Inelastic-neutron-scattering techniques have been used to measure the
low-lying phonon-dispersion curves of superconducting LuNi2B2C along t
he[xi 00] and [00 xi] symmetry directions. The most important result o
f this experiment is that the phonon frequencies of the acoustic and f
irst optical Delta(4) [xi 00] branches in the vicinity of the zone-bou
ndary point G(1) decrease with decreasing temperature. Actually these
two branches exhibit pronounced dips at low temperatures, close to G(1
). This shows that the electron-phonon interaction is quite strong and
causes an incipient lattice instability, a behavior typical of strong
ly coupled conventional superconductors. Furthermore, the phonon anoma
lies occur at wave vectors close to those of the incommensurate magnet
ically ordered structures observed in the magnetic compounds of this f
amily, which suggests that both the magnetic ordering and the incipien
t lattice instabilities are influenced by common nesting features of t
he Fermi surfaces of the rare-earth nickel boride carbides.