A Link to Absolute Intensity in WAXS

WAXS calibration for polymer materials can be simplified if one considers the fact that polymers are chain molecules. This means that for wide scattering angles in 

WAXS the scattering is completely described by the interactions of neighboring atoms along a single chain, the so-called single-chain structure factor. Cf. descriptions of the Ruland method [14] in textbooks [7,22], 

On the other hand, modern macromolecular X-ray diffraction of crystals from biological materials (protein crystallography) is frequently carried out in a rotating-crystal setup [98,99] (Alexander [7], p. 51), (Warren [97], Chap. 7), (Glocker [ 100], p. 250) using plane 2D detectors in normal transmission setup. In this case the absolute scattering intensity of reflection hkl is given by the Darwin equation (cf. Warren [97], Eq. (4.7)) 

Spinning a crystal during measurement of WAXS patterns is an old method that turns any scattering pattern into a fiber pattmi. The rotational axis becomes file principal axis. Thereafter isotropization of file scattmng data is simplified because the mafiieiiiatical treatment can resort to fiber symmetry of the measured data. In file literature file method is addressed as the rotating-crystal method or oscillating-crystal method. 

It should be clear that the Darwin equation with its special LoRENTZ-polariza-tion factor as reported by Warren ([97], Eq. (4.7)) is only valid for unpolarized laboratory sources and the rotation-crystal method. An application to different setup geometries, for example to synchrotron GIWAXS data of polymer thin films is not appropriate. 

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