PHASE TRANSFORMATIONS:

DEVELOPMENT OF MICROSTRUCTURE AND ALTERATION OF MECHANICAL PROPERTIES

• AN ALTERATION IN THE NUMBER OR CHARACTER OF THE PHASES.

Transformation Rate- reaction progress on time

VARIETY OF PHASE TRANSFORMATIONS

• Simple diffusion dependent – no change in the number or composition of phases present

Ex. Solidification & recrystallization

• Another diffusion-dependent – some alteration

Ex. Eutectoid reaction

• Diffusionless - metastable phase is produced Ex. martensitic transformation

KINETICS OF PHASE TRANSFORMATIONS

• Nucleation - appearance of very small particles, or nuclei of the new phase

• Growth - nuclei increase in size, which results in the disappearance of some (or all) of the parent phase.

NUCLEATION

• HOMEGENEOUS - form uniformly throughout the parent phase

• HETEROGENOUS - form preferentially at structural in homogeneities, such as container surfaces, insoluble impurities, grain boundaries, dislocations, and so on.

HOMOGENOUS NUCLEATION

• Take note!• free energy (or Gibbs free energy), G

• Change in free energy, ΔG

• Radius, r• volume free energy, • surface free energy, g • Activation free energy,

+4 g

0 1 2 3 4 5 6

-30

-20

-10

0

10

20

30

Free

ene

rgy

chan

ge,Δ

G

4

4 g

43 p  ΔGν  𝑟

3

ΔG∗

+4 g

Radius, r

Embryo - radius less than the critical

• Embryo - radius less than the critical will shrink and redissolve

• Nucleus – with a particle of radius greater than r*

Embryo - radius less than the critical

TOTAL FREE ENERGY CHANGE• +4 g

• d)+4 g(2 ) = 0

• r*= -

• ΔG*=

TAKE NOTE:

• D- latent heat of fusion• - equilibrium solidification temperature(Kelvin)• n* - number of stable nuclei• - frequency at w/c atoms from the liquid attach themselves to

the solid nucleus• - activation energy for diffusion• N- nucleation rate

ΔG∗2

ΔG∗1𝑇 1

𝑇 2

ΔG 𝑟

+¿

-

• = • r* = ()• = (• ==[exp ()exp ()]

NUMBER OF STABLE NUCLEI

• n*= exp ()0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-2.5

-2

-1.5

-1

-0.5

0

Tem

pera

ture

𝑇𝑚

exp ()

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

FREQUENCY OF ATTACHMENT

Tem

pera

tur

e

𝑇𝑚

exp ()]

=

NUCLEATION RATE

• N==exp () exp ()]

Tem

pera

tur

e

𝑇𝑚

Nucleation rate, frequency of attachment, number of stable nuclei

N

𝑣𝑑

n*

N==exp () exp ()]

SUPERCOOLING

• During the cooling of a liquid, an appreciable nucleation rate (i.e., solidification) will begin only after the temperature has been lowered below the equilibrium solidification (or melting) temperature (Tm).

• This phenomenon is termed supercooling (or undercooling)

COMPUTATION OF CRITICAL NUCLEUS RADIUS ANDACTIVATION FREE ENERGY• (a) For the solidification of pure gold, calculate the

critical radius r* and the activation free energy G* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are 1.16 109 J/m3 and 0.132J/m2, respectively. Use the super cooling value found in Table 10.1.

• (b) Now calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.413 nm for solid gold at its meltingtemperature.

HETEROGENEOUS

• -form on preexisting surfaces or interfaces, • -only several degrees Celsius• -activation energy is lowered

• Heterogeneous nucleation of a solid from a liquid. The solid–surface() solid–liquid ( and liquid–surface () interfacial energies are represented by vectors. The wetting angle is also () shown.

FORMULA

• =+

• = ( )S()

= S()

𝐺h𝑜𝑚∗

𝐺h𝑒𝑡∗

ΔG