Superionic Solid Electrolyte Li₇La₃Zr₂O₁₂ Synthesis and Thermodynamics for Application in All-Solid-State Lithium-Ion Batteries

Abstract

Solid-state reaction was used for Li₇La₃Zr₂O₁₂ material synthesis from Li₂CO₃, La₂O₃ and ZrO₂ powders. Phase investigation of Li₇La₃Zr₂O₁₂ was carried out by x-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDS) methods. The thermodynamic characteristics were investigated by calorimetry measurements. The molar heat capacity (C_p,m), the standard enthalpy of formation from binary compounds (Δ_oxH_LLZO) and from elements (Δ_fH_LLZO), entropy (S⁰₂₉₈), the Gibbs free energy of the Li₇La₃Zr₂O₁₂ formation (∆_f G⁰₂₉₈) and the Gibbs free energy of the LLZO reaction with metallic Li (∆_rG_LLZO/Li) were determined. The corresponding values are C_p,m = 518.135 + 0.599 × T − 8.339 × T⁻², (temperature range is 298–800 K), Δ_oxH_LLZO = −186.4 kJ·mol⁻¹, Δ_fH_LLZO = −9327.65 ± 7.9 kJ·mol⁻¹, S⁰₂₉₈ = 362.3 J·mol⁻¹·K⁻¹, ∆_f G⁰₂₉₈ = −9435.6 kJ·mol⁻¹, and ∆_rG_LLZO/Li = 8.2 kJ·mol⁻¹, respectively. Thermodynamic performance shows the possibility of Li₇La₃Zr₂O₁₂ usage in lithium-ion batteries.

1. Introduction

The commercial history of the lithium-ion battery was started in 1991 by Sony [1]. Since then, a lot of effort has been directed to improving the electrochemical performance of lithium-ion batteries [2]. One of the perspective methods of stabilizing lithium-ion battery electrochemical characteristics and safety is to apply solid-state inorganic electrolyte instead of liquid organic electrolyte as the traditional electrolyte for commercial lithium-ion batteries [3,4,5,6,7]. Some solid-state electrolytes have high ionic conductivity in an order of magnitude of ~10⁻³ S·cm⁻¹ [8] in comparison to liquid electrolyte [9].

Between all types of the solid-state electrolytes (perovskite, NASICON- and LISICON-type, LATP- and LAGP-type, garnet, sulfide and halide electrolytes, etc. [8]) garnet-type electrolytes have the most attractive electrochemical performance in combination with manufacturing costs and simplicity in commercial application. Garnet-type Li₇La₃Zr₂O₁₂ (LLZO) solid-state electrolyte has two modifications: cubic and tetragonal. The ionic conductivities are ~10⁻⁴–10⁻³ S·cm⁻¹ and ~10⁻⁷–10⁻⁶ S·cm⁻¹, respectively [10].

LLZO solid-state electrolyte attracts high attention due to its relatively high electrochemical properties. Though LLZO has lower ionic conductivity in comparison with organic liquid electrolyte (~10⁻⁴ versus ~10⁻² S·cm⁻¹, respectively [9]), it provides high safety performance, high chemical stability against metallic lithium, a wide electrochemical potential window, low electronic conductivity, and high stability with moisture in the air; LLZO prevents lithium dendrite growth due to high mechanical strength [11,12,13,14,15].

Since as LLZO was first synthesized by Murugan et al. [16], it was investigated to improve its chemical and structural stability, long life cycle, electrode/solid electrolyte interface interactions, and high energy density at room temperature. Thus, heterovalent substitution/doping with Al³⁺ from alumina crucible (or intentional incorporation) during the synthesis process allows for the enhancement of ionic conductivity up to ~10⁻³ S·cm⁻¹, but it causes higher activation energy in lithium ion conduction, which limits Li⁺ mobility [17,18,19,20,21,22,23,24]. Doped with Ga³⁺ also as Al³⁺ stabilize structure of LLZO [25,26,27,28,29,30,31,32]. The substitution of Zr⁴⁺ with Ta⁵⁺ ions allowed for an increase of the ionic conductivity, stabilization of the cubic structure, improved lithium-ion transport, lithium dendrite growth prevention, and the current density [33,34,35,36,37,38]. Ultimately, the above-mentioned elements improve electrochemical and structural stability, increase the ionic conductivity, and prevent lithium dendrite growth and penetration at the solid electrolyte structure.

