3.2.4. Pentavalent Dopants

For the pentavalent dopants V5<sup>+</sup> and Mo5+, no charge compensation is required for the substitution at the Nb5<sup>+</sup> host site, but it is required when the substitution is at the Li<sup>+</sup> host site, as shown in Tables 8 and 9.


**Table 8.** Types of defects considered due to M = V5<sup>+</sup> incorporation in LiNbO3.

The solution energies for the pentavalent (V5<sup>+</sup>) and (Mo5<sup>+</sup>) dopants with different charge compensation mechanisms were evaluated and plotted as a function of the reaction scheme. Based on the lowest energy value, it seems that the incorporation of pentavalent (V5<sup>+</sup>) and (Mo5+) ions at an Nb site is energetically more favourable than at an Li site, according to scheme (iv) as shown in Figures 6 and 7 at temperatures 0 K and 293 K. This can be attributed to the similarity between the charge of the V5<sup>+</sup> and Mo5<sup>+</sup> ions and the Nb5<sup>+</sup> host, which can contribute to a small deformation in the lattice and consequently a lower solution energy. Experimental results by Kong et al. [17] and Tian et al. [16] show that substitution occurs at the Nb5<sup>+</sup> site.

**Figure 6.** Bar chart of solution energies vs. solution schemes for pentavalent dopant (V5+) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 7.** Bar chart of solution energies vs. solution schemes for pentavalent dopant (Mo5<sup>+</sup>) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

### 3.2.5. Hexavalent Dopants

For the hexavalent dopant Mo6+, as with the pentavalent ions, there is no self-compensation mechanism and charge compensation schemes are possible when replacing Li and Nb in the LiNbO3 matrix as shown in Table 10.

**Table 10.** Types of defects considered due to Mo6<sup>+</sup> incorporation in LiNbO3.


The solution energies for the hexavalent (Mo6+) dopants with different charge-compensation mechanisms were evaluated and plotted as a function of the reaction scheme. Based on the lowest energy value, it seems that the incorporation of hexavalent (Mo6<sup>+</sup>) ions at an Nb site is energetically more favourable than at an Li site, according to scheme (iv) as shown in Figure 8 at temperatures 0 K and 293 K. This can be attributed to the similarity between the ionic radii of Mo6<sup>+</sup> ions and the Nb5<sup>+</sup> host site (0.32–0.71 Å) [40]. The ionic radii of Mo6<sup>+</sup>, taking into account the coordination number, vary between 0.42 and 0.67 Å [40], and the small difference between the Mo6<sup>+</sup> dopant ions and Nb5<sup>+</sup> ions can contribute to a small deformation in the lattice and consequently a lower solution energy. This result reveals that global trends of dopant solution energies are controlled by the combination of dopant ion size [40] and its electrostatic interactions, demonstrating that there is a relation between the energetically preferred site and the types of defect mechanisms involved in the doping process. Experimental results from Kong et al. [17] and Zhu et al. [41] show that substitution occurs at the Nb5<sup>+</sup> site.

**Figure 8.** Bar chart of solution energies vs. solution schemes for hexavalent dopant (Mo6+) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

In all cases, the energy involved in doping was obtained by calculating the solution energy, which includes all terms of the thermodynamic cycle involved in the solution process. For example, the solution energy, Esol, corresponding to the incorporation of V2<sup>+</sup> at the Li<sup>+</sup> site (second equation in Table 3) is given by:

$$\mathrm{E\_{Sol}} = \mathrm{E\_{Def}(5M\_{Li} + V\_{\mathrm{Nb}}^{\prime\prime\prime\prime})} + 2.5\mathrm{E\_{Latt}(Li\_2O)} + 0.5\mathrm{E\_{Latt}(Nb\_2O\_5)} - 5\mathrm{E\_{Latt}(MO)}\tag{2}$$

where the Elatt and EDef terms are lattice energies and defect energy.

All energies were normalised by the number of dopants, i.e., the solution energy is divided by the number of dopants involved. For example, for scheme (ii) of Table 3, the energy must be divided by five, since five lithium sites are occupied. This is done because the number of dopants varies for each mechanism. Lattice energies, Elatt, required to calculate the solution energies are given in Table 11.


**Table 11.** Lattice energies used in the solution energy calculations (eV).
