Intrinsic Defects, Diffusion and Dopants in AVSi₂O₆ (A = Li and Na) Electrode Materials

Abstract

The alkali metal pyroxenes of the AVSi₂O₆ (A = Li and Na) family have attracted considerable interest as cathode materials for the application in Li and Na batteries. Computer modelling was carried out to determine the dominant intrinsic defects, Li and Na ion diffusion pathways and promising dopants for experimental verification. The results show that the lowest energy intrinsic defect is the V–Si anti-site in both LiVSi₂O₆ and NaVSi₂O₆. Li or Na ion migration is slow, with activation energies of 3.31 eV and 3.95 eV, respectively, indicating the necessity of tailoring these materials before application. Here, we suggest that Al on the Si site can increase the amount of Li and Na in LiVSi₂O₆ and NaVSi₂O₆, respectively. This strategy can also be applied to create oxygen vacancies in both materials. The most favourable isovalent dopants on the V and Si sites are Ga and Ge, respectively.

1. Introduction

Rechargeable batteries have been the subject of considerable research for many years, to improve energy efficiency and reduce the emission of greenhouse gases [1,2,3]. There is currently much research on Li and Na ion batteries, particularly for use in electric vehicles [4,5]. Materials with a low cost, low hazard risk, high structural and chemical stability and high capacity are of great interest for preparing cathode materials for Li or Na ion batteries. A variety of materials, including phosphate (${\mathrm{PO}}_4^{3–})$-, silicate (${\mathrm{SiO}}_4^{4–})$-, and borate (${\mathrm{BO}}_3^{3–}$)-based materials, have been experimentally and theoretically screened for use as cathode materials in batteries [6,7,8,9,10,11,12,13,14,15,16,17]. The search for alternative materials continues.

Silicate-based materials have been considered as candidate cathode materials for both Li and Na ion batteries [6,18,19,20] due to the high abundance of silicon and the lattice stabilisation provided by ${\mathrm{SiO}}_4^{4–}$ units. Among them, polyanion orthosilicates such as A₂FeSiO₄ and A₂MnSiO₄ (A = Li or Na) have attracted considerable attention due to their strong electrochemical performance [12,13,21,22,23]. Li₂FeSiO₄ has attracted much interest due to its high theoretical capacity of 332 mAhg⁻¹ [18,24]. However, the performance of this material is hindered by its slow Li-ion diffusion and low electronic conductivity [18]. Many experimental and theoretical studies have focused on the modification of Li₂FeSiO₄ to improve its properties [25,26,27,28]. Li₂MnSiO₄, Na₂FeSiO₄ and Na₂MnSiO₄ materials have also been studied extensively to assess their performance as cathode materials for batteries [29,30,31,32,33].

Interest in AVSi₂O₆ (A = Li and Na) materials as cathodes for the application of rechargeable batteries has emerged in recent years due to the existence of variable oxidation states of vanadium, leading to redox reactions [34,35,36]. Li₂VSi₂O₆ was reported to be a potential cathode material for use in Li-ion batteries [34,35]. Two different high capacities of 85 mAhg^–1 and 181 mAhg^–1 were measured at 30 °C and 60 °C, respectively, due to the introduction of additional 0.42 Li⁺ ions arising from redox reactions (V³⁺/V⁴⁺ and V²⁺/V³⁺) [34]. Very recently, a sol–gel method was used to prepare a high-capacity NaVSi₂O₆ cathode material yielding a specific capacity of 80 mAhg^–1 [36]. Density functional theory simulation was used to examine the stability of Na insertion into NaVSi₂O₆, and it was concluded that poor cycle stability is directly related to the significant volume change [36]. Although a number of experimental studies have investigated the performance of AVSi₂O₆ (A = Li and Na), theoretical studies of the defects and ion transport rates are lacking in the literature. Defects are crucial because they strongly influence the performance of electrode materials.

In this study, defect properties, Li (or Na) ion diffusion and solutions of dopants in LiVSi₂O₆ and NaVSi₂O₆ are presented with the aid of classical simulations for the first time. In previous simulation studies, we used this methodology to study the defect and diffusion properties in battery materials, fuel-cell materials and minerals [37,38,39,40,41,42,43].

