#
Computer Simulation of the Incorporation of V^{2+}, V^{3+}, V^{4+}, V^{5+} and Mo^{3+}, Mo^{4+}, Mo^{5+}, Mo^{6+} Dopants in LiNbO_{3}

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{3}with V

^{2+}, V

^{3+}, V

^{4+}and V

^{5+}as well as Mo

^{3+}, Mo

^{4+}, Mo

^{5+}and Mo

^{6+}ions is of interest in enhancing its photorefractive properties. In this paper, possible incorporation mechanisms for these ions in LiNbO

_{3}are modelled, using a new set of interaction potentials fitted to the oxides VO, V

_{2}O

_{3}, VO

_{2}, V

_{2}O

_{5}and to LiMoO

_{2}, Li

_{2}MoO

_{3}, LiMoO

_{3}, Li

_{2}MoO

_{4}.

## 1. Introduction

_{3}with vanadium and molybdenum ions in different charge states, with the aim of predicting the optimum location of dopants, and charge compensation mechanisms where needed.

^{6+}ion dopes at the Nb

^{5+}site. Another study looks at LiNbO

_{3}co-doped with Mg and V, concluding that some of the vanadium dopes at the Nb site in the 5+ charge state, but that V

^{4+}

_{Li}, V

^{3+}

_{Li}and V

^{2+}

_{Li}defects are also observed [18]. Finally, another recent publication [19] has looked at the photorefractive response of Zn and Mo co-doped LiNbO

_{3}in the visible region, and concluded that the presence of Mo

^{6+}ions helps promote fast response and multi-wavelength holographic storage, which is attributed to their occupation of regular niobium sites in the lattice.

^{+}site as V

^{4+}, but that it dopes at the Nb site as a neutral defect as the Fermi level is increased. In another DFT study [21], molybdenum doping was modelled and it was concluded that the most stable configuration involves doping at the Nb

^{5+}site, in agreement with the previously mentioned experimental studies [16,17]. It is noted that in the DFT studies, predictions were made on the basis of defect formation energies, as opposed to the solution energy approach adopted in this paper.

^{2+}, V

^{3+}, V

^{4+}and V

^{5+}as well as Mo

^{3+}, Mo

^{4+}, Mo

^{5+}and Mo

^{6+}doping in LiNbO

_{3}using interatomic potentials. Such calculations enable predictions to be made of the sites occupied by dopant ions, and the form of charge compensation adopted, if needed. These calculations provide information about how the defects behave in the material, and how they influence its properties in the applications mentioned previously. It follows a series of papers by the authors on LiNbO

_{3}doped with a range of ions [22,23,24,25,26,27].

## 2. Materials and Methods

#### 2.1. Interatomic Potentials

_{ij}, ρ

_{ij}and C

_{ij}, which are constants for each interaction, q

_{i}, q

_{j}represent the charges of the ions i and j, and r

_{ij}is the interatomic distance. The parameters are determined by empirical fitting, and formal charges are used for q

_{i}and q

_{j}. The procedure by which potentials were obtained for LiNbO

_{3}is explained in the work of Jackson and Valério [22], and the derivation of the potentials for the vanadium and molybdenum dopants is described in Section 3.1 below. The potentials for LiNbO

_{3}have been the subject of recent studies on the doping of the structure with rare earth ions [23,24], doping with Sc, Cr, Fe and In [25], metal co-doping [26] and doping with Hf [27]. These papers show that modelling can predict the energetically optimal locations of the dopant ions and calculate the energy involved in the doping process. This paper extends this procedure to the study of V

^{2+}, V

^{3+}, V

^{4+}and V

^{5+}as well as Mo

^{3+}, Mo

^{4+}, Mo

^{5+}and Mo

^{6+}doped lithium niobate, with the aim of establishing the optimal doping site and charge compensation scheme for both sets of ions.

