two_lorentzian¶
This model calculates an empirical functional form for SAS data characterized by two Lorentzian-type functions.
Parameter |
Description |
Units |
Default value |
---|---|---|---|
scale |
Scale factor or Volume fraction |
None |
1 |
background |
Source background |
cm-1 |
0.001 |
lorentz_scale_1 |
First power law scale factor |
None |
10 |
lorentz_length_1 |
First Lorentzian screening length |
Å |
100 |
lorentz_exp_1 |
First exponent of power law |
None |
3 |
lorentz_scale_2 |
Second scale factor for broad Lorentzian peak |
None |
1 |
lorentz_length_2 |
Second Lorentzian screening length |
Å |
10 |
lorentz_exp_2 |
Second exponent of power law |
None |
2 |
The returned value is scaled to units of cm-1 sr-1, absolute scale.
Definition
The scattering intensity \(I(q)\) is calculated as
where \(A\) = Lorentzian scale factor #1, \(C\) = Lorentzian scale #2, \(\xi_1\) and \(\xi_2\) are the corresponding correlation lengths, and \(n\) and \(m\) are the respective power law exponents (set \(n = m = 2\) for Ornstein-Zernicke behaviour).
For 2D data the scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as
Source
References
None.
Authorship and Verification
Author: NIST IGOR/DANSE Date: pre 2010
Last Modified by: Piotr rozyczko Date: January 29, 2016
Last Reviewed by: Paul Butler Date: March 21, 2016