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The relation is the first phase relationship which will be considered
here; it estimates in centrosymmetric space groups the phase of reflection 2*H*
on the basis of the magnitudes |*E*_{H}| and |*E*_{2H}|. To start with,
geometrical considerations will be applied to reflections with simple indices.

In a centrosymmetric crystal only phases of 0 and occur; provided that the
phase of the 110 reflection is 0 the maxima of the associated electron density
wave are found at the lines I of Fig. 2 and the minima at the lines II. If the
phase of 110 is , the maxima and minima are interchanged. The lines where
the electron density wave has 0 value are marked with III. Thus in the event
|*E _{110}*| is large and = 0, the electron density is mainly
concentrated in the shaded areas of Fig. 3. For the electron density wave
associated with the 220 reflection the maxima are found at both lines I and II
in Fig. 2 in the case its phase is 0 and the minima at the lines III. Thus,
when |

The combination of the two electron density waves associated with the
reflections 110 and 220 leads to Fig. 5, in which in the areas I maxima are
found of both density waves. In the areas II the maximum of 220 coincides with
the minimum of 110, resulting in a low density. In the event that both
reflections have a large |*E*| value it is likely that the atoms are
concentrated in the double shaded area.

In case the phase = , the vertically shaded areas shift to
the blank regions of Fig. 5 and then there is no overlap between the
horizontally (110) and vertically (220) shaded areas; this implies that no
position for the atoms can be found in which they contribute strongly to both
structure factors. As a result for = and = 0 it
is not likely that both structure factor magnitudes |*E _{110}*| and |

In conclusion, for large structure factors |*E _{110}*| and |

Up to now no attention is paid to the situation = , the reader is invited to show that this gives no change in the formulation of the relation.

The comparison of *H* and 2*H* can be considered as a one-dimensional problem
which can be understood by looking along line *A* in Fig. 2. In Fig. 6 the
situation along this line is sketched with = = 0 while in
Fig. 7 = 0 and = . Areas labelled *P* in Fig. 6
denote regions of considerable positive overlap, whereas in Fig. 7 only regions
of minor positive overlap are seen. The implication is that for large |*E*_{H}|
and |*E*_{2H}| the situation depicted in Fig. 6 is more probably true and thus
= 0. When = , as denoted by the dotted line in Fig. 6
the overlap areas marked *Q* show that is still zero.

**Copyright © 1984, 1998 International Union of
Crystallography**