#### 2.2. Defect Formation Energies

## 3. Results and Discussion

#### 3.1. Derivation of Interatomic Potential Parameters

_{2}O

_{3,}VO

_{2}and V

_{2}O

_{5}as well as LiMoO

_{2}, Li

_{2}MoO

_{3}, Li

_{3}MoO

_{4}and Li

_{2}MoO

_{4}. For V

^{2+}-O

^{2−}, V

^{3+}-O

^{2−}, V

^{4+}-O

^{2−}and V

^{5+}-O

^{2−}as well as Mo

^{3+}-Li

^{+}, Mo

^{4+}-Li

^{+}, Mo

^{5+}-Li

^{+}, Mo

^{6+}-Li

^{+}, Mo

^{3+}-O

^{2−}, Mo

^{4+}-O

^{2−}, Mo

^{5+}-O

^{2−}and Mo

^{6+}-O

^{2−}interactions, a new set of potentials was derived empirically by fitting to the observed structures as shown in Table 1. The O

^{2−}-O

^{2−}potential was obtained by Sanders et al. [29] and uses the shell model for O [30], which is a representation of ionic polarisability, in which each ion is represented by a core and a shell, coupled by a harmonic spring, and the Li-O potential was taken from [22]. In all cases, the dopant-oxide potentials were obtained by fitting to parent oxide structures.

_{2}O

_{3}[32]

_{,}VO

_{2}[33] and V

_{2}O

_{5}[34] oxides as well as LiMoO

_{2}[35], Li

_{2}MoO

_{3}[36], Li

_{3}MoO

_{4}[37] and Li

_{2}MoO

_{4}[38] lithium molybdate structures, using the potentials in Table 1. It is seen that the experimental and calculated lattice parameters differ by less than 1%, confirming that the potentials can be used in further simulations of defect properties. The calculations were carried at 0 K (the default for the modelling code and used in most other theoretical studies) and at 293 K for comparison with room temperature results. In this way, we can see how the structure and energies vary with temperature.

#### 3.2. Defect Calculations

_{3}are reported. The divalent, trivalent, tetravalent, pentavalent and hexavalent dopants can substitute at Li and Nb sites in the LiNbO

_{3}matrix with charge compensation taking place in a number of ways. The proposed schemes described in the following subsections are written as solid state reactions using the Kroger–Vink notation [39]. This notation appears in the tables in Section 3.2.1, Section 3.2.2, Section 3.2.3, Section 3.2.4 and Section 3.2.5 where the dot/bullet (·) means a net positive charge and the dash/prime (′) means a net negative charge.

#### 3.2.1. Divalent Dopants

^{2+}in the Li

^{+}and Nb

^{5+}host sites requires a charge-compensating defect, which can involve Li and Nb vacancies, Nb

_{Li}anti-sites, interstitial oxygen, self-compensation and oxygen vacancies. The modes of substitution considered for divalent cations are shown in Table 3.

^{2+}) 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 (V

^{2+}) 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 V

^{2+}, which is 0.79 Å, and those of the Li

^{+}site, which varies between 0.59 and 0.74 Å, and the Nb

^{5+}site, which varies between 0.32 and 0.71 Å [40].

#### 3.2.2. Trivalent Dopants

^{2+}, the trivalent V

^{3+}and Mo

^{3+}dopants can be incorporated at the lithium and niobium sites in the LiNbO

_{3}matrix through various schemes as shown in Table 4 and Table 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.

^{3+}and Mo

^{3+}ions prefer to occupy both the Li and Nb sites according to scheme (iv) which is also observed in other trivalent ions [23,24,25]. This can be attributed to the similarity between the ionic radius of V

^{3+}which is 0.64 Å and Mo

^{3+}which is 0.67 Å [40] and that of Li

^{+}and Nb

^{5 +}. The ionic radius of Li

^{+}varies between 0.59 Å and 0.74 Å and Nb

^{5+}varies from 0.32 Å to 0. 66 Å [40]. All these ionic radii are in relation to the coordination sphere with oxygen atoms.

