= X-ray crystallographic structure inference
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<X-ray crystallographic structure inference> is an <inverse problem>: infer a <crystal structure> from measured <X-ray> <diffraction>. A proposed <unit cell> and <atomic basis of a crystal> predict a pattern; structure determination asks which proposals survive comparison with that pattern. The useful separation is between directions and strengths. Peak positions constrain the <reciprocal lattice> and hence <interplanar spacings>; relative <wave intensities> constrain the motif through the <crystal basis structure factor>. Knowing a repeat distance does not locate all the <chemical atoms> within that repeat.
The <lattice constant from two indexed reflections> example isolates the geometric inference. <Basis intensities and phase ambiguity> then holds the translations fixed while changing the motif. Even complete, noiseless <wave intensity> data need not determine all <wave phases>: this is the <phase problem>. Chemical composition, <symmetry>, and additional measurements can supply constraints beyond the original pattern.<Online Dictionary of Crystallography by International Union of Crystallography/Phase problem>[Online Dictionary of Crystallography by International Union of Crystallography; Definition and Methods of solution: intensities determine structure-factor magnitudes but not phases; additional structural information enters phase estimation]{ref}
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