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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 \(\tau\) 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

[1]
    1. Hall and D. K. Ross, Mol. Phys. 42, 673 (1981) <http://dx.doi.org/10.1080/00268978100100521>

Categories: FitFunctions | QuasiElastic

Source

Python: HallRoss.py (last modified: 2020-04-06)