Electronic structure of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ grain boundaries containing reactive element segregants

It has long been known that the addition of small quantities (“doping”) of so-called reactive elements (REs) such as Y, Zr, and Hf to high-temperature ${\text{Al}}_2{\text{O}}_3$ scale-forming alloys improves oxidation resistance. The presence of reactive elements at grain boundaries lowers the growth rate of the $\alpha \text{−}{\text{Al}}_2{\text{O}}_3$ scales, but the cause of the reduced scale growth kinetics is not fully understood. Explanations based on steric effects and explanations based on reducing the grain boundary electronic conductivity have been proposed. We have used density functional theory to study the structural and electronic properties of two $\mathrm{\Sigma }7$ bicrystal grain boundaries containing Y, Hf, and Zr substitutional defects on Al sites. The presence of RE substitutional defects plays a minimal direct role in reducing the density of electronic states near the valence-band maximum. However, ${\mathrm{Hf}}^{4+}$ or ${\mathrm{Zr}}^{4+}$ substitutions at the grain boundary repel the positively charged oxygen vacancy ${\text{V}}_{\text{O}}^{2+}$. As ${\text{V}}_{\text{O}}^{2+}$ contributes a defect state above the valence-band maximum but below the Fermi energy, this indirectly lowers the density of current-carrying holes and thus the electronic conductivity of the grain boundary. Replacing ${\mathrm{Al}}^{3+}$ ions with ${\mathrm{Hf}}^{4+}$ or ${\mathrm{Zr}}^{4+}$ ions also makes the grain boundary positively charged, further reducing the hole density.

Figure 1

Densities of states (DOSs) of (a) $\mathrm{\Sigma }7a$ and (b) $\mathrm{\Sigma }7m$ boundaries calculated using density functional theory with local (LDA) and hybrid (B3LYP) exchange-correlation functionals. The LDA conduction bands are shifted down relative to the B3LYP conduction bands, as indicated by the arrows. The solid vertical line indicates the energy of the highest occupied one-electron state.

Figure 2

Ground-state atomistic structures of pristine $\mathrm{\Sigma }7a$ [(a), (c)] and $\mathrm{\Sigma }7m$ [(b), (d)] $\alpha \text{−}{\text{Al}}_2{\text{O}}_3$ GBs. Hf- and Zr-doped GBs are shown in (a) and (b), and Y-doped GBs in (c) and (d). To aid comparison, the Al sites in the pristine boundaries substituted by RE ions in the doped boundaries are indicated by polyhedra. In (d), the two extra oxygen ions coordinated to the ${\text{Y}}_{\text{Al}}^0$ dopant are shown in yellow.

Figure 3

Calculated changes in the charge density near substitutional defects ${\text{Hf}}_{\text{Al}}^{+}$ and ${\text{Zr}}_{\text{Al}}^{+}$. The blue (yellow) isosurface indicates partial positive (negative) charge introduced by the RE species. The charge density isosurface level is $\pm 0.3{\AA }^{-3}$.

Figure 4

The densities of states of the $\mathrm{\Sigma }7a$ and $\mathrm{\Sigma }7m$ GB simulation cells in the presence of single substitutional dopants of different types. The density of states of the undoped boundary is shaded in gray. Panel (a) shows the states near the VBM and panel (b) the states near the CBM. The dashed line is proportional to the projected DOS of $\alpha \text{−}{\text{Al}}_2{\text{O}}_3$ in the “bulk” region of the GB cell, far from the GB. The VBM in the bulk region is indicated by the thin vertical line. For legibility, the bulk DOS is normalized to a lower level than the other curves.

Figure 5

Densities of states of the $\mathrm{\Sigma }7a$ unit cell with a single ${\text{Y}}_{\text{Al}}^0$ substitutional defect and with 87.5% of a monolayer of ${\text{Y}}_{\text{Al}}^0$. The dashed lines show the DOS in the bulk region of the simulation cell and the red lines show the Y-projected DOS, magnified five times for legibility. The structures of the GBs are pictured in the insets, with the Y sites highlighted in yellow. For legibility, the DOS of the bulk region is normalized to a lower level than the other curves.

Figure 6

Distributions of segregation energies of ${\text{V}}_{\text{Al}}^{3-}$ and ${\text{V}}_{\text{O}}^{2+}$ vacancies at $\mathrm{\Sigma }7a$ and $\mathrm{\Sigma }7m$ GBs.

Figure 7

${\text{V}}_{\text{O}}^{2+}$ segregation energies at oxygen sites coordinated to substitutional RE dopant sites and at the corresponding oxygen sites in the undoped GB. The vertical bars are 95% confidence intervals.

Figure 8

DOS of the $\mathrm{\Sigma }7a$ GB with ${\text{V}}_{\text{Al}}^{3-}$ (blue) and ${\text{V}}_{\text{O}}^{2+}$ (red) vacancies. The near-VBM and gap states of each defect are indicated by arrows. The undoped GB DOS (gray, shaded) is shown for comparison.