8/11/2019 Diat Htt Lect 7 8 9

1/11

HeatTreatment

Dr.SantoshS.Hosmani

Tem erature Time Transformation TTT dia rams

Phase Transformation

SolidSolid state phase

Solid 21

Physical metallurgy

Liquid Gascondensation

evaporation

What is the driving force for any phase

transformation?

> Decrease in Gibbs free energy

-

-

Gs - Gl = G If this isve, then only this transformation

will occur.

8/11/2019 Diat Htt Lect 7 8 9

2/11

G

nergy

,

G1

Energy barrierEa

Free

Reactants

G = G2 G1

ProductsG2

GGL

Gibbs free energy as a function of temperature,

GSG S

T

G

p

=

T

C

T

G p

p

=

2

2

Liquid is stableSolid is stable

GS < GL GL < GS

G

GL

TmTTfreesing

The second derivative of a function measures the

concavity of the graph of .

A function whose second deri vati ve i s osi ti ve will be

concave up, meaning that the tangent l ine wil l l ie below the

graph of the function.

Similarly, a function whose second derivat ive is negative

wil l be concave down, and its tangent l ines wil l l ie above

the graph of the function.

ef.:Wiki

The tangent line is blue where the curve is concave up, green

where the curve is concave down, and red at the inflection poin ts

How does solidification

egns

Usually at the walls of the

container

Heterogeneous

nucleation.

Why?

To be discussed later.

8/11/2019 Diat Htt Lect 7 8 9

3/11

Spherical ball of solid of radius r

in the middle of the liquid at a

temperature below Tm

Homogeneous nucleation

=

L

per unit volume

=per unit volume

= -

Change in free energy of the

system due to formation of the )(4 3

Ls GGrf = 2

4 r+so a o ra us r :

+ve: barrier to

nucleation

2

4 r+

rAt constant

Temperature

r

f

r*

)(3

4 3Ls

GGr

V

34 Grf = 24 r+Solid balls of radius r < r*canno grow as w ea

to increase in the free

energy of the system !!!

24 r+

Solid balls of radii r > r*

At constant

Temperature

r

f

*

r*

CRITICAL RADIUS OF

HOMOGENEOUS

V

3

3

4Gr

V

34 Grf = 24 r+

24 r+

f 0

*

=

=r

f*f

r

r*

V

34 Gr V

*G

r

=

3

16*f =

V

8/11/2019 Diat Htt Lect 7 8 9

4/11

Driving force for solidification:

LS GGG = V )()()( TSTTHTG =

== mmmm

mm

T

THTS

)()(

=

G (T)

)()(mTHTH = )()( mTSTS =

TSTTHTG =

m

mm

T

THTTH

)()(

=

GL GS

)(m

m

m THT

TT =

TTmT mm

HT

TG = )(

Grf = 34

24 r+

f

4 3= 2f1*

3

rr *

f2*

r *

m

m

HT

TG = )(

r = 2

* mTr =

2*

T1T2