Engineering 45
Metal Phase
Transforms (1)
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Learning Goals.1 – Phase Xforms
 Transforming one phase into another is
a Function of Time:
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
a
(ferrite)
(BCC)
 Understand How time & TEMPERATURE
(t & T) Affect the Transformation Rate
 Learn how to Adjust the Transformation
RATE to Engineer NONequilibrium
Structures
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Learning Goals.1 – PhaseX2
 Transforming one phase into another is
a Function of Time:
Fe
g
(Austenite)
C
FCC
Fe C
3
Eutectoid
transformation (cementite)
+
a
(ferrite)
(BCC)
 Understand the Desirable mechanical
properties of NONequilibrium-phase
structures
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Classes of Phase XForms
1. Diffusion Dependent – Single Phase
•
No Change in Either The Number or
Composition of Phases
•
e.g.: Allotropic Transforms, Grain-Growth
2. Diffusion Dependent – MultiPhase
•
Two-Phase Structure; e.g. α + Mg2Pb in
Mg-Pb alloy system
3. DiffusionLess – MetaStable Phase
•
NonEquil Structure “Frozen” in Place
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Phase Xform → Nucleation
 Nuclei (seeds) act as the template to
grow crystals
 For a nucleus to form the rate of
addition of atoms to the nucleus must
be greater than rate of loss
 Once nucleated, the new “structure”
grows until reaching equilibrium
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Nucleation Driving Force
 Driving force to nucleate increases as
we increase ΔT
• SuperCooling → Temp Below the eutectic
or, eutectoid
• SuperHeating → Temp Above the peritectic
 Small Super Cooling → Few & Large
Nuclei
 Large Super Cooling → Rapid
nucleation - many nuclei, small crystals
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Solid-State Reaction Kinetics
 “Kinetic” → Time Dependent
 Phase Xforms Often Require Changes
in Atom Position to Affect
• Crystal Structure
• Local Chemical Composition
 Atom Movement Requires DIFFUSION
 Diffusion is a TIME DEPENDENT
Physical Process
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Solidification by Nucleation
 Homogeneous nucleation
• Nuclei form in the bulk of liquid metal
• Requires supercooling (typically 80-300°C)
 Heterogeneous nucleation
• Much easier since stable “nucleus” is
already present at “defect” sites
– Could be wall of a casting-mold or
impurities in the liquid phase
• Allows solidification with only 0.1-10ºC
supercooling
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Homogeneous Nucleation & Energy Effects
Surface Free Energy- destabilizes
the nuclei (it takes energy to make
an interface)
DGS  4r 2 g
g = surface tension
DGT = Total Free Energy
= DGS + DGV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4 3
DGV  r DG
3
DG 
volume free energy
unit volume
r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Engineering-45: Materials of Engineering
Adapted
from Fig.10.2(b), Callister 7e.
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Solidification Quantified
 2 gTm
r* 
DH S DT
r* = critical radius
g = surface free energy
Tm = melting temperature
DHS = latent heat of solidification
DT = Tm - T = supercooling
Note: DHS = strong function of DT
g
= weak function of DT

r*
decreases as DT increases
For typical DT
Engineering-45: Materials of Engineering
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r* ca. 100Å
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Phase Xform Processes

Phase Transforms Typically Entail Two
significant Time-Regions
1. Nucleation  Formation of Very Small
New-Phase
T = const
“Starting” Particles
•
Distribution is Usually
Random, but can be
assisted by “defects”
in the Solid State
•
Also Called the
“Incubation” phase
Engineering-45: Materials of Engineering
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Incubation
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Phase Xform Processes cont.
