1. UNIT – 4 Syllabus
Solidification: Mechanism of solidification, Homogenous and
Heterogeneous nucleation, crystal growth, cast metal structures.
Phase Diagram I: Solid solutions Hume Rothary rule substitutional, and interstitial solid solutions, intermediate phases, Gibbs phase rule.

2. 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.

3. Latent heat Super heat Entropy The terms must be known
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

4. 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

5. Ice melting in a warm room is a common example of increasing entropy

6. 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

7. Transformation from liquid metal to solid metal is accompanied by a shrinkage in the volume
This volume shrinkage takes place in three stages:
Liquid – Liquid
Liquid – Solid
Solid – Solid

8. Melting of Metals Liquid Temp Solid + Liquid Tm Latent Solid
Time, Enthalpy
Temp Tm
Latent
Heat
Solid
Super Heat
Solid + Liquid
Liquid
Melting of Metals

9. Freezing of Metals Super Heat Solid + Liquid Temp Latent Heat Solid
Time, Enthalpy

10. 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

11. 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
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)

12. Undercooling (or) Supercooling in pure metals

14. 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
Begin solidification at one temp and end at another temp (Solid solution)
Begin and end solidification at a constant temp just like in pure metals (pure eutectics)
Begin solidification like a solid-solution and it like a eutectic

15. Solid solution a b
Temp c d
Time

16. Pure eutectic a b c
Temp d
Time

17. Partly solution and partly eutecticb c d
Temp e
Time

18. Understanding solidification
Nucleation
Growth

19. 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

20. a) Nucleation of crystals, b) crystal growth,
c) irregular grains form as crystals grow together,
d) grain boundaries as seen in a microscope.

21. Nuclei of the new phase form uniformly throughout the parent phase
Types of Nucleation
Homogeneous Nucleation
Heterogeneous Nucleation
Nuclei form preferentially at structural inhomogeneities, insoluble impurities, grain boundaries, dislocations, and so on.
Nuclei of the new phase form uniformly throughout the parent phase

22. Homogeneous nucleation
Prominent is pure metals
Nuclei of the solid phase form in the interior of the liquid as atoms cluster together

23. Each nucleus is spherical and has a radius ‘r’.
This situation is represented schematically
Solid
𝐴𝑟𝑒𝑎=4𝜋𝑟2
𝑉𝑜𝑙𝑢𝑚𝑒= 4 3 𝜋𝑟3
Solid-Liquid
interface

24. Latent heat released by atoms is: ∆𝑮𝒗=− 𝟒 𝟑 𝝅𝒓𝟑 ∆𝑮
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 𝝅𝒓𝟑
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=𝟒𝝅𝒓𝟐𝜸
Latent heat released by atoms is:
∆𝑮𝒗=− 𝟒 𝟑 𝝅𝒓𝟑 ∆𝑮
*Negative value is taken since the temp is considered below the equilibrium solidification temperature

25. ∆𝐺∗=∆𝑮𝒗+∆𝑮𝒔=− 𝟒 𝟑 𝝅𝒓𝟑 ∆𝑮+𝟒𝝅𝒓𝟐𝜸
Finally, the total free energy change is equal to the sum of these two contributions—that is:
∆𝐺∗=∆𝑮𝒗+∆𝑮𝒔=− 𝟒 𝟑 𝝅𝒓𝟑 ∆𝑮+𝟒𝝅𝒓𝟐𝜸
These volume, surface, and total free energy contributions are plotted schematically as a function of nucleus radius in Figures

26. 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

27. If we substitute r/r* in ∆𝑮∗
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 𝝅𝒓𝟑 ∆𝑮+𝟒𝝅𝒓𝟐𝜸 =𝟎
−𝟒𝝅𝒓𝟐∆𝑮+𝟖𝝅𝒓𝜸=𝟎
r = r* = 𝟐𝜸 ∆𝑮
If we substitute r/r* in ∆𝑮∗
∆𝑮∗ = 𝟏𝟔𝝅𝜸𝟑 𝟑 ∆𝑮∗ 𝟐

28. 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’

29. Nucleation of carbon dioxide bubbles around a finger

30. 𝛾𝑆𝐼=𝑆𝑜𝑙𝑖𝑑 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 (𝜸𝞫𝞭)
Two essential things must happen:
The substrate must be wetted by the liquid metal
The contact angle/wetting angle (𝜽) of the cap-shaped nucleus should be less than 90o
𝛾𝑆𝐼=𝑆𝑜𝑙𝑖𝑑 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 (𝜸𝞫𝞭)
𝛾SL = Solid-liquid interfacial energy (𝜸𝞪𝞫)
𝛾IL = Liquid interfacial energy (𝜸𝞪𝞭)
Substrate 𝜹
Liquid 𝜶
Cap 𝜽
Solid 𝜷
𝜽=𝟑𝟔𝟎𝒐
𝜸𝑰𝑳= 𝜸𝑺𝑰+ 𝜸𝑺𝑳 𝒄𝒐𝒔𝜽
𝜸𝞪𝞭= 𝜸𝞫𝞭+ 𝜸𝞪𝞫 𝒄𝒐𝒔𝜽 or

31. 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

32. b) Partially columnar and
partially equiaxed grains
c) Equiaxed grains
Columnar grains

33. 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.

34. Substitutional solid soln. Interstitial solid soln.
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)

35. Hari Prasad

36. Conditions for substitutional solid solution (S.S.)
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.
Hari Prasad

37. 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.

38. Common intermediate compounds
Intermetallic or valency compounds
Interstitial compounds
Electron compounds

39. Intermediate phases Intermetallic/valency compounds (Ni3Al)
Interstitial compounds (Fe3C)
Electron compounds (Cu9Al4)
Very hard in nature. Very similar to interstitial solid solutions except they have fixed compositions
These are of variable composition and don’t obey valence rules
Formed between chemically dissimilar metals.
Follow the valence rules.
Have complex crystal structure