystals

At the solidification temperature,atoms from the liquid, such asmolten metal, begin to bondtogether and start to form crystals.

The moment a crystal begins to growis know as nucleus and the pointwhere it occurs is the nucleationpoint.

When a metal begins to solidify,multiple crystals begin to grow in theliquid.

The final sizes of the individualcrystals depend on the number of

nucleation points. The crystals increase in size by the

progressive addition of atoms andgrow until they impinge uponadjacent growing crystal.

a)Nucleation of crystals, b)crystal growth, c)

irregular grains form as crystals grow together,

d)grain boundaries as seen in a microscope.


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Cooling Curve


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Cooling Curve

A cooling curve is a graphical plot of the

changes in temperature with time for a

material over the entire temperature range

through which it cools.


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Cooling Curve for Pure Metals

Under equilibrium conditions, all metals

exhibit a definite melting or freezing point.

If a cooling curve is plotted for a pure metal, It

will show a horizontal line at the melting or

freezing temperature.


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Cooling Curve of Alloys

In this method, alloys with different compositions are melted and then the

temperature of the mixture is measured at certain time intervals while

cooling back to room temperature.

A cooling curve for each mixture is constructed and the initial and final

phase change temperatures are determined.


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Cooling Curve

Then these temperatures are used for the construction of the

phase diagrams


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Undercooling during


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Cooling curve for a solid solution.

In case of alloys, the solidification does not

take place at a constant temperature.

In such cases, the solidification occure in a

range of temperature.


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Series of cooling curves for different alloys in a completely

soluble system. The dotted lines indicate the form of the phase

diagram


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Phase Diagram of Solid Solution


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Cooling Curves for Solid Solution


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Mechanism of Solidification of Metals

The solidification of metals occur by

nucleation and growth transformation.

In nucleation and growth transformation, the

nuclei of the solid phase are formed and then

they grow.


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Nucleation and Growth

Transformation

The Nucleation and Growth Transformation

may be of two types

1. Homogeneous Nucleation

2. Heterogeneous Nucleation


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Homogeneous Nucleation

Homogeneous NucleationFormation of a

critically sized solid from the liquid by

clustering together of a large number of atoms

at a high undercooling (without an externalinterface).


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The transformation temperature, as shown onthe equilibrium diagram, represents the pointat which the free energy of the solid phase is

equal to that of the liquid phase. Thus, we may consider the transition, as given

in a phase diagram, to occur when the freeenergy change, GV, is infinitesimally smalland negative, i.e. when a small but positivedriving force exists.


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Cooling curve for a pure metal showing possible

undercooling.


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Energy barrier separating structural

states.


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Free Energy Changes

The second phase has lower free energy than

the first phase

Activation energy may be required for the

transformation to occur as shown above.


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Transformation(1) The volume free energy GVfree energy difference between the liquid and solid

GV= 4/3r3Gv

(2) The surface energy Gsthe energy needed to create a surface for the spherical

particles

Gs= 4r2

specific surface energy of the particle

Total free energy Change

GT= GV+ Gs


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Transformation

Embryo - An embryo is a tiny particle of solid that

forms from the liquid as atoms cluster together.

The embryo is unstable and may either grow in to

a stable nucleus or re-dissolve. NucleusIt is a tiny particle of solid that forms

from the liquid as atoms cluster together.

Because these particles are large enough to bestable, nucleation has occurred and growth of the

solid can begin.


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Critical Size of Nucleus

The minimum size that must be formed by

atoms clustering together in the liquid before

the solid particle is stable and begins to grow.


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r* : critical radius

(where GTreaches the maximum) liquid metal is cooled below

freezing point, slow movingatoms bond together to create

homogeneous nuclei

Nucleuslarger than critical

size, can grow into a crystal Embryosmaller than critical

size, continuously beingformed and redissolved in themolten metal

For Critical size of nucleus

d(GT)/dr = 0 when r = r*

Or r* = - 2/Gv


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critical radius versus undercooling


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critical nucleus size - Example

calculate the critical radius of homogeneous

nucleus forms from pure liquid Cu.

Assume

T = 0.2Tm, = 1.77 10-7 J/cm2

Tm= 1083oC, Hf= 1826 J/cm

3

calculate the number of atoms in criticalsizednucleus at this undercooling


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critical nucleus size - Solution

T = 0.2Tm= 1356 K 0.2 = 271 K2Tm 2(1.77 10-7 J/cm

2)(1356 K )

r* = = = 9.70 10-8cm

Hf T (1826 J/cm3)(271 K)

volume of nucleus = 4/3 (9.70 10-8 cm)3= 3.82 10-21cm3

Cu: FCC structure, unit length a = 3.61 10-8 cm

4 atoms per unit cell

volume of unit cell = (3.61 10-8 cm)3

= 4.70 10-23

cm3

3.82 10-21cm3

number of atoms = 4 = 325 atoms

4.70 10-23cm3


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critical nucleus size

d(GT)/dr = 0 when r = r*

r* = - 2/Gv


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( ) Eff f l i h f f l


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(a) Effect of nucleus size on the free energy of nucleus

formation. (b) Effect of undercooling on the rate of

precipitation.


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Homogeneous Nucleation

Quantitatively, since Gvdepends on thevolume of the nucleus and GSis proportionalto its surface area, we can write for a spherical

nucleus of radius r G = (4 r3 /3) Gv+ 4 r

2

where Gvis the bulk free energy changeinvolved in the formation of the nucleus ofunit volume and is the surface energy of unitarea.