#### 3.2.3. Tetravalent Dopants

^{4+}and M

^{4+}dopant ions can also substitute at either the Li

^{+}or Nb

^{5+}sites. When these ions substitute at the Li

^{+}and Nb

^{5+}site charge compensation is required, and various schemes involving vacancies, interstitials, anti-sites and self-compensation are adopted, as shown in Table 6 and Table 7.

^{4+}prefers to be incorporated at the Li

^{+}and Nb

^{5+}sites through scheme (iv), while the Mo

^{4+}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

^{+}and Nb

^{5+}.

#### 3.2.4. Pentavalent Dopants

^{5+}and Mo

^{5+}, no charge compensation is required for the substitution at the Nb

^{5+}host site, but it is required when the substitution is at the Li

^{+}host site, as shown in Table 8 and Table 9.

^{5+}) and (Mo

^{5+}) 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 (V

^{5+}) and (Mo

^{5+}) ions at an Nb site is energetically more favourable than at an Li site, according to scheme (iv) as shown in Figure 6 and Figure 7 at temperatures 0 K and 293 K. This can be attributed to the similarity between the charge of the V

^{5+}and Mo

^{5+}ions and the Nb

^{5+}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 Nb

^{5+}site.

#### 3.2.5. Hexavalent Dopants

^{6+}, as with the pentavalent ions, there is no self-compensation mechanism and charge compensation schemes are possible when replacing Li and Nb in the LiNbO

_{3}matrix as shown in Table 10.

^{6+}) 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 (Mo

^{6+}) 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 Mo

^{6+}ions and the Nb

^{5+}host site (0.32–0.71 Å) [40]. The ionic radii of Mo

^{6+}, taking into account the coordination number, vary between 0.42 and 0.67 Å [40], and the small difference between the Mo

^{6+}dopant ions and Nb

^{5+}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 Nb

^{5+}site.

_{sol}, corresponding to the incorporation of V

^{2+}at the Li

^{+}site (second equation in Table 3) is given by:

_{latt}and E

_{Def}terms are lattice energies and defect energy.

_{latt}, required to calculate the solution energies are given in Table 11.

#### 3.2.6. Summary of Results for Vanadium and Molybdenum Dopants in LiNbO_{3}

**Divalent dopants**: the calculations predict that, for V

^{2+}, 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 V

^{2+}

_{Li}defects have been observed experimentally [18].

**Trivalent dopants**: both V

^{3+}and Mo

^{3+}ions are predicted to self-compensate. Experimental data from [18] support V

^{3+}doping at the lithium site, as with V

^{2+}.

**Tetravalent dopants**: here, different behaviour is predicted for vanadium and molybdenum. V

^{4+}is predicted to self-compensate, while Mo

^{4+}is predicted to occupy a niobium site with oxygen vacancy charge compensation. Again, [18] suggests that V

^{4+}can dope at a lithium site.

## 4. Conclusions

_{2}O

_{3}, VO

_{2}and V

_{2}O

_{5}as well as LiMoO

_{2}, Li

_{2}MoO

_{3}, Li

_{3}MoO

_{4}and Li

_{2}MoO

_{4}structures doped into LiNbO

_{3}. New interatomic potential parameters for VO, V

_{2}O

_{3,}VO

_{2}and V

_{2}O

_{5}as well as LiMoO

_{2}, Li

_{2}MoO

_{3}, Li

_{3}MoO

_{4}and Li

_{2}MoO

_{4}have been developed. It was found that divalent (V

^{2+}), trivalent (V

^{3+}, Mo

^{3+}) and tetravalent (V

^{4+}) ions are more favourably incorporated at the Li and Nb sites through the self-compensation mechanism. The tetravalent (Mo

^{4+}) ion is more favourably incorporated at the niobium site, compensated by an oxygen vacancy. The pentavalent ions (V

^{5+}, Mo

^{5+}) and hexavalent (Mo

^{6+}) ion are more favourably incorporated at the Nb site, and the lowest energy schemes involve, respectively, no charge compensation, and for the Mo

^{6+}ion, charge compensation with lithium vacancy. This is shown to be consistent with some experimental data, although future calculations involving finite V

^{5+}and Mo

^{6+}concentrations will be carried out to investigate this further.

