Synthesis Method and Thermodynamic Characteristics of Anode Material Li3FeN2 for Application in Lithium-Ion Batteries

Li3FeN2 material was synthesized by the two-step solid-state method from Li3N (adiabatic camera) and FeN2 (tube furnace) powders. Phase investigation of Li3N, FeN2, and Li3FeN2 was carried out. The discharge capacity of Li3FeN2 is 343 mAh g−1, which is about 44.7% of the theoretic capacity. The ternary nitride Li3FeN2 molar heat capacity is calculated using the formula Cp,m = 77.831 + 0.130 × T − 6289 × T−2, (T is absolute temperature, temperature range is 298–900 K, pressure is constant). The thermodynamic characteristics of Li3FeN2 have the following values: entropy S0298 = 116.2 J mol−1 K−1, molar enthalpy of dissolution ΔdHLFN = −206.537 ± 2.8 kJ mol−1, the standard enthalpy of formation ΔfH0 = −291.331 ± 5.7 kJ mol−1, entropy S0298 = 113.2 J mol−1 K−1 (Neumann–Kopp rule) and 116.2 J mol−1 K−1 (W. Herz rule), the standard Gibbs free energy of formation ΔfG0298 = −276.7 kJ mol−1.


Introduction
In the world of technological development, energy sources are being severely depleted. In this regard, the issues related to creating new energy sources, in particular renewable energy sources, are being considered.
Secondary batteries, such as lithium-ion, lithium sulfur, and hydrogen batteries, are attracting increased attention for their development and production. Probably, one of the prospective renewable sources of energy is the lithium-ion battery (LIB) as an energy source for many applications, such as electric cars and buses, laptops, mobile phones, etc. LIBs solve the problems of high energy requirements (energy and power density, cycle life), environmental efforts, and relatively low cost.
Thus, a lot of efforts were focused on the fabrication of anode materials with high theoretical specific capacity. For example, silicon has attracted the attention of the LIBs industry as an anode material with ultrahigh specific capacity (4212 mAhg −1 ), although the large volume expansion of silicon during the charge/discharge process (300%) leads to a capacity decrease and reduced cycle life [57]. Iron nanopowder and nitrogen were used as a source for Fe2N. Ceramic crucible with initial powder was put into the tube furnace (BTF−1700C, (Hefei, China). The tube has been purged by ammonia (NH3) for 30 min before synthesis. Synthesis was carried out in NH3 atmosphere at 530 °C for 6 h with a heat rate of 8 °C/min. Mechanically mixed and powder was hot pressed for 2 h at 1100 °C. The received hot-pressed sample was heated in N2 atmosphere for 10 h at 700 °C (heat rate was 5 °C/min). After heat treatment, the sample was mechanically ground into ivory-colored powder.
XRD analysis was held with a Bruker D8 Advance (Karlsruhe, Germany) with a step of 0.02°. Structural parameters were refined by the Rietveld method using TOPAS5 software. X-ray diffraction analysis (XRD) was used as the structure analysis method for the synthesized nitrides powders investigated. XRD analysis was performed with a Bruker Iron nanopowder and nitrogen were used as a source for Fe 2 N. Ceramic crucible with initial powder was put into the tube furnace (BTF−1700C, (Hefei, China). The tube has been purged by ammonia (NH 3 ) for 30 min before synthesis. Synthesis was carried out in NH 3 atmosphere at 530 • C for 6 h with a heat rate of 8 • C/min. Mechanically mixed and powder was hot pressed for 2 h at 1100 • C. The received hot-pressed sample was heated in N 2 atmosphere for 10 h at 700 • C (heat rate was 5 • C/min). After heat treatment, the sample was mechanically ground into ivory-colored powder.
XRD analysis was held with a Bruker D8 Advance (Karlsruhe, Germany) with a step of 0.02 • . Structural parameters were refined by the Rietveld method using TOPAS5 software.
X-ray diffraction analysis (XRD) was used as the structure analysis method for the synthesized nitrides powders investigated. XRD analysis was performed with a Bruker D8 ADVANCE diffractometer with a vertical goniometer and Cu K α -radiation. The diffraction angles (2θ) are 5-100 • , 10-80 • , and 5-120 • for Li 3 N, Fe 2 N, and Li 3 FeN 2 , respectively.
Calorimetric measurements were performed using a TAM IV Microcalorimeter (Shanghai, China) at 298 K with the cell volume of 20 mL. Aqueous solution of 1 mol dm −3 HCl was used for the calorimetric cell ampoule. The ampoule was broken when thermal equilibrium was established, and nitride powder began to dissolve in HCl solution. Thermo-EMF vs. time was registered during the dissolution process providing the heat dissolution curve. Integration of this curve gave the value of dissolution enthalpy. Figure 2 shows the XRD pattern of synthesized Li 3 N (a) and Fe 2 N (b) powders. All peaks are in good correlation with database one. Li 3 N has a P6/mmm space group with lattice parameters a = 3.6711 Å, b = 3.6711 Å, and c = 3.8770 Å, which are in good correlation with [74] and PDF #30-0759. Fe 2 N reflection peaks also are in good correlation with [75] and PDF #50-0978. The space group of Fe 2 N is P312 with lattice parameters a = 4.7912 Å, b = 4.7912 Å, and c = 4.416 Å.

