Download Phase Transformations

PHASE TRANSFORMATIONS
 Nucleation
 Growth
 APPLICATIONS
 Transformations in Steel
 Precipitation
 Solidification & crystallization
 Glass transition
 Recovery, Recrystallization & Grain growth
Phase Transformations in Metals and Alloys
David Porter & Kenneth Esterling
Van Nostrand Reinhold Co. Ltd., New York (1981)
PHASE TRANSFORMATIONS
Based on
Mass
transport
Diffusional
Martensitic
PHASE TRANSFORMATIONS
Based on
order
1nd order
nucleation & growth
2nd order
Entire volume transforms
Bulk Gibbs free energy ↓
Energies involved
Interfacial energy ↑
Strain energy ↑
Solid-solid transformation
New interface created
Volume of transforming material
 The concepts are illustrated using solidification of a metal
1nd order
nucleation & growth
Trasformation
→
=
Nucleation
of
 phase
+
Growth
till
 is
exhausted
Liquid → Solid phase transformation
 On cooling just below Tm solid becomes stable
 But solidification does not start
 E.g. liquid Ni can be undercooled 250 K below Tm
↑t
Solid stable
Liquid stable
G
G →
Solid (GS)
G → ve
T
G → +ve
Tm
T - Undercooling
T →
Liquid (GL)
“For sufficient
Undercooling”
Solidification
Nucleation
=
Nucleation
+
Growth
Homogenous
Nucleation
Heterogenous
 Liquid → solid
walls of container, inclusions
 Solid → solid
inclusions, grain boundaries,
dislocations, stacking faults
 The probability of nucleation occurring at point in the parent phase is
same throughout the parent phase
 In heterogeneous nucleation there are some preferred sites in the
parent phase where nucleation can occur
Neglected in L → S
transformations
Homogenous nucleation
Free energy change on nucleation 
Reduction in bulk free energy  increase in surface energy  increase in strain energy
ΔG  (Volume).( G )  (Surface). ( )


4 3
ΔG   r .(Gv )  4r 2 .( )
3

Gv  f (T )
r3
r2
1


4

ΔG   r 3 .(Gv )  4r 2 .( )
3

 By setting dG/dr = 0 the critical values (corresponding to the maximum)
are obtained (denoted by superscript *)
 Reduction in free energy is obtained only after r0 is obtained
dG
0
dr
2
r 
Gv
As Gv is ve, r*is +ve
2
*
*
r1  0 r2  
Gv
Trivial
dG
0
dr
*
G  0
3
r0  
Gv
G →
G  0
3
16

G *  
3 Gv2
r*
Embryos
r0
Supercritical nuclei
r →
Gv  f (T ) The bulk free energy reduction is a function of undercooling
Turnbull approximation
Tm
Tm2
16 3
G  
3
T 2 H 2
Decreasing G*

G →
Decreasing r*
r →
Rate of nucleation =
dN
I
dt
No. of critical sized
particles
N  Nt e
*
 G * 


 kT 


No. of particles/volume in L
x
Frequency with which they
become supercritical
 ' s  e
*
 H d 


kT


 → lattice vibration frequency (~1013 /s)
s* atoms of the liquid facing the nucleus
Critical sized nucleus
Jump taking particle to supercriticality
→ nucleated (enthalpy of activation = Hd)
Critical sized nucleus
I  Nt s  e
*
 G *  H d


kT





 G* ↑  I ↓
T↑ I ↑
T = Tm → G* =  → I = 0
T (K) →
Increasing T
Tm
0
I →
T=0→I=0
Heterogeneous nucleation
Consider the nucleation of  from  on a planar surface of inclusion 

Interfacial Energies




Created
Alens 
Created
Acircle 
Lost
Acircle 


    
Cos 
 
Surface tension force balance
  Cos      
ΔG  (Vlens )Gv  (A lens )   ( Acircle )    ( Acircle )  
Vlens = h2(3r-h)/3
Alens = 2rh
h = (1-Cos)r
rcircle = r Sin
dG
0
dr
*
hetero
r

2 
G
*
hetero
Gv
G
G*hetero / G*homo →
*
hetero
1
3
 

4
3
 
2

3
Cos


Cos

2
3 Gv

1 *
 Ghomo 2  3Cos  Cos 3
4
G*hetero (0o) = 0
no barrier to nucleation

G*hetero (180o) = G*homo
no benefit
0.75
G*hetero (90o) = G*homo/2
0.5
    
Cos 
 
0.25
Complete wetting
No wetting
Partial wetting
0
0
30
60
90

120
 (degrees) →
150
180
0
I homo  I homo
e
*
 Ghomo



 kT 


= f(number of nucleation sites)
I hetero  I
0
hetero
e
*
 Ghetero




 kT 


= f(number of nucleation sites)
~ 1026
~ 1042
BUT
the exponential term dominates
Ihetero > Ihomo






