2-Point Statistics from X-ray Scattering Data

Relationship between X-ray data and 2-point statistics

In this dataset we have both wide angle X-ray scattering plots (WAXS) and small angle X-ray scattering plots (SAXS). The WAXS provides information on the crystal orientation of the crystalline regions, while the SAXS provides information of of the orientation of the crystalline regions at a longer length scale.

The autocorrelation of the electron density is inversion Fourier transform of X-ray scattering intensity plot (see derivation). For this project, we will be using the SAXS data and attempt to recover the 2-point statistics for a microstructure function with 2 local stats used to describe the crystalline and amorphous regions of the microstrucutre.

X-ray Scatter Intensity Plots

Originial SAXS X-ray Intensity Plot

Scaled SAXS X-ray Intensity Plot

Original WAXS X-ray Intensity Plot

Scaled WAXS X-ray Intensity Plot Link to images

Image Processing

In order to have the inversion Fourier transform be real, the intensity plots need to be symmetric in both the x and y directions. In order to protect the detector while collecting data, an beam stop is place to block the X-ray beam from reaching the detector (see image below).

This image is not part of the dataset. It is only used to visual describe the image processing that will be need.

We will be using image processing to remove the line created by the beam stop used to block the beam in order to make intensity plots symmetric.

Another issue is that intensity plots contain scattering information from both the crystalline and amorphous local states. There are tools can be used to deconvolve the amorphous and crystalline contributions such as PySAXS.

Lastly, the origin of the scatter plots and the edges need to match the expected values related to the volume fraction of both the local states. The crystallinity of the polymer can be used to determine this values, and the plots will then need to be scaled accordingly.