Particle analysis in GISAXS refers to the size or shape analysis of nanoparticles on substrate.
There are various examples.
1. If particles are epitaxially grown on substrate, they may not be randomly oriented in the plane, which would requires the rotation of phi angle during the measurement. Users may like to determine particles' shape, facet, dimension, orientations and so on.
2. When substrate is not crystalline, particles are likely randomly oriented in the substrate plane. But still, due to the existence of rather flat substrate, they may have different dimensions along the vertical and horizontal directions. We typically do Guinier analysis or model fitting analysis. To come up with a right model, you may want to figure out that whether your particles are like a cylinder aligned its axis perpendicular to the substrate or an ellipsoid whose two common axes are parallel to substrate. A cylinder laying down on substrate with random orientation in the plane should be considered as the ellipsoid type. For the former case, in-plane scattering is independent to the qz. While that for the latter case is dependent. For both cases, Porod exponents are also different from each other's. In this type of work, information such as size distribution and number of particles is of interest.
In many cases, you may not need to use DWBA formula for the analyses unless you deal with pretty well defined system such as particles with monodisperse size and orientation...
Facet analysis
See my publication # 86.
When the particles on a substrate or in a thin film are not highly packed and are dispersed enough long distance so that particles does not feel the repulsive or attractive interactions, their inter-particle distance can not be regular unless their substrate is designed to do that. So particles have very short range order or they effectively can be considered dilute.
When those particles are crystalline, and they interact with substrate, the particles tend to orient or grow epitaxially in order to maximize or minimize atomic interaction between nanoparticles and substrates.
Then there will be scattering from facets of each crystalline particles. Remember that x-ray scattering is basically reflection. Any flat face will result in a x-ray streak normal to the face. The streak is called the Bragg rod scattering, facet scattering, or etc. The width of the streak will be inversely proportional to the width of the face.
How to calculate the direction of the streak?
The streak is normal to the crystallographic plane. Any vector in the reciprocal space is normal to the associated planes in the real space. Thus directions of streaks are from the direct beam position to the position of each diffraction peak.
Ex. a streak from [1-11] plane will be from (0,0) to (1-11) peak.
So if you know the orientation of your particle and its 2D powder diffraction pattern, you can get the direction of the streak.