phase transformations nucleation growth applications transformations in steel precipitation...
TRANSCRIPT
PHASE TRANSFORMATIONSPHASE TRANSFORMATIONS
Nucleation
Growth
APPLICATIONS Transformations in Steel Precipitation Solidification & crystallization Glass transition Recovery, Recrystallization & Grain growth
Phase Transformations in Metals and AlloysDavid Porter & Kenneth Esterling
Van Nostrand Reinhold Co. Ltd., New York (1981)
Diffusional
PHASE TRANSFORMATIONS
Martensitic
1nd ordernucleation & growth
PHASE TRANSFORMATIONS
2nd orderEntire volume transforms
Based onMass
transport
Based onorder
Energies involved
Bulk Gibbs free energy ↓
Interfacial energy ↑
Strain energy ↑ Solid-solid transformation
Volume of transforming material
New interface created
The concepts are illustrated using solidification of a metal
Nucleationof
phase
Trasformation
→ +
Growthtill is
exhausted
=
1nd ordernucleation & growth
Liquid → Solid phase transformation
Solid (GS)
Liquid (GL)
Tm T →
G →
T
G
Liquid stableSolid stable
T - Undercooling
↑ t
“For sufficientUndercooling”
On cooling just below Tm solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below Tm
G → ve
G → +ve
Nucleation
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
Homogenous
Heterogenous
Nucleation
NucleationSolidification + Growth=
Liquid → solid walls of container, inclusions
Solid → solid inclusions, grain boundaries, dislocations, stacking faults
Homogenous nucleation
)((Surface). )(Volume).( ΔG G
).(4 ).(3
4 ΔG 23 rGr v
r2r3
1
Neglected in L → Stransformations
)( TfGv
energystrain in increase energy surfacein increase energy freebulk in Reduction
nucleationon changeenergy Free
).(4 ).(3
4 ΔG 23 rGr v
By setting dG/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
0dr
Gd 0*1 r
vGr
2*
2
Trivial
vGr
2*
2
3*
3
16
vGG
As Gv is ve, r*is +ve
r →
G →
0dr
Gd
0G
*r0r
0GvG
r3
0Supercritical nucleiEmbryos
)( TfGv The bulk free energy reduction is a function of undercooling
r →
G →
Increasin
g T
Decreasing r*
Dec
reas
ing G
*
Tm 23
2 2
16
3 mT
GT H
Turnbull approximation
No. of critical sized particlesRate of nucleation x Frequency with which they
become supercritical=
dt
dNI
kT
G
t eNN
*
*
kT
Hd
es ' *
Critical sized nucleus
s* atoms of the liquid facing the nucleus
Critical sized nucleus
Jump taking particle to supercriticality → nucleated (enthalpy of activation = Hd)
No. of particles/volume in L → lattice vibration frequency (~1013 /s)
kT
HG
t
d
esNI
*
*
I →
T (
K)
→In
crea
sing
T
Tm
0
T = Tm → G* = → I = 0
G* ↑ I ↓
T ↑ I ↑
T = 0 → I = 0
Heterogeneous nucleation
Consider the nucleation of from on a planar surface of inclusion
)( )()(A )(V ΔG lenslens circlecirclev AAG
Alens
Acircle
Acircle
Created
Created
Lost
CosSurface tension force balance
Interfacial Energies
Vlens = h2(3r-h)/3 Alens = 2rh h = (1-Cos)r rcircle = r Sin
Cos
0
0.25
0.5
0.75
1
0 30 60 90 120 150 180
vhetero G
r
2*
32
3* 32
3
4CosCos
GG
vhetero
0
dr
Gd
3homo
* 324
1CosCosGG *
hetero
(degrees) →
G* he
tero / G
* hom
o → G*hetero (0o) = 0
no barrier to nucleation
G*hetero (90o) = G*
homo/2
G*hetero (180o) = G*
homo no benefit
Complete wetting No wettingPartial wetting
Cos
kT
G
eII
*homo
0homohomo
kT
G
eII
*hetero
0heterohetero
= f(number of nucleation sites)
~ 1042
= f(number of nucleation sites)
~ 1026
BUTthe exponential term dominates
Ihetero > Ihomo
Choice of heterogeneous nucleating agent
Small value of
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
Cos
Cos
Nucleationof
phase
Trasformation
→ +
Growthtill is
exhausted
=
Hd – vatom Gv
Hd
phase
phase
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 activationbarrier for the reverse jump is higher
Growth
rate)Growth rate,on f(Nucleatiratetion Transforma
) ,( UIfdt
dXT
3
t UI π
β
43
e 1X
I, U, T →
T (
K)
→In
crea
sing
T
Tm
0
U
T
I
Maximum of growth rate usuallyat higher temperature than maximum of nucleation rate
t →
X
→
0
1.0
0.5
3
t UI π
β
43
e 1X
Time – Temperature – Transformation (TTT) diagrams A type of phase diagram
T (rate sec1) →
T (
K)
→ T
Tm
0t (sec) →
T (
K)
→
Tm
0
Time for transformation
Small driving force for nucleation
Growth sluggish
Replot
t (sec) →
T (
K)
→
99% = finish
Increasing % transformation
TTT diagram → phase transformation
1% = start
T →
G →
Turnbull’s approximation
Tm
Solid (GS)
Liquid (GL)T
G
mm
m
T
Th
T
TThG
sionheat of fuΔh 2
3*
3
16
Th
TG m
APPLICATIONS
Phase Transformations in Steel
Precipitation
Solidification and crystallization
Glass transition
Recovery recrystallization & grain growth
Phase Transformations in Steel
%C →
T →
Fe Fe3C6.74.30.80.16
2.06
PeritecticL + →
EutecticL → + Fe3C
Eutectoid → + Fe3C
L
L +
+ Fe3C
1493ºC
1147ºC
723ºC
Fe-Cementite diagram
0.025 %C
0.1 %C
+ Fe3C
Austenite
Austenite
Pearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Not an isothermal
transformation
Ms
Mf
Coarse
Fine
t (s) →
T →
Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation
Eutectoid steel (0.8%C)
AustenitePearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
t (s) →
T →
