3.2.6. Summary of Results for Vanadium and Molybdenum Dopants in LiNbO3

In this sub-section, the results presented in the last five subsections are summarised.

**Divalent dopants**: the calculations predict that, for V2+, self-compensation (simultaneous doping at lithium and niobium sites) and doping at the lithium site with lithium vacancy compensation are most likely. It is noted that V2+Li defects have been observed experimentally [18].

**Trivalent dopants**: both V3<sup>+</sup> and Mo3<sup>+</sup> ions are predicted to self-compensate. Experimental data from [18] support V3<sup>+</sup> doping at the lithium site, as with V2<sup>+</sup>.

**Tetravalent dopants**: here, different behaviour is predicted for vanadium and molybdenum. V4<sup>+</sup> is predicted to self-compensate, while Mo4<sup>+</sup> is predicted to occupy a niobium site with oxygen vacancy charge compensation. Again, [18] suggests that V4<sup>+</sup> can dope at a lithium site.

**Pentavalent dopants**: both V5<sup>+</sup> and Mo5<sup>+</sup> are predicted to dope at the niobium site (no charge compensation is needed), agreeing with experimental results [16,17].

**Hexavalent dopants**: Mo6<sup>+</sup> is predicted to dope at the niobium site, with charge compensation by lithium vacancy formation. The occupation of the niobium site is supported by experimental data [16,17,19].

#### **4. Conclusions**

This paper has presented a computational study of VO, V2O3, VO2 and V2O5 as well as LiMoO2, Li2MoO3, Li3MoO4 and Li2MoO4 structures doped into LiNbO3. New interatomic potential parameters for VO, V2O3, VO2 and V2O5 as well as LiMoO2, Li2MoO3, Li3MoO4 and Li2MoO4 have been developed. It was found that divalent (V2<sup>+</sup>), trivalent (V3<sup>+</sup>, Mo3<sup>+</sup>) and tetravalent (V4<sup>+</sup>) ions are more favourably incorporated at the Li and Nb sites through the self-compensation mechanism. The tetravalent (Mo4<sup>+</sup>) ion is more favourably incorporated at the niobium site, compensated by an oxygen vacancy. The pentavalent ions (V5<sup>+</sup>, Mo5<sup>+</sup>) and hexavalent (Mo6<sup>+</sup>) ion are more favourably incorporated at the Nb site, and the lowest energy schemes involve, respectively, no charge compensation, and for the Mo6<sup>+</sup> ion, charge compensation with lithium vacancy. This is shown to be consistent with some experimental data, although future calculations involving finite V5<sup>+</sup> and Mo6<sup>+</sup> concentrations will be carried out to investigate this further.

Finally, to summarise, in this paper we have looked in detail at vanadium and molybdenum dopants in various charge states in LiNbO3, and through the use of solution energies, identified the energetically favoured sites and charge compensation mechanisms, while comparing the results with available experimental and theoretical work in this field.

**Author Contributions:** Conceptualisation, R.M.A.; Data curation, R.M.A. and E.F.d.S.M.; Formal analysis, R.A.J.; Supervision, M.E.G.V. and R.A.J.; Validation, M.E.G.V. and R.A.J.; Writing—original draft, R.M.A.; Writing—review & editing, M.E.G.V. and R.A.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank the peer reviewers, whose detailed comments have undoubtedly led to major improvements to this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