2. Computational Methods

We used the interatomic potential simulation code GULP (General Utility Lattice Program) [44] to examine the intrinsic defect properties, dopant solution and the diffusion of Li (or Na) ions in both LiVSi₂O₆ and NaVSi₂O₆. In this method, the interaction between the ions in the lattice is defined as the sum of long-range (Coulomb) and short-range (Pauli repulsion and van der Waals attraction) interactions. Buckingham potentials (

Table 1. Buckingham potential parameters used [30,41,47,48,49].

Interaction	A/eV	ρ/Å	C/eV·Å6	Y/e	K/eV·Å−2
LiVSi2O6
Li+–O2−	479.837	0.3000	0.00	1.00	99,999
V3+–O2−	1410.82	0.3117	0.00	2.04	196.3
Si4+–O2−	1283.91	0.32052	10.66	4.00	99,999
O2−–O2−	9547.96	0.2192	32.0	−2.04	6.3
NaVSi2O6
Na+–O2−	1497.830598	0.287483	0.00	1.00	99,999
V3+–O2−	1410.82	0.3117	0.00	2.04	196.3
Si4+–O2−	1283.91	0.32052	10.66	4.00	99,999
O2−–O2−	22,764.0	0.1490	27.89	−2.80	74.92
Three body
Bonds		K (eV. rad−2)		θ0 (o)
O2−–Si4+–O2−		2.09724		109.5

Two-body [Φ_ij (r_ij) = A_ij exp (−r_ij/ρ_ij) − C_ij/r_ij⁶, where A, ρ and C are parameters. The values of Y and K represent the shell charges and spring constants.

) were used to describe short-range interactions. Full geometry optimisation was performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [45]. The lattice relaxation around point defects and migrating ions was examined using the Mott–Littleton method [46].

This methodology divides the lattice into two regions (region I and region II). In region I (inner sphere), ions around the defects are relaxed explicitly. Ions present in region II (outer sphere) are relaxed using a quasi-quantum continuum method. In all defect calculations, there are 684 and 4801 atoms present in region I and region II, respectively. Ion migration calculations were carried out considering two nearest neighbour vacancy sites as initial and final configurations. Seven interstitial positions were selected in a direct linear route, and they were allowed to relax in different directions (x, y, z, xy, yz and xz). Activation energies were calculated considering the energy difference between the local maximum energy and the vacancy formation energy. This methodology assumes that ions are fully charged with a dilute limit. Thus, it is expected that defect energies will be overestimated. However, the relative energy trend will be consistent.

3. Results and Discussion

3.1. Crystal Structures of LiVSi₂O₆ and NaVSi₂O₆

Both LiVSi₂O₆ and NaVSi₂O₆ crystallized in a monoclinic structure with a space group of C2/c (see Figure 1). An octahedral coordination was found for Al³⁺ ions. Si⁴⁺ ions formed tetrahedral coordination with four nearest-neighbour O^2– ions. A SiO₄ unit shared its corners with adjacent VO₆ and SiO₄ units, whereas two adjacent VO₆ units share their edges. The experimentally determined lattice parameters of LiVSi₂O₆ at room temperature are reported to be a = 9.657 Å, b = 8.623 Å, c = 5.287 Å, α = γ = 90.0° and β = 110.15° [50]. In an experimental study, Ohashi et al. [51] used an X-ray diffraction technique to find the lattice constants of NaVSi₂O₆ [a = 9.634 Å, b = 8.741 Å, c = 5.296 Å, α = γ = 90.0° and β = 106.91°] at 296 K. The choice of pair-wise potentials used in this study was validated by performing full-geometry optimisation calculations on bulk LiVSi₂O₆ and NaVSi₂O₆ structures. A good agreement between calculated and experimental lattice parameters was obtained (see

Table 2. Calculated and experimental lattice parameters of bulk LiVSi₂O₆ and NaVSi₂O₆.

