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Ellipsoid

A full ellipsoid.

Constructor

Ellipsoid(R_x, R_y, R_z)

Parameters:

  • R_x, radius $R_{x}$ in $x$ direction
  • R_y, radius $R_{y}$ in $y$ direction
  • R_z, radius $R_{z}$ in $z$ direction

Usage

As for any other Form factor.

Implementation

Class Ellipsoid inherits from the interface class IFormfactor.

Form factor is computed as

$$ F(\mathbf{q})=4\pi R_xR_yR_z \exp(iq_zR_z) \dfrac{\sin(s) - s \cos(s)}{s^3} , $$ with the notation $$ s := \sqrt{(R_xq_x)^2 + (R_yq_y)^2+ (R_zq_z)^2}. $$

Volume has been validated against $$ V=\dfrac{4\pi}{3} R_xR_yR_z. $$

More special:

More general:

Example

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

Generated by Examples/ff/Ellipsoid.py .

History

Introduced in v24.