A Quantitative Comparison of the Counting Significance of van Hove Integral Spectroscopy and Quasielastic Neutron Scattering

Antonio Benedetto,Gordon J Kearley

doi:10.1038/s41598-020-63193-3

Antonio Benedetto, Gordon J Kearley

Open Access

https://doi.org/10.1038/s41598-020-63193-3

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Journal: Scientific Reports	Publication Date: Apr 14, 2020
Citations: 5	License type: open-access

Affiliation: University College Dublin

Abstract

We have recently proposed a new method to access system dynamics via neutron scattering based on measuring the elastic scattered intensity: By varying the energy band-width that impinges on the sample (also known as instrumental energy resolution), the purely elastic-scattering from this variation is the running time-integral of the intermediate scattering function (I(t)) [Benedetto and Kearley, Sci. Rep. 9, 11284, 2019]. In this correspondence we denote our method “vHI”, which stands for “van Hove Integral”. The method is now widely accepted as “valid” and here we focus on the efficiency of the vHI method compared with the standard quasi-elastic neutron scattering (QENS) method. We use a numerical Monte-Carlo simulation of an instrument that is equally capable of measuring QENS and vHI under identical conditions. For an “experiment” in which the same number of neutrons enter the instrument, we present comparisons between QENS and vHI at three levels of data-reduction. Firstly, at the raw-data level vHI achieves 100 times more neutrons at the detector than QENS. Secondly, vHI has a factor of 2 less statistical error, which would translate to an overall gain of 4 for vHI in counting-time. Lastly, we compare the distortions caused in obtaining the final I(t) via time-Fourier transform (QENS) and polynomial time-derivative (vHI). Here, the statistical error is 10 times smaller for vHI. This last comparison is the most important result where the 10 times smaller residual for vHI gives a net gain in counting time of 100 better than QENS to obtain the same underlying dynamics of the system under study.

Highlights

The study of dynamical behaviour at an atomic level plays a major role in understanding the microscopic mechanisms of materials of interest, from simple chemical molecules up to complex biomolecules
To access the vHI profile, the portion of elastic scattering from the system is computed as a function of the energy-half-width at half-maximum (HWHM) of the primary spectrometer, which is associated to an observation time, tobs[32]
The total counts of the vHI method is about 100 times more than the total counts of the quasi-elastic neutron scattering (QENS). The origin of this gain in total counts is because (i) the vHI method operates in the “elastic” regime which is usually at least an order of magnitude more probable than “inelastic” processes, and because (ii) for the vHI method the primary energy resolution, dE1, is relaxed to match the time-scale being measured

Summary

Introduction

The study of dynamical behaviour at an atomic level plays a major role in understanding the microscopic mechanisms of materials of interest, from simple chemical molecules up to complex biomolecules. The position of the band-centre on the primary monochromator is held constant, and its energy band-width is varied to obtain the elastic intensity as a function of (the observation) time, effectively the vHI profile.

Results

Conclusion