Stability of reducedV2O5(001)surfaces

The defect-free ${\mathrm{V}}_2{\mathrm{O}}_5\left(001\right)$ surface and ordered structures involving oxygen vacancies have been studied for a wide range of defect concentrations, $\Theta$ ($1∕6⩽\Theta ⩽1$ monolayer, $\mathrm{ML}$), combining density functional theory and statistical thermodynamics. At $\Theta =1∕4\mathrm{ML}$ the oxygen vacancy formation energy for the singly coordinated surface oxygen atoms (vanadyl oxygen, ${\mathrm{O}}^1$) is by $\sim 1.7\mathrm{eV}∕\mathrm{atom}$ and $\sim 2.0\mathrm{eV}∕\mathrm{atom}$ lower than the corresponding values for two- and threefold coordinated surface oxygen atoms, respectively. Between $1∕3$ and $1∕2\mathrm{ML}$ the alignment of vanadyl oxygen vacancies $\left({\mathrm{O}}_{\mathrm{vac}}^1\right)$ along the [010] direction is by $70\mathrm{meV}∕\mathrm{atom}$ $\left(\Theta =1∕3\mathrm{ML}\right)$ and $120\mathrm{meV}∕\mathrm{atom}$ $\left(\Theta =1∕2\mathrm{ML}\right)$ 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 $20\mathrm{meV}∕\mathrm{atom}$. The lowest vacancy formation energy of $1.87\mathrm{eV}∕\mathrm{atom}$ corresponds to the $\left(1\times 1\right){\text{−}\mathrm{O}}_{\mathrm{vac}}^1\left(\Theta =1∕2\mathrm{ML}\right)$ phase with defects forming a trenchlike structure with rows along the [010] direction. Above $1∕2\mathrm{ML}$ the vacancy formation energy increases up to $2.07\mathrm{eV}∕\mathrm{atom}$ $\left(\Theta =1\mathrm{ML}\right)$. 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 ${\mathrm{O}}_2$.