BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Spheroid
BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Spheroid
A full spheroid, generated by rotating an ellipse around the vertical axis.
Spheroid(R_xy, R_z)
Parameters:
Attention This has changed in BornAgain 22. Previously, the second argument was $H=2R_z$.
As for any other Form factor.
Class Spheroid inherits from the interface class Formfactor.
Form factor is computed as
$$ F(\mathbf{q})=4\pi R_{xy}^2R_z \exp(iq_zR_z) \dfrac{\sin(s) - s \cos(s)}{s^3} , $$ with the notation $$ s := \sqrt{(R_{xy}q_x)^2 + (R_{xy}q_y)^2+ (R_zq_z)^2}. $$
Volume has been validated against $$ V=\dfrac{4\pi}{3} R_{xy}^2R_z. $$
More special:
More general:
Scattering by uncorrelated, oriented spheroids for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/sas/sas-ff.py
(particle_geometry=Spheroid).
Replicates the “Full spheroid” in IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.36; Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 227, except for wrong factors of 2 in their volume formula and form factor implementation, and “Spheroid” in FitGISAXS Babonneau, FitGISAXS v130531 (2013). Up to BornAgain 1.16, our form factor computation followed IsGISAXS in using numeric integration in the $z$ coordinate.
In BornAgain, named “FullSpheroid” up to version 1.19.
Up to BornAgain 21, the second argument was $H=2R_z$.