3.2.2. Trivalent Dopants

As with the divalent ion V2<sup>+</sup>, the trivalent V3<sup>+</sup> and Mo3<sup>+</sup> dopants can be incorporated at the lithium and niobium sites in the LiNbO3 matrix through various schemes as shown in Tables 4 and 5. When these ions are substituted at Li and Nb sites, the extra positive charge can, as noted earlier, be compensated by the creation of vacancies, interstitials, anti-site defects or self-compensation.


**Table 4.** Types of defects considered due to V3<sup>+</sup> incorporation in LiNbO3.

**Table 5.** Types of defects considered due to Mo3<sup>+</sup> incorporation in LiNbO3.


According to Figures 2 and 3 for the first and second neighbours with respect to the c axis, the trivalent V3<sup>+</sup> and Mo3<sup>+</sup> ions prefer to occupy both the Li and Nb sites according to scheme (iv) which is also observed in other trivalent ions [23–25]. This can be attributed to the similarity between the ionic radius of V3<sup>+</sup> which is 0.64 Å and Mo3<sup>+</sup> which is 0.67 Å [40] and that of Li<sup>+</sup> and Nb<sup>5</sup> <sup>+</sup>. The ionic radius of Li<sup>+</sup> varies between 0.59 Å and 0.74 Å and Nb5<sup>+</sup> varies from 0.32 Å to 0. 66 Å [40]. All these ionic radii are in relation to the coordination sphere with oxygen atoms.

**Figure 2.** Bar chart of solution energies vs. solution schemes for trivalent dopant (V3<sup>+</sup>) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 3.** Bar chart of solution energies vs. solution schemes for trivalent dopant (Mo3<sup>+</sup>) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

#### 3.2.3. Tetravalent Dopants

Like other divalent and trivalent cations, tetravalent V4<sup>+</sup> and M4<sup>+</sup> dopant ions can also substitute at either the Li<sup>+</sup> or Nb5<sup>+</sup> sites. When these ions substitute at the Li<sup>+</sup> and Nb5<sup>+</sup> site charge compensation is required, and various schemes involving vacancies, interstitials, anti-sites and self-compensation are adopted, as shown in Tables 6 and 7.


**Table 6.** Types of defects considered due to M = V4<sup>+</sup> incorporation in LiNbO3.



The results obtained from these calculations are given in Figures 4 and 5. By inspecting these figures, it can be seen that the tetravalent cation V4<sup>+</sup> prefers to be incorporated at the Li<sup>+</sup> and Nb5<sup>+</sup> sites through scheme (iv), while the Mo4<sup>+</sup> ion prefers to be incorporated at the niobium site compensated by an oxygen vacancy according to scheme (ix). Similar to the divalent and trivalent dopants, this preference is related to the proximity with the ionic radii of Li<sup>+</sup> and Nb5+.

**Figure 4.** Bar chart of solution energies vs. solution schemes for tetravalent dopant (V4<sup>+</sup>) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 5.** Bar chart of solution energies vs. solution schemes for tetravalent dopant (Mo4+) at the Li and Nb sites, considering the first neighbours in relation to the c axis.
