Calculates the structure factor term ONLY from the Mass Fractal model.

Definition

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The Sinha-Mildner-Hall fractal structure factor.

The functional form of the structure factor is defined below

\begin{equation}

S(q) = \frac{\Gamma(D_m-1)\xi^{D_m-1}}{\left[1+(q\xi)^2

\right]^{(D_m-1)/2}}

\frac{sin\left[(D_m - 1) tan^{-1}(q\xi) \right]}{q}

\end{equation}

where $D_m$ is the $mass$ fractal dimension and $\xi$ is the upper fractal cutoff length, i.e. the length scale above which the system is no longer fractal.

SasView automatically appends two additional parameters $radius$_$effective$ and $volfraction$ to all $S(q)$ models. However, these are not used by this model.

The mass fractal dimension ( $D_m$ ) is only valid if $1 <= D_m <= 3$. It is also only valid over a limited $q$ range (see the references for details).

WARNING! By convention, $S(q)$ is normally dimensionless. THIS FUNCTION IS NOT DIMENSIONLESS!

References

---------------

D Mildner and P Hall, J. Phys. D: Appl. Phys.,

19 (1986) 1535-1545 Equation(9)

P Wong, Methods in the physics of porous media

San Diego; London. Academic. (1999)

Authorship and Verification

-----------------------------------

Author: Ziggy Attala and Matt D G Hughes Date: 09/09/2019

Last Modified by: Steve King Date: 18/09/2019

Last Reviewed by:

Created By |
smk78 |

Uploaded |
Sept. 18, 2019, 6:01 p.m. |

Category |
Structure Factor |

Score |
0 |

Verified |
This model has not been verified by a member of the SasView team |

In Library |
This model is not currently included in the SasView library. You must download the files and install it yourself. |

Files |
mass_fractal_sq.py |

smk78:

Wed 18 Sep 2019 at 18:04

This is a cleaned-up version of the same model submitted by Z Attala.

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