3.2.1. Divalent Dopants

The substitution of the divalent dopant V2<sup>+</sup> in the Li<sup>+</sup> and Nb5<sup>+</sup> host sites requires a charge-compensating defect, which can involve Li and Nb vacancies, NbLi anti-sites, interstitial oxygen, self-compensation and oxygen vacancies. The modes of substitution considered for divalent cations are shown in Table 3.


**Table 3.** Types of defects considered due to M = V2<sup>+</sup> incorporation in LiNbO3.

The solution energies for the divalent (V2<sup>+</sup>) dopant with different charge-compensating mechanisms were evaluated and plotted as a function of the reaction schemes. Based on the lowest energy value, it seems that the incorporation of a divalent (V2+) ion is energetically favourable at the lithium and niobium sites, taking into account the first in relation to the c axis. In schemes (i) and (iv), the energy difference in eV is small at both temperatures in the first neighbours, indicating that it can be incorporated at the lithium site compensated by a lithium vacancy as well as by self-compensation as shown in Figure 1. This can be attributed to the similarity between the ionic radius of V2<sup>+</sup>, which is 0.79 Å, and those of the Li<sup>+</sup> site, which varies between 0.59 and 0.74 Å, and the Nb5<sup>+</sup> site, which varies between 0.32 and 0.71 Å [40].

**Figure 1.** Bar chart of solution energies vs. solution schemes for divalent dopant (V2+) at the Li and Nb sites, considering the first neighbours in relation to the c axis.
