# Theory 2

### form factor F

In the following figures simulated form factors |F(qy,qz)|2 for different shapes of particles are given (log scale intensity). The scattering distribution in the patterns show, that one is able to distinguish between different form factors. By measuring the angle between the horizon and the scattering maxima in the case of a pyramidal shape one is able to calculate the angle of the facettes of the pyramid (figure 7).

**Figure 4: simulated cylindrical form factor (R=5nm; H/R=1)**

**Figure 5: simulated spherical form factor (R=5nm; H/R=2)**

**Figure 6: simulated half-spherical form factor (R=5nm; H/R=1)**

**Figure 7: simulated pyramidal form factor (R=5nm; H/R=1; φ= 54.73°)**

### interference function S (structure factor)

In the case of arranged particles in a 2D-lattice, the interference function S along qy appears. For hexagonal arranged cylinders, the interference pattern (figure 8) and the combined form factor*interference pattern (figure 9) were simulated. Only where the combination of both scattering patterns (figure 4 and figure 8) rise to a maximum, a resulting scattering is observable.

**Figure 8: simulated interference function (2Dhex,a=20 nm)**

**Figure 9:hexagonal arranged cylinders (R=5nm; H/R=1; 2Dhex,a=20 nm)**

The following patterns show the resulting scattering patterns for the same arrangement but different form factors:

**Figure 10:hexagonal arranged spheres (R=5nm; H/R=2; 2Dhex,a=20 nm)**

**Figure 11:hexagonal arranged half spheres (R=5nm; H/R=1; 2Dhex,a=20 nm)**