_{3}, 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

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Bar chart of solution energies vs. solution schemes for divalent dopant (V

^{2+}) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 2.**Bar chart of solution energies vs. solution schemes for trivalent dopant (V

^{3+}) 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 (Mo

^{3+}) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 4.**Bar chart of solution energies vs. solution schemes for tetravalent dopant (V

^{4+}) 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 (Mo

^{4+}) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 6.**Bar chart of solution energies vs. solution schemes for pentavalent dopant (V

^{5+}) 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 (Mo

^{5+}) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Figure 8.**Bar chart of solution energies vs. solution schemes for hexavalent dopant (Mo

^{6+}) at the Li and Nb sites, considering the first neighbours in relation to the c axis.

**Table 1.**Interionic potentials obtained from a fit to the VO, V

_{2}O

_{3}, VO

_{2}, V

_{2}O

_{5}, LiMoO

_{2}, Li

_{2}MoO

_{3}, Li

_{3}MoO

_{4}and Li

_{2}MoO

_{4}structures.

Interaction | A_{ij}(eV) | ρ_{ij}(Å) | C_{ij}(Å^{6} eV) |
---|---|---|---|

Li_{core}-O_{shell} | 950.0 | 0.2610 | 0.0 |

V_{core}-O_{shell} | 293.240087 | 0.475181 | 0.0 |

Mo_{core}-Li_{core} | 573.532325 | 0.369602 | 0.0 |

Mo_{core}-O^{2−}_{shell} | 3003.79 | 0.3474 | 0.0 |

Mo_{core}-O_{core} | 600.263736 | 0.328558 | 0.0 |

O^{2−}_{shell}-O^{2−}_{shell} | 22764.0 | 0.1490 | 27.88 |

Harmonic | k(eV Å^{2}) | r_{o}(Å) | |

V_{core}-O_{core} | 46.997833 | 1.942956 | |

Mo_{core}-O_{core} | 385.638986 | 2.073074 | |

Species | Y(e) | ||

Mo_{core} | 3.0 4.0 5.0 6.0 | ||

V_{core} | 2.0 3.0 4.0 5.0 | ||

O_{core} | 0.9 | ||

O_{shell} | −2.9 | ||

Spring | k(Å^{−2} eV) | ||

O_{core}-O_{oore} | 70.0 |

Oxide | Lattice Parameter | Exp. | Calc. (0 K) | Δ% | Calc. (293 K) | Δ% |

VO | a(Å) = b(Å) = c(Å) | 4.067800 | 4.108237 | 0.99 | 4.10683 | 0.98 |

V_{2}O_{3} | a(Å) = b(Å) = c(Å) | 9.393000 | 9.304757 | 0.90 | 9.346331 | 0.94 |

VO_{2} | a (Å) = b(Å) | 4.556100 | 4.569483 | 0.20 | 4.566212 | 0.22 |

c(Å) | 2.859800 | 2.866421 | 0.23 | 2.857861 | 0.07 | |

V_{2}O_{5} | a(Å) | 11.971900 | 11.99652 | 0.20 | 12.01247 | 0.33 |

b(Å) | 4.701700 | 4.722561 | 0.44 | 4.660343 | 0.88 | |

c(Å) | 5.325300 | 5.355671 | 0.57 | 5.371149 | 0.86 | |

Lithium Molybdates | Lattice Parameter | Exp. | Calc. (0 K) | Δ% | Calc. (293 K) | Δ% |

