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DiffSphere¶
Description¶
This fitting function models the dynamics structure factor of a particle undergoing continuous diffusion but confined to a spherical volume. According to Volino and Dianoux 1,
Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the \(j_l(z)\) spherical Bessel functions. Furthermore, the requirement that no particle flux can escape the sphere leads to the following boundary condition2:
The roots of this set of equations are the numerical coefficients \(x_{n,l}\).
The fit function DiffSphere has an elastic part modeled by fitting function ElasticDiffSphere, and an inelastic part modeled by InelasticDiffSphere.
Attributes (non-fitting parameters)¶
Name |
Type |
Default |
Description |
---|---|---|---|
NumDeriv |
|||
Q |
|||
f0.Q |
|||
f0.WorkspaceIndex |
|||
f1.Q |
|||
f1.WorkspaceIndex |
\(NumDeriv\) (boolean, default=true) carry out numerical derivative - \(Q\) (double, default=1.0) Momentum transfer
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
f0.Height |
1.0 |
Scaling factor to be applied to the resolution. |
f0.Centre |
0.0 |
Shift along the x-axis to be applied to the resolution. |
f0.Radius |
2.0 |
Sphere radius |
f1.Intensity |
1.0 |
scaling factor |
f1.Radius |
2.0 |
Sphere radius, in Angstroms |
f1.Diffusion |
0.05 |
Diffusion coefficient, in units of A^2*THz, if energy in meV, or A^2*PHz if energy in ueV |
f1.Shift |
0.0 |
Shift in domain |
Categories: FitFunctions | QuasiElastic
Source¶
C++ header: DiffSphere.h
C++ source: DiffSphere.cpp