Learning Objectives
• To know how does
solidification affect casting and
welding processes.
• Differentiate homogeneous and
heterogeneous nucleation.
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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.
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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
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• 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
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Ice melting in
a warm room
is a common
example of
increasing
entropy
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• 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
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• 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
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Melting of Metals
Time, Enthalpy
Temp
Tm
Latent
HeatSuper Heat
Solid + Liquid
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∆𝐆
∆𝑻
Fre
e e
ne
rg
y (
G)
Temp
Free energy
curve
for solid (Gx )
Free energy curve
for liquid(Gl)
Melting
Solidification
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• 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
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∆𝐆
∆𝑻
Free e
nerg
y (
G)
Temp
Free energy curve
for solid (Gx )
Free energy curve
for liquid(Gl)
Melting
Solidification
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• 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
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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
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• 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
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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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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
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Homogeneous nucleation
• Prominent is pure metals
• Nuclei of the solid phase form in the interior of
the liquid as atoms cluster together
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• Each nucleus is spherical and has a radius ‘r’.
• This situation is represented schematically
Solid
𝐴𝑟𝑒𝑎 = 4𝜋𝑟2
𝑉𝑜𝑙𝑢𝑚𝑒 =4
3𝜋𝑟3
Solid-Liquid
interface
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• 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
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• 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
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• 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
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• 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
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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’
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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
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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
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a) Columnar grainsc) Equiaxed grains
b) Partially columnar and
partially equiaxed grains
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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.
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• 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)
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• 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.)
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• 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.
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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.
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Common intermediate compounds
• Intermetallic or valency compounds
• Interstitial compounds
• Electron compounds
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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
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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
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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.
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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).
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