Indirect Calibration Using a Polymer Sample

The so-called Lupolen standard is a well-known secondary standard in the field of SAXS. In conjunction with the Kratky camera it is easily used, because its slit-smeared intensity J s) /V is constant over a fairly wide range, and this level is chosen as the calibration constant. In point-focus setups the SAXS of the Lupolen standard neither shows a constant intensity region, nor is the reported calibration constant of any use. 

A proper calibration constant for any beamline geometry is the invariant Q. Thus, the Lupolen standard or any other semicrystalline polymer that previously has been calibrated in the Kratky camera can be made a secondary standard for a point-focus setup, after its invariant Q has been computed in absolute units - based on a measurement of its SAXS in the Kratky camera. 

The calibration process then involves measurement of the complete scattering curve of the secondary standard and the evaluation of k by determination of PoROD s law with its asymptote Ap and the density fiuctuation background Ipi, numerical extrapolation of the function (7 s) - Ipi) towards i = 0, and finally computation of the scattering power 

The measured SAXS curve of the calibration sample must have been pre-processed in the usual way (cf. Sects. 7.3 - 7.6). Therefore it is important to have calibration samples with a well-defined thickness. Because synchrotron beamlines can be adjusted to a fairly wide range of radiation power, it is important to have thin calibration samples for a high-power adjustment (e.g., common SAXS with wide slit openings) and thick calibration samples for low-power adjustments (e.g., USAXS with microbeam). For calibration samples from synthetic polymers, thicknesses ranging between 0.2 mm and 3 mm are reasonable. It appears worth to be noted that not only polymers, but as well glassy carbon [88] can be used as a solid secondary standard for the calibration to absolute intensity. 

This evaluation is performed in minutes using my computer program TOPAS. 

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