Time-Temperature-Transformation (TTT) Diagrams

Transcription

1 Time-Temperature-Transformation (TTT) Diagrams 1

2 Classification of Phase Transformations and Plasticity Civilian transformation Military transformation 2

3 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, Type Military Civilian Effect of temperature Interface type Athermal Glissile (coherent or semicoherent) Thermally activated Non-glissile (coherent, semicoherent, incoherent, solid/liquid or solid/vapor) Composition of parent and product phases same same different Nature of diffusion processes No diffusioni Short-range diffusion (across interface) Long-range g diffusion (through lattice) Interface, diffusion, or mixed control? Interface control Interface control Mainly interface control Mainly diffusion control Mixed control Martensitic Deformation Twinning Massive Ordering Polymorphic Recrystallization ti Grain growth Condensation Evaporation Precipitation Dissolution Bainite Condensation Evaporation Precipitation Dissolution Solidification Melting Precipitation Dissolution Eutectoid Cellular precipit. 3

4 1D chain disordered phase ordered phase 1 Antiphase boundary ordered phase 2 4

5 Example of Military Transformation with Glissile Interface a b c b a c b a c b a FCC(111)planes Stacking faults Glissile interface Deformation twinning Glissile interface (111)<112> Shockley partial dislocations 5

6 Military Transformation Civilian Transformation parent parent product product Soldiers on parade ground Marching band Job search in corporate America 6

7 Short-range Diffusion Long-range Diffusion left up right down Random walk: atomic registry destroyer 7

8 Military versus civilian growth kinetics Growth speed v (velocity of interface) Collective shear athermal Higher T Short-range / long-range diffusion: linear response kinetics threshold Driving force 8

9 Bulk/Volumetric/Solution Driving Force G soln T G soln T T e -T G =(S S soln -S ) T = S T V < 0 T e S S G G T 9

10 T T e T Suppose N atoms transformed: need X 1 N type-1 atoms X 2 N type-2 atoms G soln X X X 0 X X Take them from the 2 soln matrix: 2 X 1 N (X 0 ) + X 2 N (X 0 ) 1 1 G 0 X 2 G soln 2 remix them as X 1 N (X )+ X 2 N (X ) G soln N V X T 10

11 G G G capillary r 2 T <0: nucleation impossible G soln r 3 G* r* r G capillary r 2 r T > 0: nucleation possible G soln -r 3

12 G Reason for incubation time t inc? T < 0: nucleation impossible Number of nuclei t=0 It takes time for atoms to attach to nuclei to establish quasi-steady state nuclei density ( T > 0) at r* T > 0: nucleation possible r 12

13 Kinetics of Nucleation, Growth and Coarsening Number of distinct ds nuclei uce incubation quasisteady state nucleation growth (supersaturation decreases, nucleation rate decreases) coarsening t inc t 13

14 Kinetics of Nucleation, Growth and Coarsening Number of distinct ds nuclei uce incubation quasisteady state nucleation Simplified View growth (supersaturation decreases, nucleation rate decreases) coarsening NV (t-t inc ) t inc t 14

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16 0 78k B T G* ( T) -2 T D exp(- G*/k B T) ) 16

17 0 78k B T G* ( T) -2 T N D exp(- G*/k B T) ) 17

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19 G* =16 3 /3g 2 s 19

20 V = 4 r 3 /3 (2+cos )(1-cos ) 2 /4 G soln G capillary = 4 SL r 2 (2+cos )(1-cos ) 2 /4 20

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23 diffusion 2 k B T(X 02 -X 2i )/X 2e interface 2 k B T(X 2i -X 2e )/X 2e 23

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29 Diffusion-controlled Coarsening Lifshitz-Slyozov-Wagner (LSW) mean-field theory 29

30 r i f(r,t) Living population 0 r i 0 r r * Zombie i has zero velocity r i b 1 1 ri r* ri true for living population f(r,t ) Zombie population Scaling of the living population only stretch compress i 2 i living rr i i r i living 1 0 r i living 0 * r To satisfy mass conservation and self-similarity (living pop. only), f(r,t) = r *-4 (t)g(r/r * (t)), so drr *-4 (t)g(r/r * (t)) (4 r 3 /3) = const 30

31 Grain growth kinetics Cyril Stanley Smith, MIT faculty ( ) 31

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33 Statistical Self-Similarity start finish 33

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35 G G* atom in grain 1 atom in grain 2 reaction coordinate (atom jump in x) x 35

36 signifying larger free volumes in random GB that trap solutes 36

37 Lengthscale selection due to long-range diffusion 37

38 Lengthscale selection due to long-range diffusion: Bl Balance between bt Thermodynamic and Kinetic factors 38

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40 Interface-controlled Coarsening 40

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