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EllipsoidalCylinder

An upright cylinder whose cross section is an ellipse.

Constructor

EllipsoidalCylinder(R_a, R_b, H)

Parameters:

  • R_a, radius $R_{a}$ in $x$ direction
  • R_b, radius $R_{b}$ in $y$ direction
  • H, height

Usage

As for any other Form factor.

Implementation

Class EllipsoidalCylinder inherits from the interface class Formfactor.

Form factor is computed as

$$ F(\mathbf{q})=2\pi R_aR_b H \space \exp\Big(iq_z\dfrac{H}{2}\Big) \text{sinc}\Big(q_z\dfrac{H}{2}\Big) \dfrac{J_1(\gamma)}{\gamma} , $$ with the notation $$ \gamma := \sqrt{(q_xR_a)^2 + (q_yR_b)^2}. $$

Volume has been validated against $$V=\pi R_aR_bH.$$

More special:

Example

Scattering by uncorrelated, oriented cylinders for horizontal incidence. Rotation around $z$ axis:

Generated by Examples/sas/sas-ff.py (particle_geometry=EllipsoidalCylinder).

History

Agrees with “Ellipsoid” form factor of IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.40, wrongly labeled in Fig. 2.4 and “Ellipsoidal Cylinder” Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 224