Neutron Scattering Benedetto

Neutron scattering spectroscopy for dynamics

Probing single-particle dynamics is central to the study of atomic and molecular motion across many areas of research. These dynamics can be fully described by the van Hove self-distribution function, G_self(r,t), which represents the probability that a species has diffused a distance r over time t, or equivalently, by its spatial Fourier transform, I(Q,t), known as intermediate scattering function. Current neutron-scattering spectroscopies for measuring these dynamics rely on the exchanged energy of each scattered neutron as shown by Brockhouse (Slow Neutron Spectroscopy and the Grand Atlas of the Physical World, Nobel Lecture, December 8 (1994)). Rather than these “inverse” approaches, we have recently proposed an alternative approach that uses the proportion of neutrons scattered elastically within different observation times that can be scanned by varying the energy band-width coming into the sample (Fig. 1). This new approach is based on the observation we recently made that the elastic scattering intensity corresponds to the running time-integral of I(t) up to a time inversely proportional to the selected energy band-width (Fig. 2). It turned out that our new method has several advantages in comparison to quasi-elastic neutron scattering - the standard method for dynamics - as it has 100-times more counts at the detector and a 10-times better statistical significance at the I(t)-level (Fig. 3). We are also working on instrumental designs suitable for both continuous and pulsed neutron sources (Fig. 4).

Fig. 1 - Illustration of the concept. Column 1 sketches the energy landscape of a system of particles, at three different observation times, t_obs. t_obs is the time-resolution of the measurement and is inversely proportional to the instrumental energy-resolution. At short t_obs only the rapid motions are detected, most of the system appearing at rest (1a). At intermediate t_obs other motions are detected (1b), and for long t_obs the slower motions are also detected (1c). Existing techniques require determination of many exchanged energy values, ΔE, to access I(t), typically operating at fixed t_obs. In general, our approach of obtaining the proportion of particles “at rest”, as a function of t_obs, should be more efficient. This proportion formally corresponds to the running time-integral of I(t), that is the van Hove integral vHI(t = t_obs), as sketched in column 2, in which each t_obs determines the upper integration limit of I(t). Differentiation of the measured vHI(t) (3a) provides I(t) directly (3b).

Fig. 2 - Numerical validation with counting error of several approaches to obtain I(t) from the “experimental” vHI(t). The three plots are: (a) single exponential, (b) double exponential, and (c) stretched exponential. The numerical derivative of vHI(t) is intractable, but its polynomial derivative and Gaussian-error derivative reproduce the input function well. The cosine FT is also shown for a consistency check.

Fig. 3 - Relative difference between “standard” and “perfect” outputs for quasi-elastic neutron scattering QENS (a) and van Hove Integral (vHI) neutron spectroscopy (b).

Selected publications:

A Quantitative Comparison of the Counting Significance of van Hove Integral Spectroscopy and Quasielastic Neutron Scattering
A. Benedetto and G.J. Kearley, Scientific Reports, 10, 6350, (2020)
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Dynamics from elastic neutron-scattering via direct measurement of the running time-integral of the van Hove distribution function
A. Benedetto and G.J. Kearley, Scientific Reports, 9, 11284, (2019)
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Elastic Scattering Spectroscopy (ESS): an Instrument-Concept for Dynamics of Complex (Bio-) Systems from Elastic Scattering
A. Benedetto and G.J. Kearley, Scientific Reports, 6, 34266, (2016)
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Laboratory of Biophysics of Ionic Liquids