MODEL

CoreShell

ORIGINAL AUTHOR/MODIFICATION

Steve Kline 06 NOV 1998

Alan Munter 08 JULY 1999, converted to Java

APPROVED FOR DISTRIBUTION

DESCRIPTION

Calculates the form factor, P(*q*), for a monodisperse spherical
particle with a core-shell structure. The form factor is normalized by
the total particle volume.

Resolution smeared version is also provided.

VARIABLES

Input Variables (default values):

Parameter | Variable | Value |
---|---|---|

0 | Scale | 1.0 |

1 | Core Radius (Å) | 60.0 |

2 | Shell Thickness (Å) | 10.0 |

3 | Core SLD (Å^{-2}) | 1.0e-6 |

4 | Shell SLD (Å^{-2}) | 2.0e-6 |

5 | Solvent SLD (Å^{-2}) | 3.0e-6 |

6 | incoherent Background(cm^{-1}) | 0.000 |

USAGE NOTES

The function calculated is:

where ,
, and
.
The returned value is scaled to units of [cm^{-1}].

Parameter[0] (scale) and the SLD's are multiplicative factors in the model and are perfectly correlated. No more than one of these parameters can be free during the model fitting.

If the scale factor Parameter[0] is set equal to the particle
volume fraction, *phi*, the returned value is the scattered
intensity per unit volume, I(*q*) = *phi**P(*q*).
However, no interparticle interference effects are included in this
calculation.

Scattering from monodisperse vesicles can be calculated by setting the core SLD equal to the solvent SLD.

REFERENCE

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

TEST DATASET

This example dataset is produced by calculating the CoreShell,
using 256 data points, *q*_{min} = 0.001 Å^{-1},
*q*_{max} = 0.7 Å^{-1} and the above default
coefficient values.