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A computational scheme to fully account for the core-hole relaxation effect in electron energy-loss nearedge structure has been successfully implemented. Results on ␣-Al 2 O 3 , MgO, and MgAl 2 O 4 crystals have reproduced all experimental details in all 11 edges. This is achieved by including three essential elements in the calculation: ͑1͒ A correct description of the presence of the hole in the core state of the excited atom. ͑2͒ The interaction between the excited electron in the conduction band and the hole left behind. ͑3͒ Use of large supercell for the final-state calculation. To a lesser extent, the inclusion of dipole matrix elements between the initial ground state and the final core-hole state is also important for the relative intensity of the structures. It is shown that the wave function of the excited electron in the conduction band in the presence of the core-hole state is localized to within the second-nearest-neighbor atoms, and is significantly different from the conduction-band wave function obtained from the ground-state calculation.

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The structure and properties of cubic spinel nitrides were investigated based on first-principles theoretical calculations. The lattice constants, bulk moduli, band structures, electronic bonding, and lattice stability of thirty-nine single and double nitrides were studied. The single spinel nitrides of the form c-A 3 N 4 (where A is a Group IVA element), except c-Hf 3 N 4 , are all semiconductors with band gaps ranging from an indirect gap of 0.07 eV in c-Ti 3 N 4 to a direct gap of 3.45 eV in c-Si 3 N 4 . For double nitrides of the form c-AB 2 N 4 (where A and B are Group IVA (Ti, Zr, Hf) or IVB (C, Si, Ge, Sn) elements), both metallic and insulating band structures are possible. The stability of the double spinel nitrides, relative to single nitrides, is dependent on the optimal cation radii and polyhedral volumes at the tetrahedral A sites and the octahedral B sites. Of the thirty-two double nitrides, only nine are predicted to be energetically favorable. Among the potentially stable phases, the most interesting ones are c-CSi 2 N 4 (which has an exceptionally strong covalent bonding and large bulk modulus), c-SiGe 2 N 4 (which has an energetically favorable direct band gap of 1.85 eV), and c-SiTi 2 N 4 (which is metallic).

Lattice constants, bulk moduli, band gaps, electronic bonding, and the stability of 20 new nitrides with spinel structure are studied by first-principles calculations. Double nitrides AB 2 N 4 are found to be stable when the counterparts BA 2 N 4 are metastable except for TiZr 2 N 4 . The four single nitrides C 3 N 4 , Si 3 N 4 , Ge 3 N 4 , and Sn 3 N 4 have direct band gaps at the ⌫ point ranging from 1.14 to 3.45 eV while Zr 3 N 4 and Ti 3 N 4 have small indirect gaps. For double nitrides, both metallic and insulating band structures are possible. The total bond orders of the stable double nitrides are larger than those of constituent single nitrides. Among them, CSi 2 N 4 shows exceptionally strong covalent bonding and a large bulk modulus. A simple scaling law based on bond lengths can describe the bulk moduli of these spinel nitrides quite well.