Steve Kline 06 NOV 1998
Alan Munter 08 JULY 1999, converted to Java
APPROVED FOR DISTRIBUTION
Calculates the form factor for a polydisperse spherical particle with a core-shell structure. In this model, the ratio R(core)/R(core+shell) is held constant. The form factor is normalized by the mean particle volume such that P(q) = scale*<f2>/Vol + bkg, where f is the single particle scattering amplitude and the average < > is over a Schulz distribution of radii.
Resolution smeared version is also provided.
Input Variables (default values):
|1||Average Core Radius (Å)||60.0|
|2||Average Shell Thickness (Å)||10.0|
|3||Overall Polydispersity (0-1)||0.2|
|4||Core SLD (Å-2)||1.0e-6|
|5||Shell SLD (Å-2)||2.0e-6|
|6||Solvent SLD (Å-2)||3.0e-6|
The returned value is scaled to units of [cm-1], on absolute scale.
Parameter (scale) is correlated with the SLD's that describe the particle. No more than one of these parameters can be free during model fitting.
Parameter (polydispersity) is constrained to keep it within its physical limits of (0,1). If a value larger than 1 is entered it is quietly changed to 1 for the calculation. Polydispersity, p = s/Rt, where s2 is the variance of the distribution and Rt is the total particle radius, Rt = Rc +t. For a more complete description of the Schulz distribution, see: J. Hayter in "Physics of Amphiphiles - Micelles, Vesicles and Microemulsions" V. DeGiorgio and M. Corti, Eds. (1983) p. 69.
The returned form factor is normalized by the average particle volume <V>:
where and here r denotes the total particle radius, Rc + t, and z is the width parameter of the Schulz distribution, .
If the scale factor Parameter 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.
J. B. Hayter in "Physics of Amphiphiles--Micelles, Vesicles, and Microemulsions" Eds. V. DeGiorgio; M. Corti, pp. 59-93,1983. Eqns: 32-37
This example dataset is produced by calculating the PolyCoreShellRatio using 128 data points, qmin = 0.001 Å-1, qmax = 0.7 Å-1 and the above default parameter values.