1. Byeong-Joo Lee http://cmse.postech.ac.kr Byeong-Joo Lee POSTECH - MSE calphad@postech.ac.kr Phase Equilibria in a Single- Component System

2. Byeong-Joo Lee http://cmse.postech.ac.kr Phase Diagram for H 2 O

3. Byeong-Joo Lee http://cmse.postech.ac.kr Phase Diagram for Fe

4. Byeong-Joo Lee http://cmse.postech.ac.kr Phase Diagram for Fe

5. Byeong-Joo Lee http://cmse.postech.ac.kr Equilibrium Thermal, Mechanical and Chemical Equilibrium Concept of Chemical Potential In a one component system, Temperature and Pressure dependence of Gibbs free energy

6. Byeong-Joo Lee http://cmse.postech.ac.kr Temperature Dependence of Gibbs Energy

7. Byeong-Joo Lee http://cmse.postech.ac.kr Temperature Dependence of Gibbs Energy - for H 2 O

8. Byeong-Joo Lee http://cmse.postech.ac.kr Temperature & Pressure Dependence of Gibbs Energy Clausius-Clapeyron equation For equilibrium between the vapor phase and a condensed phase constant

9. Byeong-Joo Lee http://cmse.postech.ac.kr for S/L equilibrium Phase Diagram - for H 2 O

10. Byeong-Joo Lee http://cmse.postech.ac.kr Equilibrium vapor pressures vs. Temperature

11. Byeong-Joo Lee http://cmse.postech.ac.kr Equilibrium vapor pressures vs. Temperature

12. Byeong-Joo Lee http://cmse.postech.ac.kr Gibbs Phase Rule Degree of Freedom number of variables which can be independently varied without upsetting the equilibrium F = p(1+c) – (p-1)(2+c) = c – p + 2

13. Byeong-Joo Lee http://cmse.postech.ac.kr Example - Phase Transformation of Graphite to Diamond Calculate graphite→diamond transformation pressure at 298 K, given H 298,gra – H 298,dia = -1900 J S 298,gra = 5.74 J/K S 298,dia = 2.37 J/K density of graphite at 298 K = 2.22 g/cm 3 density of diamond at 298 K = 3.515 g/cm 3