EISFDiffCylinder¶

Description¶

This fitting function models the diffusion of a particle confined in a cylinder of radius $R$ and length $L$ [1].

$A_0(Q_z) = (\frac{j_0(Q R cos(\theta))}{Q R cos(\theta)})^2 B_0^0(Q_{\perp}) = (3 \frac{j_1(Q L sin(\theta))}{Q L sin(\theta)})^2 \frac{1}{2} \int_0^{\pi} d\theta sin(\theta)$

$A_0(Q_z)$ implements diffusion along the cylinder axis. $B_0^0(Q_{\perp})$ implements diffusion perpendicular to the cylinder axis. Both diffusions are assumed to be decoupled. Finally, the integration in $\theta$ implements a powder average (spherical Bessel functions).

$R$ and $L$ units are inverse of $Q$ units.

References¶

[1]	Dianoux et al. Mol. Phys. 46:1129-37, 1982.

Usage¶

Example - fit of Q-dependence:

from __future__ import print_function

q =  [0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9]
# A=1.0, R=3.5, L=1.7
eisf = [0.8327688, 0.60447105, 0.36837178, 0.18538092, 0.07615478,
        0.02660468, 0.00973061, 0.00461192, 0.00222067]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffCylinder,A=1,R=2.0,L=1,constraints=(0.01<R,0.01<L),ties=(A=1)', w, WorkspaceIndex=0)
print(results.Function)

Output:

name=EISFDiffCylinder,A=1,R=3.5,L=1.7,constraints=(0.01<R,0.01<L),ties=(A=1)

Properties (fitting parameters)¶

Name	Default	Description
A	1.0	Amplitude, or Scaling factor
R	1.0	Cylinder radius, inverse units of Q.
L	2.0	Cylinder length, inverse units of Q.

Categories: FitFunctions | QuasiElastic

Source¶

Python: EISFDiffCylinder.py (last modified: 2019-11-13)