PHASE TRANSFORMATIONS

1
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)
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Based on Mass transport
PHASE TRANSFORMATIONS
Diffusional
Martensitic
Based on order
PHASE TRANSFORMATIONS
1nd ordernucleation growth
2nd orderEntire volume transforms
3
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

4
1nd ordernucleation growth
Growthtill? is exhausted
Nucleationof? phase
Trasformation ? ? ?


5
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
Liquid stable
Solid stable
?G
Solid (GS)
?G ? ?ve
G ?
Liquid (GL)
?T
?G ? ve
For sufficient Undercooling
Tm
T ?
?T - Undercooling
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Nucleation
Solidification
Growth


Nucleation
Homogenous
Nucleation

• Liquid ? solid walls of container,
  inclusions
• Solid ? solid inclusions, grain boundaries,
  dislocations, stacking faults

Heterogenous

• 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

7
Neglected in L ? S transformations
Homogenous nucleation
r3
r2
1
8

• 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

As ?Gv is ?ve, ris ve
Trivial
?G ?
Supercritical nuclei
Embryos
r ?
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The bulk free energy reduction is a function of
undercooling
Tm
Increasing ?T
Decreasing ?G
Decreasing r
?G ?
r ?
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No. of critical sized particles
Frequency with which they become supercritical
x
Rate of nucleation

No. of particles/volume in L
s atoms of the liquid facing the nucleus
Critical sized nucleus
Jump taking particle to supercriticality ?
nucleated (enthalpy of activation ?Hd)
Critical sized nucleus
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• ?G ? ? I ?

• T ? ? I ?

T Tm ? ?G ? ? I 0
Tm
Increasing ?T
T (K) ?
0
T 0 ? I 0
I ?
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Heterogenous nucleation
Consider the nucleation of ? from ? on a planar
surface of inclusion ?
Interfacial Energies
?
???
?
Alens ???
?
Created
???
???
Acircle ???
Created
?
Acircle ???
Lost
Surface tension force balance
Vlens ?h2(3r-h)/3
Alens 2?rh
h (1-Cos?)r
rcircle r Sin?
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?Ghetero (0o) 0no barrier to nucleation
?Ghetero (180o) ?Ghomo no benefit
?Ghetero / ?Ghomo ?
?Ghetero (90o) ?Ghomo/2
No wetting
Complete wetting
Partial wetting
? (degrees) ?
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f(number of nucleation sites) 1026
f(number of nucleation sites) 1042
BUTthe exponential term dominates
Ihetero gt Ihomo
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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

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Growthtill? is exhausted
Nucleationof? phase
Trasformation ? ? ?


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

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Tm
Maximum of growth rate usuallyat higher
temperature than maximum of nucleation rate
U
T
Increasing ?T
I
T (K) ?
0
I, U, T ?
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A type of phase diagram
Time Temperature Transformation (TTT) diagrams
Small driving force for nucleation
Tm
Tm
Replot
T
Time for transformation
T (K) ?
T (K) ?
0
0
T (rate ? sec?1) ?
t (sec) ?
Growth sluggish
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TTT diagram ? ? ? phase transformation
Increasing transformation
?
T (K) ?
99 finish
?
1 start
t (sec) ?
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Turnbulls approximation
Solid (GS)
?G
G ?
?T
Liquid (GL)
Tm
T ?
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APPLICATIONS
Phase Transformations in Steel
Precipitation
Solidification and crystallization
Glass transition
Recovery recrystallization grain growth
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Phase Transformations in Steel
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Fe-Cementite diagram
EutecticL ? ? Fe3C
Peritectic L ? ? ?
L
1493ºC
?
L ?
1147ºC
0.1 C
2.06
?
Eutectoid ? ? ? Fe3C
? Fe3C
723ºC
?
0.025 C
? Fe3C
T ?
Fe3C
Fe
6.7
0.8
0.16
4.3
C ?
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Time- Temperature-Transformation (TTT) Curves
Isothermal Transformation
Eutectoid steel (0.8C)
800
Eutectoid temperature
723
Austenite
Coarse
Pearlite
600
Fine
500
Pearlite Bainite
400
T ?
Bainite
?
300
Austenite
Ms
200
Not an isothermaltransformation
Mf
100
Martensite
1
102
103
104
0.1
10
105
t (s) ?
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Time- Temperature-Transformation (TTT) Curves
Isothermal Transformation
Eutectoid steel (0.8C)
800
Eutectoid temperature
723
Austenite
Pearlite
600
? Fe3C
500
Pearlite Bainite
400
T ?
Bainite
300
Ms
200
Mf
100
Martensite
1
102
103
104
0.1
10
105
t (s) ?
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Continuous Cooling Transformation (CCT) Curves
Eutectoid steel (0.8C)
800
Eutectoid temperature
723
Austenite
600
Pearlite
500
Original TTT lines
400
T ?
300
Ms
200
Cooling curvesConstant rate
Mf
100
Martensite
103
1
102
104
0.1
10
105
t (s) ?
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Different cooling treatments
Eutectoid steel (0.8C)
800
723
600
M Martensite
500
P Pearlite
Water quench
Full anneal
400
T ?
Normalizing
300
Oil quench
200
Coarse P
100
Fine P

M
P
M
103
1
102
104
0.1
10
105
t (s) ?
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Pearlite
? ? ? 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

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Bainite
Bainite formed at 348oC
Bainite formed at 278oC
? ? ? Fe3C

• Nucleation and growth
• Acicular, accompanied by surface distortions
• Lower temperature ? carbide could be e
  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