2. Growth  New-Phase expands from the
Nucleation “Starting” Particles to
eventually Consume the Old-Phase
•
•
If “Allowed” to
T = const
Proceed The
Equilibrium PhaseFractions Will
Eventually Emerge
This Stage of the
Xform is
characterized by the
Transformation Fraction, y
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Avrami Phase Xform Kinetics
 The Avrami Eqn
Describes the
Kinetics of Phase
Transformation
 kt n
y 1  e
• Where
– y  New-Phase
Fraction (0-1, 0-100%)
– t  Time (s)
– k, n  TimeIndependent Constants
(S-n, unitless)
Engineering-45: Materials of Engineering
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1
y
0.5
Fixed T
0
t0.5 log (t)
 RATE of Xform r
r  1 t 50%
• Where
– t0.5  Time Needed for
50% New-Phase
Formation
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Rcn Rate, r, as Fcn of T
• Where
 Temperature is a
– R  Gas Constant (8.31 J/mol-K)
Controlling Variable
– T  Absolute Temperature (K)
in the Heat Treating
– Q  Activation Energy for the
Process thru an
Reaction (J/mol)
Arrhenius Rln:
– A  Temperature-Independent
r  1 t0.5  Ae
135C 119C
1
10
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 Q RT
113C 102C
102
Scalar (1/S)
88C
43C
– e.g. Cu
Recrystallization
– In general, rate
increases as T↑
104
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
MetaStability
 The Previous Eqn. Indicates that Rcn Rates
are Thermally Activated
 Typical Equilibrium Rcn Rates are Quite
Sluggish; Too slow to Be Maintained in a
Practical Metal-Production Process
• Most Metals are cooled More Rapidly Than
Equilibrium Conditions
 Most Practical Metals are Thus SuperCooled
and do NOT Exist in Equilibrium
• They are thus MetaStable
– Quite Time-Stable; but Not Strictly in Equilibrium
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Recall Fe-C Eutectoid Xform
T(°C)
1600
 The Austenite to
L
1400
Ferrite+Cemtite
g+L
Eutectoid Rcn
1200
g
L+Fe 3C
Requires Large
austenite
Redistribution a 1000 Eutectoid: g +Fe3C
of Carbon ferrite 800
Equil.cooling: Ttransf. = 727ºC
Fe 3C
727°C
 Forms Pearlite
(Fe)
• Can Equilibrium Cool:
727.5C → 726.5C; and
SLOWLY
Engineering-45: Materials of Engineering
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1
2
3
4
5
6
Co, wt% C
• Or Can UNDERCool by
Amount DT; say 727C →
600C; and QUICKLY
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
6.7
0.77wt%C
6.7wt%C
400
0.022wt%C
0
DT
a+Fe 3C
cementite
Undercooling by DT: Ttransf. < 727ºC
0.77
600
0.022
g  a +Fe 3 C
Eutectoid Xform Rate ~ DT
 Recall the Growth of Pearlite from Cooled
Diffusive flow
Austenite
of C needed
g
 The g→Pearlite Rcn
Rate Increases with
the Degree of
UnderCooling
(larger DT)
Engineering-45: Materials of Engineering
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ferrite ( a)
a
g
pearlite
growth
direction
a
a
0
100
600°C
( DT larger)
50
0
g
650°C
50
675°C
( DT smaller)
1
% austenite
a
a
g a
a
a
a
cementite (Fe3C)
y (% pearlite)
Austenite (g)
grain
boundary
100
10 10 2 10 3
time (s)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
• Liquid Water Can be
cooled below 32 °F
(SuperCooled or
UnderCooled)
• If any Ice Nucleates
the Entire Liq body
RAPIDLY Freezes
Engineering-45: Materials of Engineering
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0
100
600°C
D
( T larger)
50
0
650°C
50
675°C
( DT smaller)
1
% austenite
 UnderCooling
Analogy
y (% pearlite)
Eutectoid Xform Rate ~ DT cont.1
100
10 10 2 10 3
time (s)
 The Greater the
SuperCooling, The
More Rapid the
Phase Transform
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
r  1 t0.5  Ae
 Q RT
0
100
600°C
( DT larger)
50
0
650°C
50
675°C
( DT smaller)
1
100
10 10 2 10 3
time (s)
Competing Process
 Lower Rcn Rate is
Countered by Higher
NUCLEATION rates
for SuperCooled
Conditions
max
Engineering-45: Materials of Engineering
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% austenite
 More RAPID Xform
at LOWER Temps
Seems to Contradict
Arrhenius
y (% pearlite)
Eutectoid Xform Rate ~ DT cont.2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Nucleation and Growth
 Transformation Rate Results from the
Combination of Nucleation AND Growth
% Pearlite
100
50 Nucleation
regime
Growth
regime
t50
log (time)
0
• Nucleation Rate INcreases
With SuperCooling (DT↑)
• Grown Rate DEcreases with
Super Cooling (DT↑)
 Examples
g
pearlite
colony
T just below TE
Nucleation rate low
Growth rate high
Engineering-45: Materials of Engineering
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g
g
T moderately below TE T way below TE
Nucleation rate med
Growth rate med
Nucleation rate high
Growth rate low
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
y,
% transformed
IsoThermal Xform Diagrams
100
 a.k.a. TIME-TEMPTRANSFORM (T-T-T)
diagram
T=675°C
50
0
102
1
T(°C)
104
Austenite (stable)
700Austenite
(unstable)
time (s)
• Example = Fe-C at
Eutectiod; C0 = 0.77
TE (727°C) Wt%-Carbon At 675C
isothermal Xform at 675°C
Pearlite
600
 0% line → Incubation
Time
500
400
1
10
time (s)
102 103 104 105
Engineering-45: Materials of Engineering
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– Moving Lt→Rt at 675C
notice intersection with
 50% line →
Transformation Rate
 100% line →
Completion
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
y,
% transformed
IsoThermal Xform Dia. cont
100
 Notice
T=675°C
50
0
102
1
T(°C)
104
Austenite (stable)
700Austenite
(unstable)
time (s)
TE (727°C)
isothermal Xform at 675°C
•
Pearlite
600
500
400
1
10
time (s)