In this work, synthesis, structure studies and thermodynamics calculations of tetragonal Li₇La₃Zr₂O₁₂ were performed.

2. Materials and Methods

Tetragonal LLZO electrolyte was produced by solid-state synthesis as one of the commonly used synthesis methods for investigation and mass manufacture [39,40,41,42,43,44,45,46,47]. Initial materials Li₂CO₃ (Xilong Sci., 99%), La₂O₃ (ReLAB, 99.99%), and ZrO₂ (Sinopharm, 99.9%) in stoichiometric ratio were used as sources for Li, La, and Zr, respectively. Excess of 10 wt.% of lithium was initially added to precursor to avoid lithium loss during the synthesis process at high temperatures. Lanthanum oxide was preliminarily dried at 900 °C for 24 h. The mentioned materials were mechanically milled in an agate mortar and then dissolved in acetic acid with subsequent magnetic stirring at 90 °C for 12 h to provide a homogeneous solution. Excess acetic acid was evaporated at 110 °C to get dry precursor powder. Dried precursor was then mechanically milled in an agate mortar and put into an alumina crucible for heat treatment. A muffle furnace (Nabertherm, Lilienthal, Germany) was used for solid-state reaction at air atmosphere. First, the precursor was slowly heated (heat rate was 0.5 °C/min) to 130 °C for 3 h to evaporate the remaining acetic acid. Then, the precursor was heated (heat rate was 2 °C/min) to 900 °C for 8 h to provide solid-state reaction.

The solid-state reaction proceeds according to next formula:

4ZrO₂ + 3La₂O₃ + 7Li₂CO₃ = 2Li₇La₃Zr₂O₁₂ + 7CO₂

(1)

X-ray diffraction structural analysis (XRD) was performed by Bruker D8 Advance (Bruker, Karlsruhe, Germany) equipment (diffraction angle step was 0.02°, Cu K_α-radiation). The Rietveld method was used for structure refinement. Diffraction angles for synthesized LLZO powder were set from 15° to 60° (2Ѳ).

Images of the microstructure performance of LLZO powder were taken with a scanning electron microscope (SEM) Tescan MAIA3 (Tescan, Brno, Czech Republic) with secondary electron detection. Bruker XFlash 6–10 (Bruker, Karlsruhe, Germany) was used for energy-dispersive X-ray spectroscopy (EDS).

TAM IV Microcalorimeter (TA Instruments, Shanghai, China) was used for calorimetric investigation. Measurement parameters were as follows: temperature is 298 K, volume of the cell is 20 mL. An aqueous solution of 1 mol·dm⁻³ HCl was filled in the ampoule at calorimetric cell. The dissolution process of the LLZO powder was started after thermal equilibrium was established. Dissolution enthalpy value was obtained from thermoelectromotive force data during the dissolution process, providing the heat dissolution curve.

3. Results

The XRD pattern of synthesized LLZO is shown at Figure 1. According to diffraction data, LLZO has a I4₁/acd space group. The vertical lines at the bottom are related to PDF #00-064-0140. The peak indexes and interplanar distances are shown in the Supplementary Materials (Table S1). Synthesized material contains 4 wt.% of La₂O₃ impurity after solid-state reaction.

SEM images of LLZO powder are shown in Figure 2, made at 2×, 3.5×, 10× and 11.5× magnification, respectively. All images were performed at 10 keV landing energy.

EDS spectra images are shown at Figure 3. The scale bar is 80 μm long for all images at Figure 3a–d. The green frame in Figure 3a shows the EDS analyzing field. Figure 3b–d show the element distributions for the La, Zr, O and C at Figure 3b; La at Figure 3c; and Zr at Figure 3d elements, respectively. The elements in Figure 3 are evenly distributed. The carbon in Figure 3b is electrically conductive carbon tape for sample holder. Elemental analysis of EDS spectra is shown at

Table 1. Elemental EDS analysis of Li₇La₃Zr₂O₁₂ powder.

