.. _lorentz:

lorentz
=======================================================

Ornstein-Zernicke correlation length model

========== =============================== ======= =============
Parameter  Description                     Units   Default value
========== =============================== ======= =============
scale      Scale factor or Volume fraction None                1
background Source background               |cm^-1|         0.001
cor_length Screening length                |Ang|              50
========== =============================== ======= =============

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


Lorentz (Ornstein-Zernicke Model)

**Definition**

The Ornstein-Zernicke model is defined by

.. math:: I(q)=\frac{\text{scale}}{1+(qL)^2}+\text{background}

The parameter $L$ is the screening length *cor_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/lorentz_autogenfig.png

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


**Source**

:download:`lorentz.py <src/lorentz.py>`
$\ \star\ $ :download:`lorentz.c <src/lorentz.c>`

**References**

#. L.S. Qrnstein and F. Zernike, *Proc. Acad. Sci. Amsterdam* 17, 793 (1914),
   and *Z. Phys.* 19, 134 (1918), and 27, 761 {1926); referred to as QZ.

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