102 103 104 105
Engineering-45: Materials of Engineering
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• Xform Lines make
Asymptotic approach
to TE
– LONG Xform Times for
Equil Cooling
Knee at Left on 0% line
– Suggests Nucleation
Rate reaches a
MAXIMUM (i.e.; it
saturates at some
large DT; perhaps
 727−550 C
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Rapid Cooling of Fe-C from g
 Eutectoid Composition; C0 = 0.77 wt%
 Cool Rapidly: ~740C → 625C
T(°C)
TE (727°C) • g Persists for about
Austenite (stable)
3S Prior to Pearlite
Nucleation
• To 50% Pearlite at
about 6S
700
Pearlite
600
g g
g g
g
g
– r = 1/6S
g
500
1
10
102
Engineering-45: Materials of Engineering
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103
104
105
• Transformation
Complete at
about 15S
time (s)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
- Smaller DT:
colonies are
larger
 TXform Just Below TE
• Higher T → C-Diffusion is
Faster (can go Further)
• Pearlite is Coarser
Engineering-45: Materials of Engineering
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10 µm
10 µm
Pearlite vs DT - Morphology
- Larger DT:
colonies are
smaller
 TXform WELL Below TE
• Lower T → C-Diffusion is
Slower (Shorter Diff-Dist)
• Pearlite is Finer
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Fe-C NonEquil Xform Products
 Bainite
• Ferrite, a, lathes (strips)
with long rods of Fe3C
800
Austenite (stable)
T(°C)
A
600
TE
P
100% pearlite
pearlite/bainite boundary
100% bainite
400
B
A
10
103
10 5
time (s)
Engineering-45: Materials of Engineering
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a(ferrite)
5 mm
 Diffusion Controlled
Formation
• Bainite & Pearlite
Compete
200
10-1
Fe 3C
(cementite)
– Bainite Forms Below
The Boundary at
About 540 °C
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Fe-C NonEquil Xform
 Spherodite
• Ferrite, a, Xtal-Matrix
with spherical Fe3C
“Globules”
800
• diffusion dependent
• heat bainite or pearlite T(°C)
600
for LONG times
– T-T-T Diagram →
seconds
• reduces a-Fe3C
Phase Boundary
(driving force)
Engineering-45: Materials of Engineering
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a
(ferrite)
Fe 3C
(cementite)
60 mm
Austenite (stable)
A
P
100% spheroidite
Spheroidite
~104
400
TE
100% spheroidite
B
A
200
10 -1
10
10 3
105time
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
(s)
Fe-C NonEquil Xform Products
• A Diffusionless, and
Hence Speed-ofSound Rapid, Xform
from FCC g
• Poorly Understood
Single Carbon-Atom
Jumps Convert FCC
Austenite to a Body
Centered Tetragonal
(BCT) Form
Engineering-45: Materials of Engineering
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60 mm
 Martensite
Martentite needles
Austenite
Fe atom
sites
x
x
x
x
x
potential
C atom sites
x
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Martensite T-T-T Diagram
 Martensite, M, is NOT
an Equil. Phase
• Does NOT Appear on
the PHASE Diagram
• But it DOES Form
– So Seen on Isothermal
Phase Xform Diagram
 xForm g→M is Rapid
• %-Xformed to M
depends ONLY on
Temperature
Engineering-45: Materials of Engineering
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800
T(°C)
Austenite (stable)
A
600
400
P
S
A
B
200
M+A
M+A
M+A
10
10-1
103
–
–
–
–
–
TE
time (s)
A = Austenite
P = Pearlite
B = Bainite
S = Spherodite
M = Martensite
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
0%
50%
90%
105
Martensite Formation
g (FCC)
slow cooling
a (BCC) + Fe3C
quench
M (BCT)
tempering
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation
BCT  few slip planes
Engineering-45: Materials of Engineering
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BCT if C > 0.15 wt%
 hard, brittle
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
WhiteBoard Work
 None Today
 Some Cool
Pearlite
• So Named
Because it Looks
Like Mother-ofPearl Oyster Shell
– Under MicroScope
with Proper Mag &
Lighting
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Appendix – 1-Xtal Turbine blds
The blades are made
out of a nickel-base
superalloy with a
microstructure
containing about 65%
of gamma-prime
precipitates in a
polycrystalline gamma
matrix. The creep life
of the blades is limited
by the grain
boundaries which are
easy diffusion paths.
The blade is made out of a
nickel-base superalloy with a
microstructure containing
about 65% of gamma-prime
precipitates in a
polycrystalline gamma
matrix. It has been
directionally-solidified,
resulting in a columnar grain
structure which mitigates
grain-boundary induced
creep.
The blade is made out of
a nickel-base superalloy
with a microstructure
containing about 65% of
gamma-prime precipitates
in a single-crystal gamma
matrix. The blade is
directionally-solidified via
a spiral selector, which
permits only one crystal to
grow into the blade.
http://www.msm.cam.ac.uk/phase-trans/2001/slides.IB/photo.html
Engineering-45: Materials of Engineering
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The blade is made out of a
nickel-base superalloy with a
microstructure containing
about 65% of gamma-prime
precipitates in a
polycrystalline gamma
matrix. It has been Spiralsolidified, resulting in a
single grain structure which
eliminates grain-boundary
induced creep.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt
Fe-C Phase Transforms
 Eutectoid Xform
• Pearlite only
 Hypo Eutectoid
• Includes
ProEeutectiod α
ProE
α
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-45_Lec-23_Metal_Phase_Xforms-1.ppt