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Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Classical Nucleation Theory.

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Presentation on theme: "Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Classical Nucleation Theory."— Presentation transcript:

1 Byeong-Joo Lee www.postech.ac.kr/~calphad Non-Classical Nucleation Theory

2 Byeong-Joo Lee www.postech.ac.kr/~calphad Y C Li et al. MSMSE (2012) Feng Yan and John Texter, 2006 Background

3 Byeong-Joo Lee www.postech.ac.kr/~calphad Introduction Refs: J.W. Cahn : Acta Met. 7, 795 (1961); J. Chem. Phys. 42, 93 (1965); Trans. AIME, 242, 166 (1968) J.E. Hilliard, "Phase Transformations," ASM (1970) ► Historically, initiated in an effort to explain uniform distribution of CuAl2 precipitates in Al-Cu alloys. ► Consider the Gibbs energy curve and stability of matrix phase against infinitesimal fluctuation of concentration. ○ Region I · stable against small local fluctuation (nothing happens) large fluctuation → nucleation of β small in extend, large in degree, "Nucleation & Growth Mechanism" ○ Region II · unstable against small local fluctuation (decrease in total energy) spontaneously goes to more fluctuation small in degree, large in extend, "Uphill Diffusion", relatively periodic microstructure

4 Byeong-Joo Lee www.postech.ac.kr/~calphad Spinodal Decomposition

5 Byeong-Joo Lee www.postech.ac.kr/~calphad Mathematical Formulation - Thermodynamics of Spinodal Decomposition

6 Byeong-Joo Lee www.postech.ac.kr/~calphad Mathematical Formulation - Thermodynamics of Spinodal Decomposition

7 Byeong-Joo Lee www.postech.ac.kr/~calphad Mathematical Formulation - Thermodynamics of Spinodal Decomposition

8 Byeong-Joo Lee www.postech.ac.kr/~calphad Mathematical Formulation - Thermodynamics of Spinodal Decomposition ► existence of minimum in wave length : for the balance between bulk energy and interfacial energy

9 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Diffusion Equation

10 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Diffusion Equation

11 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Diffusion Equation

12 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Diffusion Equation

13 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Solution of Diffusion Equation

14 Byeong-Joo Lee www.postech.ac.kr/~calphad Kinetics of Spinodal Decomposition - Solution of Diffusion Equation

15 Byeong-Joo Lee www.postech.ac.kr/~calphad Appendix - Euler’s Equation: Marion Chap. 6

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