A Generalized Semiempirical Approach to the Modeling of the Optical Band Gap of Ternary Al-(Ga, Nb, Ta, W) Oxides Containing Different Alumina Polymorphs

A generalization of the modeling equation of optical band gap values for ternary oxides, as a function of cationic ratio composition, is carried out based on the semiempirical correlation between the differences in the electronegativity of oxygen and the average cationic electronegativity proposed some years ago. In this work, a novel approach is suggested to account for the differences in the band gap values of the different polymorphs of binary oxides as well as for ternary oxides existing in different crystalline structures. A preliminary test on the validity of the proposed modeling equations has been carried out by using the numerous experimental data pertaining to alumina and gallia polymorphs as well as the crystalline ternary Ga_(1–x)Al_xO₃ polymorphs (α-Ga_(1–x)Al_xO₃ and β-Ga_(1–x)Al_xO₃) covering a large range of optical band gap values (4.50–8.50 eV). To make a more rigorous test of the modeling equation, we extended our investigation to amorphous ternary oxides anodically formed on Al-d-metal alloys (Al-Nb, Al-Ta, and Al-W) covering a large range of d-metal composition (x_d‑metal ≥ 0.2). In the last case, the novel approach allows one to overcome some difficulties experienced in fitting the optical band gap dependence from the Al-d-metal mixed anodic oxide composition as well as to provide a rationale for the departure, at the lowest d-metal content (x_d‑metal < 0.2), from the behavior observed for anodic films containing higher d-metal content.