Amplitude of structure factor

When we describe structure factors and electron density as Fourier series, we find that they are intimately related. The electron density is the Fourier transform of the structure factors, which means that we can convert the crystallographic data into an image of the unit cell and its contents. One necessary piece of information is, however, missing for each structure factor. We can measure only the intensity Ihkl of each reflection, not the complete structure factor Fhkl. What is the relationship between them It can be shown that the amplitude of structure factor Fhkl is proportional to the square root of... 

The intensities measured in detectors are proportional to the squares of the amplitudes of structure factors ... 

It is clear that the key elements for controlling the features we can get after inverse Fourier transformation are the phases of the dilfraction, which can not be obtained directly in diffractions. The easily archived data, the amplitudes of structure factors, only play very weak roles in the structures. That is the so-called phase problem . The main task of structure determinations by crystallography is to determine the lost phases. 

After the phases of all observed diffraction spots have been solved, then the structure factors can be obtained. Therefore, the inverse Fourier transformation would give the electron densities inside the crystal cell. According to the electron densities, the positions of the atoms in the crystal cell can be decided then the initial models of the structures we need can be defined. One must be sure that these initial models are very rough since the errors in measuring the diffraction intensities, and also the calculations of phases would induce a great number of errors in the positions of atoms. The next step for structure determination is to refine the positions of atoms according to the experimental data of the amplitudes of structure factors via the stereochemistry constrains of proteins to obtained the final models of proteins. 

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See also in sourсe #XX -- [ ]

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