Stable Cation Inversion at the ${\mathrm{MgAl}}_2{\mathrm{O}}_4(100)$ Surface

From an interplay of atom-resolved noncontact atomic force microscopy, surface x-ray diffraction experiments, and density functional theory calculations, we reveal the detailed atomic-scale structure of the (100) surface of an insulating ternary metal oxide, ${\mathrm{MgAl}}_2{\mathrm{O}}_4$ (spinel). We surprisingly find that the ${\mathrm{MgAl}}_2{\mathrm{O}}_4(100)$ surface is terminated by an Al and O-rich structure with a thermodynamically favored amount of Al atoms interchanged with Mg. This finding implies that so-called Mg-Al antisites, which are defects in the bulk of ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, become a thermodynamically stable and integral part of the surface.

Figure 1

(A) Side view ball model of the bulk unit cell of normal ${\mathrm{MgAl}}_2{\mathrm{O}}_4$ spinel. (b) Top view ball model showing the structure of the experimentally observed ${\mathrm{O}}_4\mathrm{\text{−}}{\mathrm{Al}}_4\mathrm{\text{−}}{\mathrm{O}}_4$ terminated surface.

Figure 2

NC-AFM images of the ${\mathrm{MgAl}}_2{\mathrm{O}}_4(100)$ surface recorded in constant height mode with a contrast reflecting (a) a positively charged tip apex and (b) negatively charged tip apex. Imaging condition for (a) is $d{f}_{\mathrm{set}}=-126\mathrm{Hz}$, $U_{\mathrm{bias}}=1.0\mathrm{V}$, $A_{p\mathrm{\text{−}}p}=10\mathrm{nm}$ and for (b) is $d{f}_{\mathrm{set}}=-30\mathrm{Hz}$, $U_{\mathrm{bias}}=3.0\mathrm{V}$, $A_{p\mathrm{\text{−}}p}=10\mathrm{nm}$. (c) Positive and (d) negative tip NC-AFM simulation of the ${\mathrm{O}}_4\mathrm{\text{−}}{\mathrm{Al}}_4\mathrm{\text{−}}{\mathrm{O}}_4$ surface. (e) Comparison of an experimental line scan with a line scan simulated with a positive tip.

Figure 3

(a) X-ray structure factors from the clean ${\mathrm{MgAl}}_2{\mathrm{O}}_4(100)$ surface (open and filled circles). The solid lines represent best fits to the data according to the structural model. Ball models of the SXRD refined structure (b) along the [100] and (c) along the [010] directions. (d) Table with occupancies for the top four layers (relative to the extended ideal flat surface) obtained from the SXRD data.

Figure 4

(a) Surface energy plot of the most relevant surfaces with or without cation inversion (inv.) and H adsorption, obtained from the DFT calculations using the chemical potential formalism. The plot reflects the stability in terms of the surface energy of the relevant phases at the experimental preparation conditions [$P({\mathrm{O}}_2)=1\times {10}^{-7}\mathrm{mbar}$ and $P({\mathrm{H}}_2)=1\times {10}^{-10}\mathrm{mbar}$] as a function of temperature. Top view ball models of the ${\mathrm{O}}_4\mathrm{\text{−}}{\mathrm{Al}}_4\mathrm{\text{−}}{\mathrm{O}}_4$ terminated ${\mathrm{MgAl}}_2{\mathrm{O}}_4(100)$ surface with (b) one antisite per unit cell, (c) most stable configuration at saturation coverage of 2H per unit cell on plain ${\mathrm{O}}_4\mathrm{\text{−}}{\mathrm{Al}}_4\mathrm{\text{−}}{\mathrm{O}}_4$, and (d) most stable configuration at saturation coverage of 2H per unit cell on the ${\mathrm{O}}_4\mathrm{\text{−}}{\mathrm{Al}}_4\mathrm{\text{−}}{\mathrm{O}}_4$ surface with one antisite (overall most stable configuration).