Choice of heterogeneous nucleating agent
 Small value of 

Cos 
    
 
 Choosing a nucleating agent with a low value of  (low energy  interface)
 (Actually the value of (  ) will determine the effectiveness of the
heterogeneous nucleating agent → high  or low )
 low value of  →
Crystal structure of  and  are similar and lattice parameters are as close as
possible
 Seeding rain-bearing clouds → AgI or NaCl → nucleation of ice crystals
 Ni (FCC, a = 3.52 Å) is used a heterogeneous nucleating agent in the
production of artificial diamonds (FCC, a = 3.57 Å) from graphite
Trasformation
→
=
Nucleation
of
 phase
+
Growth
till
 is
exhausted
Growth
 At transformation temperature the probability of jump of atom from  → 
(across the interface) is same as the reverse jump
 Growth proceeds below the transformation temperature, wherein the activation
barrier for the reverse jump is higher
Hd
Hd – vatom Gv
 phase
 phase
Transforma tion rate  f(Nucleati on rate, Growth rate)
T
dX 
dt
 f (I , U )
Tm
Increasing T
U
Xβ  1  e
 π I U3 t 4

3

Maximum of growth rate usually
at higher temperature than
maximum of nucleation rate
T
T (K) →
I
0




I, U, T →
Xβ  1  e
 π I U3 t 4

3





1.0
X →
0.5
0
t →
Time – Temperature – Transformation (TTT) diagrams
A type of phase
diagram
Small driving
force for nucleation
0
Tm
T
Replot
T (rate  sec1) →
T (K) →
T (K) →
Tm
0
Time for transformation
t (sec) →
Growth
sluggish
TTT diagram  →  phase transformation
T (K) →
Increasing % transformation

99% = finish

1% = start
t (sec) →
Turnbull’s approximation
Δh  heat of fusion
Tm  T
T
G  h
 h
Tm
Tm
Solid (GS)
G →
G
T
Liquid (GL)
Tm
T →
16 3  Tm 

G   
3
 hT 
*
2
APPLICATIONS
Phase Transformations in Steel
Precipitation
Solidification and crystallization
Glass transition
Recovery recrystallization & grain growth
Phase Transformations in Steel
Fe-Cementite diagram
Peritectic
L+→
Eutectic
L →  + Fe3C
L
1493ºC

L+

0.1 %C
1147ºC
2.06
 + Fe3C
Eutectoid
 →  + Fe3C
723ºC

 + Fe3C
T →
0.025 %C
Fe
0.16 0.8
4.3
%C →
Fe3C
6.7
Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation
Eutectoid steel (0.8%C)
800
723
Eutectoid temperature
Austenite
Coarse
Pearlite
600
Fine
Pearlite + Bainite
T →
500
400
300
Not an isothermal
transformation
200
100
Bainite

Ms
Austenite
Mf
Martensite
0.1
1
102
10
t (s) →
103
104
105
Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation
Eutectoid steel (0.8%C)
800
723
Eutectoid temperature
Austenite
Pearlite
600
 + Fe3C
T →
500
Pearlite + Bainite
400
Bainite
300
200
100
Ms
Mf
Martensite
0.1
1
102
10
t (s) →
103
104
105
Continuous Cooling Transformation (CCT) Curves
Eutectoid steel (0.8%C)
800
723
Austenite
Eutectoid temperature
600
Pearlite
T →
500
Original TTT lines
400
300
Cooling curves
Constant rate
200
100
Ms
Mf
Martensite
0.1
1
T2
T1
102
10
t (s) →
103
104
105
Different cooling treatments
Eutectoid steel (0.8%C)
800
723
M = Martensite 600
P = Pearlite
T →
500
400
300
200
Coarse P
100
M
0.1
1
Fine P
M +P
102
10
t (s) →
103
104
105
Pearlite
[1]
[1]
 →  + Fe3C
 Nucleation and growth
 Heterogeneous nucleation at grain boundaries
 Interlamellar spacing is a function of the temperature of transformation
 Lower temperature → finer spacing → higher hardness
[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962
Bainite
[1]
[1]
Bainite formed at 348oC
Bainite formed at 278oC
 →  + Fe3C**
 Nucleation and growth
 Acicular, accompanied by surface distortions
** Lower temperature →
carbide could be ε carbide (hexagonal structure, 8.4% C)
 Bainite plates have irrational habit planes
 Ferrite in Bainite plates possess different orientation relationship
relative to the parent Austenite than does the Ferrite in Pearlite
[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962
Martensite
 ( FCC )
0.8 %C

