First-Principles Investigation of the Epitaxial Stabilization of Oxide Polymorphs: TiO2 on (Sr,Ba)TiO3
Zhongnan Xu, Paul Salvador and John R. Kitchin, “First-Principles Investigation of the Epitaxial Stabilization of Oxide Polymorphs: TiO2 on (Sr,Ba)TiO3”, ACS Applied Materials & Interfaces 9(4), 4106-4118 (2017). https://doi.org/10.1021/acsami.6b11791
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Question
Earlier computational screens of oxide polymorphs for epitaxial growth, including the 20 kJ/mol window proposed by Mehta et al., relied on bulk formation energies (and in later work, strain from lattice mismatch) and never built or computed an actual film/substrate interface. This paper asks whether adding first-principles interface energies lets DFT correctly predict which polymorph grows on a given substrate, using TiO2 anatase (metastable) and rutile (stable) on low-index surfaces of cubic SrTiO3 (STO) and BaTiO3 (BTO) as a test set with many experimental observations (Xu et al. 2017).
Approach
The stability of a metastable phase II relative to stable phase I in a nucleus of thickness d was written, following continuum capillarity theory, as the difference in bulk formation plus strain energy times d, plus the difference in film/substrate interface energies, with the surface energy difference neglected. The thickness was set to 1 nm as an upper limit for nucleation layers. Orientation relationships were chosen by aligning the close-packed (eutactic) planes and directions of film and substrate on the (001), (011) and (111) perovskite facets, giving six candidate interfaces. Strain energies were computed by fixing the in-plane cell vectors to the substrate and relaxing the rest. Interface energies came from symmetric, stoichiometric supercells with two identical interfaces; to reach low-energy stoichiometric cells, poorly coordinated oxygen atoms were removed by trial and error. All quantities were computed in VASP with PBE, PBEsol and BEEF-vdW at a 500 eV cutoff. Incoherent interfaces were assigned a typical value of 1 J/m2 (Xu et al. 2017).
Key findings
Two of the six relationships, rutile (111) on perovskite (001) and rutile (110) on (011), involve misfit above 10% and were treated as incoherent. All three anatase interfaces could be coherent, which the authors attribute to the shared cubic stacking of anatase and perovskite eutactic layers, whereas hexagonally stacked rutile was coherent only on the (111) facet. With PBE, bulk anatase came out about 8 kJ/mol below rutile (-967 versus -959 kJ/mol), the known wrong ordering for GGA functionals. Biaxial strain penalties were large, mostly 8 to 16 kJ/mol, ranging from 5.76 kJ/mol for anatase (001) on STO to 21.16 kJ/mol for anatase (112) on STO (111), and so often exceeded the bulk energy difference. Strain penalties from BEEF-vdW and PBEsol were mostly within 10% of PBE.
Bulk terms alone (formation plus strain) gave predictions that mostly disagreed with experiment: for instance, they favored anatase on the (111) facets where rutile is observed. The computed interface energies were, in J/m2, about 0.25 to 0.26 for anatase (001) on (001), 0.51 to 0.78 for anatase (102) on (011), 0.33 to 0.72 for anatase (112) on (111), and 0.09 to 0.34 for rutile (100) on (111). Interfaces with more oxygen removal depended more on the functional, with PBEsol giving the largest values. Combining all terms (PBE, d = 1 nm) reversed the bulk-only picture: anatase was strongly favored on (001) of both substrates and rutile on (111), matching experiment whether strained DFT, unstrained DFT or experimental bulk energies were used. On (011), anatase was predicted on both substrates, which matches SrTiO3 but not BaTiO3; the authors attribute this to the assumed 1 J/m2 for rutile, since experiments suggest rutile forms a semicoherent interface there. Mapping anatase on STO (011) and BTO (001) onto the idealized Mehta model gave equivalent bulk penalties of 20.18 and 17.64 kJ/mol, so the observed growth of anatase on these facets supports the 20 kJ/mol window, provided that window is understood to collect bulk, strain and interface contributions together (Xu et al. 2017).
Significance
This is among the first DFT studies of the thermodynamics of a known metastable epitaxial film, and it shows that computed interface energies are needed to predict polymorph selection, because strain and interface terms are comparable in size to bulk energy differences. Trends persisted across three functionals, supporting computational guidance of substrate choice. The authors note limits: only oxygen addition or removal was explored, semicoherent and dislocated interfaces were not modeled, surface energies were neglected, and results are 0 K energies (Xu et al. 2017).