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Pyramid2

A truncated pyramid with rectangular base.

Constructor

Pyramid2(L, W, H, alpha)

Parameters:

  • L, edge length of the base
  • W, edge width of the base
  • H, height
  • alpha, dihedral angle $\alpha$ between the base and each of the four trapezoidal lateral faces.

Constraint:

$H \le \dfrac{\tan\alpha}{2} min(L,W)$

Usage

As for any other Form factor.

Implementation

Class Pyramid2 inherits from the interface class Formfactor.

Form factor computation is based on the generic form factor of a polyhedron provided by libformfactor .

Volume has been validated against $$ V=H\Big[LW-\dfrac{(L+W)H}{\tan\alpha}+\dfrac{4}{3}\dfrac{H^2}{\tan^2\alpha}\Big]. $$

More special:

Example

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

Generated by Examples/sas/sas-ff.py (particle_geometry=Pyramid2).

History

Was named “AnisoPyramid” up to BornAgain 1.19.

Agrees with the “In plane anisotropic pyramid” form factor of IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.38-2.39; Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 216-217, except for different parametrization. This is not the “Anisotropic pyramid” of FitGISAXS, which is a true pyramid with an off-center apex Babonneau, FitGISAXS v130531 (2013).