Quench
 ' ( BCT )
0.8 %C
Possible positions of
Carbon atoms
Only a fraction of
the sites occupied
FCC
Austenite
C along the c-axis
obstructs the contraction
FCC
Austenite
Alternate choice of
Cell
20% contraction of c-axis
12% expansion of a-axis
Tetragonal
Martensite
Austenite to Martensite → 4.3 % volume increase
In Pure Fe after
the Matensitic transformation
c=a
Refer Fig.9.11 in textbook
Martensite
 The martensitic transformation occurs without composition change
 The transformation occurs by shear without need for diffusion
 The atomic movements required are only a fraction of the interatomic
spacing
 The shear changes the shape of the transforming region
→ results in considerable amount of shear energy
→ plate-like shape of Martensite
 The amount of martensite formed is a function of the temperature to
which the sample is quenched and not of time
 Hardness of martensite is a function of the carbon content
→ but high hardness steel is very brittle as martensite is brittle
 Steel is reheated to increase its ductility
→ this process is called TEMPERING
Hardness (Rc) →
60
Harness of Martensite as a
function of Carbon content
40
20
% Carbon →
0.2
0.4
0.6
Properties of 0.8% C steel
Hardness (Rc)
Tensile strength (MN / m2)
Coarse pearlite
16
710
Fine pearlite
30
990
Bainite
45
1470
Martensite
65
-
Martensite tempered at 250 oC
55
1990
Constituent
Tempering
 ' ( BCT )
Martensite

Temper
 ( BCC ) Fe3C (OR )
Ferrite

Cementite
 Heat below Eutectoid temperature → wait→ slow cooling
The microstructural changes which take place during tempering
are very complex
 Time temperature cycle chosen to optimize strength and toughness
 Tool steel: As quenched (Rc 65) → Tempered (Rc 45-55)
MARTEMPERING
 To avoid residual stresses generated during quenching
 Austenized steel is quenched above Ms for homogenization of temperature
across the sample
 The steel is then quenched and the entire sample transforms simultaneously
800
 Tempering follows
Eutectoid temperature
723
Austenite
Pearlite
600
 + Fe3C
500
Pearlite + Bainite
400
Bainite
T →
Martempering
300
Austempering
AUSTEMPERING
Ms
200
Mf
100
Martensite
0.1
1
10
 To avoid residual stresses generated during quenching
 Austenized steel is quenched above Ms
 Held long enough for transformation to Bainite
102
t (s) →
103
104
105
ALLOY STEELS
 Various elements like Cr, Mn, Ni, W, Mo etc are added to plain carbon
steels to create alloy steels
 The alloys elements move the nose of the TTT diagram to the right
→ this implies that a slower cooling rate can be employed to obtain
martensite → increased HARDENABILITY
 The ‘C’ curves for pearlite and bainite transformations overlap in the
case of plain carbon steels → in alloy steels pearlite and bainite
transformations can be represented by separate ‘C’ curves
ROLE OF ALLOYING ELEMENTS
Interstitial
Segregation / phase separation
Solid solution
Substitutional
Element Added
Compound (new crystal structure)
Plain Carbon Steel
Alloying elements
• + Simplicity of heat treatment and lower cost
•  Low hardenability
•  Loss of hardness on tempering
•  Low corrosion and oxidation resistance
•  Low strength at high temperatures
• ↑ hardenability
• Provide a fine distribution of alloy carbides during tempering
• ↑ resistance to softening on tempering
• ↑ corrosion and oxidation resistance
• ↑ strength at high temperatures
• Strengthen steels that cannot be quenched
• Make easier to obtain the properties throughout a larger section
• ↑ Elastic limit (no increase in toughness)
• Alter temperature at which the transformation occurs
• Alter solubility of C in  or  Iron
• Alter the rate of various reactions
TTT diagram for Ni-Cr-Mo low alloy steel
800
Pearlite
Austenite
600
T →
500
400
300
200
100
Bainite
Ms
Mf
Martensite
~1 min
t →
Precipitation
 The presence of dislocation weakens the crystal → easy plastic deformation
 Putting hindrance to dislocation motion increases the strength of the crystal
 Fine precipitates dispersed in the matrix provide such an impediment
 Strength of Al → 100 MPa
Strength of Duralumin (Al + 4% Cu + other alloying elements) → 500 MPa
Al rich end of the Al-Cu phase diagram
L
T (ºC) →
600