Results
Thermo-EMF vs. time was registered during the dissolution process providing the heat dissolution curve. Integration of this curve gave the value of dissolution enthalpy. Figure 2 shows the XRD pattern of synthesized Li3N (a) and Fe2N (b) powders. All peaks are in good correlation with database one. Li3N has a P6/mmm space group with lattice parameters a = 3.6711 Å, b = 3.6711 Å, and c = 3.8770 Å, which are in good correlation with [74] and PDF #30-0759. Fe2N reflection peaks also are in good correlation with [75] and PDF #50-0978. The space group of Fe2N is P312 with lattice parameters a = 4.7912 Å, b = 4.7912 Å, and c = 4.416 Å.    The structure refinement defined that Li + is in 4b and 8g, Fe +3 is in 4a, and N −3 is in 8j sites. All calculations were carried out with using TOPAS 4 software by Bruker. The final structure parameters (including site occupancy) are listed in Table 2.   The structure refinement defined that Li + is in 4b and 8g, Fe +3 is in 4a, and N −3 is in 8j sites. All calculations were carried out with using TOPAS 4 software by Bruker. The final structure parameters (including site occupancy) are listed in Table 2.

Results
and single nitrides were synthesized by reactions, as described in the Experimental section: For enthalpy calculation, we used thermodynamic cycle with the following reactions, as shown in Figure 4: where (aq) means "aqueous". The standard enthalpy (∆ d H LFN ) has been determined in the calorimeter. The received value was equal to −1972.96 ± 25 J g −1 , as shown in Table 3.
Materials 2021, 14, x FOR PEER REVIEW 6 of 13 2Fe2N + 8HCl(aq) → 4FeCl2 + 2NH3 + H2, N2 + 8HCl(aq) → 2NH4Cl + 3Cl2, where (aq) means "aqueous". The standard enthalpy (ΔdHLFN) has been determined in the calorimeter. The received value was equal to −1972.96 ± 25 J g −1 , as shown in Table 3. The resulting value of ΔoxHLFN is obtained by the next equation: The values of ΔdHLi3N, ΔdHFe2N, and ΔdHN2 were also measured by the calorimetry method. Measurement results are shown in Table 3. The value of ΔoxHLFN by Equation (8) is equal to -94.833 kJ mol −1 . The negative value of ΔoxHLFN defines Li3FeN2 as a stable phase. In addition, it is it is energetically favorable to synthesize LFN from single nitrides.  The resulting value of ∆ ox H LFN is obtained by the next equation: The values of ∆ d H Li3N , ∆ d H Fe2N , and ∆ d H N2 were also measured by the calorimetry method. Measurement results are shown in Table 3. The value of ∆ ox H LFN by Equation (8) is equal to −94.833 kJ mol −1 . The negative value of ∆ ox H LFN defines Li 3 FeN 2 as a stable phase. In addition, it is it is energetically favorable to synthesize LFN from single nitrides.
At last, the enthalpy of formation of Li 3 FeN 2 from elements can now be calculated using the following equation: Standard enthalpies for the calculation were taken from the handbooks [76,77], as shown in Table 4. −661 [81] The subscripts (cryst) and (gas) mean "crystalline" and "gaseous", correspondingly.
The calculated value of the enthalpy of Li 3 FeN 2 formation by Equation (9) is −291.331 ± 5.7 kJ mol −1 , Table 4. The enthalpy of formation ∆ f H 0 for Li 3 FeN 2 has the same order as for similar compounds, namely lithium metal nitrides (Table 4). That fact indirectly confirms the correctness of measurements. The value of formation enthalpy, calculated by Equation (9), can be used in thermodynamic estimation and the modeling of Li 3 FeN 2 reactivity.

