EISFDiffSphereAlkyl

Description

../../_images/EISFDiffSphereAlkyl_1.png

This fitting function models the elastic incoherent intensity of a linear polycarbon chain (alkyl) where the local diffusion of each unit in the chain is modeled as undergoing continuous diffusion but confined to a spherical volume whose radius varies from a minimal value r to a maximum value R [1].

Ri=(Rr)(i/M)+rEISF(Q)=1Mi=1M(3j1(QRi)QRi)2(QRi)

r and R units are inverse of Q units. Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the jl(z) spherical Bessel functions.

Related functions: - EISFDiffSphere - ElasticDiffSphere - InelasticDiffSphere - DiffSphere

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=2.0, r=0.12, R=1.6, M=9
eisf = [1.96561499215648, 1.90667574712235, 1.82327109734092,
        1.72075639596568, 1.60529662348532, 1.48322421137169,
        1.36043655237770, 1.24191091785048, 1.13138963884055]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffSphereAlkyl, M=9', w, WorkspaceIndex=0)
print(results.Function)

Output:

name=EISFDiffSphereAlkyl,M=9,A=2,Rmin=0.12,Rmax=1.6

Properties (fitting parameters)

Name

Default

Description

A

1.0

Amplitude

Rmin

1.0

Minimum radius, inverse units of Q.

Rmax

2.0

Maximum radius, inverse units of Q.

Categories: FitFunctions | QuasiElastic

Source

Python: EISFDiffSphereAlkyl.py