Solidification of metals by Hari prasad

Hari Prasad-Assistant Professor

Learning Objectives

• To know how does

solidification affect casting and

welding processes.

• Differentiate homogeneous and

heterogeneous nucleation.


What is solidification?

• Solidification is the process where liquid metal

transforms into solid upon cooling

• The structure produced by solidification,

particularly the grain size and grain shape,

affects to a large extent the properties of the

products

• At any temp, the thermodynamically stable state is

the one which has the lowest free energy and

consequently, any other state tends to change the

stable form.


Latent

heatSuper

heat

The heat that is added

to convert all the solid

into liquid at the

constant temperature

The heat is further

added for the metal to

remain in molten state

Entropy

Is a thermodynamic property

that is the measure of a system’s

thermal energy per unit

temperature that is unavailable

for doing useful work

The terms

must be

known


• Gibbs free energy (G) of any system said to

be minimum when the same is at

equilibrium.

G = H-TS

• ‘G’ is a function of ‘H’ (enthalpy) and ‘S’

(entropy)

• Important parameter is change in free

energy ‘𝞓G’

• A transformation will occur spontaneously

only when G has a negative value


Ice melting in

a warm room

is a common

example of

increasing

entropy


• A crystalline solid has lower internal energy

and high degree of order, or lower entropy as

compared to the liquid-phase

i.e.,

• Liquid has higher internal energy (equal to the

heat of fusion) and higher entropy due to the

more random structure


• Transformation from liquid metal to solid metal

is accompanied by a shrinkage in the volume

• This volume shrinkage takes place in three

stages:

1. Liquid – Liquid

2. Liquid – Solid

3. Solid – Solid


Melting of Metals

Time, Enthalpy

Temp

Tm

Latent

HeatSuper Heat

Solid + Liquid


Time

Temp

Super Heat

Latent Heat

Solid + Liquid

Freezing of Metals


∆𝐆

∆𝑻

Fre

e e

ne

rg

y (

G)

Temp

Free energy

curve

for solid (Gx )

Free energy curve

for liquid(Gl)

Melting

Solidification


• If we take a simple case of pure metal

transforming to solid crystal of pure metal X as:

L X (Solid)

• A crystalline solid has the lower internal energy

and high degree of order, or low entropy as

compared to the liquid phase

i.e.,

• Liquid has higher internal energy (equal to the

heat of fusion) and higher entropy


∆𝐆

∆𝑻

Free e

nerg

y (

G)

Temp

Free energy curve

for solid (Gx )

Free energy curve

for liquid(Gl)

Melting

Solidification


• With the increase of temperature, the free-energy curve of the liquid phase falls more

steeply than the solid-phase

• At Tm, the equilibrium melting point, the free energies of both the phases are equal

• Above Tm, the liquid has a lower free energy than the crystalline solid ‘X’, i.e., liquid is more

stableThe solidification reaction will not occur

under such conditions as the free energy

change, ∆𝑮 for the reaction is positive

At the melting temperature, where the two

curves cross, the solid and liquid phases are in

equilibrium.

Below Tm, the free energy of the

crystalline solid X, is less than the liquid

phase.

The free energy change for the reaction is

negative

• In alloys, commencement of solidification is easy since

the foreign atoms act as source of nucleation

• But pure metals experience difficulties in

commencing solidification. (there are no foreign

atoms to form nuclei)

• In such cases the metal cools below its freezing

temperature and actual solidification begins at the

same point (shown in pic in the next slide)

Undercooling (or) Supercooling in pure

metals

Supercooling, also known as

undercooling, is the process of lowering

the temperature of a liquid or a gas below its

freezing point without it becoming a solid


Undercooling (or) Supercooling in pure

metals


Solidification of alloys• Solidification in alloys takes place in the same manner but

with exceptions

• They solidify over a range of temp rather than at a constanttemp

i. Begin solidification at one temp and end at anothertemp (Solid solution)

ii. Begin and end solidification at a constant temp justlike in pure metals (pure eutectics)

iii. Begin solidification like a solid-solution and end itlike a eutectic

The local solidification time can be calculated using Chvorinov's rule, which is:

𝒕 = 𝑩𝑽

𝑨

𝒏

Where t is the solidification time, V is the volume of the casting, A is the surface area ofthe casting that contacts the mould, n is a constant, and B is the mould constant.It is most useful in determining if a riser will solidify before the casting, because if theriser does solidify first then it is worthless


a

bc

d

Solid solution

Time

Temp



Solid solution

a

b c

d

Pure eutectic

Time

Temp


a

b

c d

Partly solution and partly eutectic

Time

Temp

e


Understanding solidification

Solidification

Nucleation

Growth


• The basic solidification process involves nucleation

and growth

• Nucleation involves the appearance of very small

particles, or nuclei of the new phase (often

consisting of only a few hundred atoms), which are

capable of growing.

