# 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

\[I(q) = \frac{A}{1 +(Q\xi_1)^n} + \frac{C}{1 +(Q\xi_2)^m} + \text{B}\]

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

\[q = \sqrt{q_x^2 + q_y^2}\]

Fig. 126 1D plot corresponding to the default parameters of the model.

Source

`two_lorentzian.py`

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