Rutile TiO 2 vicinal surfaces with ⟨001⟩ steps are investigated using the energy density method (EDM) based on density functional theory. In this approach, EDM provides the energy for each atom so that we can determine the stability of different step configurations correctly. Even though the energy variation due to the step is localized around the step edge, the step−step interaction is long ranged. The finite-size effect in the step−step interaction is identified using EDM. The oxygen vacancy at the step edge explains the atomic structure of the step observed by STM.
■ INTRODUCTIONThe geometries and energetics of steps on surfaces play a crucial role in a wide range of surface phenomena.Step edges influence surface morphologies and have been observed to cause surface reconstructions 1−3 and affect the shapes of islands on the surfaces. 4−7 Surface steps can be active sites for catalysis 8,9 and are preferential sites for the adsorption of adatoms and molecules 10 and nucleation for metal nanoclusters. 11,12 Steps on metal and semiconductor surfaces have been investigated extensively in experiment and theory, 13,14 but structurally and electronically complex oxide surfaces have received less attention. Recent studies have computed the steps on MgO, 15 CeO 2 , 16 SrTiO 3 , 17 and TiO 2 surfaces 3,6−9,18,19 due to their importance in catalytic applications. In particular, rutile TiO 2 step structures and energies have been the subject of both experimental and computational studies to elucidate their role in the high catalytic activity of TiO 2 .Scanning tunneling microscopy (STM) studies observed three different types of monatomic height steps on the TiO 2 (110) surfaces whose step edges are running along either [001], [111], or [110] directions. 4,10,20,21 The ⟨001⟩ and ⟨111⟩ steps form during annealing on sputtered surfaces, and ⟨111⟩ steps occurring at low annealing temperatures and ⟨001⟩ steps become favorable at high annealing temperatures. 4,20 The ⟨110⟩ steps are metastable and are formed by ion beam injection. 10 The reconstructed ⟨111⟩ step edges are reported with strand structures and oxygen vacancies. 3,8,9,22 Diebold et al. characterized the atomic structure of ⟨001⟩ steps using STM. 21 They observed two different types of ⟨001⟩ steps: one which is terminated with bridging oxygen atoms ⟨001⟩ O and the other is a reconstructed ⟨001⟩ step with exposed 5-fold titanium atoms ⟨001⟩ Ti . They reported specific (1 × 4) reconstruction on the ⟨001⟩ Ti step; however, other experimental studies show that the ⟨001⟩ step edges are rough and undercoordinated. 3,22 Density functional theory (DFT) calculates the energies of specific atomic configurations and determines their relative stability. Previous DFT studies found that the ⟨111⟩ step with reconstructed step edge is the most stable step configuration on TiO 2 vicinal surfaces. 6,7,19 The ⟨110⟩ step has the highest step energy even after it reconstructs, 7 and the ⟨001⟩ step has only two stable structures that are ⟨001⟩ O and ⟨001⟩ Ti steps. 19 Recently, Hardcast...