• During the growth stage these nuclei increase in

size, which results in the disappearance of some (or

all) of the parent phase.

• The transformation reaches completion if the

growth of these new phase particles is allowed to

proceed until the equilibrium fraction is attained


a) Nucleation of crystals,

b) crystal growth,

c) irregular grains form as

crystals grow together,

d) grain boundaries as

seen in a microscope.


Types of Nucleation

Nuclei of the

new phase

form uniformly

throughout the

parent phase

Nuclei form

preferentially at

structural

inhomogeneities,

insoluble impurities,

grain boundaries,

dislocations, and so

on.

Homogeneous

Nucleation

Heterogeneous

Nucleation


Homogeneous nucleation

• Prominent is pure metals

• Nuclei of the solid phase form in the interior of

the liquid as atoms cluster together


• Each nucleus is spherical and has a radius ‘r’.

• This situation is represented schematically

Solid

𝐴𝑟𝑒𝑎 = 4𝜋𝑟2

𝑉𝑜𝑙𝑢𝑚𝑒 =4

3𝜋𝑟3

Solid-Liquid

interface


• There are two contributions to the total free energychange that accompany a solidification transformation.

• The first is the free energy difference between the solid andliquid phases, or the volume free energy 𝞓Gv and thevolume of spherical nucleus

𝟒

𝟑𝝅𝒓𝟑

• The second energy contribution results from theformation of the solid–liquid phase boundary during thesolidification transformation.

• Associated with this boundary is a surface free energy 𝜸(positive)

∆𝑮𝒔 = 𝟒𝝅𝒓𝟐𝜸• Latent heat released by atoms is:

∆𝑮𝒗 = −𝟒

𝟑𝝅𝒓𝟑 ∆𝑮

*Negative value is taken since the temp is consideredbelow the equilibrium solidification temperature


• Finally, the total free energy change is equal

to the sum of these two contributions—that is:

∆𝐺∗= ∆𝑮𝒗+ ∆𝑮𝒔 = −

𝟒

𝟑𝝅𝒓𝟑 ∆𝑮 + 𝟒𝝅𝒓𝟐𝜸

These volume, surface, and total free energy contributions are

plotted schematically as a function of nucleus radius in

Figures


• From the fig. it is clearthat as the particle radiusincreases, the net freeenergy ∆G also increasestill the nucleus reaches acritical radius ‘r*’.

• Further increase inparticle radius the freeenergy decreases and evengoes to negative.

• In order for grain growthto take place around aparticular nucleus, itshould have reached thecritical radius


• The size of the critical radius can be estimated

by differentiating ∆𝐺∗

with respect to ‘r’ and

equating by zero𝒅

𝒅𝒓∆𝑮 ∗ =

𝒅

𝒅𝒓−𝟒

𝟑𝝅𝒓𝟑 ∆𝑮 + 𝟒𝝅𝒓𝟐𝜸 = 𝟎

−𝟒𝝅𝒓𝟐∆𝑮 + 𝟖𝝅𝒓𝜸 = 𝟎

r = r* = 𝟐𝜸

∆𝑮

If we substitute r/r* in ∆𝑮 ∗

∆𝑮 ∗ = 𝟏𝟔𝝅𝜸𝟑

𝟑 ∆𝑮∗ 𝟐


Heterogeneous nucleation

• It is easier for nucleation to occur at surfaces

and interfaces than at other sites.

• Nucleation occurs with the help of impurities

or chemical inhomogeneities.

• Impurities can be insoluble like sand particles

or alloying elements

• Nuclei are formed on the surfaces of the above

possible surfaces often called the ‘substrate’


Nucleation of carbon dioxide bubbles around a finger


Two essential things must happen:

1. The substrate must be wetted by the liquid metal

2. The contact angle/wetting angle (𝜽) of the cap-

shaped nucleus should be less than 90o

Substrate 𝜹

Liquid 𝜶

Cap

𝜽

Solid 𝜷

𝛾𝑆𝐼 = 𝑆𝑜𝑙𝑖𝑑 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 (𝜸𝞫𝞭)𝛾SL = Solid-liquid interfacial energy (𝜸𝞪𝞫)

𝛾IL = Liquid interfacial energy (𝜸𝞪𝞭)

𝜸𝑰𝑳 = 𝜸𝑺𝑰+ 𝜸𝑺𝑳 𝒄𝒐𝒔𝜽𝜸𝞪𝞭 = 𝜸𝞫𝞭+ 𝜸𝞪𝞫 𝒄𝒐𝒔𝜽 or

𝜽 = 𝟑𝟔𝟎𝒐


A typical cast metal structure

Coarse grain structure can be converted into fine grain structure by

grain refinement. This can be achieved by high cooling rates, low

pouring temp, and addition of inoculating agentHari Prasad-Assistant Professor

• The chill zone is named so because it occurs at the walls of

the mould where the wall chills the material.

