Total Scattering Pair Distribution Function (TS-PDF) Analysis

Total scattering goes beyond typical assessment of diffraction peaks to consider the diffuse intensities scattered underneath and in between. These carry further information about defects, disorder, dynamics, and morphology that underpin functional properties. The pair distribution function analysis gives an alternative perspective to the total scattering signal by trans­for­ming the data to a spatial de­pen­den­ce, allowing pro­per­ties such as bond lengths, correlated motions, and local structural features to be observed directly.

Key advantages:

• Analyzes both Bragg peaks and diffuse scattering
• Provides local structure information (bond distances, coordination)
• Works for both crystalline AND amorphous materials
• Reveals short and medium-range ordering (typically 1–30 Å)
• Can detect local distortions not visible in average structures

Target information:

• Local atomic structure: Identification of short-range ordering and coordination environments around atoms
• Bond distances: Precise measurements of interatomic distances between nearest neighbors
• Atomic pair displacements: Information about bond length distributions as affected by zero point motion, thermal vibrations, and static disorder.
• Coordination numbers: Determination of how many atoms surround each atom at specific distances. Note that this requires absolute scaling of the data, which requires additional normalization steps.
• Medium-range order: Structural correlations extending beyond nearest neighbors (typically in the range of approximately 10–30 Å), e.g. features like polyhedral connections, ring structures, and clusters at slightly higher distances.
• Coherence length: Size of locally ordered domains.
• Density information: Indirect information about atomic density and microporosity
• Local symmetry breaking: Detection of local domains with structural properties deviating from the average structure
• Phase identification: Determine if the sample is amorphous or contains nanocrystalline domains
• Structural evolution: When measurement are performed on samples that have undergone different synthesis or processing procedures, insights into relative structural changes can be determined
• Quantitative modeling: The data can be used for real space structure refinement such as small-box modeling, Reverse Monte Carlo modeling or other computational approaches to generate 3D structural models
• Composition-structure relationships: When comparing related compositions, understanding how composition affects local structure