Parameter	Calculated	Experiment	∆|(%)
LiVSi2O6 [50]
a (Å)	9.543	9.657	1.19
b (Å)	8.608	8.623	0.17
c (Å)	5.399	5.287	2.11
α = γ (°)	90.0	90.0	0.00
β (°)	109.97	110.15	0.16
V (Å3)	416.80	413.31	0.84
NaVSi2O6 [51]
a (Å)	9.634	9.634	0.00
b (Å)	8.594	8.741	1.68
c (Å)	5.249	5.296	0.88
α = γ (°)	90.0	90.0	0.00
β (°)	104.89	106.91	1.89
V (Å3)	420.04	426.72	1.57

).

3.2. Defect Properties

Point defects influence the mechanical, electronic and chemical properties of a material. Formation energies of intrinsic point defects (vacancies and interstitials) were first calculated and combined to calculate Frenkel and Schottky defect energies. Cation inter-mixing defects (anti-site defects) were also calculated, because these can govern the diffusion property. Here, we apply the Kröger–Vink notation [53] to write reaction equations to describe the intrinsic defect processes.

$$\mathrm{A} \mathrm{Frenkel} \left(\mathrm{A}=\mathrm{Li} \mathrm{or} \mathrm{Na}\right):{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}} \to V_{\mathrm{A}}^{\prime }+{ \mathrm{A}}_{\mathrm{i}}^{•}$$

(1)

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

(2)

$$\mathrm{Si} \mathrm{Frenkel}:{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X}} \to V_{\mathrm{Si}}^{••••}+{ \mathrm{Si}}_{\mathrm{i}}^{⁗}$$

(3)

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

(4)

$$\mathrm{Schottky}:{ \mathrm{A}}_{\mathrm{A} }^{\mathrm{X}}+{\mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }+2{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X}}+6{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X}}\to V_{\mathrm{A}}^{\prime }+V_{\mathrm{V}}^{‴}+2 V_{\mathrm{Si}}^{⁗}+6 V_{\mathrm{O}}^{••}+{\mathrm{AVSi}}_2{\mathrm{O}}_6$$

(5)

$${\mathrm{A}}_2\mathrm{O} \mathrm{Schottky}:2{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}}+{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X} }\to 2 V_{\mathrm{A}}^{\prime }+V_{\mathrm{O}}^{••}+{\mathrm{A}}_2\mathrm{O}$$

(6)

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

(7)

$${\mathrm{SiO}}_2 \mathrm{Schottky}:{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X}}+2{ \mathrm{O}}_{\mathrm{O}}^{\mathrm{X} }\to V_{\mathrm{Si}}^{⁗}+2 V_{\mathrm{O}}^{••}+{ \mathrm{SiO}}_2$$

(8)

$$\mathrm{A}/\mathrm{Si} \mathrm{antisite} \left(\mathrm{isolated}\right):{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}}+{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X} }\to {\mathrm{A}}_{\mathrm{Si}}^{‴}+{\mathrm{Si}}_{\mathrm{A}}^{•••}$$

(9)

$$\mathrm{A}/\mathrm{Si} \mathrm{antisite} \left(\mathrm{cluster}\right):{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}}+{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X} }\to \{{\mathrm{A}}_{\mathrm{Si}}^{‴}+{\mathrm{Si}}_{\mathrm{A}}^{•••}{\}}^{\mathrm{X}}$$

(10)

$$\mathrm{A}/\mathrm{V} \mathrm{antisite} \left(\mathrm{isolated}\right):{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}}+{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }\to {\mathrm{A}}_{\mathrm{V}}^{″}+{\mathrm{V}}_{\mathrm{A}}^{••}$$

(11)

$$\mathrm{A}/\mathrm{V} \mathrm{antisite} \left(\mathrm{cluster}\right):{ \mathrm{A}}_{\mathrm{A}}^{\mathrm{X}}+{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X} }\to \{{\mathrm{A}}_{\mathrm{V}}^{″}+{\mathrm{V}}_{\mathrm{A}}^{••}{\}}^{\mathrm{X}}$$

(12)

$$\mathrm{V}/\mathrm{Si} \mathrm{antisite} \left(\mathrm{isolated}\right):{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X}}+{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X} }\to {\mathrm{V}}_{\mathrm{Si}}^{\prime }+{\mathrm{Si}}_{\mathrm{V}}^{•}$$

