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

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.

Total scattering atomic pair distribution function: new methodology for nanostructure determination

“…[61,62] For a given initial structure model, set of structural parameters can be refined such as unit cell parameters, anisotropic atomic displacement parameters (ADPs), site occupancy level and the fractional coordinate of allowed general positions, beside particle diameter parameter in case of nanoparticle PDF study. Also, set of non-structural parameters can be refined such correction for the finite instrumental resolution, (s Q ), low-r correlated motion peak sharpening factor (d), [63,64] and scale factor. In nanostructure PDF refinement, the finite instrumental resolution and particle diameter parameters are highly correlated, [28] so in practice, it is highly recommended to choose which one to refine while fixing the other.…”

Local vibrational properties of GaAs studied by extended X-ray absorption fine structure

“…The extent of correlation can be measured by a dimensionless normalised function of temperature defined as 47,48 …”

Direct observation of charge mediated lattice distortions in complex oxide solid solutions

“…3d, solid due to uncorrelated displacements at large pair distances. This approach is commonly employed for PDF analysis [26], but without near perfect imaging enabled by RevSTEM, drift and noise would usually preclude extending precise distance measurements beyond a few angstroms (one unit-cell) in STEM.…”