LiMoO_{2} | a(Å) = b(Å) | 2.866300 | 2.880528 | 0.50 | 2.887246 | 0.73 |

c(Å) | 15.474300 | 15.409390 | 0.42 | 15.595024 | 0.78 | |

Li_{2}MoO_{3} | a(Å) = b(Å) | 2.878000 | 2.854443 | 0.82 | 2.859809 | 0.63 |

c(Å) | 14.91190 | 15.002886 | 0.61 | 15.04632 | 0.90 | |

Li_{3}MoO_{4} | a(Å) = b(Å) = c(Å) | 4.1389 | 4.107762 | 0.75 | 4.106941 | 0.77 |

Li_{2}MoO_{4} | a(Å) = b(Å) | 14.330000 | 14.301305 | 0.20 | 14.384501 | 0.38 |

c(Å) | 9.584 | 9.492067 | 0.96 | 9.632413 | 0.96 |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i) ${\mathrm{MO}+2\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022}{+\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii) ${5\mathrm{MO}+5\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {5\mathrm{M}}_{\mathrm{Li}}^{\u2022}{+\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{2.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii) ${2\mathrm{MO}+2\mathrm{Li}}_{\mathrm{Li}}\to {2\mathrm{M}}_{\mathrm{Li}}^{\u2022}{+\mathrm{O}}_{\mathrm{i}}^{\u2033}{+\mathrm{Li}}_{2}\mathrm{O}$ | |

Li^{+} and Nb^{5+} | Self-Compensation | (iv) $4{\mathrm{MO}+3\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {3\mathrm{M}}_{\mathrm{Li}}^{\u2022}{+\mathrm{M}}_{\mathrm{Nb}}^{\u2034}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Lithium Vacanciesand Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (v) ${\mathrm{MO}+2\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Nb}}^{\u2034}{+\mathrm{V}}_{\mathrm{Li}}^{\prime}+{\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+\mathrm{Li}}_{2}\mathrm{O}$ |

Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vi) $4{\mathrm{MO}+3\mathrm{Li}}_{\mathrm{Li}}{+4\mathrm{Nb}}_{\mathrm{Nb}}\to 4{\mathrm{M}}_{\mathrm{Nb}}^{\u2034}{+3\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{LiNbO}}_{3}$ | |

(vii) ${4\mathrm{MO}+3\mathrm{Li}}_{\mathrm{Li}}{+4\mathrm{Nb}}_{\mathrm{Nb}}\to {4\mathrm{M}}_{\mathrm{Nb}}^{\u2034}{+3\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | ||

Oxygen Vacancies | (viii) ${2\mathrm{MO}+2\mathrm{Nb}}_{\mathrm{Nb}}{+3\mathrm{O}}_{\mathrm{O}}\to 2{\mathrm{M}}_{\mathrm{Nb}}^{\u2034}{+3\mathrm{V}}_{\mathrm{O}}^{\u2022\u2022}{+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)$0.5{\mathrm{M}}_{2}{\mathrm{O}}_{3}{+3\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022}{+2\mathrm{V}}_{\mathrm{Li}}^{\prime}+{1.5\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)$2.5{\mathrm{M}}_{2}{\mathrm{O}}_{3}{+5\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to {5\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022}{+2\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{2.5\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${0.5\mathrm{M}}_{2}{\mathrm{O}}_{3}{+\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022}{+\mathrm{O}}_{\mathrm{i}}^{\u2033}+{0.5\mathrm{Li}}_{2}\mathrm{O}$ | |

Li^{+} and Nb^{5+} | Self-Compensation | (iv)${\mathrm{M}}_{2}{\mathrm{O}}_{3}{+\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022}{+\mathrm{M}}_{\mathrm{Nb}}^{\u2033}+{0.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Oxygen Vacancies | (v)$0.5{\mathrm{M}}_{2}{\mathrm{O}}_{3}{+\mathrm{Nb}}_{\mathrm{Nb}}{+\mathrm{O}}_{\mathrm{O}}\to {\mathrm{M}}_{\mathrm{Nb}}^{\u2033}{+\mathrm{V}}_{\mathrm{O}}^{\u2022\u2022}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vi)${\mathrm{M}}_{2}{\mathrm{O}}_{3}{+\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to {2\mathrm{M}}_{\mathrm{Nb}}^{\u2033}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+\mathrm{LiNbO}}_{3}$ | |

