Abstract
Quasi-elastic neutron scattering (QENS)—based on the seminal work of Nobel Laureate Brockhouse—has been one of the major methods for studying pico-second to nano-second diffusive dynamics over the past 70 years. This is regarded as an “inelastic” method for dynamics. In contrast, we recently proposed a new neutron-scattering method for dynamics, which uses the elastic line of the scattering to access system dynamics directly in the time domain (Benedetto and Kearley in Sci Rep 9:11284, 2019). This new method has been denoted “vHI” that stands for “van Hove Integral”. The reason is that, under certain conditions, the measured elastic intensity corresponds to the running-time integral of the intermediate scattering function, Ileft( {Q,t} right), up to a time that is inversely proportional to the energy band-width incident on the sample. As a result, Ileft( {Q,t} right) is accessed from the time derivative of the measured vHI profile. vHI has been supported by numerical and Monte-Carlo simulations, but has been difficult to validate experimentally due to the lack of a suitable instrument. Here we show that vHI works in practice, which we achieved by using a simple modification to the standard QENS backscattering spectrometer methodology. Basically, we varied the neutron-energy band-widths incident at the sample via a step-wise variation of the frequency of the monochromator Doppler-drive. This provides a measurement of the vHI profile at the detectors. The same instrument and sample were also used in standard QENS mode for comparison. The intermediate scattering functions, Ileft( {Q,t} right), obtained by the two methods—vHI and QENS—are strikingly similar providing a direct experimental validation of the vHI method. Perhaps surprisingly, the counting statistics of the two methods are comparable even though the instrument used was expressly designed for QENS. This shows that the methodology modification adopted here can be used in practice to access vHI profiles at many of the backscattering spectrometers worldwide. We also show that partial integrations of the measured QENS spectrum cannot provide the vHI profile, which clarifies a common misconception. At the same time, we show a novel approach which does access Ileft( {Q,t} right) from QENS spectra.
Highlights
Quasi-elastic neutron scattering (QENS)—based on the seminal work of Nobel Laureate Brockhouse— has been one of the major methods for studying pico-second to nano-second diffusive dynamics over the past 70 years
Neutron-scattering approaches, in particular, have a few unique a dvantages[11,12,13,14,15,16,17,18,19]. These include (i) the ability of neutrons to interact directly with the nuclei of the atoms, which facilitates comparison with molecular dynamics simulations; (ii) sensitivity to light atoms, hydrogen; (iii) ability to distinguish between isotopes, and (iv) an innate molecular spatial resolution
The information on the diffusive dynamics is contained in the spectral profile around the zero-energy exchange value—known as the elastic line—rather than in inelastic features
Summary
Quasi-elastic neutron scattering (QENS)—based on the seminal work of Nobel Laureate Brockhouse— has been one of the major methods for studying pico-second to nano-second diffusive dynamics over the past 70 years. Our vHI method measures the neutrons scattered into the elastic line as a function of the observation time, tobs , which is inversely proportional to the neutron-energy band-width incident at the sample.
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