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

Abstract

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 x O3 polymorphs (α-Ga(1–x)Al x O3 and β-Ga(1–x)Al x O3) 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.

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

“…As evidenced from the formula of garnets, RE 3 (Al x Ga (1−x) ) 5 O 12 (with RE = Y, Lu), such a general formula represents a quaternary oxide of variable composition for any value of x (0 < x < 1) different from x = 1 and x = 0, while the end terms of YAGG and LuAGG garnets are coincident with the ternary oxides Y 3 Al 5 O 12 , Y 3 Ga 5 O 12 and Lu 3 Al 5 O 12 , Lu 3 Ga 5 O 12 , respectively. According to this the modeling equations for ternary oxides, derived in our recent work 5 and accounting both for the composition and the crystallographic structure of pure and mixed oxides, will be employed to estimate the band gap value of the four end terms of YAGG and LuAGG mixed oxides. As for the quaternary oxides the modeling equations of these more complex systems will be derived in the following by using the same procedure employed for ternary oxide systems.…”

“…As extensively discussed in our previous works, 4,5 the modeling of the band gap of ternary oxides, E g,T , has been carried out by using as starting equations the relationships…”

“…eqs 6a−6d represent general relationships used for modeling ternary systems where one or both pure oxides exist as different polymorphs spanning a large range of optical band gap values, which cannot be accommodated in the initial correlation (see eq 1) by keeping constant the A and B parameters reported in eqs 2 & 3 and by varying the Pauling's electronegativity parameter within the accepted uncertainty (χ = χ 0 ± 0.05). 5,14 According to this, in the fitting procedure, band gap values derived for different polymorphs of yttria (c-…”

“…eqs 1,2 and eqs 1,3 were used to fit with reasonable accuracy, apart from some discussed exceptions, the optical band gap values, E g,opt , of binary sp-metal oxides (II and XIII-XV groups in the periodic table of the elements) and of d-metal oxides (III-XII groups), 2,3 More recently we extended such a semiempirical approach to pseudoregular (mixed s,p-s,p or d,d-metal oxides) and nonregular (s,p,d-metal oxides) ternary oxides by taking, also, into account the possible changes of band gap values for oxide systems presenting different polymorphs. 4,5 A preliminary test on the reliability of such an approach has been carried out by modeling crystalline pseudoregular ternary systems of different polymorphs α-(Ga (1−x) Al x ) 2 O 3 and β-(Ga (1−x) Al x ) 2 O 3 as well as nonregular amorphous ternary systems formed by amorphous mixed oxides, (Nb ( 1 − x ) Al x ) 2 O ( 5 − 2 x ) , Ta (1−x) Al x ) 2 O (5−2x) , and W (1−x) Al 2x O 3 , obtained by anodizing Al−Nb, Al−Ta, and Al−W metallic alloys at different compositions. 5 In this work we will extend our semiempirical approach to the modeling of the band gap of multinary oxides by discussing extensively some selected quaternary oxides for which the measured E g value is of the charge-transfer type; that is, E gap ∝ Δ, where the Δ term is directly related to the electronegativity of the anion and the Madelung potential of the solid.…”

“…4,5 A preliminary test on the reliability of such an approach has been carried out by modeling crystalline pseudoregular ternary systems of different polymorphs α-(Ga (1−x) Al x ) 2 O 3 and β-(Ga (1−x) Al x ) 2 O 3 as well as nonregular amorphous ternary systems formed by amorphous mixed oxides, (Nb ( 1 − x ) Al x ) 2 O ( 5 − 2 x ) , Ta (1−x) Al x ) 2 O (5−2x) , and W (1−x) Al 2x O 3 , obtained by anodizing Al−Nb, Al−Ta, and Al−W metallic alloys at different compositions. 5 In this work we will extend our semiempirical approach to the modeling of the band gap of multinary oxides by discussing extensively some selected quaternary oxides for which the measured E g value is of the charge-transfer type; that is, E gap ∝ Δ, where the Δ term is directly related to the electronegativity of the anion and the Madelung potential of the solid. 6,7 At this aim, the validity of quaternary oxides band gap modeling equations will be tested against aluminum garnets having general formula Y 3 (Al x Ga 1 − x ) 5 O 1 2 (YAGG) and Lu 3 (Al x Ga (1−x) ) 5 O 12 (LuAGG) and covering, according to the literature data, 8−13 a quite large range of band gap values (from ∼5.5 to ∼8.5 eV).…”