Defect Chemistry in Zn₃V₄(PO₄)₆

Abstract

Zinc-ion batteries have attracted great interest for their low cost, safety, and high energy density. Recently, Zn₃V₄(PO₄)₆ has been reported to be a promising cathode material for zinc-ion batteries. The defect chemistry, diffusion of Zn-ions, and solution of dopants are examined by advanced simulation techniques. The simulation results show that the most favorable intrinsic defect is the Zn-V anti-site. A zig-zag pattern of long-range Zn²⁺ diffusion is observed and the activation energy of 1.88 eV indicates that the ionic conductivity of this material is low. The most promising isovalent dopants on the Zn site are Ca²⁺ and Fe²⁺. Although the solution of Ga³⁺, Sc³⁺, In³⁺, Y³⁺, Gd³⁺, and La³⁺ on the V site is exoergic, the most promising is In³⁺. Different reaction routes for the formation of Zn₃V₄(PO₄)₆ are considered and the most thermodynamically favorable reaction consists of binary oxides (ZnO, V₂O₃, and P₂O₅) as reactants.

1. Introduction

The battery is a promising sustainable energy source for both mobile and stationary applications [1,2,3]. Among various rechargeable batteries, lithium-ion batteries (LIBs) have been utilized for many years in many energy storage devices such as laptops, mobile phones, and e-bikes [4,5,6,7,8,9]. Although LIBs have achieved excellent progress, factors such as limited lithium resources, safety, and cost have led to finding other monovalent ion batteries consisting of Na⁺ and K⁺ ions [10,11,12,13] and multivalent ion batteries based on Mg²⁺, Ca²⁺, and Zn²⁺ ions [14,15,16,17,18,19].

Zinc ion batteries (ZIBs) have received extensive attention owing to their high volumetric energy density, low redox potential, low cost, safety, and high abundance [20,21,22,23,24,25,26]. In order to improve energy efficiency, there is a necessity to find new materials that can be used to construct key components of ZIBs (i.e., anodes, cathodes, and electrolytes).

The cathode is an important part of ZIBs hosting Zn²⁺ ions. The most promising cathode material that has attracted many researchers is MnO₂ due to its crystal structure and different oxidation states of Mn [27,28]. Other cathode materials studied so far include vanadium oxides [29], Prussian blue analogs [30], spinel-structured oxides [31], and organic materials [32].

Phosphate-based materials have attracted great attention for constructing cathodes due to their structural rigidity provided via strong [PO₄]³⁻ units and high operating voltages [33]. NASICON-type phosphate materials (e.g., Li₃V₂(PO₄)₃ and Na₃V₂(PO₄)₃) [34,35], fluorophosphates (e.g., Na₃V₂(PO₄)₂F₃) [36], olivine-structure-based phosphates (e.g., LiFePO₄) [37], and layered phosphates (e.g., VOPO₄) [38] are expected to be candidate cathode materials for ZIBs. Recently, a vanadium-based phosphate material, Zn₃V₄(PO₄)₆ [39], was reported to be a candidate cathode material for ZIBs owing to its high stability and specific capacity. The performance of this material depends also on the diffusivity of Zn²⁺ ions in this material, and such diffusion relies on the defects. Although defects and diffusion properties of Zn₃V₄(PO₄)₆ are experimentally challenging, computational modeling techniques can provide valuable information about the most thermodynamically stable defect processes, diffusion pathways and their activation energies, and solution of dopants. In a recent classical simulation study of spinel-ZnCo₂O₄ [40], it was reported that the Co-Zn anti-site is the most stable defect type and that Zn²⁺ ion diffusion is three-dimensional with an activation energy of 0.70 eV.

In this study, we used the computational modeling technique based on the classical pair-wise potentials to examine the defect, diffusion, and dopant properties of Zn₃V₄(PO₄)₆. Many oxide materials have been modeled using this methodology and the calculated properties agree with those measured in the experiments [41,42,43,44,45]. The electronic structures of the most stable dopants were analyzed using density functional theory (DFT) simulations.

2. Computational Methods

Defect simulations were employed using a classical simulation code GULP (Generalized Utility Lattice Program) [46]. In this simulation technique, interactions between ions in the lattice are described using long-range Coulombic and short-range electron–electron repulsion (Pauli) and attractive dispersion (van der Waals) forces. Short-range interactions were modeled using Buckingham potentials (see

Table 1. Buckingham potential parameters used in the classical simulations of Zn₃V₄(PO₄)₆ [47,48]. Two-body (Φ_ij (r_ij) = A_ij exp (− r_ij/ρ_ij) − C_ij/r_ij⁶), where A, ρ, and C are parameters reproducing the experimental data. The values of Y and K are shell charges and spring constants, respectively.