• Here is where the nucleation phase of the solidification

process takes place.

• As more heat is removed the grains grow towards the

centre of the casting.

• These are thin, long columns that are perpendicular to the

casting surface, which are undesirable because they

have anisotropic properties.

• Finally, in the centre the equiaxed zone contains spherical,

randomly oriented crystals.

• These are desirable because they have isotropic properties.

• The creation of this zone can be promoted by using a low

pouring temperature, alloy inclusions, or inoculants


a) Columnar grainsc) Equiaxed grains

b) Partially columnar and

partially equiaxed grains


Coring

• In thermal equilibrium diagram, it is assumed that cooling will be slow

enough for equilibrium to be maintained.

• However, during actual operating condition where rate of cooling is more

rapid, e.g. the production of Cu-Ni alloy, there is insufficient time for

complete diffusion to take place.

• This leads to lack of uniformity in the structure of the metal. This is

termed a cored structure, which give rise to less than the optimal

properties.

• As a casting having a cored structure is reheated, grain boundary regions

will melt first in as much as they are richer in low-melting component.

• This produces a sudden loss in mechanical integrity due to the thin liquid

film that separates the grains.

• Moreover, this melting may begin at a temperature below the equilibrium

solidus temperature of the alloy.

• 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.Hari Prasad-Assistant Professor

Solid solutions

• A solid solution is asolid-state solution ofone or more solutes in asolvent.

• Such a mixture isconsidered a solutionrather than acompound when thecrystal structure of thesolvent remainsunchanged by additionof the solutes, andwhen the mixtureremains in a singlehomogeneous phase.


• The solute may incorporate into the solvent crystal

lattice substitutionally, by replacing a solvent

particle in the lattice, or interstitially, by fitting into

the space between solvent particles.

Substitutional solid soln.

(e.g., Cu in Ni)

Interstitial solid soln.

(e.g., C in Fe)


• W. Hume – Rothery rule– 1. r (atomic radius) < 15%

– 2. Proximity in periodic table

• i.e., similar electronegativities

– 3. Same crystal structure for pure metals

– 4. Valency

• Other factors being equal, a metal will have more of atendency to dissolve another metal of higher valencythan one of a lower valency.

Conditions for substitutional solid

solution (S.S.)


• A familiar example of substitutional solid solutionis found for copper and nickel to form monel.

• Polymorphous metals may possess unlimitedsolubility within a single modification of the spacelattice.

• For example, Fe𝛼 can form a continuous series ofsolid solutions with Cr (BCC lattices) and Fe𝛾, acontinuous series of solid solutions with Ni (FCClattices).

• The formation of solid solutions is alwaysassociated with an increase of electric resistanceand decrease of the temperature coefficient ofelectric resistance.

• Solid solutions are usually less plastic (except forcopper-based solid solutions) and always harderand stronger than pure metals.


Intermediate phases

• If a solid solution neither forms a substitutional

type nor interstitial type, it certainly forms an

intermediate compound.

• And the compound is said to be “intermediate

phase” or “intermediate compound” or

“intermetallic” if it has metal in it.

• If one element has more electropositivity and the

other more electronegativity, then there is greater

likelihood that they will form an intermetallic

compound instead of a substitutional solid solution.


Common intermediate compounds

• Intermetallic or valency compounds

• Interstitial compounds

• Electron compounds


Crystals formed by various elements and having their own type of

crystal lattice which differs from the crystal lattices of the component

elements are called intermediate phases.

Intermediate phases

Intermetallic/valencycompounds (Ni3Al)

Interstitial compounds

(Fe3C)

Electron compounds

(Cu9Al4)

Formed between

chemically

dissimilar metals.

Follow the

valence rules.

Have complex

crystal structure

These are of

variable

composition

and don’t

obey valence

rules

Very hard in

nature. Very

similar to

interstitial solid

solutions except

they have fixed

compositions


Intermetallic compound:

• A compound formed of two or more metals that

has its own unique composition, structure, and

properties

• Nonstoichiometric intermetallic compound A

phase formed by the combination of two

components

• into a compound having a structure and

properties different from either component.

• The nonstoichiometric compound has a variable

ratio of the components present in the compound


Interstitial compounds

• Fe3C (iron carbide), a common constituent of steels,

is an example of intermediate phase (interstitial

compound).

• It has a complex crystal structure referred to an

orthorhombic lattice and is hard and brittle.


Electron compounds

• The intermediate phases of variable composition

which do not obey the valency law are called electron

phases or electron compounds.

• Hume Rothery has shown that electron phases occur

at certain definite value of free electron to atom

ratio in the alloy such as 3 : 2, 21 : 13 and 7 : 4.

• Few typical examples of electron phases are CuZn (3 :

2), Cu5Zn8 (21 : 13) and CuZn3 (7 : 4).


Solidification of metals by Hari prasad

Engineering

Transcript of Solidification of metals by Hari prasad