Lithium Vacancies and Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vii)${0.5\mathrm{M}}_{2}{\mathrm{O}}_{3}{+3\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Nb}}^{\u2033}+{2\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{1.5\mathrm{Li}}_{2}\mathrm{O}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${\mathrm{LiMoO}}_{2}{+3\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022}{+2\mathrm{V}}_{\mathrm{Li}}^{\prime}{+2\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)$5{\mathrm{LiMoO}}_{2}{+5\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022}{+2\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}{+5\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${\mathrm{LiMoO}}_{2}{+\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022}{+\mathrm{O}}_{\mathrm{i}}^{\u2033}{+\mathrm{Li}}_{2}\mathrm{O}$ | |

Li^{+} and Nb^{5+} | Self-Compensation | (iv)${2\mathrm{LiMoO}}_{2}{+2\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022}{+\mathrm{Mo}}_{\mathrm{Nb}}^{\u2033}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Oxygen Vacancies | (v)${\mathrm{LiMoO}}_{2}{+\mathrm{Nb}}_{\mathrm{Nb}}+{\mathrm{O}}_{\mathrm{O}}\to {\mathrm{Mo}}_{\mathrm{Nb}}^{\u2033}{+\mathrm{V}}_{\mathrm{O}}^{\u2022\u2022}+{0.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vi)$2{\mathrm{LiMoO}}_{2}{+\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to 2{\mathrm{Mo}}_{\mathrm{Nb}}^{\u2033}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Lithium Vacancies and Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vii)${\mathrm{LiMoO}}_{2}{+3\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Nb}}^{\u2033}+2{\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+2\mathrm{Li}}_{2}\mathrm{O}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${\mathrm{MO}}_{2}{+4\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{V}}_{\mathrm{Li}}^{\prime}+{2\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)${5\mathrm{MO}}_{2}{+5\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{2.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${2\mathrm{MO}}_{2}{+2\mathrm{Li}}_{\mathrm{Li}}\to {2\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{O}}_{\mathrm{i}}^{\u2033}{+\mathrm{Li}}_{2}\mathrm{O}$ | |

Li^{+} and Nb^{5+} | Self-Compensation | (iv)${4\mathrm{MO}}_{2}{+\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{M}}_{\mathrm{Nb}}^{\prime}+{0.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (v)${4\mathrm{MO}}_{2}{+\mathrm{Li}}_{\mathrm{Li}}{+4\mathrm{Nb}}_{\mathrm{Nb}}\to {4\mathrm{M}}_{\mathrm{Nb}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{0.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Lithium Vacancies and Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vi)${\mathrm{MO}}_{2}{+4\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Nb}}^{\prime}{+3\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{2\mathrm{Li}}_{2}\mathrm{O}$ | |

(vii)${2\mathrm{MO}}_{2}{+3\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to {2\mathrm{M}}_{\mathrm{Nb}}^{\prime}{+2\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{LiNbO}}_{3}$ | ||

(viii)${3\mathrm{MO}}_{2}{+2\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to {3\mathrm{M}}_{\mathrm{Nb}}^{\prime}{+\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+\mathrm{LiNbO}}_{3}$ | ||

Oxygen Vacancies | (ix)${2\mathrm{MO}}_{2}{+2\mathrm{Nb}}_{\mathrm{Nb}}{+\mathrm{O}}_{\mathrm{O}}\to {2\mathrm{M}}_{\mathrm{Nb}}^{\prime}{+\mathrm{V}}_{\mathrm{O}}^{\u2022\u2022}{+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+4\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{V}}_{\mathrm{Li}}^{\prime}+{3\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)${5\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+5\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{7.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${2\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+2\mathrm{Li}}_{\mathrm{Li}}\to {2\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{O}}_{\mathrm{i}}^{\u2033}{+3\mathrm{Li}}_{2}\mathrm{O}$ | |