Element	Mass, wt.%
Lanthanum	53.19
Oxygen	22.59
Zirconium	24.22

.

EDS elemental analysis of the LLZO powder shows lanthanum excess in the solid electrolyte powder, expressed in terms of Li₇La₃Zr₂O₁₂ and La₂O₃ compounds. Elemental analysis based on Table 1 shows an excess of 3.1 wt.% of lanthanum oxide (III).

4. Discussion

4.1. The Standard Formation Enthalpy

The formation enthalpy of Li₇La₃Zr₂O₁₂ (Δ_oxH_LLZO) from Li₂CO₃, La₂O_3, and ZrO₂ is calculated according to Equation (1) from the Experimental Section. The subscript ox means “oxides”, which relates to the initial compounds from Equation (1).

The following thermodynamic cycle was used for enthalpy calculation, Figure 4:

Li₇La₃Zr₂O₁₂ + 24HCl_(aq) → 7LiCl_(aq) + 3LaCl_3(aq) + 2ZrCl_4(aq) + 12H₂↑+ 6O₂↑,

(2)

Li₂CO₃+ 2HCl_(aq) → 2LiCl + CO₂ + H₂O,

(3)

La₂O₃ + 6HCl_(aq) → 2LaCl₃ + 3H₂O,

(4)

ZrO₂ + 4HCl_(aq) → ZrCl₄ +2H₂O,

(5)

the subscript (aq) indicates “aqueous”. The calorimeter was used for the standard enthalpy (Δ_dH_LLZO) measurement. The received value after calorimetry measurement was equal to −1911 ± 37 J·g⁻¹,

Table 2. The dissolution enthalpies values of the initial components and the Li₇La₃Zr₂O₁₂ compound (p = 101 kPa, T = 298 K, 1 mol·dm⁻³ HCl_(aq)).

Compound	Molar Mass, g·mol−1	Specific Enthalpy, J·g−1	Molar Enthalpy of Dissolution, kJ·mol−1	Ref.
ZrO2	123.222	−2186 ± 19	−269.4 ± 2.34	this work
La2O3	325.837	−1927 ± 13	−627.9 ± 4.23	this work
Li2CO3	73.89	−683 ± 9	−50.5 ± 0.67	this work
Li7La3Zr2O12 (with La2O3 impurity)	-	−1758 ± 34	-	this work
Li7La3Zr2O12	839.741	−1752.6 ± 35	−1471.73 ± 29.39	this work (recalculated)

.

It was shown in the Experimental Section that LLZO has 3.1 wt.% of unreacted La₂O₃ impurity. Thereby, measured Δ_dH_LLZO should be recalculated considering the amount of La₂O₃:

$${\Delta }_d{H}_{LLZO}=\frac{{\Delta }_d{H}_{LLZO+L{a}_2{O}_3}-\omega {\Delta }_d{H}_{L{a}_2{O}_3}}{1-\omega },$$

(6)

where ω is the mass fraction of La₂O₃. It should be noted that enthalpies, mentioned in Equation (6), are supposed to be specific, not molar. The recalculated value of the dissolution enthalpy of LLZO (with 3.1 wt.% of La₂O₃) is equal to −1917.7 J·g⁻¹ or −1607.75 kJ·mol⁻¹, Table 2.

The formation enthalpy value of Δ_oxH_LLZO is estimated by the next formula:

$${\Delta }_{ox}{H}_{LLZO}=2{\Delta }_d{H}_{Zr{O}_2}+1.5{\Delta }_d{H}_{L{a}_2{O}_3}+3.5{\Delta }_d{H}_{L{i}_{2}C{O}_3}-{\Delta }_d{H}_{LLZO}$$

(7)

