BornAgain
≻ 20
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Cone
BornAgain
≻ 20
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Cone
A truncated cone (frustum) with circular base.
Cone(R, H, alpha)
Parameters:
Constraint:
$H \le R \tan\alpha$
As for any other Form factor.
Class Cone inherits from the interface class IFormFactor .
Computation involves numerical integration in radial direction, $$F(\mathbf{q})=2\pi \exp(i \tilde{q_{z}} R) \tan\alpha \int_{R_H}^R d\rho\thinspace \rho^2 \frac{J_1(q_{\parallel}\rho)}{q_{\parallel}\rho} e^{-i\tilde{q}_z \rho},$$
with notation $$\quad R_{H} := R-\dfrac{H}{\tan\alpha}, \quad q_{||} := \sqrt{q_{x}^2 + q_{y}^2}, \quad \tilde{q_{z}} := q_{z} \tan\alpha.$$
Volume has been validated against $$V=\dfrac{\pi}{3}\tan\alpha \left( R^3 - R_H^3\right).$$
More special:
Scattering by uncorrelated, oriented cones for horizontal incidence. Rotation around $y$ axis:
Generated by Examples/ff/Cone.py .
Agrees with “Cone” form factor in IsGISAXS [manual, Eq. 2.27; Renaud 2009, Eq. 225], except for a substitution $z\to\rho$ in our expression for $F$.