phase transformation chapter 2. shiva-parvati, chola bronze ball state university q: how was the...
TRANSCRIPT
Phase Transformation Chapter 2
Shiva-Parvati, Chola Bronze
Ball State University
Q: How was the statue made?
A: Invest casting
Liquid-to-solid transformation
An example of phase transformation
Czochralski crystal pulling technique
How does one produce single crystal of Si for electronic applications?
Quenching of steel componentsa solid->solid phase transformation
How does one harden a steel component?
Liquid
solid
ifica
tion
evaporation
sublimation
Solid
gas
mel
ting
condensation
Solid state phase
transformationSolid 21
Thermodynamic driving force for a phase transformation?
Decrease in Gibbs free energy
Liquid-> solid
gs - gl = g = -ve
ggL
gS
gS < gL
gL < gSLiquid is
stable
TmT
Gibbs free energy as a function of temperature, Problem 2.3
gL
gS
g
Solid is stable
Tfreezing
sT
g
p
T
c
T
g p
p
2
2
Fig. 9.1
How does solidification begins?
Usually at the walls of the container
Why?
To be discussed later.
Heterogeneous nucleation.
Spherical ball of solid of radius R in the middle of the liquid at a temperature below Tm
Homogeneous nucleation
gL = free energy of liquid per unit volumegS = free energy of solid
per unit volume
r
g = gS - gL
Change in free energy of the system due to formation of the solid ball of radius r :
r
)(3
4 3Ls ggrf
+ve: barrier to nucleation 24 r
)(3
4 3Ls ggr
rr*
f
24 r
grf 3
3
4
24 r
gr 3
3
4
rr*
f
24 rSolid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!!
Solid balls of radii r > r* will grow
r* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION
grf 3
3
4 24 r
gr 3
3
4
rr*
f
24 r
0*
rrr
f
gr
2*
*f
2
3
)(3
16*
gf
Eqn. 9.5
Eqn. 9.4
T
g
Tm
gL
gS
T
g (T)
LS ggg )()()( TsTThTg
)()( mThTh )()( mTsTs
0)()()( mmmm TsTThTg
m
mm T
ThTs
)()(
)()()( mm TsTThTg
m
mm T
ThTTh
)()(
)( mm
m ThT
TT
mm
hT
TTg
)( Eqn.
9.7
Driving force for solidification
grf 3
3
4 24 r
gr
2*
2
3
)(3
16*
gf
)(3
4)( 3 TgrTf 24 r
f
rm
m
hT
TTg
)(
m
m
hT
Tr
2*
22
23
)()(3
16*
m
m
hT
Tf
Eqn. 9.8
Eqn. 9.7
Fig. 9.3
r1*
f1*
f2*
r2*
T1T2 <
Critical particle
Fig. 9.4
Formation of critical nucleus by statistical fluctuation
Atoms surrounding the critical particle
Diffuse jump of a surrounding atom to the critical particle makes it a nucleation
The Nucleation Rate
Nt=total number of clusters of atoms per unit volumeN* = number of clusters of critical size per unit volume
By Maxwell-Boltzmann statistics
RT
fNN t
*exp*
RT
fNN t
*exp*
s*= no. of liquid phase atoms facing the critical sized particle
Hd = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequency
The rate of successful addition of an atom to a critical sized paticle
RT
Hsv dexp*' Eqn. 9.10
Eqn. 9.9
Rate of nucleation, I , (m3 s-
1)
'*NI
RT
HfsN d
t
*exp*
With decreasing T
1. Driving force increases
2. Atomic mobility decreases
= No. of nucleation events per m3 per sec
= number of critical clusters per unit volume (N*)x
rate of successful addition of an atom to the critical cluster (’)
RT
Hs
RT
fN d
t exp**
exp
Eqn. 9.11
T
I
Tm
Growth
Increase in the size of a product particle after it has nucleated
dt
drU
T
U
Overall Transformation Kinetics
),( IUfdT
dX
U
I
dX/dt
TI : Nucleation rate
U : Growth rate
dt
dr
Overall transformation rate (fraction transformed per second)
X=fraction of product phase
Fraction transformed as a function of time
ts tf
X
t
Slow due to very few nuclei
Slow due to final impingement
TTT Diagram for liquid-to-solid transformation
TStable liquid
UnderCooled liquid
crystal
Crystallization begins
L+
Crystallization ends
dX/dt
T
log t
X
log tts tf
0
1
Tm C-curves
L+
TStable liquid
UnderCooled liquid
log t
Tm
TTT Diagram for liquid-to-solid transformation
U
I
T
Coarse grained crystals
Fine grained crystals
glass
T
log t
ts metals
ts SiO2
RT
HfsNI d
t
*exp*
22
23
)()(3
16*
m
m
hT
Tf
Hd ∝ log (viscosity)
Metals: high hm, low viscosity
SiO2: low hm, high viscosity
Silica glassMetallic glass
Eqn. 9.11
Eqn. 9.8
Cooling rate 106 ºC s-1
Inert gas pressure
Molten alloy
Heater coil
Quartz tube
Rotating cooledmetal drum
Jet of molten metal
Ribbon ofglassy metal
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca
Melt Spinning for metallic glass ribbons
L+
T
log t
Tm
TTmTg
Log (viscosity Pa-s)
12
18
crystal
Stable liquid
Undercooled liquid
glass
30
Fig. 9.17
Tm
Specific volume Stable liquid
Undercooled liquid
Fast cool
Slow cool
Tgs
Tgf
crystal
Fig. 9.18
T
log t
U
I
T
L+
TStable liquidUndercooled liquid
Tm
devitrification
time
T
Glass ceramics
nucleation
growth
glass
Glass ceramic
Liquid
glass crystal
Very fine crystals
TU
TIFig. 9.16
Corning’s new digital hot plates with PyroceramTM tops.
