First-principles density functional theory calculations at the generalized gradient approximation level are performed to investigate the structures and energetics of ten stoichiometric $1\times 1$ low-index surfaces of brookite, the rarest and least understood of the natural polymorphs of titanium dioxide $\left(\mathrm{Ti}{\mathrm{O}}_2\right)$. For each surface, different possible terminations are considered, and their structural relaxations are analyzed. As a general trend, undercoordinated surface Ti atoms are found to relax inward so as to form $\mathrm{Ti}{\mathrm{O}}_x$ polyhedra with O atoms at the vertices, analogous to the $\mathrm{Ti}{\mathrm{O}}_6$ octahedra of the bulk structure. For some surfaces, very large relaxations, involving several subsurface layers, are found to occur. From the computed surface formation energies, the relative stabilities of the different terminations are determined and found to be mainly related to the concentration of exposed coordinatively unsaturated metal (Ti) atoms. The equilibrium crystal shape of brookite $\mathrm{Ti}{\mathrm{O}}_2$ is also determined, and the relative fraction of each exposed surface is estimated.

• Received 15 June 2007

DOI:https://doi.org/10.1103/PhysRevB.76.235307