# Core shell sphere filled with a cylinder in the core

## Description:

Orientationally averaged form factor for a monodisperse spherical particle with a core-shell sphere structure, filled with a circular cylinder in its center.

Output:
P(q) = \frac{\text{scale}}{V_{sph}} \int_0^{\pi/2} f^2(q,\alpha) \sin\alpha\ d\alpha + \text{background}

where
f(q,\alpha) = ( sld_{cyl}-sld_{sph,c} ) * V_{cyl} f_cyl(q,\alpha)
+ ( sld_{sph,c}-sld_{sph,sh} ) * V_{sph,c} f_sph( q*R_{sph,c} )
+ ( sld_{sph,sh}-sld_{solv} ) * V_{sph} f_sph( q*(R_{sph,c}+d_{sph,sh}) )

where
f_cyl(q,alpha) = j_0( q*L_{cyl}*\cos(\alpha)/2 ) * 2J1x( q*R_{cyl}\sin(\alpha) )
f_sph(x) = 3 * \frac{ \sin(x)-x\cos(x) }{ x^3 }

where
j_0(x) = \sin(x) / x
2J1x(x) = 2 * J_1(x) / x , where $J_1$ is the first order Bessel function
V_{cyl} = \pi R_{cyl}^2 L_{cyl}
V_{sph,c} = 4\pi/3 R_{sph,c}^3
V_{sph} = 4\pi/3 (R_{sph,c}+d_{sph,sh})^3

Parameters:
scale = scaling factor, volume fraction of particles scale phi ~ N V_{sph} / V_{irr}, with N / V_{irr} being the number density of particles in the irradiated volume
background = const. background
R_{sph,c} = core radius of sphere
d_{sph,sh} = shell thickness of sphere
NB: R_{sph,c} + d_{sph,sh} = radius of whole sphere
L_{cyl} = length of cylinder
V_{sph} = volume of whole sphere including shell
V_{sph,c} = volume of sphere core
V_{cyl} = volume of cylinder
sld_{sph,c} = scattering length density of core of sphere
sld_{sph,sh} = scattering length density of shell of sphere
sld_{cyl} = scattering length density of cylinder inside the core
sld_{solv} = scattering length density of solvent

To use the model:
-put the python and C file into the .sasview/plugin_models/ directory for plugin models
-create the .sasview/plugin_models/lib/ directory and put the following 4 files from sasmodels/models/lib/ (github) therein:
gauss76.c
polevl.c
sas_3j1x_x.c
sas_J1.c
-the model can be verified by adjusting the SLDs of sph-core, sph-shell and cyl to match the the intensity from models of a core-shell sphere or a cylinder

Literature:
-Same as for sphere and cylinders.
-A more general model of a core-shell ellipsoid with a stack of (flat) cylinders in the core has been described by S. Maric et al (2017)
https://doi.org/10.1021/acsnano.6b08089

## Details:

 Created By p3scmr Uploaded July 24, 2019, 4:12 p.m. Category Sphere 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 coreshellspherefilledwithcylinder.c coreshellspherefilledwithcylinder.py