BMEE209L: Module 3

Question 1

Process of Nucleation

Answer 1

1) Undercooling: where the liquid goes to a temp below its freezing point,Tm (Undercooling ΔT = Tm-T)

2) Atoms start to cluster into very small unstable groups called embryos

3) Now growth of embryo depends on two energies:
i) Volume Free Energy: negative value –> favours growth
ii) Surface Energy: positive values —> opposes growth

4) For small r surface energy dominates, embryo shrinks
5) For larger r volume energy dominates, embryo grows

6) Once embryo reaches the critical radius r*, it becomes a stable nucleus

7) Now, systems favours growth over shrinkage

Question 2

Total Change in energy ΔG during nucleation

Answer 2

ΔG = 4/3pir^3ΔGv + 4pir^2σsl

Question 3

Relation between undercooling and critical radius

Answer 3

Inversely proportional; as undercooling increases the critical radius required decreases

Question 4

Homogenous Nucleation

Answer 4

Happens when undercooling value is so large that it requires no surface for nucleation

Question 5

Heterogenous Nucleation

Answer 5

Happens when undercooling value is small, hence it requires a surface, often happens on impurities or mold walls

Question 6

Critical Radius (r*)

Answer 6

r* = 2σslTm/ΔHfΔT

Question 7

Planar Growth

Answer 7

When the solidification front is above Tm, such that any protrusion that tries to from is melted, hence uniform growth. The latent heat of fusion is removed through the solid as it grows

Question 8

Dendritic Growth

Answer 8

When the solidification front is undercooled, such that a small protrusion forms in the front in the form a dendrite. As the latent heat of fusion is removed through the liquid, it warms up the undercooled region thus melting the protrusion. Once all the undercooled region is warmed up, the solid grows by planar growth

Question 9

Fick’s Law of Diffusion

Answer 9

J = -Ddc/dx
where J = flux
D = diffusivity
dc/dx = conc gradient

Question 10

Diffusivity and temperature

Answer 10

D = Doexp(-Q/RT)

Question 11

Eutectic Reaction in Iron-Carbide Phase diagrams

Answer 11

Liquid –> Austenite + Cementite

Question 12

Eutectoid Reaction in Iron-Carbide Phase Diagram

Answer 12

Austenite –> Ferrite + Cementite

Question 13

Eutectoid temperature

Answer 13

723°C

Question 14

Eutectic Temperature

Answer 14

1130°C

Question 15

What is pearlite?

Answer 15

alternating lamellar structure of ferrite + cementite