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1.6.4 The Phase Problem

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The amplitude structure factor in Eq. (1.27) is a complex quantity and so can be written as the product of an amplitude and a phase:

(1.59)

where ϕhkl is the phase angle for reflection with indices hkl. The amplitude can be obtained from the square root of the intensity:

(1.60)

In general, the phase appearing in Eq. (1.59) cannot be determined in an x‐ray diffraction or SAXS experiment. There are methods in x‐ray crystallography to circumvent the problem (such as heavy atom replacement). In the study of SAXS by soft materials, the reconstruction of the electron density profile is usually only done for a limited subset of systems. In particular, it is performed for lamellar structures such as those of lipid bilayers, as discussed further in Section 4.12.

Small-Angle Scattering

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