source: sasview/src/sas/sasgui/perspectives/corfunc/media/corfunc_help.rst @ fb7fcec

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Add initial documentation for corfunc perspective

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Correlation Function Perspective

Description

This perspective performs a correlation function analysis of one-dimensional SANS data, or generates a model-independent volume fraction profile from a one-dimensional SANS pattern of an adsorbed layer.

The correlation function analysis is performed in 3 stages:

  • Extrapolation of the scattering curve to Q = 0 and Q = ∞
  • Fourier Transform of the extrapolated data to give the correlation function
  • Interpretation of the 1D correlation function based on an ideal lamellar morphology

Extrapolation

To Q = 0

The data are extrapolated to Q = 0 by fitting a Guinier model to the data points in the lower Q range. The equation used is:

I(Q) = AeBq2

The Guinier model assumes that the small angle scattering arises from particles and that parameter B is related to the radius of gyration of those particles. This has dubious applicability to polymer systems. However, the correlation function is affected by the Guinier back-extrapolation to the greatest extent at large values of R and so the back-extrapolation only has a small effect on the analysis.

To Q = ∞

The data are extrapolated to Q = by fitting a Porod model to the data points in the upper Q range.

The equation used is:

I(Q) = B + KQ − 4e − Q2σ2

Where B is the Bonart thermal background, K is the Porod constant, and σ describes the electron (or neutron scattering length) density profile at the interface between crystalline and amorphous regions (see figure 1).

fig1.gif

Figure 1 The value of σ is a measure of the electron density profile at the interface between crystalline and amorphous regions.

Smoothing

The extrapolated data set consists of the Guinier back-extrapolation up to the highest Q value of the lower Q range, the original scattering data up to the highest value in the upper Q range, and the Porod tail-fit beyond this. The joins between the original data and the Guinier/Porod fits are smoothed using the algorithm below, to avoid the formation of ripples in the transformd data.

Functions f(xi) and g(xi) where xi ∈ {x1, x2, ..., xn} , are smoothed over the range [a, b] to produce y(xi) , by the following equations:

y(xi) = hig(xi) + (1 − hi)f(xi)

where:

hi = (1)/(1 + ((xi − b)2)/((xi − a)2))
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