Li^{+} and Nb^{5+} | Self-Compensation | (iv)${4\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022}{+3\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}+{4.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Nb^{5+} | Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (v)${4\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+\mathrm{Li}}_{\mathrm{Li}}{+4\mathrm{Nb}}_{\mathrm{Nb}}\to {4\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{4.5\mathrm{Li}}_{2}\mathrm{O}+{1.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Lithium Vacanciesand Anti-site (${\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}$) | (vi)${\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+4\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}{+3\mathrm{V}}_{\mathrm{Li}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}+{3\mathrm{Li}}_{2}\mathrm{O}$ | |

(vii)${2\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+3\mathrm{Li}}_{\mathrm{Li}}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to {2\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+2\mathrm{V}}_{\mathrm{Li}}^{\prime}{+3\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{LiNbO}}_{3}$ | ||

(viii)${3\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+2\mathrm{Li}}_{\mathrm{Li}}{+3\mathrm{Nb}}_{\mathrm{Nb}}\to {3\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}{+\mathrm{Nb}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+\mathrm{V}}_{\mathrm{Li}}^{\prime}{+3\mathrm{Li}}_{2}{\mathrm{O}+2\mathrm{LiNbO}}_{3}$ | ||

Oxygen Vacancies | (ix)${2\mathrm{Li}}_{2}{\mathrm{MoO}}_{3}{+2\mathrm{Nb}}_{\mathrm{Nb}}{+\mathrm{O}}_{\mathrm{O}}\to {2\mathrm{Mo}}_{\mathrm{Nb}}^{\prime}{+\mathrm{V}}_{\mathrm{O}}^{\u2022\u2022}{+2\mathrm{Li}}_{2}{\mathrm{o}+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${0.5\mathrm{M}}_{2}{\mathrm{O}}_{5}{+5\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+4\mathrm{V}}_{\mathrm{Li}}^{\prime}+{2.5\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)${2.5\mathrm{M}}_{2}{\mathrm{O}}_{5}{+5\mathrm{Li}}_{\mathrm{Li}}{+5\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+4\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{2.5\mathrm{Li}}_{2}{\mathrm{O}+2\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${0.5\mathrm{M}}_{2}{\mathrm{O}}_{5}{+\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{M}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+2\mathrm{O}}_{\mathrm{i}}^{\u2033}+{0.5\mathrm{Li}}_{2}\mathrm{O}$ | |

Nb^{5+} | No ChargeCompensation | (iv)${0.5\mathrm{M}}_{2}{\mathrm{O}}_{5}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{M}}_{\mathrm{Nb}}^{}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${\mathrm{Li}}_{3}{\mathrm{MoO}}_{4}{+5\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+4\mathrm{V}}_{\mathrm{Li}}^{\prime}+{4\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)${5\mathrm{Li}}_{3}{\mathrm{MoO}}_{4}{+5\mathrm{Li}}_{\mathrm{Li}}{+4\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+4\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{10\mathrm{Li}}_{2}{\mathrm{O}+2\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${\mathrm{Li}}_{3}{\mathrm{MoO}}_{4}{+\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022}{+2\mathrm{O}}_{\mathrm{i}}^{\u2033}{+2\mathrm{Li}}_{2}\mathrm{O}$ | |

Nb^{5+} | No ChargeCompensation | (iv)${\mathrm{Li}}_{3}{\mathrm{MoO}}_{4}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Nb}}^{}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Site | Charge Compensation | Reaction |
---|---|---|

Li^{+} | Lithium Vacancies | (i)${\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+6\mathrm{Li}}_{\mathrm{Li}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022\u2022}{+5\mathrm{V}}_{\mathrm{Li}}^{\prime}{+4\mathrm{Li}}_{2}\mathrm{O}$ |

