Pair Distribution Function Analysis in Nanostructured Materials

Pair Distribution Function (PDF) analysis has emerged as a pivotal real‐space technique for probing atomic arrangements in nanostructured materials, where conventional crystallography often fails to capture local disorder and subtle structural motifs. By utilising total scattering data—incorporating both Bragg peaks and diffuse scattering—the PDF yields a histogram of interatomic distances, enabling the characterisation of short‐range and intermediate‐range order up to several nanometres. This approach is uniquely suited to study amorphous phases, nanocrystals, thin films and composite systems, revealing the existence of local distortions, defect clusters and transient states. Advances in instrumentation, including high‐energy synchrotron sources, spallation neutrons and ultrafast X-ray free-electron lasers (XFELs), alongside sophisticated data‐modelling frameworks, now permit in situ and time-resolved studies that unveil structural evolution under thermal, mechanical or optical stimulation. By bridging length scales from the atomic to the nanoscale and linking local structural features with functional properties, PDF analysis is driving new insights into catalysis, energy storage, electronic devices and phase‐transition dynamics.

Research from Nature Portfolio

Recent studies have harnessed ultrafast PDF measurements to resolve transient disorder during non‐equilibrium phase transitions. In one example, optical excitation of a low-temperature dimerised sulphide compound was monitored with femtosecond XFEL pulses, revealing how local Ir–Ir dimers dissolve without long-range correlation and subsequently re-order over tens of picoseconds. This work underscores the critical role of length-scale-dependent disorder in driving ultrafast structural dynamics. In another advance, three-dimensional electron diffraction coupled with 3D-ΔPDF mapping has been applied to sub-micron crystals of yttria-stabilised zirconia. By comparing difference PDFs obtained from electron, neutron and X-ray experiments, researchers have quantified local oxygen vacancy correlations and resolved three-dimensional ordering principles that govern ionic conductivity.

Pair Distribution Function Analysis in Nanostructured Materials publication trend

The graph below shows the total number of articles in pair distribution function analysis in nanostructured materials across all publications each year (not limited to Nature Index journals).

Technical terms

Pair Distribution Function (PDF): A real-space function derived from total scattering data that describes the probability of finding pairs of atoms separated by a given distance, providing insight into both ordered and disordered regions.

Total scattering: A measurement technique that collects both sharp Bragg reflections and diffuse scattering, capturing information on average periodicity and local disorder simultaneously.

3D-ΔPDF: A three-dimensional difference PDF obtained by subtracting the average crystal structure contribution, used to visualise local deviations and correlations in real space.

Ultrafast X-ray free-electron laser (XFEL): A light source delivering femtosecond X-ray pulses with extreme brightness, enabling time-resolved studies of structural dynamics on atomic length scales.

Machine learning landscape: A computational paradigm in which an algorithm iteratively explores and optimises PDF model parameters against experimental data, facilitating automated discovery of complex structures.

References

1. Resolving length-scale-dependent transient disorder through an ultrafast phase transition. Nature Materials (2024).
2. Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction. Nature Communications (2023).
3. A Machine‐Learning‐Based Approach for Solving Atomic Structures of Nanomaterials Combining Pair Distribution Functions with Density Functional Theory. Advanced Materials (2023).
4. Bridging Structural Inhomogeneity to Functionality: Pair Distribution Function Methods for Functional Materials Development. Advanced Science (2021).