400
200
Al
Sloping Solvus line
 high T → high solubility
low T → low solubility
of Cu in Al
15
30
% Cu →
45

60

+
→+
Slow equilibrium cooling gives rise to
coarse  precipitates which is not good
in impeding dislocation motion.*
4 % Cu
 ( FCC) 
  ( FCC)   CuAl2 (Tetragonal ) 

 slowcool 
 

 0.5 % Cu   
52 % Cu
 4 % Cu  

 550o C 
 RT  

RT



 

*Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max
= Gb/L
To obtain a fine distribution of precipitates the cycle A → B → C is used

Note: Treatments A, B, C are for the same
composition
B
A
C
+
4 % Cu
A
Heat (to 550oC) → solid solution 
supersaturated solution
B
C
Quench (to RT) →
Increased vacancy concentration
Age (reheat to 200oC) → fine precipitates
Hardness →
100oC
180oC
20oC
Log(t) →
 Higher temperature  less time of aging to obtain peak hardness
 Lower temperature
 increased peak hardness
 optimization between time and hardness required
Hardness →
180oC
Peak-aged
Dispersion of
fine precipitates
(closely spaced)
Coarsening
of precipitates
with increased
interparticle spacing
Overaged
Underaged
Log(t) →
Region of solid solution
strengthening
(no precipitation hardening)
Region of precipitation
hardening
(but little solid solution
strengthening)
Peak-aged
CRSS Increase →
Hardness →
180oC
Log(t) →
Particle
shearing
Particle
By-pass
1
r
r
Particle radius (r) →
1
2

r  f (t )
 Due to large surface to volume ratio the fine precipitates have a tendency
to coarsen → small particles dissolve and large particles grow
 Coarsening
 ↓ in number of particles
 ↑ in interparticle spacing
 reduced hindrance to dislocation motion (max = Gb/L)
Solidification and Crystallization
Metals
G* 
Thermodynamic ↑ Hfusion
1
H 2fusion
High → (10-15) kJ / mole
Crystallization favoured by
Kinetic
↓ Hd  Log [Viscosity ()]
Low → (1-10) Poise
Enthalpy of activation for
diffusion across the interface
Difficult to amorphize metals
Very fast cooling rates ~106 K/s are used for the amorphization of alloys
→ splat cooling, melt-spinning.
 Fine grain size bestows superior mechanical properties on the material
 High nucleation rate and slow growth rate  fine grain size
 ↑ Cooling rate  lesser time at temperatures near Tm , where the peak
of growth rate (U) lies  ↑ nucleation rate
 Cooling rates ~ (105 – 106) K/s are usually employed
 Grain refinement can also be achieved by using external nucleating agents
 Single crystals can be grown by pulling a seed crystal out of the melt
T (K) →
Tm
0
U
I
I, U →
Silicates
Thermodynamic ↑ Hfusion
low
Crystallization favoured by
Kinetic
↓ Hd  Log [Viscosity ()]
High → (1000) Poise
Enthalpy of activation for
diffusion across the interface
Easily amorphized
Certain oxides can be added to silica to promote crystallization
 In contrast to metals silicates, borates and phosphates tend to form glasses
 Due to high cation-cation repulsion these materials have open structures
 In silicates the difference in total bond energy between periodic and
aperiodic array is small (bond energy is primarily determined by the
first neighbours of the central cation within the unit
Glass-ceramic (pyroceram)
 A composite material of glass and ceramic (crystals) can have better
thermal and mechanical properties
 But glass itself is easier to form (shape into desired geometry)
Heterogenous nucleating agents (e.g. TiO2) added (dissolved) to molten glass
Shaping of material in glassy state
TiO2 is precipitated as fine particles
Held at temperature of maximum nucleation rate (I)
Heated to temperature of maximum growth rate
Growth
Tmaximum U
Nucleation
T →
Tmaximum I
Glass
t →
Partially crystallized Glass
 Even at the end of the heat treatment the material is not fully crystalline
 Fine crystals are embedded in a glassy matrix
 Crystal size ~ 0.1 m (typical grain size in a metal ~ 10 m)
 Ultrafine grain size
 good mechanical properties and thermal shock resistance
 Cookware made of pyroceram can be heated directly on flame
Glass Transition
Volume →
“All materials would amorphize on cooling unless crystallization intervenes”
Or other extensive
thermodynamic
property →
S, H, E
Glass
Crystal
T →
Tg
Tm
Glass transition temperature
Volume →
Change in slope
T →
Tf
Fictive temperature (temperature at which glass is metastable
if quenched instantaneously to this temperature)
→ can be taken as Tg
Effect of rate of cooling
Volume →
T1  T2
As more time for atoms to
arrange in closer packed
configuration
T1
T2
Slower cooling
T →
Lower volume
Slower cooling
Higher density
Lower Tg
 On crystallization the viscosity abruptly changes from ~100 → ~1020 Pa s
 A solid can be defined a material with a viscosity > 1012 Poise
Log (viscosity) →
Crystal
Glass
Supercooled
liquid
T →
Tg
Tm
Cool liquid
Heat glass
Tg
Tx
Often metallic glasses crystallize before Tg
Please read up paragraph on glassy polymers → p228 in text book
Recovery, Recrystallization & Grain Growth
Plastic deformation in the temperature range (0.3 – 0.5) Tm → COLD WORK
↑ point defect density
Cold work
↑ dislocation density
 Point defects and dislocations have strain energy associated with them
 (1 -10) % of the energy expended in plastic deformation is stored in the
form of strain energy
Annealed material
dislocation ~ (10  10 )
6
9