Interaction	A/eV	ρ/Å	C/eV·Å6	Y/e	K/eV·Å–2
Zn2+ − O2−	499.6	0.3595	0.00	2.00	99,999
V3+ − O2−	1410.82	0.3117	16.00	2.04	196.3
P5+ − O2−	897.2648	0.3577	0.00	5.000	99,999
O2 − O2−	22,764.30	0.1490	27.89	−2.80	74.92

) [47,48]. Both lattice constants and ionic positions were relaxed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [49]. Point defect modeling was carried out by a method proposed by the Mott–Littleton method [50]. Vacancy-mediated diffusion of Zn²⁺ ions was modeled considering seven interstitial positions between two Zn atomic positions in a local hop. The energy difference was between the maximum energy and the energy of the Zn vacancy. Our simulation techniques assumed that all ions were spherical and fully charged. There was an overestimation of the defect energies but the trend’s consistency was retained.

DFT simulations were employed to examine the electronic structures of the most favorable doped configurations. The plane-wave DFT simulation code VASP (Vienna Ab initio Simulation Package) [51] was used. In all cases, a plane wave basis set consisting of a cut-off of 500 eV, projected augmented wave (PAW) pseudopotentials [52], and a 4 × 4 × 4 Monkhorst–Pack [53] k-point mesh were used. The PBE-GGA (Perdew, Burke, and Ernzerhof-generalized gradient approximation) [54] was used to describe the exchange-correlation energy. Full geometry optimization was performed using the conjugate gradient algorithm [55] with a force tolerance of 0.001 eV/Å. The Bader charge analysis [56] was used to estimate the effective charges on the atoms in the relaxed configurations.

3. Results and Discussion

3.1. Crystal Structure of Zn₃V₄(PO₄)₆

Zn₃V₄(PO₄)₆ is three-dimensional with a triclinic space group of $P\overline{1}$. Its experimental lattice constants were reported to be a = 6.349 Å, b = 7.869 Å, c = 9.324 Å, α = 105.32°, β = 108.66°, and γ = 101.23° [57]. In this complex structure, phosphorous and vanadium form tetrahedral units and octahedral units with nearest-neighbor oxygen atoms (see Figure 1a). These two units share their corners and form networks in the crystal. This complex structure was energy-minimized completely to determine the equilibrium lattice constants. The calculated values were in good agreement with the values reported in the experiment showing the efficacy of potential parameters and pseudopotentials (see

Table 2. Calculated and experimental parameters of Zn₃V₄(PO₄)_6.

Parameter	Calculated		Experiment [57]	|∆| (%)
	Classical	DFT		Classical	DFT
a (Å)	6.172	6.393	6.349	2.79	0.69
b (Å)	7.960	7.975	7.869	1.16	1.35
c (Å)	9.208	9.391	9.324	1.24	0.78
α (°)	105.43	105.45	105.32	0.10	0.12
β (°)	108.31	107.20	108.66	0.33	1.34
γ (°)	102.35	101.97	101.23	1.11	0.73

).

The calculated total DOS plot shows that the Zn₃V₄(PO₄)₆ exhibits a metallic characteristic (see Figure 1b), which is one of the essential conditions for a cathode material. Figure 1c shows the charge density plot showing the ion–ion interaction in the Zn₃V₄(PO₄)₆.

Bader charges calculated on the atoms in the bulk Zn₃V₄(PO₄)₆ are reported in

Table 3. Calculated Bader charges on the atoms in bulk Zn₃V₄(PO₄)₆.

Atom	Bader Charge (e)
Zn	+1.43
V	+2.10
P	+5.00
O	−1.78

. Based on the formula of the Zn₃V₄(PO₄)₆, ionic charges on the Zn, V, P, and O are +2.00, +3.00, +5.00, and −2.00, respectively. Although the Bader charges of Zn, V, and O are not closer to the values of the full ionic charge model, the bulk Zn₃V₄(PO₄)₆ can still be considered as ionic material.

