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]	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)