Modeling of Optical Band-Gap Values of Mixed Oxides Having Spinel Structure AB2O4 (A = Mg, Zn and B = Al, Ga) by a Semiempirical Approach

Spinel oxides with the general formula AB₂O₄ comprise a large family of compounds covering a very wide range of band-gap values (1 eV < E_g < 8 eV) as a function of the nature of the metallic cations A and B. Owing to this, the physical properties of these materials have been largely exploited both from a fundamental point of view, for their variable electronic properties, and for their possible use in numerous engineering applications. Herein, the modeling of ZnAl₂O₄, ZnGa₂O₄, MgAl₂O₄, and MgGa₂O₄ cubic spinel oxides has been carried out by using the semiempirical approach based on the difference of electronegativity between oxygen and the average electronegativity of cations present in the oxides. The results of recent theoretical extensions of our semiempirical approach to ternary and quaternary oxides have been tested for spinel oxides with metallic ions occupying both octahedrally and tetrahedrally coordinated sites in different ratios. A detailed analysis of the experimental band-gap values and comparison with the theoretically estimated values has been carried out for ternary ZnAl₂O₄, ZnGa₂O₄, MgAl₂O₄, and MgGa₂O₄ spinels as well as for double spinels Mg(Al_2xGa_2–x)O₄ and Zn(Al_2xGa_2–x)O₄, and quaternary mixed oxides (Zn_xMg_(1–x))Al₂O₄ and (Zn_xMg_(1–x))Ga₂O₄. The wide range of band-gap values reported in the literature for simple or double spinels has been related to the different preparation methods affecting the grain dimension of crystalline spinel samples as well as to the presence of crystallographic defects and/or impurities in the spinel matrix. The good agreement between experimental band-gap values and the theoretical ones strongly supports the use of our semiempirical approach in the area of band-gap engineering of new materials.