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6. Systematic Enhancement, Epsilon

The third and last case of special reflections is where hR = h and ht = 0 (modulo 1). The 2 (or 3 or 4 or 6 or more) contributions are equally large and have the same phase and thus enlarge each other. The expected intensity ($I \sim F^2$) of such a reflection is 2 (or 3 or 4 or 6 or more) times as large as that of a general reflection. The factor of enhancement is called epsilon ($\varepsilon$) and is easily derived as the number of rotation matrices Ri that can be applied on h and give back h.

Example :

In P2 there are two symmetry operations:

\begin{displaymath}
\textbf{R}_1 = \left(\begin{array}
{ccc}1&0&0\\ 0&1&0\\ 0&0&...
 ...f{t}_2 = \left(\begin{array}
{c}0\\ 0\\ 0\end{array}\right).\\ \end{displaymath}

All reflections of the type (0 k 0) will fulfil the criteria hR = h and ht = 0 for both the symmetry operations, and thus these reflections have $\varepsilon$ = 2. It is clear that $\varepsilon$ is not the effect of systematic absences. See Fig. 5.



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