Algorithm for distance list extraction from pair distribution functions

Abstract

We present an algorithm to extract the distance list from atomic pair distribution functions (PDFs) in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Due to the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.

References in corpus (5)

• Relationship between the atomic pair distribution function and small angle scattering: implications for modeling of nanoparticles
• Lattice dynamics and correlated atomic motion from the atomic pair distribution function
• Structure determination of disordered materials from diffraction data
• The Nyquist-Shannon sampling theorem and the atomic pair distribution function
• Crystal structure solution from experimentally determined atomic pair distribution functions

Cited by in corpus (1)

• A fast two-stage algorithm for non-negative matrix factorization in streaming data