(13)

$$\mathrm{V}/\mathrm{Si} \mathrm{antisite} \left(\mathrm{cluster}\right):{ \mathrm{V}}_{\mathrm{V}}^{\mathrm{X}}+{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X} }\to \{{\mathrm{V}}_{\mathrm{Si}}^{\prime }+{\mathrm{Si}}_{\mathrm{V}}^{•}{\}}^{\mathrm{X}}$$

(14)

Figure 2 shows the calculated reaction energies for LiVSi₂O₆ and NaVSi₂O₆. The most dominant defect process was the V–Si anti-site defect cluster in both materials. This indicates that there will be a small concentration of V on the Si site and Si on the V site simultaneously. The isolated form of this defect is higher in energy than its cluster form. This is because of the exothermic binding of isolated defects. Previous experimental and theoretical studies have highlighted the presence of anti-site defects in various oxide materials [54,55,56]. The Li–V and Li–Si anti-defect cluster energies are higher than that of the V–Si anti-site defect cluster. This is due to the higher cation charge mismatch (Li–Si or Li–V). The Li (or Na) Frenkel was found to be the second most favourable defect. This process would expect an increase in the concentration of Li or Na vacancies, which enhances the vacancy-assisted Li or Na diffusion. The Li₂O (or Na₂O) Schottky defect is the lowest energy process among other Schottky processes. This defect process will degrade the as-prepared material, affecting the performance of batteries. Other Frenkel defects exhibit higher formation energies than the Li (or Na) Frenkel.

3.3. Diffusion of Li and Na Ions

Here, we calculate the diffusion of Li⁺ and Na⁺ ions. High ionic conductivity is one of the key features of a cathode material, because it determines the performance of batteries. The current methodology has the ability to determine the diffusion pathways together with activation energies. In previous simulations, many oxide materials have been assessed and the results from those simulations have been supportive in interpreting the experimental data [57,58,59].

Four different possible Li local hops (A, B, C and D) were identified in LiVSi₂O₆ (see Figure 3a). Local Li hops together with activation energies are provided in

Table 3. Activation energies for the migration of Li-ions and Na-ions in LiVSi₂O₆ and NaVSi₂O₆, respectively.

LiVSi2O6
Migration Hop	Separation (Å)	Activation Energy (eV)
A	4.62	2.47
B	4.96	6.41
C	5.02	3.31
D	6.23	4.49
NaVSi2O6
P	4.23	3.95
Q	4.89	2.88
R	5.88	11.78
S	6.12	7.97

. Hops A and D formed a long-range Li migration pathway (A→ D→ A→ D) with a zig-zag pattern in the ac plane. Activation energies for these hops were 2.47 eV and 4.49 eV, respectively, meaning that long-range migration requires an overall activation energy of 4.49 eV. A long-range Li migration pathway consisting of local hop B (B→ B→ B→ B) is observed in the bc plane. The overall activation energy for this pathway is 6.41 eV. A potential Li–Li hop (C) with a jump distance of 5.02 Å was also identified. This local hop forms a long-range diffusion pathway (C→ C→ C→ C) in the bc plane with a net activation energy of 3.31 eV. Energy profile diagrams plotted to calculate activation energies for Li-local hops are shown in Figure 4. Although this long-range pathway has the lowest overall migration energy, the diffusion of Li-ions in this material is expected to be very slow.

For Na-ion migration in NaVSi₂O₆, four local hops (P, Q, R and S) were identified. These hops were then allowed to construct long-range migration pathways, as shown in Figure 3b. In general, activation energies were higher than that calculated for Li-ions in LiVSi₂O₆ (see Table 3). This can partly be due to the ionic radius of Na⁺ (1.02 Å) being larger than that of Li⁺ (0.76 Å) [60]. A long-range Na-ion pathway (P→ P→ P→ P) exhibits an activation energy of 3.95 eV. This pathway can be directly compared with the long-range Li-ion pathway in LiVSi₂O₆ (C→ C→ C→ C). In both LiVSi₂O₆ and NaVSi₂O₆, the lowest ion migration pathway is the same. Although hop Q has the lowest activation energy of 2.88 eV, this hop should be combined with hop S to induce long-range diffusion. The overall activation energy for this diffusion pathway is 7.97 eV (see Table 3). The local hop R exhibits a very large activation energy of 11.78 eV. This can partly be due to the presence of V in that particular zig-zag plane. Figure 5 shows energy profile diagrams calculated for each local Na hop in NaVSi₂O₆.

