equal two. If U+V+W = odd, g-B will equal one. This

calculation applies only to the first order zone.

 Most of the CBED patterns in this study were taken

from the gamma prime phase, an L12 superlattice. In such

a superlattice, the superlattice reflections appear in the

forbidden positions for FCC. The true first order Laue

zone for U+V+W = even will consist only of superlattice

reflections. The first zone can be clearly seen in Figure

4.2, a B = (114> CBED pattern of the gamma prime phase in

alloy RSR 197. These superlattice reflections are usually

too weak to give HOLZ lines in the central disc. Only the

HOLZ lines from the B = (114> "second" order zone were

used in this study. This "second" zone will hereafter be

referred to as the first order zone (FOLZ) since it in

fact corresponds to the first order zone for a typical FCC

crystal.

 An alternate way of deriving the preceding result is

through construction of the Ewald sphere and geometrical

solution of the intersection with the reciprocal lattice.

With reference to Figure 4.3,

 the angle 0 equals 9' by similar triangles.

 Then Sin 9' = H/Igl/2R and Sin 9' = H/Igl.

 Combining these two equations gives g2 = 2RH.

 By definition, g2 = l/d2 = (h2+k2+12)/ao2.

 Substituting for igl2 gives h2+k2+12 = 2a2 RH.

 H can be shown to equal (g-B/a )(U2+V2+W2)1/2.

 Therefore, h2+k2+12 = (2aR/IBI)(g.B).