FIRST-PRINCIPLES CALCULATION OF THE LONGITUDINAL PHONON IN THE SURFACE-NORMAL DIRECTION OF A ZIRCONIUM(0001) SLAB - LOCALIZATION MODE AT THE SUBSURFACE
M. Yamamoto et al., FIRST-PRINCIPLES CALCULATION OF THE LONGITUDINAL PHONON IN THE SURFACE-NORMAL DIRECTION OF A ZIRCONIUM(0001) SLAB - LOCALIZATION MODE AT THE SUBSURFACE, Physical review. B, Condensed matter, 53(20), 1996, pp. 13772-13776
The energies and amplitudes of the longitudinal vibrational mode in th
e surface-normal [0001] direction of the fully relaxed zirconium slab
with a (0001) surface are calculated with force constants determined f
rom first-principles total-energy and force calculations. A subsurface
vibrational mode with frequency above the bulk continuum is found. We
attribute the origin of this mode to the hardness of the force consta
nt between the surface and the second layer.