The small unit cell reconstructions of SrTiO3(111)

Abstract

We analyze the basic structural units of simple reconstructions of the (111) surface of SrTiO 3 using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA+U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25eV per 1x1 unit cell, with changes of 0.5-1.0 eV per 1x1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals an unusual low-energy TiO 2 -rich configuration with an unexpected distorted trigonal biprismatic structure. This structure can act as a template for layers of either TiO or Ti 2 O 3 , consistent with experimental results as well as, in principle, Magnelli phases. The results also suggest that both the fracture surface and the stoichiometric SrTiO 3 (111) surface should spontaneously disproportionate into SrO and TiO 2 rich domains, and show that there are still surprises to be found for polar oxide surfaces.

A homologous series of structures on the surface of SrTiO3(110)

“…DFT calculations were carried out using the Wien2k code 16 , with, for improved accuracy, PBE0 and TPSSh on-site functionals as described elsewhere, with errors estimated from the differences between the functionals 20 . An RKmax parameter of 6.12 was used with RMTs of 2.36, 1.72 and 1.54 for strontium, titanium and oxygen, respectively.…”

“…The horizontal axis is the composition in terms of excess monolayers of TiO 2 at the surface; negative numbers indicate an excess of SrO. Error bars were estimated on the basis of the differences in energies using various functionals 20 .…”

Transition from Order to Configurational Disorder for Surface Reconstructions onSrTiO3(111)

“…While the approximate chemistry and topography of the surfaces is relatively well characterized as are some details of the dependence upon surface composition [21], the actual atomic structure of all these surfaces is completely unknown. A few theoretical studies in the literature focus on relatively simple structures that have not been found experimentally [22][23][24].…”

Vacant-Site Octahedral Tilings onSrTiO3(001), the(13×13)R33.7°Surface,

“…Atomic positions were optimized using the full-electron potential WIEN2k package [28] with an augmented plane wave + local orbitals (APW+lo) basis set, the PBEsol [29] generalized gradient approximation as well as the revTPSS method [30]. Similar to work for the NiO (111) surface [31], we optimized the exact-exchange parameter for the Ti-d levels using experimental energies of some TiO x molecules [32] which gave a result of 0.5. While this is not a panacea of all DFT ills, and the exactexchange fraction is surprisingly large, this gave a noticeably better value of 1.36eV for the decomposition energy of SrTiO 3 to SrO and TiO 2 compared to previous work [32], a better band-gap of ~2.8(1) eV as well as a good absolute fit to the ratio of the surface free-energy of SrTiO 3 (001) to (110) from Wulff construction measurements [33], none of these being part of the fitting.…”

“…Similar to work for the NiO (111) surface [31], we optimized the exact-exchange parameter for the Ti-d levels using experimental energies of some TiO x molecules [32] which gave a result of 0.5. While this is not a panacea of all DFT ills, and the exactexchange fraction is surprisingly large, this gave a noticeably better value of 1.36eV for the decomposition energy of SrTiO 3 to SrO and TiO 2 compared to previous work [32], a better band-gap of ~2.8(1) eV as well as a good absolute fit to the ratio of the surface free-energy of SrTiO 3 (001) to (110) from Wulff construction measurements [33], none of these being part of the fitting. Typical muffin-tin radii were 1.55, 1.75, and 2.36 Bohr for O, Ti, and Sr, respectively, a 1x1x1 k-point grid, and a plane wave cut-off of K max *min(RMT)=7.0.…”