Band structure ofTiB2:Orientation-dependent EELS near-edge fine structure and the effect of the core hole at theB Kedge

Abstract

The ceramic compound ${\mathrm{TiB}}_{2}$ has been studied by electron-energy-loss spectroscopy. Spectral shapes in the vicinity of the $\mathrm{B} K$ edge with momentum transfer $\mathbf{q}\ensuremath{\Vert}c$ and $\mathbf{q}\ensuremath{\perp}c$ have been investigated and compared with decomposed, calculated spectra. The dipole selection $(\ensuremath{\Delta}l=\ifmmode\pm\else\textpm\fi{}1)$ rule applies, so the $\mathrm{B} K$ edge provides information on p final states local to boron. For a uniaxial system like ${\mathrm{TiB}}_{2}, {\mathbf{q}}_{\ensuremath{\Vert}}$ is proportional to ${p}_{z}$ and ${\mathbf{q}}_{\ensuremath{\perp}}$ is proportional to ${p}_{x}{+p}_{y}.$ The theoretical density of states has been calculated using the ab initio full-potential linear augmented-plane-wave method, and, when combined with the relevant matrix elements, theoretical spectra have been obtained. While giving good agreement with experiment, our theoretical calculations show that the presence of the core hole must be considered in order to reproduce the experiments, especially for momentum transfer ${\mathbf{q}}_{\ensuremath{\Vert}}$ due to reduced screening in this direction. In this study the core-hole effect is calculated within the $Z+1$ supercell approximation. From the interpretation of the spectral features common hybridized electronic states between boron p and titanium d bands are observed, and the structure is highly anisotropic due to more delocalized $\ensuremath{\sigma}$ bonding within the boron planes.