78
At this point, both the graphical and calculated
methods yield a solution that is valid for a single beam
direction only. Neither method has included the effect of
the beam convergence. There are numerical methods for
including this convergence (Warren, 1979). An alternate
way is to calculate an upper and lower limit of h2+k2+l2
values for a given beam convergence angle. This approach
provides a useful and intuitive estimate of the
convergence effect. It has the shortcoming of slightly
overestimating this effect. A more rigorous method is
described in a following section.
For a given |B|, gB = |g||B|*cos.
Let K2 = Ki (gB) where Ki = 2aR/|B|.
Terms aQ, R, and B are as previously defined.
Then K2 = |g|2 = [g-B/( | B | cos) ]2
and = cos'1 (g.B/(|B|)(K2)1/2).
Two limiting values of h2+k2+l2 (limiting values of
k£), can now be calculated:
K2
1
(B_Lg)2
TfB | cos ( +<*) J 2
>
k22 = (B_ig)2
L |B|cos-<) J2 ,
where < is the convergence angle.