The Isobaric Heat Capacity
The temperature dependence of the isobaric heat capacity of the Li 3 FeN 2 is shown in Figure 5. According to XRD data (Figure 3), the obtained powder material contains a certain amount of lithium oxide Li 2 O. This impurity quantity must be taken in consideration for valuation of the heat capacity of the Li 3 FeN 2 . This impurity could appear during the synthesis process or contact with oxygen in air atmosphere. XRD quantitative methods have limitations, but the heat capacity of a two-phase system must be recalculated by additive consideration: where C p -a specific heat capacity (pressure is constant), and m-a mass. The sample weight consists of synthesized compound (Li 3 FeN 2 ) and impurity (Li 2 O). So, the heat capacity of Li 3 FeN 2 ) is expressed from Equation (10) as: . (11) plex and binary nitrides, correspondingly. For LFN, Equation (16) can be written as (according to Equation (1)): The dependence of the heat capacity by temperature calculated from Equation (17) using tabular data [77] is shown in Figure 5 and Table 5.  The temperature dependence of the heat capacity calculated by the Neumann-Kopp rule is in good correlation with the recalculated heat capacity (considering Li2O impurity amount). However, XRD quantitative analysis gives rough results for the small presence of compounds in the material. For other quantitative methods, the amount of impurities can be measured more accurately: for example, thermogravimetry or volumetric methods.
According to Equations (12) and (13), Equation (11) can be written as follows: Thereby, the heat capacity of LFN can be calculated from the experimental data and heat capacity of lithium oxide impurity. For Equation (14), it is required to know the dependence of the specific heat capacity of the lithium oxide from temperature. For this, tabulated data for the lithium oxide heat capacity [77] were used. For the temperature range of 300-900 K, the commonly used polynomial formula for the heat capacity is as follows: where a, b, and c are empirical coefficients; T is the absolute temperature. The received coefficients for lithium oxide are a = 76.666 J mol −1 K −1 , b = -13.63·10 −3 J mol −1 K −2 , and c = -18.624·10 5 J mol −1 K. The heat capacity of Li 3 FeN 2 for the 300-900 K temperature range was recalculated using Equations (15) and (16) Figure 5 and Table 5. Empirical values for heat capacity were calculated by the Neumann-Kopp rule. This rule prescribes calculating the molar heat capacity of a complex compound from the heat capacities of constituent elements by adding them in with the corresponding compound stoichiometry. However, this calculation method gives good results for room temperatures and rough results for high temperatures. For more accurate results, binary compounds were used instead of single elements: where C p -molar heat capacity, n-a stoichiometric coefficient, and CN and BN are complex and binary nitrides, correspondingly. For LFN, Equation (16) can be written as (according to Equation (1)): The dependence of the heat capacity by temperature calculated from Equation (17) using tabular data [77] is shown in Figure 5 and Table 5.
The temperature dependence of the heat capacity calculated by the Neumann-Kopp rule is in good correlation with the recalculated heat capacity (considering Li 2 O impurity amount). However, XRD quantitative analysis gives rough results for the small presence of compounds in the material. For other quantitative methods, the amount of impurities can be measured more accurately: for example, thermogravimetry or volumetric methods.

