1. Phase Transformations Spinodal Decomposition Byeong-Joo LeePOSTECH-MSE

2. 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

3. Mathematical Formulation - Thermodynamics of Spinodal Decomposition

4. Mathematical Formulation - Thermodynamics of Spinodal Decomposition

5. Mathematical Formulation - Thermodynamics of Spinodal Decomposition

6. Mathematical Formulation - Thermodynamics of Spinodal Decomposition ► existence of minimum in wave length : for the balance between bulk energy and interfacial energy

7. Kinetics of Spinodal Decomposition - Diffusion Equation

8. Kinetics of Spinodal Decomposition - Diffusion Equation

9. Kinetics of Spinodal Decomposition - Diffusion Equation

10. Kinetics of Spinodal Decomposition - Diffusion Equation

11. Kinetics of Spinodal Decomposition - Solution of Diffusion Equation

12. Kinetics of Spinodal Decomposition - Solution of Diffusion Equation

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