Temperature dependence of the lattice dynamics of chromium

Abstract

The phonon dispersion of chromium has been investigated over a large temperature range. Besides an overall decrease in the phonon frequencies the L2/3(111) mode and the ${\mathit{T}}_{1}$[\ensuremath{\xi}\ensuremath{\xi}0] branch exhibit a remarkable softening with increasing temperature. The analysis in terms of a Born--von K\'arm\'an force-constant model assuming axial symmetry yields dominating second-nearest-neighbor force constants. Their variation with temperature causes the observed phonon softening. A comparison with other transition metals shows a systematic softening of the shear motion of [111] rows against each other with decreasing d-electron density.