source: sasmodels/doc/guide/orientation/orientation.rst @ 17db833

.. _orientation:

Oriented particles
==================

With two dimensional small angle diffraction data SasView will calculate
scattering from oriented particles, applicable for example to shear flow
or orientation in a magnetic field.

In general we first need to define the reference orientation
of the particles with respect to the incoming neutron or X-ray beam. This
is done using three angles: $\theta$ and $\phi$ define the orientation of
the axis of the particle, angle $\Psi$ is defined as the orientation of
the major axis of the particle cross section with respect to its starting
position along the beam direction. The figures below are for an elliptical
cross section cylinder, but may be applied analogously to other shapes of
particle.

.. note::
    It is very important to note that these angles, in particular $\theta$
    and $\phi$, are NOT in general the same as the $\theta$ and $\phi$
    appearing in equations for the scattering form factor which gives the
    scattered intensity or indeed in the equation for scattering vector $Q$.
    The $\theta$ rotation must be applied before the $\phi$ rotation, else
    there is an ambiguity.

.. figure::
    orient_img/elliptical_cylinder_angle_definition.png

    Definition of angles for oriented elliptical cylinder, where axis_ratio
    b/a is shown >1, Note that rotation $\theta$, initially in the $x$-$z$
    plane, is carried out first, then rotation $\phi$ about the $z$-axis,
    finally rotation $\Psi$ is around the axis of the cylinder. The neutron
    or X-ray beam is along the $z$ axis.

.. figure::
    orient_img/elliptical_cylinder_angle_projection.png

    Some examples of the orientation angles for an elliptical cylinder,
    with $\Psi$ = 0.

Having established the mean direction of the particle we can then apply
angular orientation distributions. This is done by a numerical integration
over a range of angles in a similar way to particle size dispersity.
In the current version of sasview the orientational dispersity is defined
with respect to the axes of the particle.

The $\theta$ and $\phi$ orientation parameters for the cylinder only appear
when fitting 2d data. On introducing "Orientational Distribution" in
the angles, "distribution of theta" and "distribution of phi" parameters will
appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$
of the cylinder, the $b$ and $a$ axes of the cylinder cross section. (When
$\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the
instrument.) The third orientation distribution, in $\Psi$, is about the $c$
axis of the particle. Some experimentation may be required to understand the
2d patterns fully. A number of different shapes of distribution are
available, as described for polydispersity, see :ref:`polydispersityhelp` .

Earlier versions of SasView had numerical integration issues in some
circumstances when distributions passed through 90 degrees. The distributions
in particle coordinates are more robust, but should still be approached with
care for large ranges of angle.

Note that the form factors for asymmetric particles are also performing
numerical integrations over one or more variables, so care should be taken,
especially with very large particles or more extreme aspect ratios. Users can
experiment with the values of *Npts* and *Nsigs*, the number of steps used in the
integration and the range spanned in number of standard deviations. The
standard deviation is entered in units of degrees. For a rectangular
(uniform) distribution the full width should be $\pm \sqrt(3)$ ~ 1.73 standard
deviations (this may be changed soon).

Where appropriate, for best numerical results, keep $a < b < c$ and the
$\theta$ distribution narrower than the $\phi$ distribution.

Some more detailed technical notes are provided in the developer section of
this manual :ref:`orientation_developer` .

*Document History*

| 2017-10-27 Richard Heenan