Corningware PyroceramTM heat resistant cookware
ROBAX® was heated until red-hot. Then cold water was
poured on the glass ceramic from above - with NO
breakage.
Czochralski crystal pulling technique for
single crystal Si
SSPL: Solid State Physics Laboratory, N. Delhi
J. Czochralski, (1885-1953)
Polish Metallurgist
A
Steel
Hardness
Rockwell C
15 0.8
Wt% C Micro-structureCoarsepearlite
finepearlite
bainiteTempered martensite
martensite
0.8
0.8
0.8
0.8
30
45
55
65
Heattreatment
Annealing
normalizing
austempering
tempering
quenching
B
C
D
E
TABLE 9.2
HEAT TREATMENT
Heating a material to a high temperature,
holding it at that temperature for certain
length of time followed by cooling at a
specified rate is called heat treatment
A
N
AT
TQ
heati
ng
holding
time
T
Annealing Furnace cooling RC 15
Normalizing Air cooling RC 30
Quenching Water cooling RC 65
Tempering Heating after quench RC 55
Austempering Quench to an inter- RC 45mediate temp and hold
Eutectoid Reaction
CFeCo
3725
0.8 0.02
6.67
cool
Pearlite
Ammount of Fe3C in PearliteRed Tie Line below eutectoid temp
pearliteCFf
3 02.067.6
02.08.0
117.065.6
78.0
Phase diagrams do not have any information about time or rates of transformations.
We need TTT diagram for
austenite-> pearlite
transformation
Stable austenite
unstable austenite
TTT diagram for eutectoid steel
start
finish
Stable austenite
unstable austenite
start
finishAnnealing:coarse pearliteNormalizin
g:fine pearlite
U
I
TTTT diagram for eutectoid steel
Callister
Stable austenite
unstable austenite
start
finish
TTT diagram for eutectoid steel
A+M
M
Ms
Mf
Ms : Martensite start temperature
Mf : Martensite finish temperature
’: martensite (M)
' coolingrapid
QUENCHING
Hardness RC 65
Extremely rapid, no C-curves
BCT
Amount of martensite formed does not depend upon time, only on temperature.Atoms move only a fraction of atomic distance during the transformation:
1. Diffusionless (no long-range diffusion)2. Shear (one-to-one correspondence between and ’ atoms) 3. No composition change
Martensitic transformation
Problem 3.1
BCT unit cell of (austenite)
414.12 a
c
BCT unit cell of ’ (martensite)
08.100.1 a
c
0% C (BCC)
1.2 % C
Contract ~ 20%
Expand ~ 12%
Martensitic transformation (contd.)
Fig. 9.12
Hardness of martensite as a function of C content
Wt % Carbon →
20
40
60
0.2 0.4 0.6
Hard
ness
, R
C
Hardness of martensite depends mainly on C content and not on other alloying additions
Fig. 9.13
Martensitic transformation (contd.)
A
N
AT
TQ
heati
ng
T
Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling.
TEMPERING
CFetempering3
T<TE
?
Tempering (contd.)
+Fe3
CPEARLITE
A distribution of fine particles of Fe3C in matrix known as TEMPERED MARTENSITE.
Hardness more than fine pearlite, ductility more than martensite.
Hardness and ductility controlled by tempering temperature and time.
Higher T or t -> higher ductility, lower strength
Tempering Continued
Callister
AustemperingBainite
Short needles of Fe3C embedded in plates of ferrite
Problems in Quenching
Quench Cracks
High rate of cooling:
surface cooler than interior
Surface forms martensite before the interior
Austenite
martensite
Volume expansion
When interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses
But how to shift the C-curve to higher times?
