ENR116 – Mod. 3- Slide No.

ENR116 Engineering Materials

Module 3 Metals

Dr David Steele

School of Advanced Manufacturing and Mechanical Engineering

 ENR116 – Mod. 3- Slide No. 2

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 ENR116 – Mod. 3- Slide No. 3

Phase transformations
 ENR116 – Mod. 3- Slide No. 4

Intended Learning Outcomes

At the end of this section, students will be able to:-

• Understand what phase transformations are and how

they occur.

• Understand how the rate of transformation is influenced

by both temperature and time.
 ENR116 – Mod. 3- Slide No. 5

Phase transformations

• The mechanical behaviour of metals is influenced by their

microstructure

• A phase transformation is a change in the number and/or

nature of the phases present

• Phase transformations are not instantaneous, they have an

associated transformation rate

• Two main types of phase transformation :

1. Diffusion dependant (simple and altered)
2. Diffusionless
 ENR116 – Mod. 3- Slide No. 6

Nucleation

Two types of nucleation:

Heterogeneous nucleation:
Occurs in the bulk of the melt
Requires considerable supercooling

Heterogeneous nucleation:
Occurs at structural inhomogeneities
Requires very little supercooling
 ENR116 – Mod. 3- Slide No. 7

Gibbs free energy, G

ΔGs

r*

ΔG*
G = Total Free Energy
G must be negative for a reaction
to occur spontaneously ΔG
G = = GS + GV
ΔGv
4
GS  4r 2  GV  r 3 G
3
 ENR116 – Mod. 3- Slide No. 8

The critical radius

r* = critical radius
= surface free energy
Tm = melting temperature
Hf = latent heat of solidification
T = Tm - T = supercooling

Hf and  don’t change much with T

r* decreases as T increases
 ENR116 – Mod. 3- Slide No. 9

Growth
Phase transformations occur in two stages : nucleation and
growth

Growth of the new phase depends on diffusion

Rate of diffusion increases with temperature

Small supercooling Large supercooling

•Temperature close to Tm •Temperature below Tm

•Nucleation rate low •Nucleation rate high
•Large r* •Small r*
•Low growth rate •High growth rate
•(slow diffusion) •(fast diffusion)
 ENR116 – Mod. 3- Slide No. 10

Rate of phase transformations

Kinetics - study of reaction rates of phase transformations.

To determine reaction rate – measure degree of

transformation as function of time (whilst holding
temperature constant).

How can we monitor reaction progress?

• X-ray diffraction – many samples required

• Electrical conductivity – single sample
• Measuring propagation of sound waves – single sample
 ENR116 – Mod. 3- Slide No. 11

Fraction transformed, y
Rate of phase transformations

transformation complete
Fixed T
0.5 maximum rate reached – now amount
unconverted decreases so rate slows
rate increases as surface area increases
t0.5 & nuclei grow

log t Adapted from

Fig. 10.10,
Callister &
Rethwisch 8e.

Avrami equation => y = 1- exp (-kt n)

fraction time
transformed
– k & n are transformation specific parameters

By convention rate = 1 / t0.5

 ENR116 – Mod. 3- Slide No. 12

Temperature dependence of
transformation rate
Percent recrystallised

135C 119C 113C 102C 88C 43C

1 10 102 104
Time / min, log scale
Adapted from Fig. 10.11, Callister & Rethwisch 8e.
(Fig. 10.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)

Rate increases with increasing temperature

Rate = 1/t0.5

Rate often so slow that equilibrium rarely achieved – many

alloys are metastable
 ENR116 – Mod. 3- Slide No. 13

Transformations & undercooling

T(ºC)
1600

1400 L
  +L
1200 1148ºC L+Fe3C

Fe3C (cementite)
(austenite)
1000
 +Fe3C
α ferrite

800
727ºC Equilibrium Cooling: Ttransf. = 727ºC
T  +Fe3C
600
Undercooling by Ttransf. < 727C
400
0 1 2 3 4 5 6 6.7
0.76

(Fe) C, wt%C

Adapted from Fig. 9.24,Callister & Rethwisch 8e. (Fig. 9.24 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B.
Massalski (Ed.-in-Chief), ASM International, Materials Park, OH, 1990.)
 ENR116 – Mod. 3- Slide No. 14

The Fe-Fe3C eutectoid transformation

cementite (Fe3C)
Austenite () 
grain Ferrite ()
boundary 

  Diffusion of C
 during transformation



Pearlite growth
direction
Adapted from Fig. 10.14, Callister & Rethwisch 8e.

Austenite to pearlite transformation

Coarse pearlite: formed at higher temperatures
Fine pearlite: formed at lower temperatures – relatively hard
 ENR116 – Mod. 3- Slide No. 15

Generation of isothermal
transformation diagrams
Fe-Fe3C system, for C0 = 0.76 wt% C and a transformation temperature of
675ºC.

% transformed
100
y, T = 675ºC
50

0
1 10 2 10 4 time (s)
T(ºC) Austenite (stable)
TE (727ºC)
700
675
600 Pearlite
10 0
50%pearli

500
0%

400
time (s)
te

1 10 10 2 10 3 10 4 10 5
Adapted from Fig. 10.13,Callister & Rethwisch 8e. (Fig. 10.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Transformation
Diagrams, American Society for Metals, 1977, p. 369.)
 ENR116 – Mod. 3- Slide No. 16

Austenite-to-Pearlite
isothermal transformation
Eutectoid composition, C0 = 0.76 wt% C

T(ºC) Austenite (stable)

TE (727ºC)
700 Austenite
(unstable)

600 Pearlite
 
   
10 0
5 0 % r l it e

500
0%

%
pea

400

1 10 10 2 10 3 10 4 10 5
time (s)
Adapted from Fig. 10.14,Callister & Rethwisch 8e. (Fig. 10.14 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and
Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.)
 ENR116 – Mod. 3- Slide No. 17

Summary

• Phase transformations involve both nucleation and

growth.
• Nucleation can be homogeneous, or heterogeneous

• Phase transformations depend on both temperature

and time.

• Isothermal temperature diagrams allow us to

determine reaction pathways, and predict
microstructures
 ENR116 – Mod. 3- Slide No. 18

Thank you