PowerPoint 프레젠테이션

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승민 비
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1 2009 fall Phase Transformation of Materials Eun Soo Park Office: -16 Telephone: Office hours: by an appointment 1

+ eutectic lamellar - Peritectic solidification- L + α β, difficult to complete. 4.

castings Composition changes over distances - Continuous casting ertical, Curved, Horizontal contiuous casting/ Strip casting

2 Contents for previous class 4. Alloy solidification - Solidification of single-phase alloys - Eutectic solidification - Off-eutectic alloys primary (coring) + eutectic lamellar - Peritectic solidification- L + α β, difficult to complete. 4.4 Solidification of ingots and castings - Ingot structure Chill Zone, Columnar Zone, Equiaxed Zone - Segregation in ingot and castings Composition changes over distances - Continuous casting ertical, Curved, Horizontal contiuous casting/ Strip casting 4.6 Solidification during quenching from the melt * T g depends on thermal history.- Kinetic nature of the glass transition * Glass formation: Liquid stability + Formation of crystalline phase BMG * Are amorphous matal useful? At the Cutting Edge of Metals Research 2

3 Contents in Phase Transformation 상변태를이해하는데필요한배경 (Ch1) 열역학과상태도 : Thermodynamics (Ch2) 확산론 : Kinetics (Ch) 결정계면과미세조직 (Ch4) 응고 : Liquid Solid 대표적인상변태 (Ch5) 고체에서의확산변태 : Solid Solid (Diffusional) (Ch6) 고체에서의무확산변태 : Solid Solid (Diffusionless)

4 < Phase Transformation in Solids > 1) Diffusional Transformation 2) Non-diffusional Transformation (Athermal Transformation) From what we ve learned, what can we say roughly about diffusional transformation in solid? 1) Thermally-activated process: rate exp (-G * /) 2) Misfit strain energy lattice distortion ) Kinetic path for low nucleation barrier coherent or semi-coherent interfaces heterogeneous nucleation 4) Local equilibrium for incoherent (rough) interfaces diffusion-controlled growth 4

5 5. Diffusion Transformations in solid (a) Precipitation ' Homogeneous Nucleation G G A G N hom 0 Gm G* C exp exp (b) Eutectoid Transformation Composition of product phases differs from that of a parent phase. long-range diffusion Which transformation proceeds by short-range diffusion? S Heterogeneous Nucleation G ( G G ) A G het S d 적합한위치는격자결함 ( 핵생성이격자결함제거역할 ) 5

6 5. Diffusion Transformations in solid (c) Order-Disorder Transformation ' (d) Massive Transformation : 조성변화없이결정구조가다른당상또는다상으로분해 (e) Polymorphic Transformation 6 : 온도범위에따라서로다른결정구조가안정

7 Homogeneous Nucleation in Solids Free Energy Change Associated with the Nucleation Negative and Positive Contributions to G? 1) olume Free Energy : G 2) Interface Energy : A ) Misfit Strain Energy : G S G G A G S for spherical nucleation 4 2 G r ( G GS) 4r Plot of G vs r? r* =? G* =? 7

8 Homogeneous Nucleation in Solids r * 2 ( G G ) S G* 16 ( G G ) 2 S : driving force for nucleation Fig. 5.2 The variation of ΔG with r for a homogeneous nucleus. There is a activation energy barrier ΔG*. 8

9 Homogeneous Nucleation in Solids Concentration of Critical Size Nuclei : 단위체적당임계크기를갖는핵의수 C* C exp( G*/ ) 0 C 0 : number of atoms per unit volume in the phase Nucleation Rate : 각각의핵이단위시간당 f 의빈도로임계크기값보다커진다면, N f exp G hom fc* : f 는임계핵이얼마나빈번히모상 α 로부터원자를공급받는가에따라변하는함수 vibration frequency, area of critical nucleus G : activation energy for atomic migration m m N Gm G* C exp exp hom 0 9

10 N Gm G* C exp exp hom 0 : T 에민감하게변함 G* 16 ( G G ) S 2 G* G ( 화학적구동력 ) 1) For X 0, solution treatment at T 1 Liquid Solid 2) For X 0, quenching down to T 2 α α+ β : B 성분이과포화되어 β 석출 G ( 화학적구동력 ) 는조성에따라변함 10

11 Total Free Energy Decrease per Mole of Nuclei Driving Force for Precipitate Nucleation G 0 : 변태를위한전체구동력 / 핵생성을위한구동력은아님 G 1 A X A B X B G 2 : 핵의조성 (X Bβ ) 을갖는작은양이제거될때단위몰당자유 E 변화 (P point) A X A B X B : β 상생성시단위몰당자유 E 변화 (Q point) G n G 2 G 1 G G m n per unit volume of : driving force for nucleation For dilute solutions, G X where X X X G X T : driving force for nucleation 0 e 11

12 Rate of Homogeneous Nucleation aries with Undercooling 실제의평형온도 ΔGs 에의해감소 G X T G* 16 ( G G ) S 2 임계핵의증가확률 구동력 ΔGv 너무작으므로 N N Gm G* C exp exp hom 0 원자이동도 : T 시 확산이너무느리기때문에 12 N