Time- Temperature-Transformation (TTT) Curves – Isothermal Transformation
Eutectoid steel (0.8%C)
+ Fe3C
Continuous Cooling Transformation (CCT) Curves Eutectoid steel (0.8%C)
Austenite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
t (s) →
T →
Original TTT lines
Cooling curvesConstant rate
Pearlite
1T 2T
Eutectoid steel (0.8%C)
100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
t (s) →
T →
Water quench O
il quench
Norm
alizing
Full anneal
Different cooling treatments
M = Martensite
P = Pearlite
Coarse P
P M M + Fine P
Pearlite
Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar spacing is a function of the temperature of transformation Lower temperature → finer spacing → higher hardness
→ + Fe3C
[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962
[1] [1]
Bainite
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
→ + Fe3C**
Bainite formed at 348oC Bainite formed at 278oC
[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962
[1] [1]
Martensite
FCCAustenite
FCCAustenite
Alternate choice of Cell
Tetragonal Martensite
Austenite to Martensite → 4.3 % volume increase
Possible positions of Carbon atoms
Only a fraction ofthe sites occupied
20% contraction of c-axis12% expansion of a-axis
Refer Fig.9.11 in textbook
In Pure Fe after the Matensitic transformation
c = a
C along the c-axis obstructs the contraction
C
BCT
C
FCC Quench
% 8.0
)( '
% 8.0
)(
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 towhich 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
% Carbon →
Har
dnes
s (
Rc)
→
20
40
60
0.2 0.4 0.6
Harness of Martensite as a function of Carbon content
Properties of 0.8% C steel
Constituent 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
Tempering
Heat below Eutectoid temperature → wait→ slow cooling
The microstructural changes which take place during temperingare very complex
Time temperature cycle chosen to optimize strength and toughness
Tool steel: As quenched (Rc 65) → Tempered (Rc 45-55)
Cementite
ORF
Ferrite
BCC
Martensite
BCT Temper )( Ce)( )( ' 3
AustenitePearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
t (s) →
T →
+ Fe3C
MARTEMPERING
AUSTEMPERING
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 Tempering follows
To avoid residual stresses generated during quenching Austenized steel is quenched above Ms Held long enough for transformation to Bainite
Martempering
Austempering
ALLOY STEELS
Various elements like Cr, Mn, Ni, W, Mo etc are added to plain carbonsteels 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 ELEMENTSROLE OF 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
Plain Carbon Steel
Element Added
Segregation / phase separationSolid solution
Compound (new crystal structure)
• ↑ 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)
Alloying elements
• Alter temperature at which the transformation occurs• Alter solubility of C in or Iron• Alter the rate of various reactions
Interstitial
Substitutional
Austenite Pearlite
Bainite
Martensite100
200
300
400
600
500
800
Ms
Mf
t →
T →
TTT diagram for Ni-Cr-Mo low alloy steel
~1 min
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% Cu →
T (
ºC)
→
200
400
600
15 30 45 60
L
Sloping Solvus line high T → high solubility low T → low solubilityof Cu in Al
Al rich end of the Al-Cu phase diagram
4 % Cu
+
→ + Slow equilibrium cooling gives rise tocoarse precipitates which is not goodin impeding dislocation motion.*
RT
Cu
TetragonalCuAl
RT
Cu
FCC
C
Cu
FCCcoolslow
o
% 52
)(
% 5.0
)(
550
% 4
)( 2
*Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max = Gb/L
C
A
B
Heat (to 550oC) → solid solution
Quench (to RT) →
Age (reheat to 200oC) → fine precipitates
4 % Cu
+
CA
B
To obtain a fine distribution of precipitates the cycle A → B → C is used
Note: Treatments A, B, C are for the samecomposition
supersaturated solution
Increased vacancy concentration
Log(t) →
Har
dnes
s → 180oC
100oC
20oC
Higher temperature less time of aging to obtain peak hardness
Lower temperature increased peak hardness
optimization between time and hardness required
Log(t) →
Har
dnes
s →
180oC
OveragedUnderaged
Peak-aged
Region of solid solution strengthening
(no precipitation hardening)
Region of precipitation hardening
(but little solid solution strengthening)
Dispersion of fine precipitates(closely spaced)
Coarsening of precipitateswith increased
interparticle spacing
Log(t) →
Har
dnes
s →
180oC Peak-aged
Particle radius (r) →
CR
SS
Inc
reas
e →
2
1
r r
1
Particle shearing
Particle By-pass
)(tfr
Coh
eren
t (G
P zo
nes) In-coherent (precipitates)
Due to large surface to volume ratio the fine precipitates have a tendencyto 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
↑ Hfusion
↓ Hd Log [Viscosity ()]
Crystallization favoured by
High → (10-15) kJ / mole
Low → (1-10) Poise
Metals
Enthalpy of activation for diffusion across the interface
Difficult to amorphize metals
Thermodynamic
Kinetic
Very fast cooling rates ~106 K/s are used for the amorphization of alloys → splat cooling, melt-spinning.
