B. B. Rath Symposium Thermodynamics of Interfaces in Mechanically Alloyed Metals

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B. B. Rath SymposiumThermodynamics of
Interfaces in Mechanically Alloyed Metals
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Mechanically Alloyed Oxide Dispersion
Strengthened Metals
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Atom probe image of MA957
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MA956
Chou Bhadeshia, 1994
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MA956
Chou Bhadeshia, 1994
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Mechanical Mixture
free energy of
mechanical
o
m
mixture
B
G
o
m
Gibbs free energy per mole
A
x
1-x
A
B
Concentration x of B
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free energy of
mechanical
o
m
mixture
B
G
Gibbs free energy per mole
o
m
A
?G
M
Gx
free energy
of solution
A
B
x
Composition
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Entropy
P
P / 2
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For a random mixture, number of configurations
given by
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Boltzmann
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Badmos and Bhadeshia, 1997
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Classical theory for entropy of mixing
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Solution-like behaviour when particles about 1000
atoms in size
Free energy of mixing due to configurational
entropy alone
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Enthalpy
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Surface per unit volume
Sv
Solution formation impossible!
Particle size
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coherent
coherent
incoherent
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Single barrier to solution formation when
components attract
Badmos and Bhadeshia, 1997
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Double barrier to solution formation when
components immiscible
Badmos and Bhadeshia, 1997
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o
m
B
o
m
A
Gibbs free energy per mole
A
B
Paradox at concentration extremities vanishes in
the discrete model of concentration
Concentration x of B
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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
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MA957, 1330 - 30 C
Capdevila Bhadeshia, 2000
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Normal Grain Size
Sub Micron Grain Size
Grain junctions powerful pinning points for small
grains, which are no longer topologically
independent
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Evolution of SolutionsThermodynamics 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.