13 The Effect of ΔT on G* het & G* hom? Plot G* het & G* hom vs ΔT and N vs ΔT. ΔT hom c 임계과냉도 N hom 1 cm - 1 s Fig. 4.9 (a) ariation of G* with undercooling ( T) for homogeneous and heterogeneous nucleation. (b) The corresponding nucleation rates assuming the same critical value of G* 1

14 Rate of Homogeneous Nucleation aries with Undercooling 실제의평형온도 ΔGs 에의해감소 G X T G* 16 ( G G ) S 2 임계핵의증가확률 중간정도과냉에서 N 최대 구동력 ΔGv 너무작으므로 N N Gm G* C exp exp hom 0 원자이동도 : T 시 확산이너무느리기때문에 14 N

15 Homogeneous Nucleation in Solids The Effect of Alloy Composition on the Nucleation Rate Compare the two plots of T vs N(1) and T vs N(2). 15

16 Heterogeneous Nucleation in Solids 대부분의핵생성이해당, 적합한위치는격자결함 ( 핵생성이격자결함제거역할 ) G ( G G ) A G het S d Nucleation on Grain Boundaries 가정 : G S ( 불일치변형에너지 )= 0, 입계에서핵생성이일어날때입계에서핵생성의크기 핵의모양전체계면자유에너지를최소로하는상태 cos / 2 G G A A 주형벽에서불균일핵생성에의한응고와유사구형모자형태핵의임계반경 r* 2 / G 불균일핵생성에필요한활성화에너지장벽 G* het * G* * hom het hom S( ) 1 S( ) (2cos )(1cos )

17 Barrier of Heterogeneous Nucleation G G A A A het S v SL SL SM SM SM ML G * 16 2 G SL 16 S ( ) 2 G SL (2 cos cos 4 ) S(θ) has a numerical value 1 dependent only on θ (the shape of the nucleus) G S() G * * het hom 2 SL 16 r * and G * 2 G G SL S ( ) A * * 2cos cos Gsub Ghomo 4 B A A B 2cos cos 4 S( ) 17

18 Heterogeneous Nucleation in Solids * G het ~ cos ~ / How can * and G* be reduced even further? By nucleation on a grain edge or a grain corner. 18

19 Heterogeneous Nucleation in Solids * G het / G * hom vs cos Compare the plots of for grain boundaries, edges and corners S( ) Activation Energy Barrier 19

20 Heterogeneous Nucleation in Solids High-angle grain boundaries are particularly effective nucleation sites for incoherent precipitates with high. If the matrix and precipitate make a coherent interface, * and G* can be further reduced. < Nucleus with Coherent Interface > - 전위혹은과잉공공은핵생성시불일치변형에너지를감소시킴으로써핵생성을도와준다. 20

21 Heterogeneous Nucleation in Solids Rate of Heterogeneous Nucleation Decreasing order of G* 1) homogeneous sites 2) vacancies ) dislocations 4) stacking faults (Activation Energy Barrier for nucleation) : 아래로갈수록핵생성이빨리일어난다. 5) grain boundaries and interphase boundaries 6) free surfaces Gm G* Nhet C1 exp exp nuclei m s 1 C 1 : concentration of heterogeneous nucleation sites per unit volume Gm G* Nhom C0 exp exp 21 : 단위체적당임계크기를갖는핵의수

22 Heterogeneous Nucleation in Solids The Rate of Heterogeneous Nucleation during Precipitation : 매우작은구동력에서도핵생성발생 균일핵생성과불균일핵생성의상대적인크기 > Nhet C G* G* N C 1 hom het exp hom 0 > 1 C 1 /C 0 for GB nucleation? C C 1 0 ( GB thickness) D( grain size) For D = 50 m, = 0.5 nm C C 1 0 D

23 2 C 1 /C 0 for arious Heterogeneous Nucleation Sites C for nucleation on grain edge C D 1 0 C for nucleation on grain corner C D Heterogeneous Nucleation in Solids 불균일핵생성이상대적으로우세해지려면앞선식에서뒤의 exp 항의영향이위의비보다더커져야만함.

24 Heterogeneous Nucleation in Solids In order to make nucleation occur exclusively on the grain corner, how should the alloy be cooled? 1) At small driving forces (ΔG v ), when activation energy barriers for nucleation are high, the highest nucleation rates will be produced by grain-corner nucleation. 2) Grain edge or Grain boundary ) At very high cooling rate? At very high driving forces it may be possible for the (C 1 /C 0 ) term to dominate and then homogeneous nucleation provides the highest nucleation rates. 24

PowerPoint 프레젠테이션

PowerPoint 프레젠테이션 Diffusion Transformations in solid (a) Precipitation ' Homogeneous Nucleation Heterogeneous Nucleation G V G A VG N hom 0 V Gm G* C exp exp kt kt (b) Eutectoid Transformation S G V ( G G ) A G het V S