On the use of negative quartets

The number of negative quartets (NQ) φ_h + φ_k + φ_l + φ _{- h - k - l} = π is small compared with the number of Σ₂-triplets. Also the associated weights B = 2N^-1|E_hE_kE_lE _{- h - k - l}| are small relative to the weights of the triplets. Therefore negative quartets cannot be used to find phases of reflexions. However, in symmorphic space groups they are very useful for selecting the correct phase set from all sets produced by a multisolution procedure. Negative quartets can also be employed to remove most of the errors in a normal quartet list, so that for quartets a reliability can be obtained better than for triplets. This error cleaning procedure can be used to improve the reliability of the strengthened quartet relation.