1. Evolution of Solutions Thermodynamics of Mechanical Alloying
A. Badmos and H. K. D. H. Bhadeshia, Metall. & Mater. Trans. A, 18A (1997) 2189.
H. K. D. H. Bhadeshia,
Proceedings of the Royal Microscopical Society, 35 (2000) 95.
Materials Science and Technology, 16 (2000) 1404.
H. K. D. H. Bhadeshia & H. Harada, Applied Surface Science, 67 (1993) 328.

2. Oxide Dispersion Strengthened Metals
Mechanically Alloyed
Oxide Dispersion Strengthened Metals

3. Normal Grain Size
Sub Micron Grain Size
Grain junctions powerful pinning points for small grains, which are no longer topologically independent

4. Fe-20Cr-5Al-0.5Ti-0.3 yttria wt%
90% reduction
Capdevila & Bhadeshia, 2000

6. Helical grains
Capdevila & Bhadeshia, 2000

7. Capdevila & Bhadeshia, 2000

8. Atom probe image of MA957

9. MA956
Chou & Bhadeshia, 1994

10. MA956
Chou & Bhadeshia, 1994

11. Mechanical Mixture Gibbs free energy per mole Concentration x of B m
free energy of
mechanical m o
mixture B G* m o
Gibbs free energy per mole A x
1-x A B
Concentration x of B

12. Gibbs free energy per mole
free energy of
mechanical m o
mixture B G*
Gibbs free energy per mole m o A ∆G M
G{x}
free energy
of solution A B x
Composition

13. Entropy P
P / 2

14. + =

15. For a random mixture, number of configurations given by:

16. Boltzmann

18. Classical theory for entropy of mixing

19. Solution-like behaviour when particles about 1000 atoms in size
Free energy of mixing due to configurational entropy alone

20. Enthalpy

21. Sv Surface per unit volume Solution formation impossible!
Particle size

22. coherent
coherent
incoherent

23. Single barrier to solution formation when components attract
Badmos and Bhadeshia, 1997

24. Double barrier to solution formation when components immiscible
Badmos and Bhadeshia, 1997

25. Barrier to solution formation
Badmos and Bhadeshia, 1997

26. Barrier to solution formation, especially in rich solutions
Badmos and Bhadeshia, 1997

27. m o B m o A
Gibbs free energy per mole A B
Paradox at concentration extremities vanishes in the discrete model of concentration
Concentration x of B

28. Molar Gibbs free energy
ferrite
cementite
Molar Gibbs free energy m o Fe Fe x x x a q
Concentration of carbon

30. Atom probe image of Scifer,
5.5 GPa steel wire
Bhadeshia and Harada, 1993

31. Scifer, 5.5 GPa with ductility!
Kobe Steel

32. Mechanical tempering a a¢ m Molar Gibbs free energy of ferrite Fe x x
Concentration of carbon

33. Amorphous phase formation during mechanical alloying of Cu and Cd powders
….contribution from Cu/d interfaces, and accompanying increase in free energy, provide additional driving force for amorphisation….
Zhang & Massalski
Metall. & Mater. Trans. 29A (1998) 2425