The document discusses solidification during metal casting. It begins by explaining the processes of nucleation and growth of solid crystals in the melt, and how impingement of growing crystals forms grains and grain boundaries. It then provides details on the mechanisms of solidification, including homogeneous and heterogeneous nucleation, planar and dendritic growth, development of ingot structure, and the effects of cooling rate. Key concepts covered are the thermodynamics and energetics of solidification, the roles of undercooling and grain structure formation.

1. Lecture 7

2. Solidification in metal casting. (a) Nucleation and growth of solid crystals in the melt.
(b) Impingement of growing solid crystals forms the grains and grain boundaries.
Overview of solidification
Development of ingot During casting
1/10/2023 2

4. Overview of solidification
Solidification
1. Nucleation
2. Growth
Homogeneous Nucleation
Heterogeneous Nucleation
Planar Growth
Dendritic Growth
1/10/2023 4

5. At any temperature, the thermodynamically stable state is the one
which has the lowest free energy.
Gibbs free energy, G = H − TS
(constant volume V)
Helmholtz free energy F = U −TS
(constant pressure P)
For most solid-liquid or solid-solid transitions it is usually more practical to
work at constant pressure, so G is the appropriate thermodynamic
potential.
Minimize
Thermodynamic equilibrium
Thermodynamic equilibrium = Temperature at which the two states
have same free energy
1/10/2023 5

6. 1/10/2023 6
• A crystalline solid has lower internal energy and high
degree of order, or lower entropy
• liquid has higher internal energy (equal to heat of
fusion) and higher entropy due to its more random
structure
• with the increase of temperature, the free-energy curve
for the liquid phase falls more steeply than the free
energy curve of solid-phase
• At the Tm, the equilibrium melting point, the free
energies of both the phases are equal. Solidification
does not occur as (free energy change), ∆g = 0, even
when kept for indefinite time.
• Above Tm, the liquid has a lower free energy than the
crystalline solid X, i.e., liquid is more stable.

7. The solidification reaction cannot occur under such
conditions as the free energy change, ∆g for the reaction
is positive.
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,
just below Tm, the magnitude of ∆g , the free energy
change is very small, and the solidification occurs very
slowly,
but at much lower temperature than Tm, that is, at large
supercooling, the magnitude of ∆g is quite large, and thus,
solidification occurs at a fast rate.

8. Energetics of solidification
L S
1/10/2023 8

9. Undercooling/Supercooling
Theoretical Actual
1/10/2023 9

10. Total free energy change for a solidification transformation
There are two contributions to the total free energy
change that accompany a solidification
transformation
surface free
energy
volume
free energy
Nucleation
1/10/2023 10

11. Nucleation
The first step of metal solidification is the creation of tiny, stable, nuclei
in the liquid metal.
 Cooling the liquid below its equilibrium freezing temperature, or
undercooling, provides the driving force for solidification.
 Once a cluster reaches a critical size, it becomes a stable nucleus and
continues to grow.
The mold walls and any solid particles present in the liquid make
nucleation easier.
Cluster of atoms Embryo Nuclei Crystals Grains
r > r*
r < r* r* = critical radius
1/10/2023 11

12. Homogeneous Nucleation and Heterogeneous Nucleation:
The distinction between them is made according to the site at which nucleating
events occur
• For the homogeneous type, nuclei of the new phase form uniformly throughout
the parent phase
• for the heterogeneous type, nuclei form preferentially at structural
inhomogeneities, such as container surfaces, insoluble impurities, grain
boundaries, dislocations, and so on

13. Nucleation
Homogeneous
Heterogeneous
Nuclei of the new phase
form uniformly
throughout the
parent phase
nuclei form at
Structural inhomogeneities,
such as container surfaces
1/10/2023 13

14. 14
Solidification: Nucleation Types
• Homogeneous nucleation
• nuclei form in the bulk of liquid metal
• requires considerable supercooling
(typically 80-300°C)
• Heterogeneous nucleation
– much easier since stable “nucleating surface” is already present —
e.g., mold wall, impurities in liquid phase
– only very slight supercooling (0.1-10°C)

