# Chapter 10 Phase Transformations in Metals ... Phase Transformations in Metals Development of...

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1

Phase Transformations

in Metals Development of Microstructure and

Alteration of Mechanical Properties

2

3

Introduction

The development of microstructure in

alloys involves phase transformation:

Phase transformation need time, and cooling

rate greatly modify the phase transformation.

4

Phase Transformation

Basic Concepts

Phase transformation as well as the

transformation rate are important to develop a

specific microstructure which in turn affect the

mechanical properties of materials.

For example, the tensile strength of Fe-C

eutectoid alloy can be 700 MPa to 2000 MPa

depending on heat treatment condition.

5

Basic Concepts

Three classifications of phase transformations:

No change in composition, simple diffusion-

dependent transformation

Composition change, diffusion-dependent

transformation

Diffusionless transformation

6

The 1st kind of phase transformation

No change in composition, simple

diffusion-dependent transformation

Solidification

Allotropic transformation (αγ)

Recrystallization and grain growth

No change in composition of phases.

7

Composition change, diffusion-dependent

transformation

Eutectoid reaction (γ pearlite)

The 2nd kind of phase transformation

8

The 3rd kind of phase transformation

Diffusionless transformation

Metastable phase

Martensitic transformation

9

The Kinetics of Phase

Transformation

The progress of a phase transformation can be broken down into two distinct stages:

Nucleation

Growth

There are two types of nucleation :

Homogeneous

Hetergeneous

The growth begins once an embryo has exceeded the critical size, r*

10

Solidification: Nucleation Processes

Homogeneous nucleation

nuclei form in the bulk of liquid metal

requires supercooling (typically 80-300°C max)

Heterogeneous nucleation much easier since stable “nucleus” is already present

Could be wall of mold or impurities in the liquid phase

allows solidification with only 0.1-10ºC supercooling

11

The Kinetics of Phase

Transformation

Homogeneous nucleation

Nuclei of the new phase form uniformly throughout

the parent phase.

Will occur spontaneously only when free energy

change G is negative.

Fig. 10.1 solidification of a pure material from liquid

phase.

12

The Kinetics of Phase

Transformation

13

The Kinetics of Phase

Transformation

The are two contributions to the total free

energy change that accompany a solidification

transformation:

Free energy difference between the solid and

liquid phase: Volume free energy : Gv < 0

Formation of the solid-liquid phase boundary:

surface free energy : >0

23 4 3

4 rGrG v

14

The Kinetics of Phase

Transformation

15

r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

Homogeneous Nucleation & Energy Effects

GT = Total Free Energy

= GS + GV

Surface Free Energy- destabilizes

the nuclei (it takes energy to make

an interface)

24 rGS

= surface tension

Volume (Bulk) Free Energy –

stabilizes the nuclei (releases energy)

GrGV 3

3

4

volume unit

energy free volume G

16

The Kinetics of Phase

Transformation

The subcritical particle is an embryo, whereas

the particle of radius greater than r* is termed a

nucleus.

Since r* and G* appear at the maximum on the

free energy-versus-radius curve of Fig. 10.2b,

derivation of expressions for these two

parameters is a simple matter. equation 10.3

and 10.4

The Kinetics of Phase

Transformation

17

vG r

2 *

2

3

)(3

16 *

vG G

m

mf

v T

TTH G

)(

) 1

)( 2

(* TTH

T r

mf

m

22

23

)(

1 )

3

16 (*

TTH

T G

mf

m

18

The Kinetics of Phase

Transformation

T1>T2

The Kinetics of Phase

Transformation The number of stable nuclei n* (radii greater than r*) is

a function of temperature:

Another temperature-dependent parameter is also

important for nucleation: rate of diffusion, the

frequency atoms from the liquid attach to the solid

nucleus.

19

) *

exp(* 1 kT

G Kn

)exp(2 kT

Q Kv dd

20

The Kinetics of Phase

Transformation

)exp()

* exp(* 3213

kT

Q

kT

G KKKvnKN dd

21

The Kinetics of Phase

Transformation

22

The Kinetics of Phase

Transformation

Example Problem

Computation of critical nucleus radius and

activation free energy

Computing the number of atoms in a critical

nucleus.

The Kinetics of Phase

Transformation

Heterogeneous Nucleation

The activation energy (energy barrier) for nucleation

(△G* ) is lowered when nuclei form on preexisting surfaces or interfaces.

The surface free energy is reduced.

23

24

The Kinetics of Phase

Transformation

Hetergeneous Nucleation

cosSLSIIL

The Kinetics of Phase

Transformation

25

v

SL

G r

2 *

)()( )(3

16 hom

*

2

3

*

SGS G

G v

SL het

=30-90o, S()=0.01~0.5

26

The Kinetics of Phase

Transformation

27

The Kinetics of Phase

Transformation

The nucleation

rate is shifted to

higher temperature

for heterogeneous.

The Kinetics of Phase

Transformation

The growth rate is determined by the rate of

diffusion and its temperature dependence is the

same.

The overall phase transformation rate is equal to

some product of N and G

28

)exp( kT

Q CG

29

The Kinetics of Phase

Transformation

The Kinetics of Phase

Transformation

The rate of transformation and the time required

for the transformation (say 50%) is inversely

proportional to one another.

Rate of transformation : r = 1/ t0.5

t 0.5 = time required for halfway to completion.

30

31

10.3 The Kinetics of Phase

Transformation

32

Rate of transformation

33

The Kinetics of Phase Transformation-

Kinetic considerations of solid-state transformation

Rate of transformation : r = 1/ t0.5

t 0.5 = time required for halfway to completion.

Temperature will affect the rate of transformation:

Q = activation energy

Phase transformation is a thermal activated process.

)( RT

Q

eAr

34

The Kinetics of Phase Transformation-

Kinetic considerations of solid-state

transformation

Solid-state transformation did not occur instantly.

Need composition redistribution or atomic

rearrangement

Energy increase for nucleation or new phase

boundaries.

Time-dependent process (kinetics): Avrami equation.

k, n = time-independent constant ; k relates to r.

)exp(1 nkty

35

Rate of transformation

36

Metastable versus Equilibrium

states

Phase transformation is a time-dependent

process, long time is required to reach

equilibrium stage.

Speed or rate of cooling

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