Lattice vibrations at (111) surfaces and stacking faults in transition metals: Ni

The Falicov and Yndurain transfer matrix formalism is extended to study the lattice vibrations near surfaces and stacking faults. A simple nearest-neighbour central force harmonic potential appropriate to Ni is considered. The bulk density of states obtained is in good agreement with the experimental findings. Modes localised around the (111) surface are found and analysed in detail. Lattice vibrations densities of states around: (i) intrinsic stacking fault, (ii) extrinsic stacking fault and (iii) twin fault, are calculated. Bona flde localised modes are found in the three faults studied.