# mass_fractal

Mass Fractal model

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

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

background |
Source background |
cm |
0.001 |

radius |
Particle radius |
Å |
10 |

fractal_dim_mass |
Mass fractal dimension |
None |
1.9 |

cutoff_length |
Cut-off length |
Å |
100 |

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

Calculates the scattering from fractal-like aggregates based on the Mildner reference.

**Definition**

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

where \(R\) is the radius of the building block, \(D_m\) is the **mass** fractal
dimension, \(\zeta\) is the cut-off length, \(\rho_\text{solvent}\) is the
scattering length density of the solvent, and \(\rho_\text{particle}\) is the
scattering length density of particles.

Note

The mass fractal dimension ( \(D_m\) ) is only valid if \(1 < mass\_dim < 6\). It is also only valid over a limited \(q\) range (see the reference for details).

**Source**

`mass_fractal.py`

\(\ \star\ \) `mass_fractal.c`

\(\ \star\ \) `sas_gamma.c`

\(\ \star\ \) `sas_3j1x_x.c`

**References**

D Mildner and P Hall,

*J. Phys. D: Appl. Phys.*, 19 (1986) 1535-1545 Equation(9)

**Authorship and Verification**

**Author:****Last Modified by:****Last Reviewed by:**