3.2. Intrinsic Defect Properties

Here, we calculated the Frenkel, Schottky, and anti-site defect formation energy processes. These defects are crucial as they determine the properties of materials. As point defect (vacancy and interstitial) energies are necessary to calculate the defect process energies, vacancy and interstitial formation energies were first calculated. The defect processes are written using Kröger–Vink notations [58]. In a Schottky defect process, vacancies are introduced in the lattice. A Frenkel defect consists of a vacancy–interstitial pair. The concentration of these two defect processes is temperature-dependent. In general, the concentration of these defects will increase with increasing temperature. The Frenkel defect process controls the ionic conductivity of a material as explained in a previous experimental study on AgI [59]. An enhancement in the electronic conductivity was explained in the presence of Schottky defects in LaFeO₃ [60]. Point defect energies were combined to calculate Frenkel, Schottky, and anti-site defect formation energies.

$$\mathrm{Zn} \mathrm{Frenkel}:{ \mathrm{Zn}}_{\mathrm{Zn}}^{\mathrm{X}} \to V_{\mathrm{Zn}}^{″}+{ \mathrm{Zn}}_{\mathrm{i}}^{••}$$

(1)

$$\mathrm{V} \mathrm{Frenkel}:{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X}} \to V_{\mathrm{V}}^{‴}+{ \mathrm{V}}_{\mathrm{i}}^{•••}$$

(2)

$$\mathrm{P} \mathrm{Frenkel}:{ \mathrm{P}}_{\mathrm{P}}^{\mathrm{X}} \to V_{\mathrm{P}}^{•••••}+{ \mathrm{P}}_{\mathrm{i}}^{″″\prime }$$

(3)

$$\mathrm{O} \mathrm{Frenkel}:{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X}} \to V_{\mathrm{O}}^{••}+{ \mathrm{O}}_{\mathrm{i}}^{″}$$

(4)

$$\mathrm{Schottky}:3{ \mathrm{Zn}}_{\mathrm{Zn} }^{\mathrm{X}}+4{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }+6{ \mathrm{P}}_{\mathrm{P}}^{\mathrm{X}}+24{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X}}\to 3 V_{\mathrm{Zn}}^{″}+4 V_{\mathrm{V}}^{‴}+6 V_{\mathrm{P}}^{″″\prime }+12 V_{\mathrm{O}}^{••}+{ \mathrm{Zn}}_3{\mathrm{V}}_4{({\mathrm{PO}}_4)}_6$$

(5)

$$\mathrm{ZnO} \mathrm{Schottky}:{ \mathrm{Zn}}_{\mathrm{Zn}}^{\mathrm{X}}+{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X} }\to V_{\mathrm{Zn}}^{″}+V_{\mathrm{O}}^{••}+\mathrm{ZnO}$$

(6)

$${\mathrm{V}}_2{\mathrm{O}}_3 \mathrm{Schottky}: 2{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X}}+3{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X} }\to 2 V_{\mathrm{V}}^{″″\prime }+3 V_{\mathrm{O}}^{••}+{\mathrm{V}}_2{\mathrm{O}}_3$$

(7)

$${\mathrm{P}}_2{\mathrm{O}}_5 \mathrm{Schottky}: 2{ \mathrm{P}}_{\mathrm{P}}^{\mathrm{X}}+5{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X} }\to 2 V_{\mathrm{P}}^{″″\prime }+5 V_{\mathrm{O}}^{••}+{\mathrm{P}}_2{\mathrm{O}}_5$$

(8)

$$\mathrm{Zn}/\mathrm{V} \mathrm{anti}–\mathrm{site} \left(\mathrm{isolated}\right):{ \mathrm{Zn}}_{\mathrm{Zn}}^{\mathrm{X}}+{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }\to {\mathrm{Zn}}_{\mathrm{V}}^{\prime }+{\mathrm{V}}_{\mathrm{Zn}}^{•}$$

(9)

$$\mathrm{Zn}/\mathrm{V} \mathrm{anti}–\mathrm{site} \left(\mathrm{cluster}\right):{ \mathrm{Zn}}_{\mathrm{Zn}}^{\mathrm{X}}+{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }\to {\{{\mathrm{Zn}}_{\mathrm{V}}^{\prime }+{\mathrm{V}}_{\mathrm{Zn}}^{•}\}}^X$$

(10)

