Atomic arrangement and impurity bonding at a $\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(001\right)∕\mathrm{Al}\left(771\right)$ interface: First-principles calculations

First-principles optimization of a $\kappa$-alumina–Al(771) superlattice shows that the incompliant oxide causes substantial disorder in the adjacent, soft metal layers. A H “probe atom” is found to bind best in the disrupted metal region, suggesting that this is the locus of initial failure of a protective oxide layer.

Figure 1

(Color) Comparison of starting (left) and DFT-converged (right) unit cells from an $\mathrm{Al}\left(771\right)–\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(001\right)$ superlattice structural optimization. For clarity, hard spheres representing Al and O atoms are plotted with radii of 0.8 and $1.3\mathrm{\AA }$. (Their closed-shell, ionic radii are 0.45 and $1.46\mathrm{\AA }$.) Al and O atoms belonging initially to the oxide are shown in cyan and yellow. Al atoms initially of the metal are colored according to layer proximity to the oxide. A metal step of the starting superlattice is highlighted by the green line through blue Al atoms in the left panel. The red atoms in the right panel show that relaxation has greatly disturbed the initially stepped surface. Even among the blue atoms, one layer deeper inside the metal, the initial geometry is greatly perturbed. Green atoms were held fixed in the course of geometry optimization, accounting in part for the weakness of the disturbance among the magenta and gray Al’s. The arrow in the left panel indicates a representative Al-O atom pair separated by only $1.44\mathrm{\AA }$, compared to a minimum Al-O distance of $1.76\mathrm{\AA }$ in bulk, DFT, $\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$. After relaxation (right panel), the separation of the same pair is $1.86\mathrm{\AA }$, and, indeed, all atom pairs are at separations compatible with atomic radii.

Figure 2

Hard sphere model of the Al(771) surface, showing the primitive surface lattice vectors, $\mathbf{\alpha }=(2.862,0.0)\mathrm{\AA }$ and $\mathbf{\beta }=(-1.431,14.238)\mathrm{\AA }$. The surface is characterized by a repeating sequence of (110) terraces four close-packed atom rows across, followed by a so-called “$A$-type step” [or (111) microfacet]. The left panel of Fig. 1 shows a side view of this surface (with reduced sphere radii), abutting a $\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(001\right)$ slab.

Figure 3

Computed energy and stress of the relaxed superlattice as a function of its repeat distance. In the starting geometry (left panel of Fig. 1), the periodicity of the superlattice was $25.76\mathrm{\AA }$. After searching for a repeat such that the diagonal stress tensor component, $S_{zz}=0$, where the $z$ coordinate runs normal to the repeats, the repeat distance was found to be 7.26% greater than the starting guess, or $27.63\mathrm{\AA }$. Straight line segments in the figure show the consistency of the computed stress zero and energy minimum.

Figure 4

(Color) The final supercell rotated, and with Al sphere radii reduced to $0.5\mathrm{\AA }$ to make it easier to see the substantial reorganization of the right-hand metal-oxide interface occasioned by the relaxation procedure described in the main text. The blue arrow points to what was a second layer Al atom, now lying 1.83 and $1.87\mathrm{\AA }$ from two O-atom neighbors, Al-O distances characteristic of bulk $\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$. Thus, it is judged to have left the metal and become part of the oxide. The magenta arrow points to the third layer Al atom that replaced it, leaving the vacancy, indicated by the white arrow. Substantial Al atom displacements are also evident higher up in the illustration.

Figure 5

Smoothed by a Gaussian broadening of half-width 0.5°, the distributions of nearest-neighbor bond angles in the second layers from the interfaces (Al atoms colored blue in Fig. 1), in the third layers (atoms colored magenta), and in the central layers (colored green).

Figure 6

(Color) Four optimized, relative minimum energy locations of an impurity H atom in the left hand $\kappa \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(001\right)–\mathrm{Al}\left(771\right)$ interface of Fig. 1. For clarity, Al atoms are displayed in “ball and stick” mode. In panel (a), the radius of one of the (yellow) O-atom spheres is reduced to make it possible to see the attached H atom. Black arrows point to the H atom in each panel. Of interest is that the H binding is weakest to an O atom of the oxide [panel (a)] and strongest in bridging a pair of second-layer Al atoms on the metal side of the interface. This trend is consistent with the idea that interface formation most seriously weakens near-interface metal bonds, leaving Al atoms most likely to benefit energetically from the presence of a new neighbor. On the specifics of the bridging geometries: the H atom in panel (b) has Al neighbors 1.68 and $1.82\mathrm{\AA }$ distant, and an O nearest neighbor $2.64\mathrm{\AA }$ from it. In panel (c) the H atom is near three Al atoms, at distances from it of 1.85, 2.01, and $2.05\mathrm{\AA }$. The nearest O atoms are 2.58 and $2.90\mathrm{\AA }$ away. In the most favorable geometry, that of panel (d), the closest (blue) Al atoms are at distances of 1.67 and $1.73\mathrm{\AA }$ from the H, and the nearest O atoms are 2.67 and $2.72\mathrm{\AA }$ away.