Electronic band structures and x-ray photoelectron spectra of ZrC, HfC, and TaC

Abstract

The band structures and densities of states (DOSs) of ZrC, HfC, and TaC were calculated by the augmented-plane-wave method, and the x-ray photoelectron spectra of valence bands of these compounds were observed. The theoretical energy distribution curves (EDCs) were in good agreement with the experimental EDCs. These band structures resemble each other and also those of TiC obtained by our previous work. This fact suggests that the rigid-band model is applicable to the transition-metal carbides with the rock-salt structure. Their DOSs are divided into three parts. Peak I derived from the $\mathrm{C} 2s$ state is isolated from the higher valence-band peak II arising from the $\mathrm{C} 2p$ and the valence electrons of the metal atom. Peak III derived from the $d$ and $s$ states of the metal atom is separated by the Fermi level from peak II. The Fermi level lies at the minimum point of the DOS for the group IV carbides, but for TaC it lies at a relatively large DOS point. The DOS at the Fermi level of ZrC, HfC, and TaC are 0.18, 0.16, and 0.65 electrons/(eV primitive cell), respectively. The characteristic mutual differences among these compounds are a stronger localization of $d$ electrons in ZrC and HfC compared with TiC and an enhancement of the photoelectron spectrum intensity of TaC around the Fermi level.