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EISFDiffCylinder

Description

This fitting function models the diffusion of a particle confined in a cylinder of radius \(R\) and length \(L\) [1]. \(A_0(Q_z)\) implements diffusion along the cylinder axis.

\[A_0(Q_z) = (j_0(Q L \cos(\theta)))^2 = (\frac{\sin(Q L \cos(\theta))}{Q L \cos(\theta)})^2\]

\(B_0^0(Q_{\perp})\) implements diffusion perpendicular to the cylinder axis.

\[B_0^0(Q_{\perp}) = (2 \frac{J_1(Q R \sin(\theta))}{Q R \sin(\theta)} )^2\]

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]

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

Usage

Example - fit of Q-dependence:

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=3.11497,L=1.68724,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