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
0Scale1.0
1Average Radius (Å)60.0
2Polydispersity (0-1)0.12
3Contrast (Å-2)3.0e-6
4Incoherent 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:

the (normalized) rectangular distribution

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 Equation 1. The polydispersity, equation 2.

The form factor is normalized by the average volume, using

equation 3.

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, qmin = 0.001 Å-1, qmax = 0.7 Å-1 and the above default parameter values.

Example Dataset