.. _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.

References

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

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.

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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