Lattice dynamics and correlated atomic motion from the atomic pair distribution function

TL;DR

This paper investigates atomic pair motions in crystals using the atomic pair distribution function, comparing models and experiments to understand lattice vibrational effects and atomic correlations.

Contribution

It introduces a comparative analysis of BvK and Debye models for lattice vibrations and their impact on PDF peak widths, highlighting the importance of vibrational effects in disordered systems.

Findings

Strong correlation of near-neighbor atomic motions.

Debye model effectively describes average MSRD behavior.

Good agreement between BvK model calculations and experiments.

Abstract

The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born von-Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRD of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.