In Figure 2, calculated defect energies are reported. The Zn-V anti-site cluster exhibits the lowest defect formation energy. In this defect process, a small amount of Zn²⁺ ions will be on the V site and vice versa. The defect formation energy difference between the anti-site (isolated) and anti-site (cluster) is defined as the binding energy (−0.18 eV). Exoergic binding shows that isolated defects (${\mathrm{Zn}}_{\mathrm{V}}^{\prime }{ \mathrm{and} \mathrm{V}}_{\mathrm{Zn}}^{•}$) will aggregate as soon as the isolated defects are present in this material. This defect has been determined in a variety of oxide materials both experimentally and theoretically [61,62,63,64,65]. The influence of the cation anti-site defect has been discussed in an experimental study on LiFePO₄ [66]. The electrochemical performance of LiNiPO₄ upon the Li-Ni anti-site defect has been discussed by Kempaiah et al. [67]. The cycled structure of Li₂FeSiO₄ exhibited Li-Fe ion mixing and the Li-ion diffusion pathways and activation energies were different to those found in its as-prepared structure [68]. In a recent study, defect and diffusion properties of spinel-ZnCo₂O₄ were examined using classical simulation [40]. It was found that the Zn-Co anti-site cluster is the lowest-energy defect with a binding energy of −0.14 eV.

Partial Schottky (ZnO and V₂O₃) and Zn Frenkel defect energies are closer to each other. The Zn Frenkel is an important defect energy process as it can govern the vacancy-assisted Zn-ion migration in this material. This defect energy is 2.82 eV, much lower than that calculated in ZnCo₂O₄. The O Frenkel has a defect energy of 3.00 eV. This is higher only by ~0.30 eV than that calculated in the partial Schottky or Zn Frenkel. Other Schottky or Frenkel defects are higher-defect-energy processes and do not form under normal temperatures. In particular, the P Frenkel has the highest defect energy of 10.60 eV.

3.3. Diffusion of Zn²⁺ Ions

The understanding of Zn²⁺ ion diffusion is important as it determines the overall performance of Zn₃V₄(PO₄)₆. Here, we used classical simulation techniques to calculate the energies of activation of local Zn hops and construct diffusion pathways with long range. In a previous classical simulation study [69], it was reported that Li⁺ ion migration in LiFePO₄ is one-dimensional with a curve that was later confirmed in a neutron diffraction study [70].

Five local Zn hops were found. In the first hop (A), Zn diffuses in the bc plane having an activation energy of 1.05 eV (see Figure 3). A jump distance of 3.98 Å and its activation energy 1.88 eV were calculated in the second hop. Both activation energies are quite high and, therefore, the diffusion of Zn²⁺ would be slow.

Table 4. Calculated activation energies of different Zn hops.

Hop	Distance (Å)	Activation Energy (eV)
A	3.55	1.05
B	3.98	1.88
C	5.87	3.48
D	5.94	3.62
E	6.24	3.80

lists the activation energies of each hoping distance. In particular, longer hop distances (>4.00 Å) have higher activation energies (>3 eV). This means that Zn²⁺ ions would diffuse very slowly via those hops. The slow diffusivity of Zn²⁺ can be due to several reasons including the high positive charge of 2+, long Zn hop distance, and the crystal structure. Morkhova et al. [71] recently employed DFT simulations to calculate activation energies of some Zn²⁺ ion conductors. The most promising structures were found to be spinel compounds with the chemical formula of ZnM₂O₄ (M = Fe, Co, Cr, and V) and their activation energies ranged between 0.54 eV and 0.68 eV. In the crystal structure of Zn₃S₂O₉, the activation energy of Zn²⁺ is high (1.55 eV), although this compound consists of three Zn²⁺ ions per formula unit. In a previous classical simulation study of spinel-ZnCo₂O₄, it was reported that the Zn²⁺ ions migrate in a linear pathway having an activation energy of 0.71 eV [40].

An improvement of Zn²⁺ ion diffusion can be made by preparing materials at the nanoscale, lowering the Zn-Zn separation. The polymerization intercalation method has also been applied to enhance the rate of diffusion of Zn²⁺ ions [72]. In this method, the electrostatic interaction between Zn²⁺ and O²⁻ ions is weakened to overcome the sluggish diffusion of Zn²⁺ ions. A combined experimental and DFT study of ZnCo₂O₄ showed that the oxygen vacancy formation can improve the Zn²⁺ ion diffusion by enlarging channels [73]. A facile hydrothermal method was applied to prepare a composite consisting of Zn_xV₂O₅ and graphene oxide to form a stabilized structure and enhance the diffusion of Zn²⁺ ions [74].

