Chapter 10

Chapter 10

Phase Transformations

Kinetics and Phase Transformations

• Phase diagrams show which phases are in equilibrium under certain conditions, such as temperature– A change in the external conditions makes the phases

unstable, and drives phase transformation• A system cannot change instantaneously, i.e. phase

transformations occur over a period of time.• Kinetics deals with the rates of transformations

– A diffusion controlled process involves the movement of atoms over “long” distances (more than a few lattice constant lengths) to form the new more stable phase(s)

Phase Transformations

• When the external conditions (e.g. temperature) is changed, the stable phase(s) may change

• Transformation typically occurs in two steps– Nucleation : Formation of stable nuclei of the more

stable phase– Growth of nuclei : Increase in size of the nuclei to

form a grain structure• Nucleation can occur in one of two ways

– Homogeneous nucleation occurs in the bulk– Heterogeneous nucleation occurs at grain

boundaries and other defects

Phase Transformation: Solidification

• Homogenous Nucleation:– As temperature is reduced below the melting point,

the liquid becomes more and more unstable– The atoms in the liquid, as they are moving around,

may locally arrange themselves to form clusters of the solid and establish a solid-liquid interface

• The interface has a higher energy than the bulk• The additional energy required to form the

interface must be overcome by the energy released when the liquid changes to solid

– The smallest viable particle of the solid phase is called a nucleus

Nucleation during Solidification

Volume free energy Gv

• Released by liquid to solid transformation.

• ΔGv is the change in free energy per unit volume between liquid and solid– ΔGv is negative– This is the energy that

drives the transformation• The free energy change for a

spherical cluster of radius r is given by

Surface energy Gs

• Required to form new solid surface

• ΔGs is energy needed to create a surface

• γ is the surface free energy per unit area, then

• ΔGs is a retarding energy

vGr 33

4

2s 4G r

Homogeneous Nucleation

23

3

16*

2*

0

V

V

T

GG

and

Gr

orr

G

• As the size of the cluster of atoms increases, total free energy change increases up to a size r*

• Any further increase in size results in a decrease in free energy change

• A cluster of critical size is called a nucleus

– Smaller clusters will redissolve into the liquid

– Once a cluster reaches critical size it can grow

• At the critical cluster size

Total free energy change is given by

23 43

4rGrG vT

r

+

- ΔGv

ΔGs

ΔGT

r*

ΔGT

Homogeneous Nucleation

• The magnitude of GV increases as temperature decreases below the melting point, while does not change significantly

• It can be shown that the radius, r*, of the cluster of critical size at a transformation temperature T decreases as T decreases, i.e., with increasing undercooling

where Tm is the melting temperature in Kelvin, L is the latent heat of fusion and T is the under-cooling

• As a result, it becomes easier to form nuclei, and the number of nuclei per unit volume increases as the temperature T drops further and further below the melting point

T

1

LT2

TT

1

LT2

= G

2 = r m

m

m

V

*

Effect of undercooling on nucleation

Decrease in critical nucleus size

Decrease in activation energy to form nuclei

Increase in nucleation rate

Maximum observed undercooling during Homogeneous Nucleation

Heterogeneous Nucleation

• Occurs at a preexisting imperfection, such as a grain boundary (during solid state transformation) or the mold wall (during solidification of an ingot)

• During nucleation, two types of interfaces that require energy are formed– Solid-liquid (SL) and Solid-Imperfection (SI)

• One type of interface, the Liquid-Imperfection (IL) interface is removed. This provides additional energy to drive the transformation

Homo- and Heterogeneous Nucleation Rates

• At low under-cooling, the additional energy provided by the removal of the IL interfaces aids heterogeneous nucleation

• At higher under-cooling, the homogeneous nucleation rate becomes higher than heterogeneous nucleation rate because there are many more potential sites for homogeneous nucleation to occur

• At very high under-cooling, the nucleation rate drops off because atoms are not able to diffuse fast enough for nucleation to occur

Diffusion controlled growth

• Once stable nuclei have formed, they grow by diffusion of atoms to the interface, and their migration across the interface from the liquid to the solid phase

• It can be shown that the radius of a spherical particle will increase according to the equation below, where D is the diffusion coefficient

• As the temperature T decreases, the diffusion coefficient decreases exponentially. This results in a rapid decrease in growth rate

RT

QDD

where

Dt = r

dexp0

Overall Transformation Kinetics

• The overall rate of transformation depends on both nucleation and growth

• At low under-cooling, nucleation rate is low resulting in a low transformation rate

• At high under-cooling, the growth rate is low, also resulting in a low transformation rate

• The fastest transformation occurs at an intermediate temperature

Transformation rate and time

• The time that a transformation takes is proportional to the inverse of the transformation rate

• The figure above shows schematically, the rate and time for 50% of the transformation to complete– i.e., half of the liquid has solidified

• The time-temperature-transformation curve shows a characteristic “C” shape

Isothermal Transformation Diagram

• The isothermal transformation diagram has the typical “C” shape because– At high temperatures, close to the transformation temperature

(melting point, solvus temperature, eutectoid temperature, etc) the nucleation rate is low because T is small, while growth rate is high. Transformation is slow because there simply aren’t enough nuclei to grow

– At low temperatures well below the transformation temperature, nucleation rate is very high, and a large number of small nuclei will form, but growth rate is low. The nuclei are generally too small to be observed, and the transformation is therefore sluggish

