TruncatedSpheroid

A vertically oriented, horizontally truncated spheroid.

Constructor

TruncatedSpheroid(R, H, f_p, dh)

Parameters:

  • R, radius
  • H, height
  • f_p, height flattering $f_p$
  • dh, top removal

Constraint:

$ dh < H \le 2f_pR $

Usage

As for any other Form factor.

Implementation

Class TruncatedSpheroid inherits from the interface class IFormFactor .

Computation involves numerical integration in vertical direction,

$$ F(\mathbf{q})=2\pi \exp[iq_z(H-f_pR)] \int_{f_pR-H}^{f_pR-dh} \text{d}z \space R_z^2 \frac{J_1(q_{||}R_z)}{q_{||}R_z} \exp(iq_z z), $$

with the notation

$$ q_{||} := \sqrt{q_x^2 + q_y^2}, \quad R_z:=\sqrt{R^2-z^2/f_p^2} $$

Volume has been validated against $$ V=\dfrac{\pi}{3f_p^2} [ 3f_pR(H^2-dh^2) + dh^3 -H^3 ]. $$

More special:

Example

Scattering by uncorrelated, oriented truncated spheroids for horizontal incidence. Rotation around $y$ axis:

Generated by Examples/ff/TruncatedSpheroid.py .

History

Agrees with the IsGISAXS form factor “Spheroid” [manual, Eq. 2.42].