BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Cylinder
BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Cylinder
An upright circular cylinder.
Cylinder(R, H)
Parameters:
As for any other Form factor.
Class Cylinder inherits from the interface class Formfactor.
Form factor is computed as
$$ F(\mathbf{q})=2\pi R^2H \space \exp\Big(iq_z\dfrac{H}{2}\Big) \text{sinc}\Big(q_z\dfrac{H}{2}\Big) \dfrac{J_1(q_{\parallel}R)}{q_{\parallel}R} , $$ with the notation $$ q_{||} := \sqrt{q_x^2 + q_y^2}. $$
Volume has been validated against $$V=\pi R^2H.$$
More general:
Scattering by uncorrelated, oriented cylinders for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/sas/sas-ff.py
(particle_geometry=Cylinder).
This form factor is well known; it goes back to Lord Rayleigh.
In IsGISAXS and FitGISAXS, it has been implemented as form factor “Cylinder” Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.26; Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 223; Babonneau, FitGISAXS v130531 (2013).