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In a space group with *n* equivalent positions (**R**_{i}**x** +
*t*_{i}), *i* = 1, 2, , *n* the structure factor can be calculated through
summing up the contributions to it in the following way:

| |
(4) |

i.e. first all the atoms of the first equivalent position are added, then those
atoms related to the first ones through **R**_{2} + **t**_{2} are
added, and so on until all atoms within the unit cell are added.
According to (1) every equivalent position can be written as **Rx** +
**t**. If this expression is inserted into (4), and we for the sake of
simplicity look at a space group with 2 equivalent positions, we obtain:

| |
(5) |

The second of these sums can be rewritten, since

| |
(6) |

If (5) and (6) are combined we get:

| |
(7) |

It is obvious that in the general case the contributions from the two parts of
the structure differ, both in amplitude and phase. If, however, the two
contributions are equally large, i.e. have identical amplitudes, there will be
several interesting situations. The amplitudes of two (or more) parts of the
structure are equal if and only if or
for at least one , .

** Next:** 4. Phase Restrictions
**Up:** Rotation Matrices and Translation Vectors in
** Previous:** 2. The Structure Factor

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