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Next: The |E|'s of H and 2H:
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Note: in this text FH designates the structure factor corrected for thermal
motion and brought to an absolute scale; generally this is done using a Wilson
plot. Since the scattering factor of any atom decreases for larger reflection
angle , and the expected intensity of a
reflection is given by
| |
(1) |
reflections measured at different -values can not be compared directly.
Expression (1) can be used to calculate the so called normalized structure
factor
| |
(2) |
It is obvious from a comparison of (1) and (2) that E2H =
1 for all values of .
The structure-factor expression in terms of the normalized structure factor is
then:
| |
(3) |
If the form factor fj has the same shape for all atoms (fj = Zjf),
expression (3) can be written as
| |
(4) |
This is clearly the structure factor formula of a point atom structure, because
no -dependent factors are present any more.
In order to find the maximum value of |E|, let us consider an equal atom
structure for which the structure factor (4) further reduces to
| |
(5) |
The maximum possible value of |EH| is N/N1/2 = N1/2.
The unitary structure factor U was used extensively in the early literature on
Direct Methods:
| |
(6) |
The denominator represents the maximum possible value of FH and thus UH
varies between 0 and 1. In the equal atom case the relation between UH and
|EH| is given by
which can easily be verified by the reader from (6) and (2).
Next: The |E|'s of H and 2H:
Up: An Introduction to Direct Methods. The
Previous: Strong and Weak Structure Factor Magnitudes FH
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