We have investigated the structural and electronic properties of the (001)-(1x1) surface of the refractory hard metal HfC, using the density functional theory and the pseudopotential method. The mos important feature of the HfC(001) surface relaxation is that both in the surface and subsurface layer C atoms move out of the surface and Hf atoms move inward. In good agreement with previous experimental and theoretical works [1,2], the spacings between the C and Hf atoms in the first and second layers are found to be 0.12 Å and 0.05 Å. Our results clearly indicate that the electronic structure for HfC(001) is metallic, with at least one band crossing the Fermi level in the gap
region of the projected bulk electronic spectrum. Using our calculated atomic and electronic structures, zone-center and zone edge surface phonon modes are calculated by employing a linear response approach based on the density functional perturbation theory[3]. Interesting surface-localized phonon modes are found in the gap region between the acoustic and optical bulk states. At the X point, the energy of this phonon mode is found to be 51.80 meV which compares
very well with the corresponding experimental value[4] of 52.0 meV. The highest lying phonon mode has been identified at 74.06 and 82.56 meV at the Γ and X points, respectively. These values can be compared with their experimental values of 78.0 and 83.0 meV in the work of
Wuttig et al [4]. The atomic displacement patterns corresponding to these phonon modes have been detailed.
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[2] F. Vines, C. Sousa, P. Liu, J. A. Rodriguez and F. Illas, J. Chem. Phys. 122 (2005) 174709.
[3] S. Baroni, S. de Gironcoli, and A. Dal. Corso and P. Giannozzi, Rev. Mod. Phys. 73 (2001) 515.
[4] M. Wuttig, C. Oshima, T. Aizawa, R. Souda, S. Otani, Y. Ishizawa, Surf. Sci. 192, (1987) 573. |