APPENDIX B
INTERPLANAR ANGLES
If the interplanar angles for the 931 lines are
calculated and summed, the sum will not total 180
degrees. For example, for the interplanar angles a (see
Figure 4.8) (angle between 193 and 391), b (angle between
391 and 931), c (angle between 931 and 913), and d (angle
between 913 and 193), the calculated interplanar angles
are a = 27.113 degrees, b = 54.38 degrees, c = 27.113
degrees, and d = 72.74 degrees. The sum of these angles
is 181.35 degrees. Figure 4.8 clearly shows that this
value should be 180 degrees. The discrepancy of 1.35
degrees arises because the calculated values of the
interplanar angles are not the interplanar angles in the
114 plane, the plane in which the diffracted information
appears. The calculated angles are calculated in a plane
perpendicular to the zone axis of the two intersecting
planes. This zone axis, for high order Laue zone lines,
is not perpendicular to the 114 plane. As an example,
consider the angle formed by the intersection of the 111
plane and the 111 plane. The calculated angle between
these two planes is 70.53 degrees. The angle of
intersection projected onto the 001 plane is clearly 90
degrees. A vector common to both the 001 plane and either
111 plane is the cross product of these two vectors. For
199