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Temperature dependence of the lattice dynamics of chromium.

The phonon dispersion of chromium has been investigated over a large temperature range. Besides an overall decrease in the phonon frequencies the L 1 /3(111) mode and the T 1 [ξξ0] branch exhibit a remarkable softening with increasing temperature. The analysis in terms of a Born-von Karma 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