Entropy
Entropy is another thermodynamic function that should be calculated. 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: where S is entropy, ∆H k is enthalpy of the k-th phase transition, and T k is temperature of the k-th phase transition (0 < T k < T). Since the entropy can be calculated by the Neumann-Kopp rule, if there is no phase transition until the calculation temperature, entropy can be also calculated by the Neumann-Kopp rule: where BN is the binary nitride compound (see Equation (16)). According to Equations (16) and (17), Equation (19) can be written in the following way: The entropy of Li 3 FeN 2 at room temperature is 113.2 J mol −1 K −1 according to Equation (20) and tabular data [82]. The additive rule for entropy calculation is suitable if the sum of the molar volumes of binary compounds differs a bit from the molar volume of the complex compound [83]. Thus, the molar volume for Li 3 N is 27.2 cm 3 mol −1 (ρ = 1.28 g cm −3 [83]), for Fe 2 N is 19.8 cm 3 mol −1 (ρ = 6.35 g cm −3 [83]), and for Li 3 FeN 2 is 33.9 cm 3 mol −1 (ρ = 3.09 g cm −3 [84]). The sum of the molar volumes of binary nitrides with their corresponding coefficients is 37.1 cm 3 mol −1 and differs about 9% from the LFN molar volume, which allows usage of an additive scheme.
In addition, the LFN entropy can be calculated by the W. Herz rule [85]: where K H is Herz constant (K H = 20.5), M is molar mass, C p,298 is isobaric heat capacity, and m is atoms per formula. According to Equation (21) and considering C p,298 from Table 5, the LFN entropy is 116.2 J mol −1 K −1 . Thus, the LFN entropy calculated by the Herz rule is in good correlation with the Neumann-Kopp rule result.

The Standard Gibbs Free Energy
The enthalpy of formation and entropy calculated above allows evaluating the standard Gibbs free energy of Li 3 FeN 2 formation (at T = 298 K): The resulting value of the Gibbs free energy for Li 3 FeN 2 at room temperature is −276.7 kJ mol −1 .
The next reaction is suggested for the determination of stability against metallic lithium with subsequent calculation of the Gibbs free energy at room temperature: 3Li + Li 3 FeN 2 = 2Li 3 N + Fe.
To determine the Gibbs free energy of the reaction, it is required to subtract from ∆ f G 0 298 values of the Gibbs energy for initial reagents of the reaction. The ∆ f G 0 298 for single elements is equal to zero, and for Li 3 N, it is −128.6 kJ mol −1 [82]. The Li 3 FeN 2 Gibbs free energy has been calculated above. Thus, the Gibbs free energy for reaction (23) is 19.5 kJ mol −1 , and this reaction is thermodynamically impossible. Finally, Li 3 FeN 2 is stable against metallic lithium at room temperature.

Conclusions
The thermodynamic characteristics were determined for Li 3 FeN 2 anode material for a lithium-ion battery. The two-step synthesis method allowed producing a highly pure compound with less than 3 wt % of Li 2 O impurity according to XRD data. The enthalpy of Li 3 FeN 2 formation from binary nitrides was determined according to the measured enthalpy of dissolution of reagents and product of Li 3 FeN 2 formation reaction. The obtained value is equal to −206.5 ± 2.8 kJ mol −1 . The Li 3 FeN 2 standard enthalpy of formation from single elements is equal to −291.3 ± 5.7 kJ mol −1 . This value can be used in further thermodynamic modeling and determinations.
The heat capacity value was recalculated considering the presence of Li 2 O impurity. The temperature dependence of the heat capacity is in good correlation with calculation by the Neumann-Kopp rule. Finally, the heat capacity can be described by formula C p (T) = 78.997 + 0.132 × T + 4.654·10 5 × T −2 , where T is absolute temperature. The LFN entropy is equal to 113.2 J mol −1 K −1 , and the Gibbs free energy of Li 3 FeN 2 formation is −276.7 kJ mol −1 . The calculations confirm that the Li 3 FeN 2 material is stable against metallic lithium. All thermodynamic values and functions can be used for modeling and further calculations.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.