Evolution of Solutions Thermodynamics of Mechanical Alloying

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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.
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Mechanically Alloyed Oxide Dispersion
Strengthened Metals
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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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Fe-20Cr-5Al-0.5Ti-0.3 yttria wt 90 reduction
Capdevila Bhadeshia, 2000
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Helical grains
Capdevila Bhadeshia, 2000
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Capdevila Bhadeshia, 2000
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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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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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Barrier to solution formation
Badmos and Bhadeshia, 1997
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Barrier to solution formation, especially in rich
solutions
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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ferrite
cementite
o
Molar Gibbs free energy
m
Fe
Fe
x
x
x
q
a
Concentration of carbon
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Atom probe image of Scifer, 5.5 GPa steel wire
Bhadeshia and Harada, 1993
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Scifer, 5.5 GPa with ductility!
Kobe Steel
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Mechanical tempering
o
m
Fe
Molar Gibbs free energy of ferrite
Fe
x
x
x
a
a
Concentration of carbon
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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