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Critical Size of Nucleus

When the nuclei are small the positive surface energy term predominates,while when they are large the negative volume term predominates, sothat the change in free energy as a function of nucleus size. This indicatesthat a critical nucleus size exists below which the free energy increases asthe nucleus grows, and above which further growth can proceed with alowering of free energy; Gmax may be considered as the energy or work

of nucleation W. Both rcand W may be calculated since

d G/dr = 4 r2Gv+ 8 r= 0 when r = rcand thus

rc= -2/ G v

Substituting for rc gives

W =16 3/3 Gv2


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The probability of an atom having sufficientenergy to jump the barrier is given, from theMaxwellBoltzmann distribution law, asproportional to exp [Q/kT] where k isBoltzmanns constant, T is the temperature and

Q is usually expressed as the energy per atom inelectron volts.1

The rate of reaction is given byRate = A exp [- Q/kT]

where A is a constant


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The surface energy factor is not strongly dependent ontemperature, but the greater the degree of undercooling orsupersaturation, the greater is the release of chemical freeenergy and the smaller the critical nucleus size and energyof nucleation.

This can be shown analytically sinceGv= H - TS,

and at T = Te, Gv= 0, so that H = Te S.

It therefore follows that

Gv =(Te -T) S = TS and because Gv is proportional to T, then

W is proportional to S3/ T2


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Heterogeneous Nucleation


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Heterogeneous NucleationFormation of a

critically sized solid from the liquid on an

impurity surface.

heterogeneous nucleation occurs in a liquid

on the surface of its container, insoluble

impurities and other structural materials that

lower the critical free energy required to forma stable nucleus


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Heterogeneous Transformation

In practice, homogeneous nucleation rarely

takes place and heterogeneous nucleation

occurs either on the mould walls or on

insoluble impurity particles.

A reduction in the interfacial energy would

facilitate nucleation at small values of T.

This occurs at a mould wall or pre-existingsolid particle


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Chill-cast ingot structure


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crystal growth and grain formation

nuclei crystals grains polycrystallinesolidified metal containing many crystals

grainscrystals in solidified metal

grain boundariesthe surfaces between the grains

two major types of grain structures:(1) equiaxed grainscrystals grow about equally in alldirections, commonly found adjacent to a cold moldwall

(2) columnar grainslong, thin, coarse grains, created

when metal solidifies rather slow in the presence of asteep temperature gradient. columnar grains growperpendicular to the mold surface


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Ingot Structure

Al ingot

N l ti d G th


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Transformation in solid solution

N l ti d G th


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Transformation in solid solution

wt% Ni20

120 0

130 0

3 0 4 0 5 0110 0

L(liquid)

a

(solid)

T(C)

A

35C0

L: 35wt%Ni

46354332

a: 43 wt% Ni

L: 32 wt% Ni

Ba: 46 wt% Ni

L: 35 wt% Ni

C

EL: 24 wt% Ni

a

: 36 wt% Ni

24 36D

N l ti d G th


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Transformation

The factors which determine the rate of phase

change are:

(1) the rate of nucleation, N (i.e. the number

of nuclei formed in unit volume in unit time)

and

(2) the rate of growth, G (i.e. the rate of

increase in radius with time)


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Dendrites

In metals, the crystals that form in the liquid during freezinggenerally follow a pattern consisting of a main branch with manyappendages. A crystal with this morphology slightly resembles apine tree and is called a dendrite, which means branching.

The formation of dendrites occurs because crystals grow in definedplanes due to the crystal lattice they create.

The figure to the right shows how a cubic crystal can grow in a meltin three dimensions, which correspond to the six faces of the cube.

For clarity of illustration, the adding of unit cells with continuedsolidification from the six faces is shown simply as lines.

Secondary dendrite arms branch off the primary arm, and tertiary

arms off the secondary arms and etcetera.


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Dendrites


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Dendrites

During freezing of a polycrystalline material, manydendritic crystals form and grow until they eventuallybecome large enough to impinge upon each other.

Eventually, the interdendriticspaces between the

dendrite arms crystallize to yield a more regular crystal. The original dendritic pattern may not be apparent

when examining the microstructure of a material.

However, dendrites can often be seen in solidification

voids that sometimes occur in castings or welds, asshown in the next slide..


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Dendrites

Computer simulated image of dendritic growth using a cellular automata technique.


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Notice the branching on the dendrites. Photograph courtesy of the Institute of

Materials, based on the work of U. Dilthey, V. Pavlik and T. Reichel, Mathematical

Modelling of Weld Phenomena III, eds H. Cerjak and H. Bhadeshia, Institute of

Materials, 1997.


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(A) Time evolution of the interface morphology for SCN/rhodamine 6G at constant pulling


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(A) Time evolution of the interface morphology for SCN/rhodamine 6G at constant pulling

speed V (V = 3.11 m/s, G = 2.8 K/cm, C = 0.325 wt%).

Losert W et al. PNAS 1998;95:431-438

1998 by National Academy of Sciences


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Shrinkage

Most materials contract or shrink during solidification and cooling.Shrinkage is the result of: Contraction of the liquid as it cools prior to its solidification

Contraction during phase change from a liquid to solid

Contraction of the solid as it continues to cool to ambient temperature.

Shrinkage can sometimes cause cracking to occur in component as it

solidifies. Since the coolest area of a volume of liquid is where it contacts a mold or

die, solidification usually begins first at this surface.

As the crystals grow inward, the material continues to shrink.

If the solid surface is too rigid and will not deform to accommodate theinternal shrinkage, the stresses can become high enough to exceed thetensile strength of the material and cause a crack to form.

Shrinkage cavitation sometimes occurs because as a material solidifiesinward, shrinkage occurred to such an extent that there is not enoughatoms present to fill the available space and a void is left.

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