Niobium Vacancies | (ii)${\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022\u2022}{+\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (iii)${2\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+2\mathrm{Li}}_{\mathrm{Li}}\to 2{\mathrm{Mo}}_{\mathrm{Li}}^{\u2022\u2022\u2022\u2022\u2022}{+5\mathrm{O}}_{i}^{\u2033}{+3\mathrm{Li}}_{2}\mathrm{O}$ | |

Nb^{5+} | Lithium Vacancies | (iv)${\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+\mathrm{Li}}_{\mathrm{Li}}{+\mathrm{Nb}}_{\mathrm{Nb}}\to {\mathrm{Mo}}_{\mathrm{Nb}}^{\u2022}{+\mathrm{V}}_{\mathrm{Li}}^{\prime}+{1.5\mathrm{Li}}_{2}\mathrm{O}+{0.5\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Niobium Vacancies | (v)${5\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+6\mathrm{Nb}}_{\mathrm{Nb}}\to 5{\mathrm{Mo}}_{\mathrm{Nb}}^{\u2022}{+\mathrm{V}}_{\mathrm{Nb}}^{\u2033\u2034}{+5\mathrm{Li}}_{2}{\mathrm{O}+3\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ | |

Oxygen Interstitial | (vi)${2\mathrm{Li}}_{2}{\mathrm{MoO}}_{4}{+2\mathrm{Nb}}_{\mathrm{Nb}}\to {2\mathrm{Mo}}_{\mathrm{Nb}}^{\u2022}{+\mathrm{O}}_{\mathrm{i}}^{\u2033}{+2\mathrm{Li}}_{2}{\mathrm{O}+\mathrm{Nb}}_{2}{\mathrm{O}}_{5}$ |

Compound | Lattice Energy | Lattice Energy |
---|---|---|

0 K | 293 K | |

LiNbO_{3} | −174.45 | −174.66 |

Li_{2}O | −33.16 | −32.92 |

Nb_{2}O_{5} | −314.37 | −313.39 |

VO | −22.06 | −22.07 |

V_{2}O_{3} | −124.37 | −124.39 |

VO_{2} | −111.54 | −111.57 |

V_{2}O_{5} | −315.65 | −274.18 |

LiMoO_{2} | −98.07 | −97.09 |

Li_{2}MoO_{3} | −150.38 | −149.10 |

Li_{3}MoO_{4} | −181.28 | −178.88 |

Li_{2}MoO_{4} | −234.06 | −234.12 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Araujo, R.M.; dos Santos Mattos, E.F.; Valerio, M.E.G.; Jackson, R.A.
Computer Simulation of the Incorporation of V^{2+}, V^{3+}, V^{4+}, V^{5+} and Mo^{3+}, Mo^{4+}, Mo^{5+}, Mo^{6+} Dopants in LiNbO_{3}. *Crystals* **2020**, *10*, 457.
https://doi.org/10.3390/cryst10060457

**AMA Style**

Araujo RM, dos Santos Mattos EF, Valerio MEG, Jackson RA.
Computer Simulation of the Incorporation of V^{2+}, V^{3+}, V^{4+}, V^{5+} and Mo^{3+}, Mo^{4+}, Mo^{5+}, Mo^{6+} Dopants in LiNbO_{3}. *Crystals*. 2020; 10(6):457.
https://doi.org/10.3390/cryst10060457

**Chicago/Turabian Style**

Araujo, Romel Menezes, Emanuel Felipe dos Santos Mattos, Mário Ernesto Giroldo Valerio, and Robert A. Jackson.
2020. "Computer Simulation of the Incorporation of V^{2+}, V^{3+}, V^{4+}, V^{5+} and Mo^{3+}, Mo^{4+}, Mo^{5+}, Mo^{6+} Dopants in LiNbO_{3}" *Crystals* 10, no. 6: 457.
https://doi.org/10.3390/cryst10060457