The calorimetry-measured values of Δ_dH_ZrO2, Δ_d$H_{L{a}_2{O}_3}$, and Δ_d$H_{L{i}_{2}C{O}_3}$ are shown in Table 2. The recalculated value of the enthalpy of dissolution of Li₇La₃Zr₂O₁₂ was used for Δ_oxH_LLZO evaluation. The value of Δ_oxH_LLZO given by Equation (7) is equal to −186.4 kJ mol⁻¹. The negative value of the enthalpy of Li₇La₃Zr₂O₁₂ formation indicates that Li₇La₃Zr₂O₁₂ is a stable phase; the chemical reaction of Li₂CO₃, La₂O₃, and ZrO₂ is energetically favorable for Li₇La₃Zr₂O₁₂ synthesis. The values for various lithium zirconates were added to Table 2 to compare with the measured and calculated values in this work. The value of the formation enthalpy from binary oxides Δ_oxH_LLZO has the same order as corresponding values for lithium zirconate compounds and complex oxides (

Table 3. Standard enthalpies of formation of complex oxides from binary oxides (Δ_oxH⁰).

Compound	ΔoxH°298.15, kJ·mol−1	Reference
Li7La3Zr2O12 (s)	−186.4 ± 7.3	this work
Li2ZrO3 (s)	−304.1 ± 1.4	[48]
Li6Zr2O7 (s)	−112.86	[49]
La2Zr2O7 (s)	−135.6	[50]
Li2TiO3 (s)	−238.5 ± 1.5	[48]
LiAlO2 (s)	−209.0 ± 3.2	[4]
LiCoO2 (s)	−143.99 ± 1.38	[51]
BaZrO3 (s)	−114.6	[52]

The subscripts (s) mean “solid”.

), thus it can be concluded that the measurements are correct.

Finally, the enthalpy of Li₇La₃Zr₂O₁₂ formation from elements can be calculated by the following formula:

$${\Delta }_f{H}_{LLZO}=3.5{\Delta }_f{H}_{L{i}_{2}C{O}_3}+1.5{\Delta }_f{H}_{L{a}_2{O}_3}+2{\Delta }_f{H}_{Zr{O}_2}+{\Delta }_{ox}{H}_{LLZO}$$

(8)

The corresponding handbook’s materials were used to define the standard enthalpies [53],

Table 4. Standard enthalpies of formation from elements (Δ_fH⁰).

Material	ΔfH°298.15, kJ·mol−1	Ref.
Li2CO3 (s)	−1214.1 ± 1.0	[53]
La2O3 (s)	−1794.2 ± 2.0	[53]
ZrO2 (s)	−1100.3 ± 0.7	[53]
Li7La3Zr2O12 (s)	−9327.65 ± 7.9	this work

The subscripts (s) mean “solid”.

.

The formation enthalpy value of the Li₇La₃Zr₂O₁₂ compound, calculated by formula (8) is −9327.65 ± 7.9 kJ·mol⁻¹, Table 4. The enthalpy of formation value, rated by Equation (8), can be recommended for use in further thermodynamic calculations of Li₇La₃Zr₂O₁₂ reactivity.

4.2. The Isobaric Heat Capacity

Figure 5 shows the isobaric heat capacity of the Li₇La₃Zr₂O₁₂ as a function of temperature (C_p = f(T)). Pay attention to the certain amount of La₂O₃ (Figure 1 and Table 1) in LLZO synthesized powder material, the measured isobaric heat capacity for the two-phase system must be recalculated by the following additive rule:

$$m{C}_p=m\left(LLZO\right)C_p\left(LLZO\right)+m\left(L{a}_2{O}_3\right)C_p\left(L{a}_2{O}_3\right),$$

(9)

where C_p is a specific heat capacity (p = const), and m is mass. In our case, the two-phase system consists of the solid electrolyte compound (LLZO) and La₂O₃. Thus, the heat capacity of Li₇La₃Zr₂O₁₂ is expressed from Equation (9) as:

$$C_p\left(LLZO\right)=\frac{m{C}_p-m\left(L{a}_2{O}_3\right)C_p\left(L{a}_2{O}_3\right)}{m\left(LLZO\right)}$$

(10)

