sequence may start, as indicated in Fig. 4.7(b). The Monte Carlo calcula-
tion of the percolation threshold for the long-range diffusion by this vari-
ant of the ASB mechanism yields about 11% of the antistructure atoms as
the critical concentration.
During the ASB sequence of jumps, only one species of atoms moves
(see Fig. 4.7). Therefore, the diffusivities of the two components are not
coupled.
In a strict sense, the genuine ASB mechanism operates only after the
percolation threshold is reached. However, in combination with another
mechanism (usually the sublattice diffusion mechanism), the ASB mech-
anism [for example, jump sequence 1 → 2 in Fig. 4.7(b)] can substantially
contribute to long-range diffusion without any percolation threshold.
[7, 8,39]
We will therefore use the term ASB mechanism in such cases as well,
referring to the specific sequence presented in Fig. 4.7.
Other Diffusion Mechanisms. Several other mechanisms, which may
be relevant in some specific cases, were proposed for ordered intermetal-
lic compounds. The next-nearest neighbor jump mechanism was shown to
correspond to the lowest activation energy of single Ni vacancy migration
in Al-rich NiAl.
[22]
The divacancy mechanism, with both vacancies
belonging to the same sublattice in NiAl, was considered by Divinski
et al.
[40]
After the given sequence of four atomic jumps, the initial order is
completely restored and the divacancy has moved by one step.
4.4 Experimental Results on Bulk Diffusion
in Ordered Aluminides
A common feature of all aluminides is that there are practically no
direct tracer measurements of Al self-diffusion in these compounds. This
problem is related to the very high price and the low specific activity of
the only available
26
Al radioisotope and to the difficulty of avoiding oxi-
dation of this isotope during a diffusion study. The only directly measured
Al-diffusion data
[41]
are considered to be unreliable.
There exist, however, two approaches to overcome this difficulty.
First, by combining interdiffusion and transition metal tracer diffusion
data (D
∼
and D
*
TM
, respectively), the diffusivity of the Al component D
*
Al
in
a binary system can be evaluated by applying the Darken-Manning for-
malism,
[42, 43]
neglecting the volume effects:
D
∼
∼
(N
Al
D
*
TM
N
TM
D
*
Al
)ΦS. (3)
Here, N
TM
and N
Al
are the mole fractions of the transition metal element
and Al in the compound, respectively; Φ is the thermodynamical factor;
188 DIFFUSION PROCESSES IN ADVANCED TECHNOLOGICAL MATERIALS