MODEL

ProlateCoreShell

AUTHOR/MODIFICATION

Steve Kline 06 NOV 1998

Alan Munter 08 JULY 1999, converted to Java

APPROVED FOR DISTRIBUTION

DESCRIPTION

Calculates the form factor for a monodisperse prolate ellipsoid
particle with a core/shell structure. The form factor is averaged
over all possible orientations of the ellipsoid. The form factor is
normalized by the total particle volume such that P(*q*) =
scale*<*f*^{2}>/Vol + bkg, where *f* is the
single particle scattering amplitude and the < > represent
the orientational average.

Resolution smeared version is also provided.

VARIABLES

Input Variables (default values):

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

0 | Scale | 1.0 |

1 | Major Core Radius (Å) | 100.0 |

2 | Minor Core Radius (Å) | 50.0 |

3 | Major Shell Radius (Å) | 110.0 |

4 | Minor Shell Radius (Å) | 60.0 |

5 | Contrast (core-shell) (Å^{-2}) | 1.0e-6 |

6 | Contrast (shell-solvent) (Å^{-2}) | 2.0e-6 |

7 | Incoherent Background (cm^{-1}) | 0.0 |

**USAGE** **NOTES**

The function calculated is P(*q*):

The returned value is in units of [cm^{-1}]

Scattering contrast = SLD (core) - SLD (shell) or SLD (shell - solvent) as marked

Parameter[0] (scale), and contrasts (Parameter[5] and Parameter[6]) are both multiplicative factors in the model and are perfectly correlated. No more than one of these parameters can be free during model fitting.

If the scale factor Parameter[0] is set equal to the particle
volume fraction, *phi*, then 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.

It is the users' responsibility to ensure that shell radii are larger than core radii, and that major radii are larger than minor radii.

76-point Gaussian quadrature is used to perform the orientational averaging, and may be slow on older machines.

REFERENCE

Kotlarchyk, M.; Chen, S.-H. *J. Chem. Phys*., **1983**,
*79*, 2461.

Berr, S. *J. Phys. Chem.*, **1987**, *91*, 4760.

TEST DATASET

This example dataset is produced by calculating the ProlateCoreShell
using 128 data points, *q*_{min} = 0.001 Å^{-1},
*q*_{max} = 0.7 Å^{-1} and the above default
parameter values.