surface_fractal¶
Fractal-like aggregates based on the Mildner reference
Parameter |
Description |
Units |
Default value |
---|---|---|---|
scale |
Scale factor or Volume fraction |
None |
1 |
background |
Source background |
cm-1 |
0.001 |
radius |
Particle radius |
Å |
10 |
fractal_dim_surf |
Surface fractal dimension |
None |
2 |
cutoff_length |
Cut-off Length |
Å |
500 |
The returned value is scaled to units of cm-1 sr-1, absolute scale.
This model 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, \(D_S\) is the surface fractal dimension, \(\xi\) 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 surface fractal dimension is only valid if \(1<D_S<3\). The result is only valid over a limited \(q\) range, \(\tfrac{5}{3-D_S}\xi^{\,-1} < q < R^{-1}\). See the reference for details.
Source
surface_fractal.py
\(\ \star\ \) surface_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
Authorship and Verification
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