40
model which explains the gamma prime alignment and uniform
size by considering the coarsening behavior of gamma prime
precipitates under the influences of mutual elastic
interactions between the coarsening gamma prime
precipitates. Ardell's model provides the most reasonable
explanation for the development of the microstructures in
alloys like those discussed in Chapter 5 of this
dissertation.
2.3 Diffraction Patterns: NiyMo Phases/Ni^Al
The reciprocal lattices of the various NixMo phases
can be constructed easily based on the crystallography of
each precipitate type. Since it is easiest to relate the
diffraction patterns of each to the parent FCC lattice,
(here the disordered gamma phase), this will be done for
the DO22 N3M0 phase. The other diffraction patterns were
similarly constructed.
2.3.1 DO?? Reciprocal Lattice
The DO22 is a tetragonal cell with atom positions at
Mo (000), (1/2, 1/2, 1/2);
Ni (1/2, 1/2, 0), (1/2, 0, 1/4), (1/2, 0, 3/4)
(0, 1/2, 1/4), (0, 0, 1/2), (0, 1/2, 3/4).
The structure factor can then be written as the summation:
F= Mof (1+exp ("IT i (h-f-k+1) ) + wif t (exP 71" i (h+k) ) +
exp(TTi(l)) + exp(tt(h+1 /2)) + exp(tr i(k+l/2)) +
exp(TTi(h+3l/2)) + exp(rr i(k+31/2)) L