The impurity compound weight can be recalculated from the total weight of the sample, with the known mass fraction of lanthanum oxide, $\omega \left(L{a}_2{O}_3\right)$:

$$m\left(L{a}_2{O}_3\right)=m\omega \left(L{a}_2{O}_3\right)$$

(11)

and

$$m\left(LLZO\right)=m\left[1-\omega \left(L{a}_2{O}_3\right)\right]$$

(12)

Considering Equations (11) and (12), Equation (13) can be expressed as follows:

$$C_p\left(LLZO\right)=\frac{C_p-C_p\left(L{a}_2{O}_3\right)\omega \left(L{a}_2{O}_3\right)}{1-\omega \left(L{a}_2{O}_3\right)}$$

(13)

Equation (13) shows, that the Li₇La₃Zr₂O₁₂ heat capacity $C_p\left(LLZO\right)$ can be evaluated by the measured heat capacity (C_p), tabulated heat capacity of La₂O₃ $C_p\left(L{a}_2{O}_3\right),$ and La₂O₃ mass fraction $\omega \left(L{a}_2{O}_3\right)$. The dependence of La₂O₃ specific heat capacity from temperature is required for Equation (13) calculation. For this, tabular data is required to define temperature dependence for the lanthanum oxide heat capacity [53]. The heat capacity polynomial, commonly used for the low temperature range (for 300–800 K in our case) can be expressed as follows:

C_p = a + bT − cT⁻²

(14)

where a, b, and c are empirical coefficients, and T is the absolute temperature. The La₂O₃ received coefficients are a = 119.604 J·mol⁻¹·K⁻¹, b = 14.514 × 10⁻³ J·mol⁻¹·K⁻², and c = 13.452 × 10⁵ J·mol⁻¹·K. Considering the La₂O₃ impurity presence, the LLZO heat capacity can be recalculated via Equations (13) and (14) for the 300–800 K temperature interval. According to XRD and EDS data (Figure 1 and Table 1, respectively) LLZO contains about 3.1 ± 0.12 wt.% La₂O₃. Figure 5 and Table 5 shows measured and recalculated LLZO heat capacity temperature dependence. The Neumann-Kopp (N-K) rule was used for the empirical value calculation of the heat capacity. The N-K rule approves “that the molecular heat capacity of a solid compound is the sum of the atomic heat capacities of the elements composing it; the elements having atomic heat capacities lower than those required by the Dulong–Petit law retain these lower values in their compounds.” [54]. This rule commonly gives reproducible results for room temperatures, not for high temperatures. To achieve more accurate results, binary materials were used instead of single elements (accurate results are usually obtained for the same aggregate state of materials):

$$C_p\left(CO\right)={{\displaystyle \sum }}^{\text{}}n\left(BO\right)C_p\left(BO\right)$$

(15)

C_p is a molar heat capacity (p = const), n is a stoichiometric coefficient, and CO and BO are complex and binary oxide, respectively. Equation (15), considering Equation (1), can be expressed for LLZO as follows:

$$C_p\left(LLZO\right)=3.5C_p\left(L{i}_{2}C{O}_3\right)+1.5C_p\left(L{a}_2{O}_3\right)+2C_p\left(Zr{O}_2\right)$$

(16)

The calculated from tabular data [53] heat capacity from Equation (16) is shown on Figure 5 and Table 5.

Table 5. The Li₇La₃Zr₂O₁₂ (s) heat capacities of experimental C_p(exp.), recalculated by Equation (15) C_p(rec.) and calculated by the (N-K) rule C_p(N-K) values as a function of temperature.

T, K	Cp(exp.), J·K−1·mol−1	Cp(rec.), J·K−1·mol−1	Cp(N-K), J·K−1·mol−1
300	-	-	621.1
400	778.6	709.7	708.1
500	851.8	784.7	778.8
600	936.7	857.4	843.1
700	1002.8	925.0	904.3
800	1035.4	971.1	964.0

Table 5. The Li₇La₃Zr₂O₁₂ (s) heat capacities of experimental C_p(exp.), recalculated by Equation (15) C_p(rec.) and calculated by the (N-K) rule C_p(N-K) values as a function of temperature.

