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Hall-Ross¶
Description¶
Models the Q dependence of the QENS line width (Gamma (hwhm)), diffusion coefficients (D), residence times (tau) and jump lengths (l) to extract the associated long range diffusive motions of molecules.
The Hall-Ross Jump diffusion model [1] has the form:
\[Gamma(Q) = \frac{\hbar}{\tau} \cdot (1-\exp(-\frac{l^2 Q^2}{2}))\]
Units of \(l\) are inverse units of \(Q\).
Units of \(Gamma\) are meV if units of \(\tau\) are ps. Alternatively, units of \(Gamma\) are \(\mu`eV if units of :math:\)tau` are ns.
Mean square diffusion jump length \(= 3 l^2 \ \AA^2\).
Diffusion coefficient \(D = \frac{l^2}{2 \tau} \ \AA^2 ps^{-1}\).
Properties (fitting parameters)¶
Name |
Default |
Description |
|---|---|---|
Tau |
1.0 |
Residence time |
L |
0.2 |
Standard deviation of jump lengths |
References¶
Categories: FitFunctions | QuasiElastic
Source¶
Python: HallRoss.py