A spherical harmonics method for processing anisotropic X-ray atomic pair distribution functions

In this work, a general spherical harmonics method for the extraction of anisotropic pair distribution functions (PDFs) is described. In the structural study of functional crystallized materials, there is an urgent need for investigation of local structures under the application of external stimuli, such as an electric field and stress. A well established technique for local structural studies is PDF analysis, but the extraction of X-ray PDF data is usually based on angular integrations of isotropic X-ray structure functions, which is no longer valid for the anisotropic responses of materials under orientation-dependent stimuli. Therefore, an advanced spherical harmonics method has been developed, to transform 2D X-ray total-scattering data into anisotropic PDF data on the basis of the 3D diffraction geometry and a Fourier transform. The electric-field-induced local structural change in PbZr0.54Ti0.46O3 ceramics is presented to demonstrate the effectiveness of this method.

Automated summary

This work presents a general spherical harmonics method for extracting anisotropic pair distribution functions (PDFs). It addresses the need for investigating local structures under external stimuli in studies of functional crystallized materials. The traditional method of extracting X-ray PDF data based on isotropic X-ray structure functions is no longer valid for materials with orientation-dependent responses. To overcome this limitation, an advanced spherical harmonics method is developed to transform 2D X-ray total-scattering data into anisotropic PDF data based on 3D diffraction geometry and Fourier transform. The effectiveness of this method is demonstrated through the analysis of electric-field-induced local structural changes in PbZr0.54Ti0.46O3 ceramics.