The Band Structure of Polycrystalline Al₂O₃ and Its Influence on Transport Phenomena

Abstract

The electronic (band) structure of polycrystalline Al2O3, in particular the density of near‐band edge grain‐boundary localized states, plays a significant role in a host of high‐temperature phenomena, including sintering, high‐temperature creep, oxygen permeability in dense “dry” Al2O3 ceramics, and Al2O3 scale formation on Al2O3 scale‐forming alloys. All these phenomena involve creation or annihilation of charged point defects (vacancies and/or interstitials) at grain boundaries and interfaces, and must of necessity involve electrons and holes. Thus, the density of states associated with grain boundaries in Al2O3 assume great importance, and has been calculated using DFT for both nominally undoped and Y‐doped Σ7 bi‐crystal boundaries. These quantum mechanical calculations must be taken into account when considering why Y2O3 segregation to Al2O3 grain boundaries is so effective in enhancing high‐temperature creep resistance of polycrystalline Al2O3, and in understanding the reactive element effect in Al2O3 scale‐forming alloys. Finally, a case will be made that grain‐boundary diffusion is mediated by the migration of a class of grain‐boundary ledge defects called disconnections, which are characterized by a step height h and a Burgers vector b.

Reactive Element Effects in High-Temperature Alloys Disentangled

“…These observations support RE-induced oxidation slowdown by pinning impurity states in the band gap, cf. [2] and also [32][33][34]. Greater suppression by RE(IV) than RE(III) is consistent with greater stability in case of the former, cf.…”

“…Linear is Δm ∝ √ t. Sublinear is Δm ∝ t the outer cathode, i.e., by O 2 reduction. It is achieved by the enhanced electronic conductivity across the scale emerging from the top-of-valence-band to the bottom-of-conduction-band electronic excitations that in turn become facilitated by chemical disruptions in high-angle grain boundaries [32][33][34], and/or by employing oxygen vacancies as generic impurity states in the band gaps of the grain boundaries [2,16,38]. In [2], bipolaron-mediated redox processes among V O sites were shown to drastically enhance V O mobility and thus to facilitate thermal oxide growth.…”

“…In a subsequent study, the Σ7 grain boundary was subject to extended in-depth analysis by means of modeling [33]. Building on the latter study, but notwithstanding that high temperatures increasingly disfavor cooperative processes, their emerging working hypothesis regarding the RE effect still envisioned the moderation of cooperative migration at high temperatures, mainly as jogs along grain boundary disconnections, but this time also together with other conceivable cooperative mechanisms, the possible viability of any or all to be assessed by atomistic simulations [34].…”

Grain Boundary Engineering of Alumina Ceramics

“…According to the GB disconnection model, [1,2,31] oxygen vacancies are created by the reverse reaction of Eq. (11.1) at P O2 (lo) surface ledges and migrate by surface diffusion to the closest GBs, where they are annihilated at jogs on disconnections to form positively charged jogs.…”

A model for time-dependent grain boundary diffusion of ions and electrons through a film or scale, with an application to alumina

“…While the slowest process is rate-determining for consecutive processes, like dissociation of oxygen molecules and their transport through the oxide, the fastest process is rate-determining for parallel processes, like bulk and grain boundary diffusion through the oxide. The measured oxygen and aluminum diffusion coefficients in α-alumina are found to be several orders of magnitude greater at the grain boundaries than in the bulk material [5][6][7]. The fact that grain boundaries provide the dominant transport mechanism underlines the importance of including their geometric and transport properties in a realistic model of the process.…”