MODEL

PolyRectSphere

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 polydisperse population of spheres
with uniform scattering length density. The distribution of radii is
a rectangular (box) distribution. The form factor is normalized by
the average particle volume such that P(*q*) =
scale*<*f***f*>/Vol + bkg, where *f* is the single
particle scattering amplitude and the < > denote an average over
the size distribution.

Resolution smeared version is also provided.

VARIABLES

Input Variables (default values):

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

0 | Scale | 1.0 |

1 | Average Radius (Å) | 60.0 |

2 | Polydispersity (0-1) | 0.12 |

3 | Contrast (Å^{-2}) | 3.0e-6 |

4 | Incoherent Background(cm^{-1}) | 0.000 |

USAGE NOTES

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

contrast = SLD (sphere) - SLD (solvent)

The (normalized) rectangular distribution is:

with the constraint that *w* <= R. Here R is the average
radius specified by parameter[1] above.

R is the mean of the distribution and *w* is the half-width.
The root mean square deviation is
. The polydispersity,
.

The form factor is normalized by the average volume, using

.

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.

Parameter[0] (scale) and Parameter[3] (contrast) are multiplicative factors in the model and are perfectly correlated. Only one of these parameters should be left free during model fitting.

REFERENCE

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

TEST DATASET

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