BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Prism3
BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Prism3
A prism based on equlateral triangle.
Prism3(L, H)
Parameters:
As for any other Form factor.
Class Prism3 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 provided by libformfactor .
Volume has been validated against $$ V=\dfrac{\sqrt3}{4}HL^2. $$
More general:
Scattering by uncorrelated, oriented prisms for horizontal incidence. Rotation around $z$ axis:
Generated by Examples/sas/sas-ff.py
(particle_geometry=Prism3).
Has been validated against the “Prism3” form factor of IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.28 and “Prism with three fold symmetry” Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 219. Note the different parametrization $L = 2R_{IsGISXAXS}$. In FitGISAXS Babonneau, FitGISAXS v130531 (2013) just called “Prism”. In BornAgain 1.6, redefined to let the $x$ axis point along a symmetry axis (rotated by $30^{\circ}$ with respect to the previous version).
Reimplemented in BornAgain 1.6 using the generic form factor of a polygonal prism Wuttke, J Appl Cryst 54, 580 (2021) to achieve numerical stability near the removable singularity at $q \to 0$.