Phase problem

The phase problem in crystallography is the inability to reconstruct an electron density map due to the lack of phase information of the diffracted rays.

Recall that the modulus of a complex function is \left | z \right |=\left | re^{ix} \right |=\left | rcosx+irsinx \right |=\sqrt{r^2cos^2x+r^2sin^2x}=r. Since the structure factor Fhkl is a complex function of the form z = re, where r = IzI ,

F_{hkl}=\left | F_{hkl} \right |e^{i\phi_{hkl}}\; \; \; \; \; \; \; (49)

Hence, Fhkl is composed of two factors, the modulus IFhklI and the phase e^{i\phi_{hkl}}. If we replace Fhkl in eq48 with just the modulus factor, information with regard to the phase is lost. Without phase information, it is impossible to reconstruct an electron density map. This is known as the phase problem, which fortunately can be overcome by a few methods, one of which is the Patterson method.


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