Surface phonon dispersion of HfC(100)

Abstract

The dispersion of vibrational modes for the clean HfC(100) surface has been measured by high resolution electron energy loss spectroscopy. Five different branches have been observed both in the Γ ¯ Μ ¯ - and Γ ¯ Χ ¯ -direction. For a quantitative discussion of the experimental data a shell model with free electron screening has been used. This analysis shows that the S 2 ′ mode which is attributed to the perpendicular motion of second layer carbon atoms appears as a localized vibration due to an increase of the force constant between first layer metal and second layer carbon atoms. The frequency of the S 2 mode can be explained by decreasing the force constant between first layer carbon and second layer metal atoms. These two findings strongly suggest a surface rumpling where the carbon atoms at the surface are displaced outwards. Such a tendency also exists for TiC(100) but for HfC(100) this effect is strongly enhanced.