BornAgain
≻ 21
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Spheroid
BornAgain
≻ 21
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Spheroid
A full spheroid, generated by rotating an ellipse around the vertical axis.
Spheroid(R, H)
Parameters:
As for any other Form factor.
Class Spheroid inherits from the interface class IFormFactor .
Form factor is computed as
$$ F(\mathbf{q})=4\pi R^2h \exp(iq_zh) \dfrac{\sin(s) - s \cos(s)}{s^3} , $$ with the notation $$ h:=H/2, \quad s := \sqrt{(Rq_x)^2 + (Rq_y)^2+ (hq_z)^2}. $$
Volume has been validated against $$ V=\dfrac{2\pi}{3} R^2H. $$
More special:
More general:
Scattering by uncorrelated, oriented spheroids for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/ff/Spheroid.py .
Replicates the “Full spheroid” in IsGISAXS [manual, Eq. 2.36; Renaud 2009, Eq. 227], except for wrong factors of 2 in their volume formula and form factor implementation, and “Spheroid” in FitGISAXS [Babonneau 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.