Temperature-dependent work function, thermionic emission and bulk modulus of TiC: a study on the identification of free valence electrons and localized valence electrons and their roles played in carbides.

Abstract

By analyzing the projected states of valence electrons (fatband structures), the localized valence electrons and the free valence electrons of TiC were identified, respectively. After defining the volumes and the magnitudes of localized valence electrons and free valence electrons, the influences of the temperature, including the thermal expansion and the atomic thermal vibration, on the localized valence electron density and the free valence electron density were investigated, respectively. Based on the metallic plasma model (MPM), the temperature-dependent work functions and the thermionic emission current densities of TiC were calculated in terms of temperature-dependent free valence electron densities. The results were in good agreement with experimental results. Furthermore, as it was observed, the linear dependence of the bulk modulus on the localized valence electron density demonstrated that the bulk modulus of TiC was determined by the localized valence electron density. The different roles played by the free valence electrons and the localized valence electrons in the work function and the bulk modulus of TiC could be attributed to their different contributions to the kinetic energy density of valence electrons. The influences of the temperature on the work function, thermionic emission and bulk modulus of TiC indicated that the transition metal carbides with lower free valence electron density, higher localized valence electron density and heavier atomic mass were desired to achieve lower work function, higher current density and higher stability.