15. 15
r* = critical nucleus: for r < r* nuclei shrink; for r > r* nuclei grow (to reduce energy)
Adapted from Fig. 10.2(b), Callister & Rethwisch 10e.
Homogeneous Nucleation & Energy Effects
ΔGT = Total Free Energy
= ΔGS + ΔGV
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
γ = surface tension
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
DGV
=
4
3
pr3
DGu
DGu
=
volume free energy
unit volume

16. 16
Solidification
Note: ΔHf and γ are weakly dependent on ΔT
 r* decreases as ΔT increases
For typical ΔT r* ~ 10 nm
ΔHf = latent heat of solidification
Tm = melting temperature
γ = surface free energy
ΔT = Tm - T = supercooling
r* = critical radius

20. Homogeneous vs. Heterogeneous
This lower ∆G* for heterogeneous means that a smaller energy must
be overcome during the nucleation process (than for homogeneous)
Therefore, heterogeneous nucleation occurs more readily
1/10/2023 20

21. Growth
 Once solid nuclei form, growth occurs as atoms are attached to the solid
surface.
Growth is the physical process by which a new phase increases in size. In
the case of solidification, this refers to the formation of a stable solid
particle as the liquid freezes.
 Nature of growth of solid depends on how heat is removed from the
system.
The manner in which the latent heat is lost determines the growth
mechanism
There are 2 growth mechanisms:
1. Planar growth
2. Dendritic growth
The differences in planar and dendritic growth
arises because of the differences in sink for the
latent heat.
1/10/2023 21

22. Planar growth
The heat is dissipated through the crystal, i.e. the
growing crystal is colder than the melt. Here a solid
bulge into the liquid would melt again because the
temperature in the bulge is above Tm . Therefore,
one obtains a stable flat solidification front
Any small protuberance that begins to grow on the
interface is surrounded by liquid above the freezing
temperature.
The growth of the protuberance stops until the
remainder of the interface catches up with it.
This planar growth occurs by the movement of a
smooth solid-liquid interface into the liquid.
Growth
1/10/2023 22

23. Dendritic growth
For a strongly undercooled melt the heat of
crystallization can also be dissipated through the melt.
Under these conditions a small solid protuberance
called a dendrite which forms at the interface is
encouraged to grow.
As the solid dendrites grow the latent heat of fusion is
conducted into the undercooled liquid
Raising the temperature of the liquid towards freezing
temperature.
Dendritic growth continues until the undercooled
liquid warms to the freezing temperature.
Any remaining liquid then solidifies by planar growth.
These are thermal dendrites different from dendrites
in alloys
Growth
c = specific heat of the
liquid
1/10/2023 23

24. Grain structure in Casting
Development of the ingot
structure of a casting during
solidification:
(a) Nucleation begins,
(b) the chill zone forms,
(c) preferred growth produces the
columnar zone, and
(d) additional nucleation creates
the equiaxed zone.
1/10/2023 24

25. Effect of cooling rates
• Slow cooling rates (on the order of 102 K/s) or long local solidification
times result in coarse dendritic structures with large spacing between
dendrite arms.
• For higher cooling rates (on the order of 104 K/s) or short local
solidification times, the structure becomes finer with smaller dendrite
arm spacing.
• For still higher cooling rates (on the order of from 106 to 108 K/s) the
structures developed are amorphous
1/10/2023 25

26. Directional solidification
1/10/2023 26

27. Test your knowledge…
Define the following terms: nucleation, embryo, heterogeneous nucleation, and
homogeneous nucleation.
1. Differentiate between nucleation and growth
2. State the conditions for the formation of
1. Dendrites
2. Central equiaxed zone
3. Chill zone
4. Stable interface growth
3. Differentiate between homogeneous and heterogeneous nucleation
Sketch a cooling curve for a pure metal and label
different regions carefully.
1/10/2023 27