Mechanically Alloyed Metals

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Presentation transcript:

Mechanically Alloyed Metals thermodynamics of particulate solutions

Oxide Dispersion Strengthened Metals Mechanically Alloyed Oxide Dispersion Strengthened Metals

Atom probe image of MA957

MA956 Chou & Bhadeshia, 1994

MA956 Chou & Bhadeshia, 1994

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

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

Entropy P P / 2

+ =

For a random mixture, number of configurations given by:

Boltzmann

Badmos and Bhadeshia, 1997

Classical theory for entropy of mixing

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

Enthalpy

Sv Surface per unit volume Solution formation impossible! Particle size

coherent coherent incoherent

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

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

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

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.