  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.
