Editing Phase problem (section)

=== [[Direct methods (crystallography)|Direct (''ab initio)'' methods]] ===
If the crystal diffracts to high resolution (<1.2 Å), the initial phases can be estimated using direct methods.<ref name=":0" />  Direct methods can be used in  [[x-ray crystallography]],<ref name=":0" /> [[neutron crystallography]],<ref>{{Cite journal|last=Hauptman|first=H.|date=1976-09-01|title=Probabilistic theory of the structure invariants: extension to the unequal atom case with application to neutron diffraction|journal=Acta Crystallographica Section A |language=en|volume=32|issue=5|pages=877–882|doi=10.1107/S0567739476001757|bibcode=1976AcCrA..32..877H|doi-access=free}}</ref> and [[electron crystallography]].<ref name=":2" /><ref name=":3" />

A number of initial phases are tested and selected by this method. The other is the Patterson method, which directly determines the positions of heavy atoms.  The [[Patterson function]] gives a large value in a position which corresponds to interatomic vectors. This method can be applied only when the crystal contains heavy atoms or when a significant fraction of the structure is already known.  

For molecules whose crystals provide reflections in the sub-Ångström range, it is possible to determine phases by [[brute-force search|brute force]] methods, testing a series of phase values until spherical structures are observed in the resultant electron density map.  This works because atoms have a characteristic structure when viewed in the sub-Ångström range.  The technique is limited by processing power and data quality.  For practical purposes, it is limited to "small molecules" and peptides because they consistently provide high-quality diffraction with very few reflections.