small angle X-ray scattering abbr., SAXS (rus. малоугловое рентгеновское рассеяние abbr., МРР) — an elastic scattering of X-rays by inhomogeneities in the substance, whose dimensions substantially exceed the radiation wavelength, which is λ = 0.1-1 nm; the directions of the scattered beam only slightly (to a small angle) deviate from the direction of the incident beam.


The presence in a polydisperse system of evenly distributed inhomogeneities, whose sizes range from 1 to 100 nm, leads to the scattering of X-rays at small angles (<30 degrees). Analysis of the dependence between the intensity of scattered radiation and the scattering angle (Fig. a) makes it possible to determine such characteristics of nano-sized elements, as their shape and size, phase composition, internal structure, orientation and distribution.

X-ray sources used in the experiments include X-ray tubes (wavelength λ = 0.1-0.2 nm) and synchrotron radiation (λ = 0.03-0.35 nm). Monochromaticity of the primary narrow beam is achieved by using special collimation systems. The beam passing through the sample is scattered and registered by the detectors. The size and shape of the particles are determined on the basis of the dependence between the scattered radiation intensity and the scattering angle (Fig. a). For example, in an isotropic dispersed system the X-ray scattering intensity is determined using the Guinier equation: 

where is the scattering wave vector, is the wavelength, is the radiation scattering angle ( is the radius of gyration of a particle about its centre of mass).

Then, for plotting a Guinier curve (showing the dependence ), the size and shape of the scattering particle can be determined from the slope of the line (Fig. b).

The method is widely used for obtaining information about the shape and structure of various materials, such as protein molecules, surfactants, various dispersed systems (such as pigments in paint, blood cells), emulsions, fibres, catalysts, polymers and nanocomposites, and liquid crystals.


a — Small angle X-ray scattering spectrum of NADPH oxidase protein molecule. b
a — Small angle X-ray scattering spectrum of NADPH oxidase protein molecule. 
b — Guignet chart to define the size of NADPH oxidase protein molecule. 
Authors: R. P. Rambo, G. L. Hura, A. L. Menon, M. Hamel, M.W. Adams, J. A. Tainer. Quoted from Biosis portal,, devoted to the research in macromolecular compounds using the small angle X-ray scattering technique.


  • Streletskiy Alexey V.


  1. Small angle X-ray scattering // Physical encyclopedia (in Russian). V. 3 Ed. by А. М. Prohorov . — Moscow: Bol'shaja Rossijjskaja ehnciklopedija, 1992. P. 41–44.
  2. Suzdalev I.P. Nanotechnology: Physics and Chemistry of Nanoclusters, Nanostructures and Nanomaterials (in Russian). — Moscow: KomKniga, 2006. — 592 pp.

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