Time-Temperature-Transformation (TTT) Diagrams

1

Classification of Phase Transformations and Plasticity

Civilian transformation

Military transformation

2

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

3

DissolutionEutectoid

Cellular precipit.SolidificationMelting

BainiteCondensationEvaporation

RecrystallizationGrain growthCondensationEvaporation

DeformationTwinning

disordered phase 1D chain

ordered phase 1

chainordered phase 2Antiphase

boundary

4

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

5

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

6

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

12

37 9

4 5 610 11 12

R d lk

7

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

9

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

12

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

15

078kBT

0G* (T)-2

TT

exp(-G*/kBT)

16

p( B ) D

078kBT

0G* (T)-2

TTN

exp(-G*/kBT)

17

p( B ) D

18

∆G* = 163 / 3g 2∆G = 16 / 3gs

19

3 2V = 4r3/3 × (2+cos)(1-cos)2/4 Gsoln

20

Gcapillary = 4SLr2 × (2+cos)(1-cos)2/4

21

22

diffusion2 ≈ kBT(X02-X2i)/X2e

interface2 ≈ kBT(X2i-X2e)/X2e

23

24

25

26

27

28

Diffusion-controlledCoarsening

Lifshitz-Slyozov-Wagner (LSW) mean-field theory

29

·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

30

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)

32

Statistical Self-Similarity

start finish

33

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

36

37

Lengthscale selection due to long-range diffusion

Lengthscale selection due to long-range diffusion:

B l b tBalance betweenThermodynamic and

Kinetic factors

38

39

Interface-controlled Coarsening

40

41