6.3

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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

[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