MODEL

CoreShellCylinder

ORIGINAL AUTHOR/MODIFICATION

Steve Kline 20 JAN 1999

Alan Munter 08 JULY 1999, converted to Java

APPROVED FOR DISTRIBUTION

DESCRIPTION

Calculates the form factor for a monodisperse, right circular
cylinder with a core-shell scattering length density profile. The
shell thickness, *t*, is considered to be uniform over the entire
surface of the core. The form factor is normalized by the total
particle volume such that P(*q*) =
scale*<*f***f*>/Vol + bkg, where *f*
is the scattering amplitude and the < > denote an average over
all possible orientations of the cylinder. Resolution smeared version
is also provided.

VARIABLES

Input Variables (default values):

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

0 | Scale | 1.0 |

1 | Core Radius (Å) | 20.0 |

2 | Shell Thickness (Å) | 10.0 |

3 | Core Length (Å) | 400.0 |

4 | Core SLD (Å^{-2}) | 1.0e-6 |

5 | Shell SLD (Å^{-2}) | 4.0e-6 |

6 | Solvent SLD (Å^{-2}) | 1.0e-6 |

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

USAGE NOTES

The function calculated is:

, and;

where *r* is the radius of the core of the cylinder as shown below, and
J_{1}(*x*) is the first order bessel
function. Alpha is defined as the angle between the cylinder axis and the
scattering vector, **q**. The integral over alpha averages the form
factor over all possible orientations of the cylinder. The returned value
is scaled to units of [cm^{-1}],
on absolute scale.

The shell thickness is uniform over the entire particle. This means
that for the default case above, the total *diameter* of the
cylinder is 2*20 + 2*10 = 60 Å and that the total *length* is 400
+ 2*10 = 420 Å. The calculated cylinder volume is based on these total
cylinder dimensions.

The constrasts in the default case correspond to scattering from a cylindrical shell.

Parameter[0] (scale) and Parameter[4], Parameter[5], and Parameter[6] (SLD's) are multiplicative factors in the model and are perfectly correlated. Only one of these four parameters should be left free during model fitting.

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

REFERENCE

TEST DATASET

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