# core_shell_cylinder

Right circular cylinder with a core-shell scattering length density profile.

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Source intensity | None | 1 |

background | Source background | cm^{-1} |
0.001 |

sld_core | Cylinder core scattering length density | 10^{-6}Å^{-2} |
4 |

sld_shell | Cylinder shell scattering length density | 10^{-6}Å^{-2} |
4 |

sld_solvent | Solvent scattering length density | 10^{-6}Å^{-2} |
1 |

radius | Cylinder core radius | Å | 20 |

thickness | Cylinder shell thickness | Å | 20 |

length | Cylinder length | Å | 400 |

theta | In plane angle | degree | 60 |

phi | Out of plane angle | degree | 60 |

The returned value is scaled to units of cm^{-1} sr^{-1}, absolute scale.

**Definition**

The output of the 2D scattering intensity function for oriented core-shell cylinders is given by (Kline, 2006 [2]). The form factor is normalized by the particle volume.

where

and

and \(\alpha\) is the angle between the axis of the cylinder and \(\vec q\),
\(V_s\) is the volume of the outer shell (i.e. the total volume, including
the shell), \(V_c\) is the volume of the core, \(L\) is the length of the core,
\(R\) is the radius of the core, \(T\) is the thickness of the shell, \(\rho_c\)
is the scattering length density of the core, \(\rho_s\) is the scattering
length density of the shell, \(\rho_\text{solv}\) is the scattering length
density of the solvent, and *background* is the background level. The outer
radius of the shell is given by \(R+T\) and the total length of the outer
shell is given by \(L+2T\). \(J1\) is the first order Bessel function.

To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles \(\theta\) and \(\phi\). (see cylinder model)

NB: The 2nd virial coefficient of the cylinder is calculated based on the radius and 2 length values, and used as the effective radius for \(S(q)\) when \(P(q) \cdot S(q)\) is applied.

The \(\theta\) and \(\phi\) parameters are not used for the 1D output.

**Reference**

[1] | see, for example, Ian Livsey J. Chem. Soc., Faraday Trans. 2, 1987,83, 1445-1452 |

[2] | S R Kline, J Appl. Cryst., 39 (2006) 895 |

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Last Modified by:**Paul Kienzle**Date:**Aug 8, 2016**Last Reviewed by:**Richard Heenan**Date:**March 18, 2016