3.4. Solution of Dopants

Substitutional doping of elements is an important process to modify the properties of a material [75]. The ionic conductivity of zirconia was enhanced by the doping of yttria [76]. Such an enhancement was shown to associate with the point defects controlling the oxygen diffusion at grain boundaries. Ru doping on the Fe site reduced the Li-Li hop distances and enhanced the Li-ion diffusion in LiFePO₄ [77]. Here, we considered alkali earth (Mg, Ca, Sr, and Ba), divalent transition metal (Co, Mn, Fe, and Ni), and trivalent (Al, Ga, Gd, In, Sc, Y, and La) dopants to predict candidate dopants that can be tried experimentally. Appropriate lattice energies of dopant oxides and charge-compensating defects were introduced to construct defect reaction equations.

Table 5. Interatomic potential parameters used for dopants in the atomistic simulations of Zn₃V₄(PO₄)₆. Two-body (Φ_ij (r_ij) = A_ij exp (−r_ij/ρ_ij) − C_ij/r_ij⁶).

Interaction	A (eV)	ρ (Å)	C (eV·Å6)	Y (e)	K (eV·Å−2)
Mg+ − O2−	946.627	0.31813	0.000	2.000	99,999
Ca2+ − O2−	1090.40	0.3372	0.000	1.260	34.00
Sr2+ − O2−	776.84	0.35867	0.000	1.526	11.406
Ba2+ − O2−	931.79	0.3949	0.000	1.460	14.78
Ni2+ − O2−	683.5	0.3332	0.000	2.000	8.77
Co2+ − O2−	696.3	0.3362	0.000	2.000	10.74
Fe2+ − O2−	1207.6	0.3084	0.000	2.000	99,999
Mn2+ − O2−	715.80	0.3464	0.000	3.000	81.20
Al3+ − O2−	1725.20	0.28971	0.000	3.000	99,999
Ga3+ − O2−	2901.12	0.2742	0.000	3.000	99,999
Sc3+ − O2−	1575.85	0.3211	0.000	3.000	99,999
In3+ − O2−	1495.65	0.3327	4.33	3.000	99,999
Y3+ − O2−	1766.40	0.33849	19.43	3.000	99,999
Gd3+ − O2−	1885.75	0.3399	20.34	3.000	99,999
La3+ − O2−	2088.79	0.3460	23.25	3.000	99,999

reports the potential parameters used for dopant oxides in this study.

First, alkali earth dopants (R = Mg, Ca, Sr, and Ba) were substitutionally doped on the Zn site. The following equation explains the doping process.

$$\mathrm{RO} +{ \mathrm{Zn}}_{\mathrm{Zn}}^{\mathrm{X}}\to {\mathrm{R}}_{\mathrm{Zn}}^{\mathrm{X}}+ \mathrm{ZnO}$$

(11)

Solution energies are reported in Figure 4a. The Ca²⁺ is found to be the most favorable dopant. A negative solution energy (−0.16 eV) is calculated for this dopant. The solution energy calculated for the Mg²⁺ is also negative but lower by 0.05 eV than that calculated for the Ca²⁺. These dopants are favored partly due to their ionic radii (Mg²⁺: 0.89 Å and Ca²⁺: 1.12 Å) closely matching with the ionic radius of Zn²⁺ (0.88 Å). The solution of Sr²⁺ is endoergic with the solution energy of 0.41 eV. The Ba²⁺ exhibits a high positive solution energy of 1.73 eV, meaning that this dopant can be doped only at high temperatures. The total DOS plot shows that the Ca-doped Zn₃V₄(PO₄)₆ is still metallic (see Figure 4b). The states of the Ca lie in the deeper level of the valence band (see Figure 4c).

Next, divalent transition metal ions (Ni²⁺, Co²⁺, Fe²⁺, and Mn²⁺) were considered on the Zn site. The most promising dopant is Fe²⁺ and its solution energy is –1.30 eV (see Figure 5a). The negative solution energy indicates that the Fe²⁺ on the Zn site is thermodynamically stable. The second most favorable dopant is Mn²⁺. The solution energy for this dopant is negative (−0.08 eV), meaning that this dopant is also promising. Both Ni²⁺ and Co²⁺ exhibit positive solution energies. The most unfavorable dopant is Ni²⁺. The metallic characteristic of Zn₃V₄(PO₄)₆ is retained upon Fe-doping (see Figure 5b). The states in the Fermi energy level are significantly affected by the d-states of Fe (see Figure 5c).

