Dab

Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which is a measure of the average spacing between regions of phase 1 and phase 2. **The model also assumes smooth interfaces between the phases** and hence exhibits Porod behavior $(I \sim q^{-4})$ at large $q$, $(qL \gg 1)$.

The DAB model is ostensibly a development of the earlier Debye-Bueche model.

Definition

$$ I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q\cdot L)^2)^2} + \text{background}
$$
where scale is

$$ \text{scale} = 8 \pi \phi (1-\phi) \Delta\rho^2
$$
and the parameter $L$ is the correlation length.

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

#. P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 #. P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518

Source

`dab.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/dab.py>`_

Authorship and Verification

**Author:**
**Last Modified by:**
**Last Reviewed by:** Steve King & Peter Parker **Date:** September 09, 2013
**Source added by :** Steve King **Date:** March 25, 2019