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In the following table numbers of relations are given together with their
percentage of correct indications for triplets, quartets and negative quartets
above variable thresholds of respectively the triplet product *E _{3}* and a
quartet product

Triplets | Positive quartets | Negative quartets | |||||

E_{3} |
no. relations | % correct relations | E_{4} |
no. | % | no. | % |

6.0 | 21 | 100 | 6.0 | 185 | 100 | ||

4.0 | 143 | 100 | 4.0 | 1213 | 100 | ||

3.0 | 353 | 100 | 3.0 | 3295 | 100 | 1 | 100 |

2.5 | 583 | 99.8 | 2.5 | 5813 | 99.8 | 2 | 100 |

2.0 | 980 | 99.7 | 2.0 | 10,006 | 99.5 | 17 | 100 |

1.5 | 1823 | 99.2 | 1.5 | 13,114 | 98.8 | 38 | 100 |

1.0 | 3395 | 96.9 | |||||

As can be seen many relations are available to solve this small *N* = 40
structure. As a rule the number of useful triplets and quartets diminishes as
*N* increases; this effect is quite noticeable for quartets.

One comment regarding the use of negative quartets. If phase relationships such as the triplet relation

are used exclusively and there is no translational symmetry, the trivial solution with all phases = 0 is the most consistent one. To find phases equal to (e.g. in space group ) it is necessary to use relations of the type

Thus relations such as negative quartets (34), although few in number, play an important role in these structure determinations.

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