.. _core_shell_sphere:

This model provides the form factor, $P(q)$, for a spherical particle with a core-shell structure. The form factor is normalized by the particle volume.

For information about polarised and magnetic scattering, see the `magnetism` documentation.

Definition

The 1D scattering intensity is calculated in the following way (Guinier, 1955)

$$ P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background}

$$

where

$$ F(q) = \frac{3}{V_s}\left[ V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3} + V_s(\rho_s-\rho_\text{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3} \right]

$$

where $V_s$ is the volume of the whole particle, $V_c$ is the volume of the core, $r_s$ = $radius$ + $thickness$ is the radius of the particle, $r_c$ is the radius of the core, $\rho_c$ is the scattering length density of the core, $\rho_s$ is the scattering length density of the shell, $\rho_\text{solv}$, is the scattering length density of the solvent.

The 2D scattering intensity is the same as $P(q)$ above, regardless of the orientation of the $q$ vector.

NB: The outer most radius (ie, = radius + thickness) is used as the effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied.

Validation

Validation of our code was done by comparing the output of the 1D model to the output of the software provided by NIST (Kline, 2006). Figure 1 shows a comparison of the output of our model and the output of the NIST software.

References

A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)

Authorship and Verification

**Author:**

**Last Modified by:**

**Last Reviewed by:**

Created By |
sasview |

Uploaded |
Sept. 7, 2017, 3:56 p.m. |

Category |
Sphere |

Score |
0 |

Verified |
Verified by SasView Team on 07 Sep 2017 |

In Library |
This model is included in the SasView library by default |

Files |
core_shell_sphere.py core_shell_sphere.c |

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