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
heat
Super
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
Heat
Super Heat
Solid + Liquid

Time
Temp
Super Heat
Latent Heat
Solid + Liquid
Freezing of Metals

∆𝐆
∆𝑻
Freeenergy(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
Freeenergy(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
stable
The 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 constant
temp
i. Begin solidification at one temp and end at another
temp (Solid solution)
ii. Begin and end solidification at a constant temp just
like in pure metals (pure eutectics)
iii. Begin solidification like a solid-solution and end it
like a eutectic
The local solidification time can be calculated using Chvorinov's rule, which is:
𝒕 = 𝑩
𝑽
𝑨
𝒏
Where t is the solidification time, V is the volume of the casting, A is the surface area of
the 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 the
riser does solidify first then it is worthless

a
b
c
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
3
𝜋𝑟3
Solid-Liquid
interface

• There are two contributions to the total free energy
change that accompany a solidification transformation.
• The first is the free energy difference between the solid and
liquid phases, or the volume free energy 𝞓Gv and the
volume of spherical nucleus
𝟒
𝟑
𝝅𝒓 𝟑
• The second energy contribution results from the
formation of the solid–liquid phase boundary during the
solidification transformation.
• Associated with this boundary is a surface free energy 𝜸
(positive)
∆𝑮𝒔 = 𝟒𝝅𝒓 𝟐 𝜸
• Latent heat released by atoms is:
∆𝑮𝒗 = −
𝟒
𝟑
𝝅𝒓 𝟑 ∆𝑮
*Negative value is taken since the temp is considered
below the equilibrium solidification temperature

• Finally, the total free energy change is equal
to the sum of these two contributions—that is:
∆𝐺
∗
= ∆𝑮 𝒗 + ∆𝑮 𝒔 = −
𝟒
𝟑
𝝅𝒓 𝟑 ∆𝑮 + 𝟒𝝅𝒓 𝟐 𝜸
These volume, surface, and total free energy contributions are
plotted schematically as a function of nucleus radius in
Figures

• From the fig. it is clear
that as the particle radius
increases, the net free
energy ∆ G also increases
till the nucleus reaches a
critical radius ‘r*’.
• Further increase in
particle radius the free
energy decreases and even
goes to negative.
• In order for grain growth
to take place around a
particular nucleus, it
should have reached the
critical radius

• The size of the critical radius can be estimated
by differentiating ∆𝐺
∗
with respect to ‘r’ and
equating by zero
𝒅
𝒅𝒓
∆𝑮 ∗
=
𝒅
𝒅𝒓
−
𝟒
𝟑
𝝅𝒓 𝟑 ∆𝑮 + 𝟒𝝅𝒓 𝟐 𝜸 = 𝟎
−𝟒𝝅𝒓 𝟐∆𝑮 + 𝟖𝝅𝒓𝜸 = 𝟎
r = r* =
𝟐𝜸
∆𝑮
If we substitute r/r* in ∆𝑮 ∗
∆𝑮 ∗
=
𝟏𝟔𝝅𝜸 𝟑
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
𝛾 𝑆𝐼 = 𝑆𝑜𝑙𝑖𝑑 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 ( 𝜸 𝞫𝞭)
𝛾SL = Solid-liquid interfacial energy (𝜸 𝞪𝞫)
𝛾IL = Liquid interfacial energy (𝜸 𝞪𝞭)
𝜸𝑰𝑳 = 𝜸 𝑺𝑰 + 𝜸 𝑺𝑳 𝒄𝒐𝒔𝜽𝜸 𝞪𝞭 = 𝜸 𝞫𝞭 + 𝜸 𝞪𝞫 𝒄𝒐𝒔𝜽 or
𝜽 = 𝟑𝟔𝟎 𝒐

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 agent

• 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 grains
c) 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.

Solid solutions
• A solid solution is a
solid-state solution of
one or more solutes in a
solvent.
• Such a mixture is
considered a solution
rather than a
compound when the
crystal structure of the
solvent remains
unchanged by addition
of the solutes, and
when the mixture
remains in a single
homogeneous 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 a
tendency to dissolve another metal of higher valency
than one of a lower valency.
Conditions for substitutional solid
solution (S.S.)

• A familiar example of substitutional solid solution
is found for copper and nickel to form monel.
• Polymorphous metals may possess unlimited
solubility within a single modification of the space
lattice.
• For example, Fe 𝛼 can form a continuous series of
solid solutions with Cr (BCC lattices) and Fe 𝛾, a
continuous series of solid solutions with Ni (FCC
lattices).
• The formation of solid solutions is always
associated with an increase of electric resistance
and decrease of the temperature coefficient of
electric resistance.
• Solid solutions are usually less plastic (except for
copper-based solid solutions) and always harder
and 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/valency
compounds (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

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