Time-Temperature-Transformation (TTT)...
Transcript of Time-Temperature-Transformation (TTT)...
Time-Temperature-Transformation (TTT) Diagrams
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Classification of Phase Transformations and Plasticity
Civilian transformation
Military transformation
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Table 3.5 Classification of Nucleation and Growth Transformations
Adapted from J.W. Christian, “Phase transformations in metals and alloys – an introduction”, in Phase Transformations,Vol. 1, p. 1, Institute of Metallurgists, 1979.
Type Military Civilian
Thermally activatedAthermalEffect of temperaturetemperature
Interface typeGlissile
(coherent orsemicoherent)
Non-glissile(coherent, semicoherent, incoherent, solid/liquid or solid/vapor)
Composition of parent and
product phasessame same different
Nature of N diff i
Short-range Long-rangediffusion processes
No diffusion diffusion (across interface)
g gdiffusion (through lattice)
Interface, diffusion, or Interface
control Interface controlMainly
interface Mainly
diffusion Mixed controlmixed control? control control control
PrecipitationDissolution
PrecipitationDissolution
PrecipitationDissolution
MassiveOrdering
PolymorphicR t lli ti
Martensitic
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DissolutionEutectoid
Cellular precipit.SolidificationMelting
BainiteCondensationEvaporation
RecrystallizationGrain growthCondensationEvaporation
DeformationTwinning
disordered phase 1D chain
ordered phase 1
chainordered phase 2Antiphase
boundary
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Example of Military Transformation with Glissile Interface
li il i f
bc
aGlissile interface Glissile interface
c
c
ba
cab Stacking
faults(111)<112>
Shockley partialdislocations
ab
FCC (111) planesDeformation
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FCC (111) planes twinning
Military Transformation Civilian Transformation
1 2 3 4
5 6 7 8
parent
1 2 3 4
5 6 7 8
parent9 10 11 12
13 14 15 16
parent9 10 11 12
13 14 15 16
parent
12 4111 2 3 4
5 6 7 8
product product
12
3
4
5 6 7
10
11
12139 10 11 12
13 14 15 16
product product 3
89
10 1213
14 1516
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Soldiers on parade groundMarching band
Job search in corporate America
Short-range Diffusion Long-range Diffusion
up1 2 37 9
4 5 610 11 12
up
down
left right
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37 9
4 5 610 11 12
R d lk
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Random walk: atomic registry destroyer
G th d
Military versus civilian growth kinetics
Growth speed v(velocity of interface) Collective shear
“athermal”athermal
HigherTT
Short-range /long-range diffusion:
linear response kinetics
8Driving forcethreshold
Bulk/Volumetric/Solution Driving Force
GGsoln
∆T
∆Gsoln
GS
∆G = (S S) ∆T
∆T ≡ Te-T
S∆Gsoln = (S-S) ∆T
= ∆S ∆T V
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TG
Te
< 0
T Suppose N atoms transformed: need X Nt 1 t
∆T
TeX1
Ntype-1 atomsX2
Ntype-2 atoms
X2Gsoln
∆X
X0X X Take them from the matrix:soln 2 X1
N(X0) + X2
N(X0)
∆Gsoln
remix them asX N (X) +
soln
∆G0
1
X1N(X) +
X2N(X)
10X2
1
2
1
∆Gsoln N V
∆X ∆T
∆Gcapillary r2∆G∆G
∆G*∆T < 0:rr*
∆G*∆Gsoln r3∆T < 0:nucleationimpossible
∆Gcapillary r2
impossible
∆T > 0:nucleation
∆Gsoln -r3r
nucleationpossible
Reason for incubation time tinc?
Number of nuclei
∆G∆T < 0:nucleationimpossible of nucleiimpossible
t=0
r
∆T > 0:It takes time for atoms to attach to
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nucleationpossible
nuclei to establish quasi-steady state nuclei density (∆T > 0) at r*
Kinetics of Nucleation, Growth and Coarsening
Number of distinct nuclei
id s c uc e
quasi-steadystate
incubationstate
nucleation growth(supersaturation
ddecreases,nucleation rate
decreases) coarsening
13ttinc
Kinetics of Nucleation, Growth and Coarsening
Number of distinct nuclei
iSimplified View
d s c uc equasi-steadystate
incubationstate
nucleation growth(supersaturation
ddecreases,nucleation rate
decreases) coarsening
NV(t-tinc)
14ttinc
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078kBT
0G* (T)-2
TT
exp(-G*/kBT)
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p( B ) D
078kBT
0G* (T)-2
TTN
exp(-G*/kBT)
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p( B ) D
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∆G* = 163 / 3g 2∆G = 16 / 3gs
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3 2V = 4r3/3 × (2+cos)(1-cos)2/4 Gsoln
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Gcapillary = 4SLr2 × (2+cos)(1-cos)2/4
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diffusion2 ≈ kBT(X02-X2i)/X2e
interface2 ≈ kBT(X2i-X2e)/X2e
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Diffusion-controlledCoarsening
Lifshitz-Slyozov-Wagner (LSW) mean-field theory
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·rif(r,t)
ri0 r0*
Livingpopulation
Z bi ir* Zombiepopulation
true for living
Zombiehas zerovelocity
f(r,t’)Scaling of the
living population only1 1*i
brr r r
true for living population
stretch
compressliving20 *
i i
ii
i i
r r r
rr r r
r0livingliving
01i i
ii
r r r
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To satisfy mass conservation and self-similarity (living pop. only), f(r,t) = r*-4(t)g(r/r*(t)), so ∫dr r*-4(t)g(r/r*(t)) (4r3/3) = const
Grain growth kinetics
31Cyril Stanley Smith, MIT faculty (1961-1992)
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Statistical Self-Similarity
start finish
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start finish
http://www.geology.um.maine.edu/geodynamics/Microdynamics/
GG*
atom ingrain 2
atom ingrain 1
reaction coordinate(atom jump in x)
35x
signifying larger“free volumes”in random GB that trap solutes
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Lengthscale selection due to long-range diffusion
Lengthscale selection due to long-range diffusion:
B l b tBalance betweenThermodynamic and
Kinetic factors
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Interface-controlled Coarsening
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