# barbell

Cylinder with spherical end caps

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

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
0.001 |

sld |
Barbell scattering length density |
10 |
4 |

sld_solvent |
Solvent scattering length density |
10 |
1 |

radius_bell |
Spherical bell radius |
Å |
40 |

radius |
Cylindrical bar radius |
Å |
20 |

length |
Cylinder bar length |
Å |
400 |

theta |
Barbell axis to beam angle |
degree |
60 |

phi |
Rotation about beam |
degree |
60 |

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

**Definition**

Calculates the scattering from a barbell-shaped cylinder. Like capped_cylinder, this is a spherocylinder with spherical end caps that have a radius larger than that of the cylinder, but with the center of the end cap radius lying outside of the cylinder. See the diagram for the details of the geometry and restrictions on parameter values.

The scattered intensity \(I(q)\) is calculated as

where the amplitude \(A(q,\alpha)\) with the rod axis at angle \(\alpha\) to \(q\) is given as

The \(\left<\ldots\right>\) brackets denote an average of the structure over all orientations. \(\left<A^2(q,\alpha)\right>\) is then the form factor, \(P(q)\). The scale factor is equivalent to the volume fraction of cylinders, each of volume, \(V\). Contrast \(\Delta\rho\) is the difference of scattering length densities of the cylinder and the surrounding solvent.

The volume of the barbell is

and its radius of gyration is

Note

The requirement that \(R \geq r\) is not enforced in the model! It is up to you to restrict this during analysis.

The 2D scattering intensity is calculated similar to the 2D cylinder model.

**Source**

`barbell.py`

\(\ \star\ \) `barbell.c`

\(\ \star\ \) `gauss76.c`

\(\ \star\ \) `sas_J1.c`

\(\ \star\ \) `polevl.c`

**References**

H Kaya,

*J. Appl. Cryst.*, 37 (2004) 223-230H Kaya and N R deSouza,

*J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata)Onsager,

*Ann. New York Acad. Sci.*, 51 (1949) 627-659

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Last Modified by:**Paul Butler**Date:**March 20, 2016**Last Reviewed by:**Richard Heenan**Date:**January 4, 2017