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Martensite
Possible positions of Carbon atoms Only a
fraction ofthe sites occupied
FCC Austenite
Bain distortion
C along the c-axis obstructs the contraction
FCC Austenite Alternate choice of Cell
In Pure Fe after the Matensitic transformation c
a
Tetragonal Martensite
20 contraction of c-axis 12 expansion of a-axis
Austenite to Martensite ? 4.3 volume increase
Refer Fig.9.11 in textbook
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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

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60
Harness of Martensite as a function of Carbon
content
Hardness (Rc) ?
40
20
Carbon ?
0.2
0.4
0.6
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Tempering

• 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)

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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
• Tempering follows

Martempering
Austempering
AUSTEMPERING

• To avoid residual stresses generated during
  quenching
• Austenized steel is quenched above Ms
• Held long enough for transformation to Bainite

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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

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ROLE OF ALLOYING ELEMENTS
Interstitial
Segregation / phase separation
Solid solution
Substitutional
Element Added
Compound (new crystal structure)

• 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

• ? 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

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TTT diagram for Ni-Cr-Mo low alloy steel
800
Pearlite
Austenite
600
500
400
T ?
300
Bainite
Ms
200
Mf
100
Martensite
1 min
t ?
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Precipitation
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• 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

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Al rich end of the Al-Cu phase diagram
L
600
?
400
T (ºC) ?
?
Sloping Solvus line? high T ? high solubility
low T ? low solubility of Cu in Al
200
30
45
60
Al
15
Cu ?
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• ? ? ? ?
• Slow equilibrium cooling gives rise tocoarse ?
  precipitates which is not goodin impeding
  dislocation motion.

? ?
4 Cu
Also refer section on Double Ended Frank-Read
Source in the chapter on plasticity ?max Gb/L
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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
A
Heat (to 550oC) ? solid solution ?
supersaturated solution
B
Quench (to RT) ?
Increased vacancy concentration
C
Age (reheat to 200oC) ? fine precipitates
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100oC
180oC
Hardness ?
20oC
Log(t) ?

• Higher temperature ? less time of aging to
  obtain peak hardness
• Lower temperature ? increased peak hardness ?
  optimization between time and hardness required

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Peak-aged
180oC
Hardness ?
Coarsening of precipitateswith
increasedinterparticle spacing
Dispersion of fine precipitates(closely spaced)
Overaged
Underaged
Log(t) ?
Region of precipitation hardening(but little
solid solution strengthening)
Region of solid solution strengthening(no
precipitation hardening)
Tm
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Peak-aged
180oC
Coherent (GP zones)
Hardness ?
In-coherent (precipitates)
Log(t) ?
Particle shearing
Particle By-pass
CRSS Increase ?
Particle radius (r) ?
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• Due to large surface to volume ration 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)

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Solidification and Crystallization
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Metals
? ?Hfusion
High ? (10-15) kJ / mole
Thermodynamic
Crystallization favoured by
Low ? (1-10) Poise
? ?Hd ?? Log Viscosity (?)
Kinetic
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.
50

• 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

Tm
U
T (K) ?
I
0
I, U ?
51
Silicates
? ?Hfusion
low
Thermodynamic
Crystallization favoured by
High ? (1000) Poise
? ?Hd ?? Log Viscosity (?)
Kinetic
Enthalpy of activation for diffusion across the
interface
Easily amorphized
Certain oxides can be added to silica to promote
crystallization
52

• 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

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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
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• 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

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Glass Transition
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All materials would amorphize on cooling unless
crystallization intervenes
Liquid
Glass
Volume ?
Crystal
Tm
Tg
T ?
Or other extensivethermodynamic property ? S,
H, E
Glass transition temperature
57
Change in slope
Volume ?
T ?
Tf
Fictive temperature (temperature at which glass
is metastableif quenched instantaneously to this
temperature)? can be taken as Tg
58
Effect of rate of cooling
As more time for atoms to arrange in closer
packedconfiguration
Volume ?
Slower cooling
Lower volume
T ?
Slower cooling
Higher density
Lower Tg
59

• On crystallization the viscosity abruptly
  changes from 100 ? 1020 Pa s
• A solid can be defined a material with a
  viscosity gt 1012 Poise

Crystal
Glass
Log (viscosity) ?
Supercooledliquid
Liquid
T ?
Tm
Tg
60
Cool liquid
Heat glass
Tg
Tx
Often metallic glasses crystallize before Tg
61
Please read up paragraph on glassy polymers ?
p228 in text book
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Recovery, Recrystallization Grain Growth
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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

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? point defect density
Material tends to lose the stored strain energy
Anneal
Cold work
? dislocation density
Increase in strength of the material
Softening of the material
Low temperature
Recovery
Anneal
Cold work
Recrystallization
High temperature
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Anneal
Cold work
Recovery
Recrystallization
Grain growth
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? 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

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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

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POLYGONIZATION
Bent crystal
Polygonization
Low angle grain boundaries
69
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 density
Region of higherdislocation density
Direction of grainboundary migration
70
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)

71

• 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

72
Hot Work and Cold Work

• Hot Work ? Plastic deformation above
  TRecrystallization
• Cold Work ? Plastic deformation below
  TRecrystallization

Hot Work
Recrystallization temperature ( 0.4 Tm)
Cold Work
73
Grain growth

• Globally ? Driven by reduction in grain
  boundary energy
• Locally ? Driven by bond maximization
  (coordination number maximization)

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Direction of grainboundary migration
JUMP
Boundary moves towards itscentre of curvature
75
Electical conductivity
Internal stress
Ductility
Tensile strength
Cold work
Recovery
Recrystallization
Grain growth
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