Solution to Quench cracks
Shift the C-curve to the right (higher times)
More time at the nose
Slower quenching (oil quench) can give martensite
By alloying
All alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right.
Exception: Co
Substitutional diffusion of alloying elements is slower than the interstitial diffusion of C
Plain C steel
Alloy steel
Alloying shifts the C-curves to the right.Separate C-curves for pearlite and bainite
Fig. 9.10
Hardenability
Ability or ease of hardening a steel by formation of martensite using as slow quenching as possible
Alloying elements in steels shift the C-curve to the right
Alloy steels have higher hardenability than plain C steels.
Hardnenability Hardness
Ability or ease of hardening a steel
Resistance to plastic deformation as measured by indentation
Only applicable to steels
Applicable to all materials
Alloying additions increase the hardenability of steels but not the hardness.
C increases both hardenability and hardness of steels.
High Speed steel
Alloy steels used for cutting tools operated at high speeds
Cutting at high speeds lead to excessive heating of cutting tools
This is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edge
Alloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels.
Airbus A380 to be launched on October 2007
A shop inside Airbus A380
Alfred Wilm’s Laboratory 1906-1909
Steels harden by quenching
Why not harden Al alloys also by quenching?
time
Wilm’s Plan for hardening Al-4%Cu alloy
Sorry! No increase in hardness.
550ºC
T
Heat
Quench
Hold
Check hardness
Eureka ! Hardness
has Increased
!!
One of the greatest technological achievements of 20th century
Hardness increases as a function of time: AGE HARDENING
Property = f (microstructure)
Wilm checked the microstructure of his age-hardened alloys.
Result: NO CHANGE in the microstructure !!
As- quenched hardness
Hardness
time
Peak hardness
Overaging
Hardness initially increases: age hardening
Attains a peak value
Decreases subsequently: Overaging
+
: solid solution of Cu in FCC Al: intermetallic compound CuAl2
4
Tsolvus
supersaturated saturated +
FCC FCC Tetragonal
4 wt%Cu 0.5 wt%Cu 54 wt%Cu
Precipitation of in
Stable
unstable
Tsolvus
As-quenched
start finsh
+
Aging
TTT diagram of precipitation of in
A fine distribution of precipitates in matrix causes hardening
Completion of precipitation corresponds to peak hardness
-grains
As quenched
-grains +
Aged
Peak aged
Dense distribution of fine
overaged
Sparse distribution of coarse
Driving force for coarsening
/ interfacial energy
0.1 1 10 100
hardness
Aging time
(days)
180ºC
100ºC 20ºC
Aging temperature
Peak hardness is less at higher aging temperaturePeak hardness is obtained in shorter time at higher aging temperature
Fig. 9.15
U
I
T Stable
unstable
As-quenched
start finsh
+
Aging
Tsolvus
1
hardness
180ºC
100ºC 20ºC
100 ºC
180 ºC
Recovery, Recrystallization and grain growth
Following slides are courtsey
Prof. S.K Gupta (SKG)
Or Prof. Anandh Subramaniam (AS)
Cold work
↑ dislocation density
↑ point defect density
Plastic deformation in the temperature range above(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
AS
Cold work↑ Hardness
↑ Strength
↑ Electrical resistance
↓ Ductility
AS
Cold work Anneal
Recrystallization
Recovery
Grain growth
AS
Recovery, Recrystallization and Grain Growth
During recovery
1. Point Defects come to Equilibrium
2. Dislocations of opposite sign lying on a slip plane annihilate each other
(This does not lead to substantial decrease in the dislocation density)
SKG
POLYGONIZATION
Bent crystal
Low angle grain boundaries
Polygonization
AS
Recrystallization
Strained grains Strain-free grains
Driving force for the Process =
Stored strain energy of dislocations
SKG
Recrystallization Temperature:
Temperature at which the 50% of the cold-worked material recrystallizes in one hour
Usually around 0.4 Tm (m.p in K)
SKG
Factors that affect the recrystallization temperature:
1. Degree of cold work
2. Initial Grain Size
3. Temperature of cold working
4. Purity or composition of metal
Solute Drag Effect
Pinning Action of Second Phase Particle
SKG
Solute Drag Effect
SKG
Grain Boundary Pinning
SKG
Grain Growth
Increase in average grain size following recrystallization
Driving Force reduction in grain boundary
energy
Impurities retard the process
SKG
Grain growth
Globally► Driven by reduction in grain boundary energy
Locally► Driven by bond maximization (coordination number maximization)
AS
Bonded to4 atoms
Bonded to 3 atoms
Direction of grainboundary migration
Boundary moves towards itscentre of curvature
JUMP
AS
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)
AS
Cold work Recovery Recrystallization Grain growth
Tensile strength
Ductility
Electical conductivityInternal stress
Fig. 9.19
%CW Annealing Temperature
AS