Surface-phonon dispersion of the NbC(001) and TaC(001) surfaces: Double-shell-model analysis

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Abstract
Using the double-shell model in a slab geometry, we calculate the surface phonons on the NbC (001) and TaC(001) surfaces for what we believe to be the first time. A small anomaly is found in the dispersion curve of the Rayleigh mode along the Γ¯–M¯ symmetry axis. Its magnitude is very small for NbC and is not inconsistent with recent observations. Moreover, the observed above-bulk mode is very well reproduced by our model. On the other hand, the agreement with the experiment is not so good for the optical modes. We propose possible changes of the shell-model parameters at the surface to resolve this disagreement.