.. _dab:

dab
=======================================================

DAB (Debye Anderson Brumberger) Model

========== ================== ======= =============
Parameter  Description        Units   Default value
========== ================== ======= =============
scale      Source intensity   None                1
background Source background  |cm^-1|         0.001
cor_length correlation length |Ang|              50
========== ================== ======= =============

The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale.


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**

.. math::

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

where scale is

.. math:: \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

.. math:: q = \sqrt{q_x^2 + q_y^2}



.. figure:: img/dab_autogenfig.png

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

**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

*2013/09/09 - Description reviewed by King, S and Parker, P.*