byeong-joo lee calphad non-classical nucleation theory

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

Non-Classical Non-Classical Nucleation TheoryNucleation Theory

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

Y C Li et al. MSMSE (2012)

Feng Yan and John Texter, 2006

BackgroundBackground

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

IntroductionIntroductionRefs: 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

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Spinodal DecompositionSpinodal Decomposition

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Mathematical Formulation Mathematical Formulation - Thermodynamics of Spinodal Decomposition- Thermodynamics of Spinodal Decomposition

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

Mathematical Formulation Mathematical Formulation - Thermodynamics of Spinodal Decomposition- Thermodynamics of Spinodal Decomposition

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

Mathematical Formulation Mathematical Formulation - Thermodynamics of Spinodal Decomposition- Thermodynamics of Spinodal Decomposition

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

Mathematical Formulation Mathematical Formulation - Thermodynamics of Spinodal Decomposition- Thermodynamics of Spinodal Decomposition

► existence of minimum in wave length : for the balance between bulk energy and interfacial energy

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Diffusion Equation- Diffusion Equation

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Diffusion Equation- Diffusion Equation

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Diffusion Equation- Diffusion Equation

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Diffusion Equation- Diffusion Equation

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Solution of Diffusion Equation- Solution of Diffusion Equation

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

Kinetics of Spinodal Decomposition Kinetics of Spinodal Decomposition - Solution of Diffusion Equation- Solution of Diffusion Equation

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

Appendix Appendix - Euler’s Equation: Marion Chap. 6- Euler’s Equation: Marion Chap. 6

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