The effect of transverse wavefront width on specular neutron reflection.

In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions that are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases, such as specular neutron reflectometry, in which the structural length scales of the scattering object require that the wavefunction of an individual neutron in the beam be described by a spatially localized packet - in particular with respect to the transverse extent of its wavefronts (i.e. normal to the packet's mean direction of propagation). It is shown in the present work that neutron diffraction patterns observed for periodic transmission phase gratings, as well as specular reflection measurements from patterned thin films with repeat units of the order of micrometres, can be accurately described by associating an individual neutron with a wave packet and treating a beam as a collection of independent packets. In these cases, accurate analysis requires that the transverse spatial extent of a neutron packet wavefront be accounted for in addition to the angular divergence of the beam that is characterized by a distribution of packet mean wavevector directions. It is shown how a measure of the effective transverse spatial extent of the neutron packet - over which its wavefronts are of sufficient uniformity to produce coherent scattering - can be determined by employing reference diffraction gratings and patterned thin films of known structure and composition.

Analysis of multibeam data for neutron reflectivity.

We offer mathematical proof that multiple-beam neutron reflectivity, corresponding to simultaneous collection of data at multiple angles (wavevector transfers) does not perform better, errorwise for counting noise, than single-beam data collection for the same total number of reflected neutrons-and may perform much worse, depending on the beam modulation strategy used. The basic idea is that the nominal statistical benefit of summing data at, say, N different wavevector transfers is undone by needing to collect N differently modulated (i.e., weighted) sums in order to extract the reflectivities. To our knowledge, a general proof of this behavior for arbitrary strategies has been lacking. The formal result can be summarized by saying that the best nondiagonal matrix modulation strategies are orthogonal (unitary) matrices, or constant multiples thereof, and that these can do no better than diagonal--i.e., single-beam--strategies.

Statistical analysis of phase-inversion neutron specular reflectivity.

The phase-inversion approach to neutron specular reflection is elucidated in a formal setting, in order to emphasize its conceptual coherence and to facilitate study of some of its statistical properties in the context of real data. An operational notion of data degradation is introduced and illustrated with the randomizing effects of shot noise ("counting" noise) and the systematic "bias" induced by data truncation. Some basic statistical effects of phase-inversion are worked out in the new formalism and illustrated by simulated examples. A principal is advanced that phase-inversion sets the limit of available information from specular reflection.

Progress in the development of phase-sensitive neutron reflectometry methods.

It has been a number of years since phase-sensitive specular neutron reflectometry (PSNR) methods employing reference layers were first introduced to help remove the ambiguity inherent in the reconstruction of scattering length density (SLD) depth profiles (Majkrzak, C. F.; Berk, N. F. Physica B 2003, 336, 27) from specular reflectivity measurements. Although a number of scientific applications of PSNR techniques have now been successfully realized (Majkrzak, C. F.; Berk, N. F.; Perez-Salas, U. A. Langmuir 2003, 19, 7796 and references therein), in certain cases practical difficulties remain. In this article, we describe possible solutions to two specific problems: (1) the need for explicit, detailed knowledge of the SLD profile of a given reference layer of finite thickness; and (2) for a reference layer of finite thickness in which only two density variations are possible, how to identify which of two mathematical solutions corresponds to the true physical structure.

Hydration state of single cytochrome c monolayers on soft interfaces via neutron interferometry.

Yeast cytochrome c (YCC) can be covalently tethered to, and thereby vectorially oriented on, the soft surface of a mixed endgroup (e.g., -CH3/-SH = 6:1, or -OH/-SH = 6:1) organic self-assembled monolayer (SAM) chemisorbed on the surface of a silicon substrate utilizing a disulfide linkage between its unique surface cysteine residue and a thiol endgroup. Neutron reflectivities from such monolayers of YCC on Fe/Si or Fe/Au/Si multilayer substrates with H2O versus D2O hydrating the protein monolayer at 88% relative humidity for the nonpolar SAM (-CH3/-SH = 6:1 mixed endgroups) surface and 81% for the uncharged-polar SAM (-OH/-SH = 6:1mixed endgroups) surface were collected on the NG1 reflectometer at NIST. These data were analyzed using a new interferometric phasing method employing the neutron scattering contrast between the Si and Fe layers in a single reference multilayer structure and a constrained refinement approach utilizing the finite extent of the gradient of the profile structures for the systems. This provided the water distribution profiles for the two tethered protein monolayers consistent with their electron density profile determined previously via x-ray interferometry (Chupa et al., 1994).

First-principles determination of hybrid bilayer membrane structure by phase-sensitive neutron reflectometry.

The application of a new, phase-sensitive neutron reflectometry method to reveal the compositional depth profiles of biomimetic membranes is reported. Determination of the complex reflection amplitude allows the related scattering length density (SLD) profile to be obtained by a first-principles inversion without the need for fitting or adjustable parameters. The SLD profile so obtained is unique for most membranes and can therefore be directly compared with the SLD profile corresponding to the chemical compositional profile of the film, as predicted, for example, by a molecular dynamics simulation. Knowledge of the real part of the reflection amplitude, in addition to enabling the inversion, makes it possible to assign a spatial resolution to the profile for a given range of wavevector transfer over which the reflectivity data are collected. Furthermore, the imaginary part of the reflection amplitude can be used as a sensitive diagnostic tool for recognizing the existence of certain in-plane inhomogeneities in the sample. Measurements demonstrating the practical realization of this phase-sensitive technique were performed on a hybrid bilayer membrane (self-assembled monolayer of thiahexa (ethylene oxide) alkane on gold and a phospholipid layer) in intimate contact with an aqueous reservoir. Analysis of the experimental results shows that accurate compositional depth profiles can now be obtained with a spatial resolution in the subnanometer range, primarily limited by the background originating from the reservoir and the roughness of the film's supporting substrate.

Neutron reflectivity studies of single lipid bilayers supported on planar substrates.

Neutron reflectivity was used to probe the structure of single phosphatidylcholine (PC) lipid bilayers adsorbed onto a planar silicon surface in an aqueous environment. Fluctuations in the neutron scattering length density profiles perpendicular to the silicon/water interface were determined for different lipids as a function of the hydrocarbon chain length. The lipids were studied in both the gel and liquid crystalline phases by monitoring changes in the specularly-reflected neutron intensity as a function of temperature. Contrast variation of the neutron scattering length density was applied to both the lipid and the solvent. Scattering length density profiles were determined using both model-independent and model-dependent fitting methods. During the reflectivity measurements, a novel experimental set-up was implemented to decrease the incoherent background scattering due to the solvent. Thus, the reflectivity was measured to Q approximately 0.3 A-1, covering up to seven orders of magnitude in reflected intensity, for PC bilayers in D2O and silicon-matched (38% D2O/62% H2O) water. The kinetics of lipid adsorption at the silicon/water interface were also explored by observing changes in the reflectivity at low Q values under silicon-matched water conditions.

Outline of Neutron Scattering Formalism.

Neutron scattering formalism is briefly surveyed. Topics touched upon include coherent and incoherent scattering, bound and free cross-sections, the Van Hove formalism, magnetic scattering, elastic scattering, the static approximation, sum rules, small angle scattering, inelastic scattering, thermal diffuse scattering, quasielastic scattering, and neutron optics.

Microstructural Characterization of Ceramic Materials by Small Angle Neutron Scattering Techniques.

The use of small angle neutron scattering (SANS) techniques for ceramic materials is discussed. Two areas are emphasized: 1) diffraction for microstructural phenomena of less than 100 nm, and 2) beam broadening for microstructural phenomena greater than 90 nm.