# fractal

Calculates the scattering from fractal-like aggregates of spheres following theTexiera reference.

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

scale | Source intensity | None | 1 |

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

volfraction | volume fraction of blocks | None | 0.05 |

radius | radius of particles | Å | 5 |

fractal_dim | fractal dimension | None | 2 |

cor_length | cluster correlation length | Å | 100 |

sld_block | scattering length density of particles | 10^{-6}Å^{-2} |
2 |

sld_solvent | scattering length density of solvent | 10^{-6}Å^{-2} |
6.4 |

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

**Definition**
This model calculates the scattering from fractal-like aggregates of spherical
building blocks according the following equation:

where \(\phi\) is The volume fraction of the spherical “building block” particles of radius \(R_0\), \(V_{block}\) is the volume of a single building block, \(\rho_{solvent}\) is the scattering length density of the solvent, and \(\rho_{block}\) is the scattering length density of the building blocks, and P(q), S(q) are the scattering from randomly distributed spherical particles (the building blocks) and the interference from such building blocks organized in a fractal-like clusters. P(q) and S(q) are calculated as:

where \(\xi\) is the correlation length representing the cluster size and \(D_f\) is the fractal dimension, representing the self similarity of the structure. Note that S(q) here goes negative if \(D_f\) is too large, and the Gamma function diverges at \(D_f=0\) and \(D_f=1\).

**Polydispersity on the radius is provided for.**

For 2D data: The 2D scattering intensity is calculated in the same way as
1D, where the *q* vector is defined as

**References**

[1] | J Teixeira, J. Appl. Cryst., 21 (1988) 781-785 |

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Converted to sasmodels by:**Paul Butler**Date:**March 19, 2016**Last Modified by:**Paul Butler**Date:**March 12, 2017**Last Reviewed by:**Paul Butler**Date:**March 12, 2017