T, K	Cp(exp.), J·K−1·mol−1	Cp(rec.), J·K−1·mol−1	Cp(N-K), J·K−1·mol−1
300	-	-	621.1
400	778.6	709.7	708.1
500	851.8	784.7	778.8
600	936.7	857.4	843.1
700	1002.8	925.0	904.3
800	1035.4	971.1	964.0

The Neumann-Kopp rule and recalculated heat capacity of Li₇La₃Zr₂O₁₂ are in good correlation. Experimental data is for the LLZO compound with La₂O₃ impurity. The heat capacity temperature dependence (Equation (16)) was calculated using tabular data [53,55]. XRD and EDS quantitative analysis gives accurate enough results to define a small quantity of impurity compounds in the material.

4.3. Entropy

The Third Law of Thermodynamics states, “The entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (0 K).” Thus, the entropy absolute value can be valued by the equation:

$$S\left(T\right)=\underset{0}{\overset{T_1}{{\displaystyle \int }}}\frac{C_p\left(T\right)}{T}dT+\frac{\Delta H_1}{T_1}+\underset{T_1}{\overset{T_2}{{\displaystyle \int }}}\frac{C_p\left(T\right)}{T}dT+\frac{\Delta H_2}{T_2}+\dots +\underset{T_k}{\overset{T}{{\displaystyle \int }}}\frac{C_p\left(T\right)}{T}dT,$$

(17)

where S is entropy, T_k is temperature of the k-th phase transition (0 < T_k < T), and ΔH_k is enthalpy of the k-th phase transition. The Neumann-Kopp rule for entropy calculation can be expressed as follows (considering absence of phase transition at calculating temperature range):

$$S\left(T\right)=\underset{0}{\overset{T}{{\displaystyle \int }}}\frac{{{\displaystyle \sum }}^{\text{}}{C}_p\left(T, BO\right)}{T}dT={{\displaystyle \sum }}^{\text{}}\underset{0}{\overset{T}{{\displaystyle \int }}}\frac{C_p\left(T, BO\right)}{T}dT={{\displaystyle \sum }}^{\text{}}S\left(T,BO\right),$$

(18)

where BO is the binary oxide compound (see Equation (15)). Equation (18) can be rewritten taking into account Equations (15) and (16):

S (LLZO) = 3.5S(Li₂CO₃) + 1.5S(La₂O₃) + 2S(ZrO₂)

(19)

The Li₇La₃Zr₂O₁₂ entropy is equal to 607.18 J·mol⁻¹·K⁻¹ (T = 298 K) by calculating Equation (19) using tabulated data [53,55]. The additive rule for entropy calculation can be used if the following term is met: the complex compound molar volume slightly differs of the molar volumes sum of binary compounds [55]. Thus, the molar volume for Li₂CO₃ is 35.0 cm³·mol⁻¹ (density is ρ = 2.11 g·cm⁻³ [56]), for La₂O₃ is 50.1 cm³·mol⁻¹ (density is ρ = 6.51 g·cm⁻³ [57]), for ZrO₂ is 21.2 cm³·mol⁻¹ (density is ρ = 5.56 g·cm⁻³ [57]), and for Li₇La₃Zr₂O₁₂ is 165.0 cm³·mol⁻¹ (density is ρ = 5.09 g·cm⁻³ [58]). The sum of the molar volumes of Li₂CO₃, La₂O_3, and ZrO₂ with their corresponding stoichiometric coefficients is 240.05 cm³·mol⁻¹ and differs about 45.5% of the LLZO molar volume, which does not allow one to apply the additive rule.

Excepting the additive calculation rule, the W. Herz rule can be used for the LLZO entropy calculation [59]:

$$S_{298}^0=K_H{\left(M/C_{p,298}\right)}^{1/3}m,$$

(20)

where K_H is the Herz constant, M is molar mass, C_p,298 is isobaric heat capacity, and m is atoms per formula.

The Herz constant K_H has a good correlation with average values of anion molar mass [60]:

$$K_H=\frac{33.5x^2{e}^x}{{\left(e^x-1\right)}^2},$$

(21)

where x = 42.4/$M_{L{a}_{3}Z{r}_2{O}_{12}}$, and M_A is an anion (La₃Zr₂O₁₂⁷⁻) molar mass. For Li₇La₃Zr₂O₁₂, anion molar mass $M_{L{a}_{3}Z{r}_2{O}_{12}}$ is 791.154 g·mol⁻¹. Thus, K_H constant is equal to 33.5.

