BornAgain
≻ git-main
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ TruncatedSphere
BornAgain
≻ git-main
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ TruncatedSphere
A spherical segment, obtained from a spherical ball by two parallel cuts.
TruncatedSphere(R, H, dh)
Parameters:
Constraint:
$ dh < H \le 2R $
As for any other Form factor.
Class TruncatedSphere inherits from the interface class IFormfactor .
Computation involves numerical integration in vertical direction,
$$ F(\mathbf{q})=2\pi \exp[iq_z(H-R)] \int_{R-H}^{R-dh} \text{d}z \space R_z^2 \frac{J_1(q_{||}R_z)}{q_{||}R_z} \exp(iq_z z), $$
with the notation
$$ q_{||} := \sqrt{q_x^2 + q_y^2}, \quad R_z:=\sqrt{R^2-z^2} $$
Volume has been validated against $$ V=\dfrac{\pi}{3} [ 3R(H^2-dh^2) + dh^3 -H^3 ]. $$
More general:
More special:
Scattering by uncorrelated, oriented truncated spheres for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/ff/TruncatedSphere.py .
Agrees with the IsGISAXS form factor “Sphere” [manual, Eq. 2.32] and “Truncated sphere” [Renaud 2009, Eq. 228]. It is not “Truncated sphere” of FitGISAXS, which is without top removal [Babonneau 2013].