BornAgain
≻ git-main
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ SpheroidalSegment
BornAgain
≻ git-main
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ SpheroidalSegment
A vertically oriented, horizontally truncated spheroid.
SpheroidalSegment(R_xy, R_z, t, b)
Parameters:
Constraint:
$ t+b \le 2R_z $
As for any other Form factor.
Class SpheroidalSegment inherits from the interface class IFormfactor.
Computation involves numerical integration in vertical direction,
$$ F(\mathbf{q})=2\pi \exp[iq_z(R_z-b)] \int_{-R_z+b}^{R_z-t} \text{d}z \space r_z^2 \frac{J_1(q_{||}r_z)}{q_{||}r_z} \exp(iq_z z), $$
with the notation
$$ q_{||} := \sqrt{q_x^2 + q_y^2}, \quad r_z:=R_{xy}\sqrt{1-z^2/R_z^2} $$
Volume has been validated against $$ V=\dfrac{\pi}{3} \Big(\frac{R_{xy}}{R_z}\Big)^2 [ 4R_z^3 - 3R_z(t^2+b^2) + (t^3 + b^3) ]. $$
More special:
Scattering by uncorrelated, oriented truncated spheroids for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/ff/SpheroidalSegment.py .
Agrees with the IsGISAXS form factor “Spheroid” [manual, Eq. 2.42].