Research into determining what intrinsic characteristics cause materials to be hard is imperative if one would like to design future materials with a hardness exceeding that of diamond. Measuring the hardness of materials in order to obtain a fundamental quantity independent of extrinsic factors is difficult, if not impossible. However, many theories have been proposed pertaining to the quantification of hardness as a fundamental property. While it is clear that the hardness of a material will strongly depend on its crystal structure, another fundamental quantity, the electronic band gap, has also been linked to the intrinsic hardness of materials. The electronic band gap is a seemingly simple quantity, but is difficult to de- termine for novel or complicated materials. Core-level spectroscopy techniques that probe the occupied and unoccupied density of states separately allow for an indirect determination of the electronic band gap. These methods have several advantages over conventional tech- niques in that they do not strongly depend on the extrinsic material properties such as defects and impurities. The electronic band gap has been determined in this way for several novel materials. These include group 14 nitrides with spinel structure that were recently studied over the last decade. The electronic band gap of three synthesized binary spinel nitrides γ-Si3N4, γ-Ge3N4 and γ-Sn3N4 are determined using core-level spectroscopy to be 4.8 ± 0.2 eV, 3.5 ± 0.2 and 1.6 ± 0.2 eV, respectively. These measurements agree with the calculated values of 4.97, 3.59 and 1.61 eV for γ-Si3N4, γ-Ge3N4 and γ-Sn3N4, respectively. We have also extended these measurements and calculations to include the solid solutions γ-(GexSi1−x)3N4 and γ-(SnxGe1−x)3N4 showing these spinel-structured nitrides form a multi-functional class of semiconductors. This band gap measurement technique has also been applied successfully to the phosphor converting light emitting diode material Ba3Si6O12N2 and the novel semicon- ductor MnNCN. This shows that using core-level spectroscopy is a very effective method to determine the electronic band gap where there are no other feasible techniques. Aside from the electronic band gap, core-level spectroscopy is also a complementary technique to deter- mine the crystal structure, which is also an important parameter with regard to hardness. The crystal structure, particularly aspects such as anion ordering and vacancy ordering, have been determined for the spinel-structured oxonitride Ga3O3N and a novel phase of calcium nitride Ca3N2. These results show that core-level spectroscopy is a powerful technique to determine the anion ordering in oxonitrides and was further applied to the material class β-sialons, allowing for the determination of the electronic band gap as well as ascertaining both the anion and cation ordering. Combining all of these aspects we show that the electronic band gap is not only useful for predicting the hardness of materials, but in some cases can be used to predict the existence of certain materials. We use theoretical methods, combined with experimental measurements, to calculate the hardness and electronic band gap of all possible binary and ternary group 14 spinel-structured nitrides. Through the correlation of the hardness and electronic band gap we show that only the three already synthesized binary group 14 spinel-structured nitrides are stable along with their solid solutions and that the elusive spinel-structured carbon nitride γ-C3N4 will be never synthesized
