# two_lorentzian

This model calculates an empirical functional form for SAS data characterized by two Lorentzian-type functions.

Parameter Description Units Default value
scale Source intensity 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 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 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

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

References

None.

Author: NIST IGOR/DANSE on: pre 2010

Last Modified by: Piotr rozyczko on: January 29, 2016

Last Reviewed by: Paul Butler on: March 21, 2016