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# Neutron Reflectometry

Neutron Reflectometry is a laboratory technique for measuring the structure of thin films, similar to the often complementary techniques of X-ray reflectivity and ellipsometry. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, polymer and surfactant adsorption, structure of thin film magnetic systems, biological membranes, etc.

## Technical details

The technique involves shining a highly collimated beam of neutrons onto an extremely flat surface and measuring the intensity of reflected radiation as a function of angle. The exact shape of the reflectivity profile provides detailed information about the structure of the surface, including the thickness, density, and roughness of any thin films layered on the substrate.

Neutron reflectometry is a specular reflection technique, where the angle of the incident beam is equal to the angle of the reflected beam. The reflection is usually described in terms of a momentum transfer vector, denoted qz, which describes the change in momentum of a neutron after reflecting from the material. Conventionally the z direction is defined to be the film normal direction, and for specular reflection, the scattering vector has only a z-component. A typical neutron reflectometry plot displays the reflected intensity (relative to the incident beam) as a function of the scattering vector:

$q_z = \frac{4\pi}{\lambda}\sin ( \theta )$

where λ is the neutron wavelength, and θ is the angle of incidence. The Abeles matrix formalism can be used to describe the specular signal arising from the interface.

The wavelength of the neutrons used for reflectivity are typically on the order of 0.2 to 1 nm (2 to 10 Å). This technique requires a neutron source, which may be either a research reactor or a spallation source (a particle accelerator). Like all neutron scattering techniques, neutron reflectometry is sensitive to contrast arising from different nuclei (as compared to electron density, which is measured in x-ray scattering). This allows the technique to differentiate between various isotopes of elements. Neutron reflectometry measures the neutron scattering length density (SLD) and can be used to accurately calculate material density if the atomic composition is known.

## Comparison to other reflectometry techniques

Although other reflectivity techniques (in particular optical reflectivity, x-ray reflectometry) operate using the same general principles, neutron measurements are advantageous in a few significant ways. Most notably, since the technique probes nuclear contrast, rather than electron density, it is more sensitive for measuring some elements. In particular neutron measurements can probe lighter elements (hydrogen, carbon, nitrogen, oxygen, etc.) with more sensitivity than other techniques. Sensitivity to isotopes allows contrast to be greatly (and selectively) enhanced for some systems of interest. Multiple experiments that differ only by isotopic substitution can also be used to resolve the phase problem that is general to scattering techniques. Neutrons are typically non-perturbing: x-ray exposure may damage some materials, and laser light can modify some materials (e.g. photoresists). Also, optical techniques may include ambiguity due to optical anisotropy (birefringence), which complimentary neutron measurements can resolve.

Disadvantages of neutron reflectometry include the higher cost of the required infrastructure, the fact that some materials may become radioactive upon exposure to the beam, and insensitivity to the chemical state of constituent atoms. The relatively lower flux and higher background of the technique also limit the maximum value of qz that can be probed, as compared to x-ray reflectivity.

## Partial list of operating neutron reflectometers

• Platypus at ANSTO
• D17 at the Institut Laue-Langevin
• SURF and CRISP at ISIS neutron source
• NG1, NG7 and AND/R at the NIST Center for Neutron Research (NCNR)
• Liquids and Magnetism Reflectometers at the Spallation Neutron Source
• Polarized Neutron Reflectometer (PNR) at Dhruva, Bhabha Atomic Research Centre, Mumbai 400085, India
• Apparatus for Multi Option Reflectometry AMOR at Paul-Scherrer Institute (PSI), Villigen, Switzerland
• V6 reflectometer at HMI, Berlin, Germany
• C5 spectrometer at NRC Canada Chalk River Labs.

## Partial list of neutron reflectometry software

• Reflred and reflfit (NIST Center for Neutron Research)
• Motofit
• Parratt32 (HMI)
• Yanera (Brock University)