Nanoparticle size
and size distribution

Looking at mean particle size, number or volume-weighted particle size distribution

What is measured?

The measured quantity is the diameter of globular shaped particles and the related number- or volume-weighted size distribution. The quantitative analysis in terms of volume fraction or mass concentration is possible due to scattering intensities being normalized to absolute units.

Range of diameters accessible with SAXS measurements:

  • 1 to 300 nm
  • Up to 5 µm with the USAXS extension
  • Applicable to multimodal distributions
Figure 1. Size distribution of dilute silver nanoparticles in aqueous suspension obtained from SAXS data acquired on the Nano-inXider. The data analysis was performed with XSACT software.

The availability of the scattering intensity in absolute units enables the accurate determination of volume fractions.
The histogram is normalized with respect to the bin size. The size distributions corresponding to two distinct bin definitions can therefore be compared directly.
Cumulated values are displayed to facilitate the readout.


Typical samples for this measurement are:

  • Dispersions and suspensions

  • Dry powders

  • Nanostructured solids

  • Gels and pastes

Have a look at the following examples:

Methods & standards

Standards & methods used for particle size & size distribution:

  • Size determination by Guinier analysis and model fitting
    Ref: ISO 17867:2015 – Particle Size Analysis – Small-angle X-ray scattering
  • Guinier analysis
    Ref: A. Guinier, G. Fournet Small-Angle Scattering of X-rays. John Wiley, New York, 1955
  • Expectation Maximization (EM)
    Ref: F. Benvenuto, H. Haddar and B. Lantz, SIAM J. Appl. Math., 2016, 76(1), 276-292

XSACT analysis software implements the above methods and standards.

SAXS Data Analysis

Advantages of SAXS

Why use SAXS for measurement of particle size & size distribution ?

  • Exceptional resolution power even for smallest nanoparticles and bimodal populations.

  • Reliable statistical properties due to ensemble averaging.

  • Minimal sample preparation is required. You can work with a wide range of concentrations and samples, even on opaque suspensions or dry powders. No dilution step is required.

  • With SAXS, you can do in situ and dynamics studies.


All these measurements are possible directly in your lab.


Smart nanoscale characterization

Nanoparticle Size Distribution

Xeuss 3.0

The Next Generation
(GI-)SAXS/WAXS/USAXS beamline for the laboratory

Nanoparticle Size Distribution

Nanoparticle Size Distribution

Nanoparticle Size Distribution

Nanoparticle Size Distribution – Representative Measurement With SAXS

Nanoparticle Size Distribution – Representative Measurement With SAXS – PSD From 1nm to 300nm On Bulk Or Thin Film. No Sample Form Limitation