Transition Metal Oxides: Extra Thermodynamic Stability as Thin Films

The oxides of many transition metals wet their own metal surface. The adhesion energy at this interface ($E_{\mathrm{adh},\mathrm{ox}/\mathrm{m}}$) provides extra stabilization, which lowers the ${\mathrm{O}}_2$ pressure required for oxide stability as a thin film below that required for bulk-oxide stability by the factor $\exp [(2{\gamma }_{\mathrm{g}/\mathrm{ox}}-E_{\mathrm{adh},\mathrm{ox}/\mathrm{m}})/(t{N}_{\mathrm{ox}}RT)]$, where ${\gamma }_{\mathrm{g}/\mathrm{ox}}$ is the surface energy of the oxide, $t$ is the oxide film thickness, and $N_{\mathrm{ox}}$ is the oxygen concentration in the bulk oxide (moles ${\mathrm{O}}_2$ per volume). For oxide films only $\sim 1\mathrm{nm}$ thick, this correction can be many orders of magnitude. This may extend to other compounds.

Figure 1

Plot of the equilibrium ${\mathrm{O}}_2$ dissociation pressure for ${\mathrm{Ag}}_2\mathrm{O}(s)$ versus temperature in van’t Hoff format. The top line is experimental data for bulk ${\mathrm{Ag}}_2\mathrm{O}(s)$ [10]. The two lower lines are predicted for thin films of ${\mathrm{Ag}}_2\mathrm{O}(s)$ of thickness 2 and 1 nm covering $\mathrm{Ag}(s)$ using Eq. (7), assuming a reasonable value for $2{\gamma }_{g/\mathrm{ox}}-E_{\mathrm{adh},\mathrm{ox}/m}(-50\mu \mathrm{J}/{\mathrm{cm}}^2)$. The real value of $2{\gamma }_{g/\mathrm{ox}}-E_{\mathrm{adh},\mathrm{ox}/m}$ could be determined from an experimental measurement of the equilibrium pressure at one thickness.