EISFDiffCylinder

Description

This fitting function models the diffusion of a particle confined in a cylinder of radius R and length L [1]. A0(Qz) implements diffusion along the cylinder axis.

A0(Qz)=(j0(QLcos(θ)))2=(sin(QLcos(θ))QLcos(θ))2

B00(Q) implements diffusion perpendicular to the cylinder axis.

B00(Q)=(2J1(QRsin(θ))QRsin(θ))2

Both diffusions are assumed to be decoupled. Finally, the integration in θ implements a powder average (spherical Bessel functions).

R and L units are inverse of Q units.

References

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