Band Gap Modeling of Different Ternary and Quaternary Alumina Garnet Phases Y3(AlXGa1-X)5O12 (YAGG) and Lu3(AlXGa1-X)5O12 (LuAGG). A Semiempirical Approach

A further generalization to quaternary oxide systems of the modeling equation of optical band gap values, based on the semiempirical correlation between the differences in the electronegativity of oxygen and the average cationic electronegativity, proposed some years ago, has been carried out by expanding the approach recently employed for ternary mixed oxides. The choice of oxide polymorphs and their influence on the fitting procedure of an experimental data set is evidenced by a detailed discussion of the fitting process of the literature's experimental band gap data pertaining two quaternary oxide systems of the garnet family, namely, Y3(AlxGa1-x)5O12 (YAGG) and Lu3(AlxGa1-x)5O12 (LuAGG), playing an important role in several engineering applications. The two investigated systems, moreover, span a quite large range of band gap energy values (from similar to 5.5 to similar to 7.5 eV), as a function of the Al/Ga ratio, allowing a rigorous test of the proposed modeling equation. Based on the wide existing literature on the presence of excitonic effects in the investigated systems some empirical correlations between an optical gap and a band gap in the presence of excitonic effects are suggested, too, which could provide some rationale to overcome the discrepancies frequently encountered in comparing band gap values reported in the literature for the same materials. The results of this work confirm the ability of this semiempirical approach in providing good agreement between experimental and theoretical band gap values also for very complex systems, where more sophisticated density functional theory-based methods face some difficulties in predicting the correct values.