74
To solve equation (1), only the value of g*B needs to
be derived (we assume here that the other information is
at hand). The values of gB will depend on the specific
cubic Bravais lattice.
For an FCC crystal, as for both the matrix and the
gamma prime phase in the RSR alloys, diffraction pattern
planar indices cannot be mixed. The three values of g in
g*B will thus be all odd or all even. Indices for the
beam direction can be reduced to three combinations of
terms: B is odd, odd, odd; B is odd, even, even; and B is
odd, odd, even. The following cases are constructed to
show values for the dot products of unmixed g indices and
the three combinations of B terras given above.
Case 1) B h,k,l Case 2) B h,k,l Case 3) B h,k,l
0
E
0
E
lQ
E
0
0
E
0
0
E
0
0
E
0
0
E
E
E
E
0
0
E
0
0
E
E
E
E
E
E
E
The first case will be used as an example. If B is all
odd, for example, B = (111), the individual terms in the
dot product of this B and an odd set of g indices will
contain all odd terms. The algebraic sum of all odd terms
is odd. For this case, g*B can equal one, since one is an
odd term. The results in Case 2 are the same. For
Case 3, the algebraic sum will always be even. For this
case, g*B will equal two. These results can be
generalized as follows: if U+V+W = even, g*B will