1. Mechanically Alloyed Metals
thermodynamics of particulate solutions

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

3. Atom probe image of MA957

4. MA956
Chou & Bhadeshia, 1994

5. MA956
Chou & Bhadeshia, 1994

6. 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

7. 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

8. Entropy P
P / 2

9. + =

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

11. Boltzmann

12. Badmos and Bhadeshia, 1997

13. Classical theory for entropy of mixing

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

15. Enthalpy

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

17. coherent
coherent
incoherent

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

19. 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

20. 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

21. 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.