SAXS notes

Small-Angle X-Ray Scattering (SAXS)

SAXS is an analytical technique used to determine the structure of particles at a nanoscale. It provides information about average particle sizes, shapes, and distribution, as well as pore structures.


SAXS operates on the principle of elastic scattering of X-rays by particles or structural inhomogeneities within a sample.
The technique is sensitive to variations in electron density, requiring a contrast between the particles and the surrounding matrix.

Main modes

Transmission Mode: X-rays penetrate through the sample, and the scattering signal is contributed by all irradiated particles within the sample volume.
Grazing-Incidence Mode: X-rays strike the sample surface at a shallow angle, slightly greater than the critical angle, optimizing for surface or near-surface structures (reflection mode).

Contrast requirement

A key requirement in SAXS is the presence of electron density contrast between the particles and the surrounding matrix. This contrast is what leads to scattering and allows for the analysis of the sample’s internal structure.

SAXS advantages

Non-Destructive: SAXS does not alter or damage the sample.
Minimal Sample Preparation: Requires little to no special preparation of the sample.
No Standard Measurement Needed: Typically, there’s no need to measure a standard for comparison.

SAXS instrument components

Source: X-ray source, e.g., copper and molybdenum.
Collimation System: Ensures that the X-ray beam is well-defined and directed at the sample.
Sample Chamber: Where the sample is placed for analysis.
Beam Stopper: Prevents the primary beam from directly hitting the detector, which is crucial for weakly scattering samples and to avoid detector damage.
Detector: Records the scattered X-rays.

Challenges and considerations

Beam Stopper Necessity: In the absence of a beam stopper, the primary beam can overshadow weak scattering signals and potentially damage the detector.
Sample Thickness: For transmission mode, sample thickness needs to be optimized to avoid excessive absorption or insufficient scattering.


SAXS is widely used in material science, biology, and chemistry for the characterization of a wide range of materials including polymers, biological macromolecules, and nanoparticles.

Nanoparticles: Characterization of size, shape, and distribution of nanoparticles in various media.
Porous Materials: Analysis of pore size distribution, porosity, and surface area in materials like catalysts, membranes, and aerogels.
Polymer Science: Studying the structural organization in polymers, polymer blends, to understand micelle formation, phase separation, and crystallinity.
Proteins and Biomolecules: Determining the size and shape of proteins in solution, studying protein folding, conformational changes, and interaction

Data interpretation

Intensity Profile: The primary data from a SAXS experiment is an intensity profile, which is a plot of scattered intensity versus the scattering angle (most often in q-value). This pattern reflects the size, shape, and distribution of the scatterers (e.g., particles, pores) in the sample.
Guinier Region: At very small angles (low q values, where q is the scattering vector), the plot often shows a linear region when plotted on a log-log scale. This is known as the Guinier region and is used to determine the radius of gyration (Rg) of particles, providing insight into their size.

Radius of Gyration (Rg): Rg is a measure of the distribution of electron density within the particle. It can give an approximation of the size of particles or molecular weight in the case of macromolecules.
Porod’s Law: At higher angles, the intensity decay follows Porod’s law, which can be used to deduce information about surface roughness and the overall shape of the scatterers.

Form Factor (P(q)): Describes the scattering from a single particle and depends on its shape. By fitting the experimental data to theoretical models of different shapes (spheres, rods, etc.), one can infer the shape of the scatterers.
Structure Factor (S(q)): Accounts for the interference effects due to the spatial arrangement of particles. It’s important in concentrated systems where particle-particle interactions influence the scattering.


Ambiguity in Data Interpretation: The interpretation of SAXS data can sometimes be ambiguous due to the indirect nature of the measurements.
Requirement for Complementary Techniques: Often, SAXS data is combined with other techniques (like electron microscopy) for more conclusive interpretations.