Next, trivalent dopants were substituted on the V site. This doping process, as other processes mentioned above, requires no charge-compensating defects as defined by the following equation.

$${\mathrm{R}}_2{\mathrm{O}}_3+2{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X}}\to 2{ \mathrm{R}}_{\mathrm{V}}^{\mathrm{X}}+{\mathrm{V}}_2{\mathrm{O}}_3$$

(12)

The solution energies reported in Figure 6a indicate that most of the dopants except Al³⁺ exhibit an exoergic solution. The most promising dopant of In³⁺ has the solution energy of −1.10 eV. The least promising dopant of Al³⁺ exhibits an endothermic solution energy of 0.30 eV. There is an increase in solution energy with increasing ionic radius from Al³⁺ to In³⁺. Then, there is a gradual drop in the solution energy up to Ga³⁺. The solution energy of La³⁺ becomes more negative than that calculated for Gd³⁺.

The total DOS plot shows that In-doped Zn₃V₄(PO₄)₆ is metallic (see Figure 6b) and the states occupied at the Fermi energy level are a mixture of s, p, and d states of In (see Figure 6c).

A deformation charge density plot associated with the most favorable dopants interacting the lattice structure is provided in Figure 7.

3.5. Synthetic Routes for the Formation of Zn₃V₄(PO₄)₆

The synthesis of Zn₃V₄(PO₄)₆ was carried out using a high-temperature roasting method. In this complex method, CH₃COO)₂Zn·2H₂O, NH₄VO₃, and H₂C₂O₄·2H₂O are used as starting materials [39]. Here, we consider some chemical reactions and calculate the formation energies by optimizing different oxides containing Zn, V, and P. In all cases, the formation of one mole of Zn₃V₄(PO₄)₆ is considered and the reaction energies are exothermic (see

Table 6. Different reaction routes for the synthesis of Zn₃V₄(PO₄)₆.

Reaction Number	Reaction	Reaction Energy (eV)
1	3 ZnO + 2 V2O3 + 3P2O5 → Zn3V4(PO4)6	−6.27
2	3 ZnO + 4 VPO4 + P2O5 → Zn3V4(PO4)6	−3.12
3	1.5 Zn2(P2O7) + 2 V2O3 + 1.5 P2O5 → Zn3V4(PO4)6	−2.30
4	3 ZnO + V4(P2O7)3 → Zn3V4(PO4)6	−1.72
5	3 Zn(PO3)2 + 2 V2O3 → Zn3V4(PO4)6	−1.10
6	Zn3(PO4)2 + 4 VPO4 → Zn3V4(PO4)6	−0.29

). This means all five routes are theoretically feasible. In the first reaction, the reaction liberates energy (−6.27 eV) in the form of heat. In this reaction route, binary oxides are taken as reactants. The second reaction has two binary oxides and one ternary oxide. The inclusion of a ternary oxide results in a lower reaction energy of −3.12 eV. In the third reaction, a ternary oxide consisting of Zn, P, and O (Zn₂P₂O₇) is considered as a reactant. This reaction is still exothermic and its reaction energy is lower than those of reactions 2 and 3. In the least feasible reaction, a ternary oxide consisting of high Zn content (Zn₃(PO₄)₂) is used. This reaction is exothermic with a reaction energy of −0.29 eV. Although all the reaction energies are thermodynamically exoergic, the availability, abundance, cost of materials, and ease of experiments should also be considered. In addition, kinetic feasibility is also important as the start of the reaction depends on the activation energy. The kinetic barrier can be dealt with by using appropriate catalysts.

4. Conclusions

In conclusion, we have studied the nature of defects, migration of Zn²⁺ ions, a solution of isovalent dopants, and the thermodynamic stability of different reaction routes for the synthesis of Zn₃V₄(PO₄)₆ using computational modeling techniques. The Zn-V anti-site is the most energetically favorable defect process. The diffusion of Zn²⁺ ions is low in this material. The Ca²⁺ and Fe²⁺ ions are the most promising dopant ions on the Zn site, while the V site prefers the In³⁺ dopant ion. The formation of Zn₃V₄(PO₄)₆ is favored by the reaction between binary oxides (ZnO, V₂O₃, and P₂O₅).