Safinya Group Research
Small Angle X-Ray Scattering and Diffraction

One of the main research tools of the Safinya group is X-ray scattering, in particular small angle X-ray scattering and diffraction (SAXS and SAXD). Our group regularly performs SAXS experiments at the Stanford Synchrotron Radiation Laboratory (SSRL), taking advantage of the high-flux X-ray beam available there. After building our own setup on site at the SSRL for years, we are now using the designated small angle beamline 4-2. We also have recently performed experiments at the Advanced Light Source (ALS). Concurrently, the Safinya group houses several custom-built in-house X-ray instruments. For a comprehensive discussion of concepts in X-ray scattering see references [1,2]

In contrast to the "real-space" images provided by optical microscopy or X-ray transmission measurements (such as those taken to identify, e.g., bone fractures), X-ray diffraction (XRD) data (which is collected at varied angles away from the transmitted beam) has to be transformed back from reciprocal space to yield real-space structural information. As a consequence, XRD yields structural information that averages over all the material the beam passes through. In this aspect, the information gained by XRD is complementary to similar information from microscopy techniques (e.g. AFM or EM), which provide local structural information. Wide angle X-ray diffraction further allows to determine structures at a finer resolution than any microscopy technique.

Bragg's law, which is a fundamental equation for the interpretation of X-ray diffraction data, states that a reflection / scattering peak resulting from an ordered structure with a repeat distance d will be observed when the condition nλ = 2d sinθ is fulfilled. Here, n is an integer, λ the wavelength of the X-ray radiation, and θ the angle at which the scattered beam is observed. Thus, d is inversely proportional to sinθ, meaning that the larger the repeat distance d, the smaller the angle at which scattering is observed. Consequently, SAXS is ideally suited for the study of ordered systems with large repeat distances, such as liquid crystalline mesophases, complex fluids and nano- to mesoporous materials. In addition, the elastic scattering of X-rays that can be observed at small and very small angles gives information about the shape and size of macromolecules.

A typical SAXS setup with a 2D (area) detector is shown below. An appropriate source emits a beam of X-rays which is focused and monochromated by special X-ray optics. The size of the beam is adjusted by a system of slits, hits the sample and enters the flight path. The flight path, which has to be under vacuum because air scatters the beam, provides the long distance between detector and sample that is essential to detect X-rays scattered at small angles. Unoriented samples yield a centrosymmetric pattern on the 2D detector, which is radially averaged to give the typical plots of diffracted intensity vs. scattering vector q (= 4π sinθ/λ).

The Safinya Lab is home to three custom-built X-ray scattering instruments built around one Rigaku rotating anode source and one XENOCS GENIX microfocus X-ray tube, with focusing multilayer optics and 2D detectors. These instruments, which are part of the MRL X-ray facility, cover a wide range of flightpath length (and thus scattering angles) down to very small angles, with observable scattering vectors q (= 4π sinθ/λ) from 30 down to 0.1 nm-1. This corresponds to observable real space distances of about 0.2 nm to 60 nm.

For more information:

Visit the website of the MRL's X-Ray Facility (managed by Youli Li) for further information on and signup for the available X-ray instruments.

Several websites give a more detailed introduction to SAXS and scattering theory, e.g. at the University of Oklahoma, or this PDF from the SSRL.

The following monographs provide a comprehensive discussion of concepts in X-ray scattering

[1]   J. Als-Nielsen, D. McMorrow: Elements of Modern X-Ray Physics; Wiley, New York, 2001.
[2]   O. Glatter, O. Kratky: Small Angle X-Ray Scattering; Academic Press, London, 1982.