Our calculations show that the ionic conductivity in both LiVSi₂O₆ and NaVSi₂O₆ is low. A possible way of increasing ion diffusion can be achieved by preparing these materials at nano scales. Appropriate doping strategies (see Section 3.4) can also be introduced to increase the concentration of ions (Li⁺ or Na⁺) in the form of interstitial defects.

3.4. Solution of Dopants

Dopants can play a significant role in governing the performance of materials. Here, we consider monovalent (M = Li⁺, Na⁺, K⁺ and Rb⁺), trivalent (M = Al³⁺, Ga³⁺, Sc³⁺, In³⁺, Y³⁺, Gd³⁺ and La³⁺) and tetravalent dopants (M = Ge⁴⁺, Ti⁴⁺, Sn⁴⁺, Zr⁴⁺ and Ce⁴⁺) on the Li (or Na), V (or Si) and Si sites, respectively. The lowest solution energy dopant is predicted for future experimental verification. Necessary charge-compensating defects and energies of lattices were included in the reaction equations. Buckingham potentials used for dopants are given in the electronic supplementary materials (see Table S1).

3.4.1. Monovalent Dopants

Monovalent dopants were considered on the Li site in LiVSi₂O₆ and the Na site in NaVSi₂O₆. The defect reaction process used for LiVSi₂O₆ is given by the following equation:

$${\mathrm{M}}_2\mathrm{O} +2{ \mathrm{Li}}_{\mathrm{Li}}^{\mathrm{X}}\to 2{\mathrm{M}}_{\mathrm{Li}}^{\mathrm{X}}+{ \mathrm{Li}}_2\mathrm{O}$$

(15)

An exoergic solution energy of –0.35 eV was determined for Na⁺ in LiVSi₂O₆ (see Figure 6a). This is partly due to the ionic radius of Li⁺ (0.76 Å) matching with the ionic radius of Na⁺ (1.02 Å) [60]. It is possible to synthesise Li_1−xVSi₂O₆ (0.0 < x < 1.0). However, the exact concentration should be verified experimentally. The solution energy increases with the increasing ionic radius. The largest solution energy is calculated for the Rb⁺. In the case of NaVSi₂O₆, the most favourable dopant is Li⁺. The solution energy for this dopant is 0.83 eV. Although this dopant is not thermodynamically feasible, the doping process can be performed at high temperatures. Solution energies for K⁺ and Rb⁺ are higher than that calculated for Li⁺ due to their larger ionic radii than that of Li⁺.

3.4.2. Trivalent Dopants

A range of trivalent dopants were substituted on the vanadium site. Vanadium has a charge of +3 in this material; therefore, charge-compensating defects were not necessary. The following reaction equation explains the doping process:

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

(16)

Solution energies are shown in Figure 7. In both LiVSi₂O₆ and NaVSi₂O₆, the most favourable dopant is Ga. The preference of Ga in both materials is due to the close ionic radius match between V³⁺ (0.64 Å) and Ga³⁺ (0.62 Å) [60]. Al exhibits positive solution energies in both materials, although its ionic radius (0.54 Å) is smaller than that of V³⁺. The solution energy increases with the increasing ionic radius from Sc to La. A similar trend in the solution energies is noted for both materials, although the solution energies are slightly lower in LiVSi₂O₆ than in NaVSi₂O₆. The most unfavourable dopant is La³⁺.

In order to create Li interstitials in LiVSi₂O₆ or Na interstitials in NaVSi₂O₆, the Si site was substituted by trivalent dopants, as described by defect Equation (17). The incorporation of a trivalent cation onto a tetravalent cation lattice site results in two potential compensating defects (Li+ interstitial ion and a host lattice oxygen vacancy) and a second phase material (SiO₂), in contrast to the experiment.

$${\mathrm{M}}_2{\mathrm{O}}_3+2{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X}}+{\mathrm{Li}}_2\mathrm{O}\to 2{ \mathrm{M}}_{\mathrm{Si}}^{\prime }+2{ \mathrm{Li}}_{\mathrm{i}}^{•}+2{ \mathrm{SiO}}_2$$

