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Mechanically Alloyed
Oxide Dispersion Strengthened Metals
Atom probe
image of MA957
1008060402000
20
40
60
80
100
Cluster Number (50 Ion Clusters)
Fe
Cr
MA956
Chou & Bhadeshia, 1994
0
5
10
15
20Atom-Probe
Binomial
Iron / at%
Total Ions : 12006 Fe ions : 8229
0
5
10
15
20Atom-Probe
Binomial
Chromium / at%
Total Ions : 12006 Cr ions : 2434
0
5
10
15
20
Atom-Probe
Binomial
Aluminium / at%
Total Ions : 12006 Al ions : 1231
MA956
Chou & Bhadeshia, 1994
A B
(1-x) x
o
o
A
B
A B
1-x
Gib
bs
free e
nerg
y p
er
mole
Concentration x of B
free energy of mechanical mixture
G*
x
Mechanical Mixture
o
o
A
B
A Bx
Gib
bs
free e
nerg
y p
er
mole
Composition
G{x}
free energy of mechanical mixture
∆G M
free energy of solution
G*
A B+
Solution
atomic solution
+ =
For a random mixture, number of configurations given by:
Boltzmann
Classical theory for entropy of mixing
10410310210110010 -1
10 0
10 1
10 2
10 3
10 4
Atoms per particle
Solution-like behaviour when particles about 1000 atoms in size
Free energy of mixing due to configurational entropy alone
Enthalpy
Surface per unit volume
SvParticle size
Solution formation impossible!
coherent
coherent
incoherent
Single barrier to solution formation when components attract
Badmos and Bhadeshia, 1997
1e+00 1e+02 1e+04 1e+06 1e+08 1e+10-100
-50
0
50
100
-100
-50
0
50
100 x = 0.02 x = 0.14 x = 0.50
Atoms per particle
(b)
Ω - 100 J mol- 1
= 1000 T K
1e+00 1e+02 1e+04 1e+06 1e+08 1e+10-100
-50
0
50
100
-100
-50
0
50
100 x = 0.02 x = 0.14 x = 0.5
Atoms per particle
Ω = 100 J mol- 1
= 1000 T K
Double barrier to solution formation when components immiscible
Badmos and Bhadeshia, 1997
o
o
A
B
A B
Composition
free energy of solution
o
o
A
B
A B
Gib
bs
free e
nerg
y p
er
mole
Concentration x of B
Paradox at concentration extremities vanishes in the discrete model of concentration