Considering C_p,298 from Table 5 and Equation (21), calculated by Equation (20) the LLZO entropy is equal to 362.3 J mol⁻¹·K⁻¹. The calculated value of LLZO entropy by the W. Herz rule is in good correlation with Ref. [60]. Hence, the N-K rule cannot be used for the entropy calculations, as follows from molar masses principle.

4.4. The Standard Gibbs Free Energy

Calculated formation enthalpy and entropy allows one to rate the standard Gibbs free energy (${\Delta }_f{G}_{298}^0$) of LLZO formation (T = 298 K):

$${\Delta }_f{G}_{298}^0={\Delta }_f{H}_{298}^0-298{\Delta }_f{S}_{298}^0,$$

(22)

For Equation (22), the ${\Delta }_f{G}_{298}^0$ value of LLZO is equal to −9435.6 kJ·mol⁻¹.

The stability against metallic lithium can be estimated by the Gibbs free energy calculation of the following reaction at room temperature:

$$3Li+L{i}_{7}L{a}_{3}Z{r}_2{O}_{12}=7.5L{i}_{2}O+1.5L{a}_2{O}_3+2Zr$$

(23)

The Gibbs free energy of reaction (∆_rG_LLZO/Li) can be expressed as the difference between the and the Gibbs energy values of reactants and resultants of the reaction. The ${\Delta }_f{G}_{298}^0$ for single elements is equal to zero, for Li₂O is −561.2 kJ·mol⁻¹, and for La₂O₃ is −1706.7 kJ·mol⁻¹ [53]. The Li₇La₃Zr₂O₁₂ Gibbs free energy has been calculated above. Thus, the Gibbs free energy for reaction (23) is ∆_rG_LLZO/Li = 8.2 kJ·mol⁻¹; this means that the reaction is thermodynamically impossible. Finally, Li₇La₃Zr₂O₁₂ is stable against metallic lithium at room temperature.

5. Conclusions

The thermodynamic characteristics were determined for Li₇La₃Zr₂O₁₂ solid-state electrolyte material for lithium-ion battery. Solid-state reaction was used as the synthesis method of Li₇La₃Zr₂O₁₂ from Li₂CO₃, La₂O_3, and ZrO₂. The synthesized material had 3.1 wt.% of the lanthanum oxide (La₂O₃) impurity according to XRD and EDS data. Probably, this amount of La₂O₃ is unreacted oxide from the synthesis process. The enthalpy of Li₇La₃Zr₂O₁₂ formation from binary oxides (and from Li₂CO₃) Δ_oxH_LLZO and from the elements Δ_fH_LLZO were calculated according to the measured enthalpy of dissolution of reagents and the products of the Li₇La₃Zr₂O₁₂ formation reaction. The obtained values are equal to −186.4 ± 7.3 kJ·mol⁻¹ and −9327.65 ± 7.9, respectively. The formation enthalpy from binary oxides Δ_oxH_LLZO is in good correlation with similar zirconate compounds, which confirms the correctness of the measurements.

The recalculated LLZO heat capacity considering La₂O₃ presence is in good correlation with that calculated by the Neumann-Kopp rule. Finally, the temperature dependence of the LLZO heat capacity can be expressed by the formula C_p(T) = 518.135 + 0.599 × T − 8.339 × T⁻² (T is absolute temperature). The LLZO entropy is S⁰₂₉₈ = 362.3 J·mol⁻¹·K⁻¹, the Gibbs free energy of formation of Li₇La₃Zr₂O₁₂ is −9435.6 kJ mol⁻¹. Li₇La₃Zr₂O₁₂ material is stable against metallic lithium, according to the Gibbs free energy of the LLZO reaction with metallic Li. All thermodynamic values and functions measured and calculated for Li₇La₃Zr₂O₁₂ can be used for modelling and further calculations of all-solid-state batteries.