2* 1
fusionHG
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 peakof 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
I, U →
T (
K)
→
Tm
0
U
I
↑ Hfusion
↓ Hd Log [Viscosity ()]
Crystallization favoured by
low
High → (1000) Poise
Silicates
Enthalpy of activation for diffusion across the interface
Easily amorphized
Thermodynamic
Kinetic
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
A composite material of glass and ceramic (crystals) can have betterthermal and mechanical properties
But glass itself is easier to form (shape into desired geometry)
Glass-ceramic (pyroceram)
Shaping of material in glassy state
Heterogenous nucleating agents (e.g. TiO2) added (dissolved) to molten glass
TiO2 is precipitated as fine particles
Held at temperature of maximum nucleation rate (I)
Heated to temperature of maximum growth rate
t →T
→
Nucleation
Growth
Tmaximum I
Tmaximum U
Glass 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
“All materials would amorphize on cooling unless crystallization intervenes”
T →
Vol
ume
→
Or other extensivethermodynamic property → S, H, E
Liquid
Glass
Crystal
Tg Tm
Glass transition temperature
T →
Vol
ume
→Change in slope
Tf
Fictive temperature (temperature at which glass is metastableif quenched instantaneously to this temperature)
→ can be taken as Tg
T →
Vol
ume
→Effect of rate of cooling
1T
2T
21 TT
Slower cooling
Slower cooling Higher density
Lower Tg
Lower volume
As more time for atoms to arrange in closer packedconfiguration
T →
Log
(vi
scos
ity)
→
Glass
Crystal
Tg Tm
Supercooledliquid Liquid
On crystallization the viscosity abruptly changes from ~100 → ~1020 Pa s
A solid can be defined a material with a viscosity > 1012 Poise
Tg
Heat glass
Cool liquid
Tx
Often metallic glasses crystallize before Tg
Please read up paragraph on glassy polymers → p228 in text book
Recovery, Recrystallization & Grain Growth
Cold work
↑ dislocation density
↑ point defect density
Plastic deformation in the temperature range (0.3 – 0.5) Tm → COLD WORK
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
)1010(~
)1010(~
1412
ndislocatio
96
ndislocatio
materialStrongermaterialAnnealed workCold
Cold work
↑ dislocation density
↑ point defect density
AnnealMaterial tends to lose the stored strain energy
Increase in strength of the material Softening of the material
Cold work Anneal
Recrystallization
RecoveryLow temperature
High temperature
Cold work Anneal
Recrystallization
Recovery
Grain growth
Cold work↑ Hardness
↑ Strength
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
↑ Electrical resistance
↓ Ductility
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
Polygonization
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 lower dislocation densityRegion of higher
dislocation density
Direction of grainboundary migration
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 theirmotion → Solute drag (can be used to retain strength of materials athigh temperatures)
The impurity atoms seggregate to the grain boundary and retard theirmotion → 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
Cold Work Plastic deformation below TRecrystallization
Col
d W
ork
Hot
Wor
k
Recrystallization temperature (~ 0.4 Tm)
Grain growth
Globally► Driven by reduction in grain boundary energy
Locally► Driven by bond maximization (coordination number maximization)
Bonded to4 atoms
Bonded to 3 atoms
Direction of grainboundary migration
Boundary moves towards itscentre of curvature
JUMP
Cold work Recovery Recrystallization Grain growth
Tensile strength
Ductility
Electical conductivityInternal stress