– At an intermediate temperature, nucleation rate is high, and the growth rate is also sufficiently high that the overall transformation occurs rapidly

Diffusion controlled transformation

• The extent of transformation varies with time in a sigmoidal fashion

• Avrami equation is often used to describe such transformations

• where k and n are time independent constants that depend on the temperature and geometry of the transformation process.

nkty exp1

5.0

1

trtiontransformaofrate

Kinetics of transformation

Rate of a transformation occurs depends upon temperature

Q = activation energy for transformation T = absolute temperature (in Kelvin) R = universal gas constant

t0.5

Recrystallization of rolled copper

RT

QAr exp Arrhenius Equation

Kinetics of Phase Transformation

• Typically, phase transformations do not start immediately after the temperature crosses a phase boundary (solidus, liquidus or solvus line) on the phase diagram

• For example, when a liquid solidifies under normal conditions, undercooling or supercooling of several degrees below the freezing temperature may occur before nuclei of the solid are observed.

• In solid state transformations, both supercooling and superheating can occur.

Isothermal transformation Diagram

• The Iron-Carbon system is very significant for industrial applications, and has been widely studied.

• The formation of pearlite from austenite has been extensively investigated under both isothermal transformation and continuous cooling conditions– Isothermal transformation: samples are held at

constant temperature below the eutectoid temperature and the transformation is observed

– Continuous cooling: samples are allowed to cool continuously from a temperature above the eutectoid temperature

Isothermal Transformation Diagram

• Several samples are first austenitized above eutectoid temperature, quickly transferred to a salt bath held at the desired temperature and then quenched in water after different time intervals.

Repeat procedure

at

progressivelower

temperatures

727ºC

727ºC

0.76%

0.76%

Quenching stops any diffusional transformation that is occurring, and the extent of transformation can be observed under a microscope

Isothermal Transformation Diagram

Also calledTime Temperature Transformation orT-T-T diagrams

Diffusion Controlled ProcessesNucleation – rate increases as T decreasesGrowth – rate decreases as T decreases

Isothermal Transformation Diagram

Diffusion Controlled ProcessesNucleation – rate increases as T decreasesGrowth – rate decreases as T decreases

Bainite

Bainite forms below the “nose” or “knee”

Very rapid cooling produces Martensite

Martensite

Diffusion Controlled ProcessesNucleation – rate increases as temperature drops below Teutectic

Growth – rate decreases as T decreases

Initially the transformation rate increases due to increased nucleation rate, but then slows down due to decreased growth rate giving the TTT curve a characteristic “C” shape

Formation of Martensite

• Very fast cooling results in the formation of a new phase called Martensite

• For the eutectoid composition, 0.76wt% C is dissolved in the fcc austenite phase.

• Limit of solid solubility in the bcc ferrite phase is 0.022wt%C• Upon “slow cooling” below the eutectoid temperature, the excess

carbon forms Fe3C or cementite in a diffusion controlled process

• During quenching, the carbon does not have time to get out of the fcc matrix, and the alloy transforms to Martensite in a diffusion-less or athermal transformation

Formation of Martensite

• The carbon position remains unchanged

• Instead of the bcc ferrite phase, a new phase with a body centered tetragonal (bct) structure is formed

• This can be thought of as a bcc structure that has been stretched in one direction by the trapped carbon atoms

• During quenching, austenite starts changing to martensite at the M(start) temperature and the extent of transformation depends on how far below this temperature the sample is quenched and not on how long it is held at a particular temperature

• Martensite is a very hard phase

Austenite unit cell

Ferrite unit cell

Martensite unit cell

TTT curves for different steels

Hypereutectoid steel

Alloy steel type 4340

Microstructure can be controlled by changing the heat treatment process

A = AusteniteP = PearliteB = BainiteM = MartensiteF = FerriteC = Cementite

Continuous Cooling Transformation

• The sample is withdrawn from the furnace and allowed to cool continuously

• The cooling rate depends upon the cooling medium

– Furnace cooling– Air cooling (still air or forced air)– Oil quenching– Water quenching– Iced brine quenching– …– The start and finish lines for

pearlite transformation get shifted to lower temperatures and longer times

• Bainite transformation is not observed for eutectoid PC steel because it occurs below the “nose” or “knee”

Continuous Cooling Transformation

•Slow to moderate cooling produces coarse or fine pearlite

•Fast cooling produces martensite•Quenching at rates > than critical cooling rate of 140ºC/s produces 100% Martensite

Continuous Cooling of Alloy Steel 4340

• Two “noses” or “knees” makes the transformation behavior more complex

• Critical cooling rate is smaller. Air cooling will produce 100% martensite

Mechanical Properties of plain carbon steels (PC Steels)

Mechanical Properties of PC steels

Mechanical Properties of PC steels

Eutectoid Steel

Martensite

Tempering of Martensite

• Martensite is an extremely hard and brittle phase• It is thermodynamically unstable phase. Upon reheating

and holding over extended periods of time, the carbon atoms diffuse out of the bct lattice and form Fe3C

• This process is called tempering, and the resultant structure consisting of the a (bcc) phase and Fe3C is called tempered martensite

Effect of tempering temperature and time

•Strength and hardness decrease while ductility increases•This is a diffusional process, and properties also depend upon tempering time

Summary of phase transformations in PC Steels

Shape Memory Alloys

Ordered CubicComplex Monoclinic