(17)

This efficient strategy can improve the capacity of the batteries. Al³⁺ is a promising dopant for this strategy. In a previous simulation study on Li₂MnSiO₄ cathode material, Al³⁺ was identified as a candidate dopant for generating Li interstitials [30]. In general, there is a gradual increase in the solution energy with increasing ionic radii in both materials (see Figure 8). Slightly favourable solution energies were calculated for NaVSi₂O₆, although the solution process is endoergic. The promising dopant Al³⁺ can be tested and validated experimentally. The lowest solution energy calculated for Al³⁺ can partly be due to the small difference between the ionic radii of Al³⁺ (0.39 Å) and Si⁴⁺ (0.26 Å) [60]. Endoergic solution energies are due to the quadruply charged Si being occupied by triply charged dopants.

As mentioned earlier, trivalent doping on the Si site can also generate oxygen vacancies as charge-compensating defects, as defined by the following equation:

$${\mathrm{M}}_2{\mathrm{O}}_3+2{ \mathrm{Si}}_{\mathrm{Si}}^{\mathrm{X}}+{\mathrm{Li}}_2\mathrm{O}\to 2{ \mathrm{M}}_{\mathrm{Si}}^{\prime }+{\mathrm{V}}_{\mathrm{O}}^{••}+2{ \mathrm{SiO}}_2$$

(18)

The oxygen vacancies can promote vacancy-assisted Li or Na migration via Li₂O or Na₂O formation. Al³⁺ is a suitable dopant for this as well (see Figure 9). The trend in the solution energies is almost the same as that observed for the formation interstitials (see Figure 8). The solution energies are higher by ~1.50 eV for each dopant than that calculated for interstitials, meaning that high temperature should be applied for the oxygen vacancy formation process.

3.4.3. Tetravalent Dopants

Finally, tetravalent cations were doped on the Si site. This doping process produces no charge-compensating defects, as explained by Equation (19):

$${\mathrm{MO}}_2+{ \mathrm{Si}}_{\mathrm{Si} }^{\mathrm{X}}\to {\mathrm{M}}_{\mathrm{Si} }^{\mathrm{X}}+{\mathrm{SiO}}_2$$

(19)

The results show that the most favourable dopant for this process is Ge⁴⁺ (see Figure 10). The favourability of this dopant is due to the smaller ionic radius of Ge⁴⁺ (0.39 Å), closer to that of Si⁴⁺ (0.26 Å). There is a big jump in the solution energy for Ti⁴⁺. Solution energy then increases with the increasing ionic radius. Both LiVSi₂O₆ and NaVSi₂O₆ exhibit almost similar solution energies. The possible composition that can be prepared by experiments is LiVSi_2-xGe_xO₆ or NaVSi_2−xGe_xO₆ (x = 0.0 < x < 1.0). The largest solution energy is calculated for Ce⁴⁺, suggesting that this dopant requires high temperatures. The migration of Li-ions was calculated in the presence of Ge⁴⁺ dopant. The doping was reflected in the activation energies of local hops. In all cases, there were small reductions in the activation energies (LiVSi₂O₆: A-4.53 eV, B-4.88 eV, C-5.10 eV and D-4.40 eV; NaVSi₂O₆: P-3.89 eV, Q-2.80 eV, R-11.67 eV and S-7.90 eV). In all cases, long-range diffusion pathways were unaffected.

4. Conclusions

In conclusion, we used atomistic simulation based on the classical pair potentials to examine the defects, diffusion and dopant properties of LiVSi₂O₆ and NaVSi₂O₆. The dominant defect in both materials is the V–Si anti-site defect, suggesting that a small amount of cation inter-mixing will be present. The Li or Na ionic conductivity is slow in both materials, indicating that the as-prepared materials should be modified to increase the rate of Li-ion (or Na-ion) diffusion. The doping of Al on the Si site is an efficient strategy to increase the concentration of Li and Na in LiVSi₂O₆ and NaVSi₂O₆, respectively. Such doping can also create oxygen vacancies in both materials. The candidate isovalent dopants on the V and Si sites are Ga and Ge, respectively.