Transcript Kinetics – time dependence of transformation rate

Kinetics – time dependence of
transformation rate
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Kinetics of Solid-State
Reactions
• Most reactions involve impedance
–
–
–
–
Formation of a new phase
Composition different from parent
Atomic rearrangement via diffusion required
Energy increase at new boundaries
• Processes in microstructural transformation
– Nucleation is first process in phase transformation
– Occurs at imperfection sites, grain boundaries
– Growth (until equilibrium)
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Typical kinetic behavior for
most solid-state reactions
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Fraction of transformation
(Avrami equation)
y  1  exp(kt )
n
Rate of transformation
r
1
t 0 .5
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For most reactions rate
increases with temperature:
r  Ae
 Q / RT
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Isothermal Transformation
Diagrams (Pearlite)
cooling
• (0.76 wt% C)
(0.022 wt% C)+Fe3C(6.70 wt%
heating
C)
• Upon cooling  (intermediate carbon content)
transforms to  (much lower carbon content) and Fe3C
(much high carbon content)
• Pearlite =  + Fe3C
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Pearlite (Eutectoid Composition)
Reaction v. Log of Time
Temperature kept constant throughout course of experiment
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More Convenient Analysis
Only valid for
eutectoid
composition
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Note from Figure 11.4
• Derived from series of S-curves
• Plot of temperature (y-axis ) v. log time in seconds
(x-axis)
• Austenite transformation only upon cooling below
eutectoid temperature
• Beginning curve, 50% transformation, and
completion curve
• Austenite to left: pearlite to right
• Start and finish curves are nearly parallel, and
they approach eutectic line asymptotically
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Reaction Rate
r 1
t0.5
• At temperature just below eutectic line rate is very slow
• Apparent contradiction to r = Ae-Q/RT – increase in temperature
causes increase in rate of reaction
• Between about 540 0C and 727 0C – transformation is controlled
by pearlite nucleation
• Nucleation rate decreases with rising temperature (less
supercooling)
• Activation energy (Q) of nucleation increases with temperature
• But, at lower temperatures austenite decomposition –
transformation is diffusion controlled (as predicted by equation
11.3)
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Isothermal Transformation Diagram
(Time–Temperature–Transformation, T-T-T)
Very rapid cooling (AB)
Isothermal (BCD)
C (3.5s is beginning)
D (15s is completion)
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Compute the mass fractions of
 ferrite and cementite in
pearlite
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This problem asks that we compute the mass fractions of ferrite
and cementite in pearlite. The lever-rule expression for ferrite is
W 
C Fe3 C  Co
C Fe3 C  C
And, since CFe3C = 6.70 wt% C, Co = 0.76 wt% C, and C = 0.022
wt% C
6.70  0.76
W 
 0.89
6.70  0.022
Similarly, for cementite
WFe3C
Co  C 0.76  0.022


 0.11
CFe3C  C 6.70  0.022
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Morphology of Pearlite
• Ferrite to cementite (approximately 8:1)
• At temperature just below eutectoid –
relatively thick  and Fe3C layers (coarse
pearlite)
• Diffusion rates are relatively high and
carbon diffuses over long distances
• With decreasing temperature, carbon
diffusion rate decreases and layers become
thinner (fine pearlite)
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Bainite – another product of
austenite transformation
• Needles or plates – needles of ferrite separated by
elongated particles of the Fe3C phase
• Bainite forms as shown on the T-T-T diagram at
temperatures below those where pearlite forms
• Pearlite forms – 540 to 727 0C
• Bainite forms – 215 to 540 0C
• Bainite and pearlite are competitive with each other –
once some portion of an alloy is transformed to either
pearlite or bainite, transformation to the other
microconstituent is not possible without reheating to
form austentite
• Unlike pearlite – kinetics of bainite obey Arrhenius
equiation – why?
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Pearlite – nucleation
controlled
Maximum rate of
transformation
Bainite – diffusion
controlled
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Spheroidite
• Steel alloy having either pearlite or bainite
microstructure heated to and left at a
temperature below eutectic line for long period
of time (18 to 24h)
• Microstructure formed is sphere like particles
embedded in a continuous -phase
• Transformation due to additional carbon
diffusion with no change in composition
• Driving force- reduction of -Fe3C boundary
line
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Martensite
• Formed when austenite cools rapidly (or is
quenched) to a relatively low temperature (near
ambient) – instantaneous
• Diffusionless transformation of austenite
• Competitive with pearlite and banite
• Occurs when quenching rate is rapid enough to
prevent carbon diffusion
• Must be formed from austenite; cannot be
formed from pearlite or bainite
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Martensite, (cont’d)
• FCC austenite experiences
polymorphic transformation to
BCT – diffusionless transformation
from austentite – almost
instantaneous since not dependent
on diffusion
• Martensite structure typically
maintained indefinately at room
temperatures
• Supersaturated solid solution
capable of rapidly transforming to
other structures if heated to
temperatures at which diffusion
rates become appreciable
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Needle-shaped
Portion is Martensite –
Rest is austensite
Martensite does not appear on iron-rich
phase diagram because it is metastable
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• Martensite shown on isothermal
transformation diagram
• Independent of time – not depicted
in the same way as pearlite or
bainite
• Function of temperature temperature must be low enough
to make carbon diffusion virtually
nonexistant
• Presence of alloying elements other
than carbon cause significant
changes in positions and shapes of
curves including shifting to longer
times and formation of a separate
bainite nose
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(a) Rapidly cool to 350C, hold for
10,000s, and quench to RT
(b) Rapidly cool to 250C, hold
for 100s, and quench to RT
(c) Rapidly cool to 650C, hold for
20s, rapidly cool to 400C, hold
For 1,000s, and quench to RT
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Mechanical Properties of Pearlite
• Fe3C is harder and more brittle than ferrite
• Increasing Fe3C content increases hardness
• Fine pearlite is harder and stronger than coarse
pearlite
– Greater Fe3C boundary are per unit volume
– Phase boundaries serve as barriers to dislocation motion
– Fine pearlite has more boundaries through which a
dislocation must pass during plastic deformation
• Coarse pearlite – more ductile than fine pearlite
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Spheroidite
•
•
•
•
Less boundary area
Plastic deformation not constrained
Ductile
tough
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Bainite
• Fine structure (smaller  and Fe3C
particles than pearlite
• Stronger and harder than pearlite
• Combination of strength and ductility
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Martensite
• Hardest and strongest
• Most brittle
• Strength and hardness not related to
microstructure – attributed to interstitial
carbon atoms hindering dislocation
motion
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Tempered Martensite
• Martensite is so brittle that its utility is limited
• Ductility and toughness may be enhanced by relieving
internal stresses by heat tempering
– Heat to below eutectoid
– Matensite (BCT, single phase)  tempered martensite ( +
Fe3C phases)
– Forms structure similar to spherodite expect cementite
particles are smaller
– Large ferrite phase boundary area around very fine and
numerous cementite particles
– Increasing cementite particle size decreases boundary area and
thus results in softer, weaker materail
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Polymer Crystallization
• Upon cooling through melting temperature, nuclei form
wherein small regions of tangled and random molecules
become ordered and align in the manner of chainfolded layers
• Nuclei grow by the continued ordering and alignment
of additional molecular chain segments
• Crystallization rate obeys Avrami equation:
– Y = 1 – exp (-ktn)
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