Cold work
Stronger material
 dislocation ~ (1012  1014 )
↑ point defect density
Anneal
Cold work
Material tends to lose
the stored strain energy
↑ dislocation density
Increase in strength
of the material
Low temperature
Cold work
Softening of the material
Recovery
Anneal
High temperature
Recrystallization
Cold work
Anneal
Recovery
Recrystallization
Grain growth
↑ Strength
↑ Hardness
Cold work
↑ Electrical resistance
↓ Ductility
 Changes occur to almost all physical and mechanical properties
 X-Ray diffration
► Laue patterns of single crystals show pronounced asterism
→ due to lattice curvatures
► Debye-Scherrer photographs show line broadning
→ Residual stresses + deformations
Recovery
 Recovery takes place at low temperatures of annealing
 “Apparently no change in microstructure”
 Excess point defects created during Cold work are absorbed:
► at surface or grain boundaries
► by dislocation climb
 Random dislocations of opposite sign come together and annihilate each
other
 Dislocations of same sign arrange into low energy configurations:
► Edge → Tilt boundaries
► Screw → Twist boundaries
 POLYGONIZATION
 Overall reduction in dislocation density is small
POLYGONIZATION
Bent crystal
Low angle grain boundaries
Recrystallization
 Trecrystallization  (0.3 – 0.5) Tm
 “Nucleation” and growth of new, strain free crystals
 Nucleation of new grains in the usual sense may not be present and
grain boundary migrates into a region of higher dislocation density
 G (recrystallization) = G (deformed material) – G (undeformed material)
 TRecrystallization is the temperature at which 50 % of the material
recrystallizes in 1 hour
Region of higher
dislocation density
Direction of grain
boundary migration
Region of lower
dislocation density
Further points about recrystallization
 Deformation ↑  recrystallization temperature (Trecrystallization) ↓
 Initial grain size ↓  recrystallization temperature ↓
 High cold work + low initial grain size  finer recrystallized grains
 ↑ cold work temperature  lower strain energy stored
 ↑ recrystallization temperature
 Rate of recrystallization = exponential function of temperature
 Trecrystallization = strong function of the purity of the material
Trecrystallization (very pure materials) ~ 0.3 Tm
Trecrystallization (impure) ~ (0.5 – 0.6) Tm
►
Trecrystallization (99.999% pure Al) ~ 75oC
Trecrystallization (commercial purity) ~ 275oC
 The impurity atoms segregate to the grain boundary and retard their
motion → Solute drag (can be used to retain strength of materials at
high temperatures)
 The impurity atoms seggregate to the grain boundary and retard their
motion → Solute drag (can be used to retain strength of materials
at high temperatures)
 Second phase particles also pin down the grain boundary during its
migration
Hot Work and Cold Work
 Hot Work  Plastic deformation above TRecrystallization
Hot Work
 Cold Work  Plastic deformation below TRecrystallization
Cold Work
Recrystallization temperature (~ 0.4 Tm)
Grain growth
 Globally
► Driven by reduction in grain boundary energy
 Locally
► Driven by bond maximization (coordination number maximization)
Bonded to
4 atoms
Bonded to
3 atoms
Direction of grain
boundary migration
Boundary moves towards its
centre of curvature
JUMP
Electical conductivity
Internal stress
Ductility
Tensile strength
Cold work
Recovery
Recrystallization
Grain growth