Scattering depth correction of evanescent waves in inelastic neutron scattering using a neutron prism

Abstract

Grazing Incidence Neutron Spin Echo Spectroscopy (GINSES) has recently been applied to measure the dynamics of surfactant membranes close to a hydrophilic silicon wall. The scattering depth of the evanescent wave inside the microemulsion depends strongly on the angle of incidence and the wavelength. The inherently low scattering intensity of GINSES measurements, however, requires the integration over a rather broad wavelength band. In particular, at a pulsed source the instrument operates with a broad wavelength band covering all neutrons within one frame between two pulses. In order to yield viable counting statistics it is highly desirable to integrate data corresponding to significant fractions of the wavelength band. Therefore, in a normal reflectometry setup the penetration length would be smeared and blur the depth dependence of the experimental results. Here we describe a new method to strongly mitigate this effect and show its application in a GINSES experiment at the neutron spin echo instrument at the Spallation Neutron Source (SNS). A prism in front of the sample was introduced in order to adapt the angle of the incoming beam according to the wavelength by this optical component. As an example an experiment on a bicontinuous microemulsion using these neutron optics is presented.

Introduction

Neutron spin echo (NSE) spectroscopy achieves the highest resolution in inelastic neutron scattering [1], [2], [3]. The neutron velocity is encoded and decoded by a number of spin precessions in solenoids. The polarization of the neutron beam at the end of the decoding precession path is the intermediate scattering function $S(q,\tau )$ multiplied by a resolution function. In soft matter physics, the main fields of application are Brownian motion type processes, such as polymer chain dynamics in melts or membrane fluctuations in microemulsion systems [4]. Grazing incidence small angle neutron scattering (GISANS) is a technique which allows to study structural properties close to an interface. The incident neutron beam is strongly collimated in one direction and enters a silicon block from the side. It then hits the flat Si-liquid interface at a very small angle below the critical angle ${\alpha }_c$. Such studies allowed to resolve a lamellar structure close to the Si-interface of a bulk bicontinuous microemulsion [5]. The concept of probing the sample close to the interface has recently also been applied to studies of the dynamics of surfactant membranes in microemulsions as a function of scattering depth [6]. When transferring this technique to a spallation neutron source with a pulsed beam, the acquired data gain in complexity due to the time-of-flight nature of the measurement, hence the data reduction process is more elaborate. Due to the wavelength spread during the pulse, one naturally probes a certain q-range according to $q=4\pi /\lambda \sin (\theta /2)$ and a Fourier time range, since the Fourier time $\tau \propto {\lambda }^3$. Fortunately the approximate q³ dependence of the relaxation rates [7] implies a matching compensation of space and time scales and results in a remarkable independence of observed relaxation curves on wavelength width. For the GINSES experiment, however, the variation of the scattering depth into the sample adds additional complexity to the experiment. For intensity reasons it is absolutely necessary to integrate over the broad wavelength band. Regrouping of time tagged wavelength bins is difficult since the scattering vector q, the Fourier-time $\tau$ and the scattering depth have different $\lambda$ dependences. This is different from a plain SANS experiment at a pulsed source where large sections of time bins and detector positions can be grouped to yield the same q value which in that case is the single parameter. Here we demonstrate that the wavelength-dependence of the scattering depth in a GINSES experiment can be corrected to a constant scattering depth for the whole wavelength band by using a neutron prism, which deflects the long wavelengths stronger than the short ones.