Theoretical study of the (110) surface of Sn_{1 - X}Ti _xO₂ solid solutions with different distribution and content of Ti

The composition and thermodynamic stability of the (110) surface of Sn _{1 - x}Ti_xO₂ rutile solid solutions was investigated as a function of Ti-distribution and content up to the formation of a full TiO₂ surface monolayer. The bulk and (110) surface properties of Sn_{1 - x}Ti_xO₂ were compared to that of the pure SnO₂ and TiO₂ crystal. A large supercell of 720 atoms and a localized basis set based on the Gaussian and plane wave scheme allowed the investigation of very low Ti-content and symmetry. For the bulk, optimization of the crystal structure confirmed that up to a Ti-content of 3.3 at.%, the lattice parameters (a, c) of SnO₂ do not change. Increasing further the Ti-content decreased both lattice parameters down to those of TiO₂. The surface energy of these solid solutions did not change for Ti-substitution in the bulk of up to 20 at.%. In contrast, substitution in the surface layer rapidly decreased the surface energy from 0.99 to 0.74 J/m ² with increasing Ti-content from 0 to 20 at.%. As a result, systems with Ti atoms distributed in the surface (surface enrichment) had always lower energies and thus were thermodynamically more favorable than those with Ti homogeneously distributed in the bulk. This was attributed to the lower energy necessary to break the TiO bonds than SnO bonds in the surface layer. In fact, distributing the Ti atoms homogeneously or segregated in the (110) surface led to the same surface energy indicating that restructuring of the surface bond lengths has minimal impact on thermodynamic stability of these rutile systems. As a result, a first theoretical prediction of the composition of Sn _{1 - x}Ti_xO₂ solid solutions is proposed.