broad-peak (SASfit)

This file has been automatically generated by sasfit_convert and manually edited by Wojciech Potrzebowski, ESS on 2017-12-05.

The model calculates an empirical functional form for SAS data characterized by broad_peak (as defined in SASfit: https://github.com/SASfit/SASfit/)

Definition:
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Many SANS spectra are characterized by a broad peak even though they are from amorphous soft materials.
The d-spacing corresponding to the broad peak is a characteristic distance between the scattering inhomogeneities (such as in lamellar, cylindrical, or spherical morphologies or for bicontinuous structures).
The following simple functional form reproduces the broad peak feature:

$$ I(q) = \frac{I_0}{({1 + (|q - q_0|\xi)^m})^p}$$

where $I_0$: forward scattering
$\xi$: correlation length
$q_0$:peak position which is related to the d-spacing as $q_0 = 2\pi/d$
$m$: exponent m
$p$: exponnent p

Here the peak position is related to the d-spacing as $q_0 = 2\pi/d$.
Soft systems that show a SANS peak include copolymers, polyelectrolytes, multiphase systems, layered structures, etc.

Note:
For $q_0 = 0$, $m = 2$ and $p = 1$ one gets the Ornstein-Zernike model.
For $q_0 = 0$, $m = 2$ and $p = 2$ The Broad-Peak model is identical to the
Debye-Anderson-Brumberger model.

For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector element for given x and y is defined as

$$ q = \sqrt{q_x^2 + q_y^2}$$

References:
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https://github.com/SASfit/SASfit/
Original SASfit file: /src/plugins/non_particulate/sasfit_ff_broad_peak.c

A paper about SASfit has been published in J. Appl. Cryst. (2015). 48, 1587-1598 doi:10.1107/S1600576715016544

Example Data: