Stability of reducedV2O5(001)surfaces

The defect-free ${\mathrm{V}}_{2}{\mathrm{O}}_{5}(001)$ surface and ordered structures involving oxygen vacancies have been studied for a wide range of defect concentrations, $\ensuremath{\Theta}$ ($1∕6\ensuremath{\leqslant}\ensuremath{\Theta}\ensuremath{\leqslant}1$ monolayer, $\mathrm{ML}$), combining density functional theory and statistical thermodynamics. At $\ensuremath{\Theta}=1∕4\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$ the oxygen vacancy formation energy for the singly coordinated surface oxygen atoms (vanadyl oxygen, ${\mathrm{O}}^{1}$) is by $\ensuremath{\sim}1.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{atom}$ and $\ensuremath{\sim}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{atom}$ lower than the corresponding values for two- and threefold coordinated surface oxygen atoms, respectively. Between $1∕3$ and $1∕2\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$ the alignment of vanadyl oxygen vacancies $({\mathrm{O}}_{\mathrm{vac}}^{1})$ along the [010] direction is by $70\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{atom}$ $(\ensuremath{\Theta}=1∕3\phantom{\rule{0.3em}{0ex}}\mathrm{ML})$ and $120\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{atom}$ $(\ensuremath{\Theta}=1∕2\phantom{\rule{0.3em}{0ex}}\mathrm{ML})$ more favorable than along the [100] direction, with the concentration-induced change of the vacancy formation energy for structures with vacancies aligned along the [100] direction being smaller than $20\phantom{\rule{0.3em}{0ex}}\mathrm{meV}∕\mathrm{atom}$. The lowest vacancy formation energy of $1.87\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{atom}$ corresponds to the $(1\ifmmode\times\else\texttimes\fi{}1){\text{\ensuremath{-}}\mathrm{O}}_{\mathrm{vac}}^{1}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\Theta}=1∕2\phantom{\rule{0.3em}{0ex}}\mathrm{ML})$ phase with defects forming a trenchlike structure with rows along the [010] direction. Above $1∕2\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$ the vacancy formation energy increases up to $2.07\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{atom}$ $(\ensuremath{\Theta}=1\phantom{\rule{0.3em}{0ex}}\mathrm{ML})$. The ease of formation of nonrandom vacancy structures with a favored alignment along the [010] direction is discussed in terms of special vacancy-induced lattice distortions. It is also argued that the trenches along the [010] direction provide preferred paths for continuous reduction of the surface starting from isolated defect sites. However, this missing-row structure would be stable only at very low oxygen partial pressures close to conditions for which ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ decomposes into ${\mathrm{VO}}_{2}$ and ${\mathrm{O}}_{2}$.