Rigaku logo
Rigaku Journal Winter 2026 Vol.42 No.1 cover
Read Article

Total X-ray Scattering

Masatsugu Yoshimoto

Winter 2026 Volume 42, No. 1 , 25-31

Total scattering measurement is widely used to evaluate the local structure of the cathode and the solid electrolyte for Li-ion batteries. The observed pair distribution function Gobs(r) obtained from the Fourier transform of the structure factor S(Q) has information not only about neighboring distances but also about the coordination numbers and the number density of sample. Herein, we discuss deviations in Gobs(r) arising from the standard deviation of S(Q) and the termination error of the measurable maximum and minimum scattering vector in Gobs(r) using the basic theory of total scattering analysis.

Highlights

  • Total X-ray scattering and pair distribution function (PDF) analysis reveal local atomic structure in both crystalline and amorphous materials, including interatomic distances, coordination numbers, and atomic density.
  • Measurement quality depends on both the maximum scattering vector (Qmax) and the minimum scattering vector (Qmin), with each affecting the resulting PDF in different ways.
  • Propagating measurement uncertainty from the structure factor S(Q) into the PDF makes it possible to distinguish meaningful structural features from measurement noise.
  • Applying corrections for Qmin termination error significantly improves density estimation accuracy, reducing errors from as much as 11% to about 1% in the demonstrated examples.
  • Short-wavelength laboratory X-ray sources such as Ag Kα and Mo Kα provide higher spatial resolution for total scattering measurements than Cu Kα radiation.

Summary

Total X-ray scattering is a technique that helps scientists study how atoms are arranged in materials, even when those materials are not perfectly crystalline. Instead of looking only at long-range crystal order, it provides information about the local arrangement of neighboring atoms through a pair distribution function (PDF).

The quality of the PDF depends heavily on the quality of the measured scattering data. Random measurement noise can create uncertainty in the results, while limits in the measurable scattering range introduce mathematical artifacts called termination errors. The work explains how these effects arise, how they can be estimated, and how they influence the interpretation of atomic structure.

Special attention is given to the roles of the maximum scattering vector (Qmax) and minimum scattering vector (Qmin). A larger Qmax improves spatial resolution, while correcting for Qmin-related artifacts reduces unwanted oscillations and leads to more accurate estimates of material density.

Examples using silica glass and liquid argon demonstrate that careful measurement conditions combined with appropriate data corrections produce clearer PDFs and more reliable structural information, helping users distinguish real atomic features from processing artifacts.

Frequently asked questions

Total X-ray scattering is used to study the local atomic structure of materials. Unlike conventional X-ray diffraction, which primarily analyzes well-ordered crystals, it can also characterize amorphous materials, glasses, and locally disordered structures by showing how atoms are arranged over short distances.

The PDF shows the distances between neighboring atoms and also contains information about coordination numbers and the atomic number density of a material. Together, these properties help describe the local structure even when long-range crystal order is absent.

A larger maximum scattering vector (Qmax) improves the spatial resolution of the PDF, producing sharper peaks that better separate nearby atomic distances. However, simply increasing Qmax is not enough, because other sources of error must also be managed.

Termination errors occur because scattering data can only be collected over a finite Q range. These limitations introduce artificial oscillations, or side lobes, into the PDF that can resemble real structural features. Mathematical corrections and window functions help reduce these artifacts.

Noise in the measured scattering intensity propagates into the calculated PDF. By calculating the uncertainty in the PDF, it becomes possible to determine whether small peaks represent actual structural information or are simply the result of measurement noise.

While Qmax determines spatial resolution, Qmin influences low-frequency oscillations in the PDF. Correcting for Qmin-related termination errors removes unwanted modulation, resulting in cleaner data and more accurate structural analysis.

Correcting for Qmin termination errors produces more accurate estimates of atomic number density. In the demonstrated examples, the corrected method reduced density estimation errors substantially, bringing calculated values much closer to known reference values.

Related products

Subscribe to the Bridge newsletter

Stay up to date with materials analysis news and upcoming conferences, webinars and podcasts, as well as learning new analytical techniques and applications.

Contact Us

Whether you're interested in getting a quote, want a demo, need technical support, or simply have a question, we're here to help.

Contact Sales
Contact Service
Office Locations