Inelastic Neutron Scattering Analysis with Time-Dependent Gaussian-Field Models

TL;DR

This paper introduces time-dependent Gaussian-field models for analyzing inelastic neutron scattering data, enabling the extraction of dynamic real-space structures in disordered systems through novel correlation functions and modeling approaches.

Contribution

The paper develops new time-dependent Gaussian-field models and analytical expressions for neutron scattering, allowing detailed analysis of dynamic structures in complex multiphase systems.

Findings

Static large-scale structure of oil/water domains identified

Interfaces exhibit thermal fluctuations with ~6 nm amplitude

Models successfully analyze data across various contrasts and q, τ ranges

Abstract

Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing time-dependent clipped Gaussian field models. General expressions are derived for all space- and time-correlation functions relevant to coherent inelastic neutron scattering, for multiphase systems and arbitrary scattering contrasts. Various dynamic models are introduced that enable one to add time-dependence to any given spatial statistics, as captured e.g. by small-angle scattering. In a first approach, the Gaussian field is decomposed into localised waves that are allowed to fluctuate in time or to move, either ballistically or diffusively. In a second approach, a dispersion relation is used to make the spectral components of the field time-dependent. The various models lead to qualitatively different dynamics, which can be discriminated by neutron scattering. The methods of the paper are illustrated with oil/water microemulsion studied by small-angle scattering and neutron spin-echo. All available data - in both film and bulk contrasts, over the entire range of $q$ and $\tau$- are analyzed jointly with a single model. The analysis points to static large-scale structure of the oil and water domains, while the interfaces are subject to thermal fluctuations. The fluctuations have an amplitude around 6 nm and contribute to 30 % of the total interface area.