BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Prism6
BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Prism6
A prism based on regular hexagon.
Prism6(L, H)
Parameters:
As for any other Form factor.
Class Prism6 inherits from the interface class Formfactor.
Form factor is computed as
$$ F(\mathbf{q})=H \space \exp\Big(iq_z\dfrac{H}{2}\Big) \space \text{sinc}\Big(q_z\dfrac{H}{2}\Big) \space F_{||}(\mathbf{q}_{||}) $$
where the form factor $F_{||}(\mathbf{q}_{||}) $ computation is based on the generic form factor of a planar polygon with two-fold symmetry $(S_2)$ provided by libformfactor .
Volume has been validated against $$ V=\dfrac{3\sqrt3}{2}HR^2. $$
More general:
Scattering by uncorrelated, oriented prisms for horizontal incidence. Rotation around $z$ axis:
Generated by Examples/sas/sas-ff.py
(particle_geometry=Prism6).
Has been validated against the “Prism6” form factor of IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.30 and “Prism with six fold symmetry” Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 221, which has different parametrization and lacks a factor $H$ in $F(\mathbf{q})$. Reimplemented in BornAgain 1.6 using the generic form factor of a polygonal prism with symmetry $S_{2}$ Wuttke, J Appl Cryst 54, 580 (2021) to achieve numerical stability near the removable singularity at $q \to 0$.