Calorimetric Studies on Chemically Delithiated LiNi_0.4Mn_0.4Co_0.2O₂: Investigation of Phase Transition, Gas Evolution and Enthalpy of Formation

Abstract

Li_1.11(Ni_0.4Mn_0.4Co_0.2)O₂ powders were chemically delithiated by (NH₄)₂S₂O₈ oxidizer to obtain Li_x(Ni_0.4Mn_0.4Co_0.2)O₂ powders. The thermal behavior of two delithiated specimens, Li_0.76Ni_0.41Mn_0.42Co_0.17O_2.10 and Li_0.48Ni_0.38Mn_0.46Co_0.16O_2.07, was studied compared to the pristine specimen. Phase transitions at elevated temperatures were investigated by simultaneous thermal analysis (STA) and the gas evolution accompanying the phase transitions was analyzed by mass spectroscopy and an oxygen detector. The enthalpy of two delithiated samples and a pristine specimen were measured by a high temperature drop solution calorimeter. Based on these results, the enthalpies of formation were calculated.

1. Introduction

Among the key parameters of Li ion batteries—namely power, lifetime, and cost—safety is also important and remains the main challenge for their application [1,2]. The layered Li(Ni, Mn, Co)O₂ (NMC) is widely commercially applied as a positive electrode material, due to its high energy density and good rate performance [3,4]. However, when the Li ion cell is fully charged, the delithiated NMC can be thermally unstable. In its delithiated state, phase transitions are prone to take place at elevated temperatures, accompanied with gas evolution [5,6,7]. The electrochemical performance and safety are deteriorated by storage or operation at high temperatures. Therefore, a detailed understanding of the thermal behavior and phase transitions of delithiated NMC materials is essential to improve the thermal stability.

The method of chemical delithiation is often used [8,9,10] for the synthesis of pure delithiated active cathode materials, which avoids the interaction with binder and carbon black in composite cathode electrode. Since the assembly and later disassembly of a cell can be avoided, there is also no contact/reaction between cathode electrode and liquid electrolyte which could introduce reaction products. Additionally, the amount of delithiated sample is not limited by disassembly of cells. Zheng et al. [8] investigated chemically delithiated NMC samples by ab initio computation and experimental methods. Tian et al. [9] studied the thermal behavior of NMC-622 under a delithiated status by surface-sensitive techniques, revealing the chemical and structural characteristics of the bulk and surface of NMC particles after heating. Ma et al. [10] investigated the thermal stability of NMC with different Co contents. NMC samples were chemically delithiated by five kinds of acids to achieve a range of lithium content. With increasing Co content in NMC, a better thermal stability of the delithiated sample was exhibited.

In this work, we attempted to obtain the delithiated positive electrode active material (NMC442) via chemical delithiation using (NH₄)₂S₂O₈ as an oxidizer. Medium- and high degree delithiated specimens were prepared with two different Li contents. The thermal behavior of the delithiated specimens was investigated by using simultaneous thermal analysis (STA) combined with mass spectroscopy (MS) and an oxygen detector. The enthalpy was measured by a high temperature oxide melt drop solution calorimeter (Alexsys-1000). Enthalpies of formation from oxides and elements of delithiated and pristine materials are calculated.

2. Experimental

The investigated Li_1.11(Ni_0.42Mn_0.41Co_0.17)O₂ (NMC442) powders and the oxidizer powder (NH₄)₂S₂O₈ were purchased from MTI (MTI Coop., Richmond, CA, USA) and Alfa Aesar (Thermo Fisher Scientific, Kandel, Germany), respectively (

Table 1. Chemical specification: commercial NMC442 positive electrode materials and oxidizer powder (NH₄)₂S₂O₈.

Raw Material	Chemical Formula	Source	Initial Mass Fraction Purity
Lithium nickel manganese cobalt oxide	Li1.11Ni0.42Mn0.41Co0.17O2	MTI	0.9776
Ammoniumpersulfat	(NH4)2S2O8	Alfa Aesar	0.98

). (NH₄)₂S₂O₈ powders were dissolved in distilled water, preparing 0.5 mol/L oxidizing solvent. In order to obtain medium- and high degree delithiated specimens, two pristine specimens with a mass of 1 g were immersed in 250 mL and 500 mL oxidizing solvent with a concentration of 0.5 mol/L. After 65 h and 96 h reactions, the delithiated specimens Li_xNMC442 were washed with distilled water three times and filtered. Finally, the samples were dried in a vacuum oven at 120 °C for 24 h. One medium degree delithiated (65 h and 250 mL solvent) and one high degree delithiated specimen (96 h and 500 mL solvent) were obtained.

The compositions of the delithiated samples were quantitatively determined by inductively coupled plasma with optical emission spectroscopy (ICP-OES) and carrier gas hot extraction (CGHE) measurements. Approximately 5 mg solid specimen was dissolved in 6 mL hydrochloric acid and 2 mL nitric acid at 80 °C for four hours. To measure the contents of transition metal elements (TM: Ni, Co, and Mn) and lithium, the chemical digestion solution was diluted and, thereafter, an internal standard solution was added. For each element analysis, a calibration curve was adopted, which was determined by four selected concentrations. The calibration was conducted within one decade. Two to three different wavelengths of each element have been used for the ICP-OES analysis of the composition. Oxygen contents were determined by CGHE measurements.

The crystal structure of specimens before/after thermal measurements was determined by X-ray diffraction (XRD, Bruker-AXS GmbH, Ettlingen, Germany). The measurements were made in the 2θ angle range of 10–110°, with a step size increment of 0.02. Rietveld profile refinements were carried out using the software Maud 2.67 and Jade 5.

Phase transitions were studied by the combination of simultaneous thermal analysis (STA, NETZSCH, Hanau, Germany), mass spectroscopy (QMS 403C, NETZSCH, Germany), and an oxygen detector (SGM 5T, Zirox GmbH, Greifswald, Germany). Ar gas (purity 99.9999%) with a flow rate of 50 mL/min was used as a protective gas. The produced gases and Ar were collected and investigated by a mass spectrometer (MS) and an oxygen detector. The specimens were heated up to 800 °C with 5 K/min. The masses of pristine, medium, and highly delithiated specimens were 58.62, 56.90, and 59.59 mg, respectively.

The measurements of the enthalpy of the drop solution of pristine and delithiated specimens were performed in a high temperature drop solution calorimeter (Alexsys-1000 calorimeter, Setaram (KEP technologies SA), Caluire-et-Cuire, France). Here, 5–8 mg powder specimens were pressed into pellets with a diameter of 3 mm. The masses of the specimens were carefully controlled to ensure that heat effects were in the range of 5–10 J, where one drop took approximately 45 min. Between drops, it would take about 1.5 h for the stabilization of the baseline [11]. The specimens were dropped into the right and left cell of the calorimeter alternately from ambient temperature into the molten oxide (sodium molybdate at 701 °C). During the drops Ar gas was introduced as a flushing gas to maintain a constant atmosphere, with a flow rate of 40 mL/min. Moreover, Ar gas was also used to stir the solution to prevent local solvent saturation by bubbling it into the melt with a flow rate of 5 mL/min.

3. Results and Discussion

3.1. ICP-OES and CGHE Results for Pristine and Chemically Delithiated Samples

The results of the ICP-OES measurements are shown in

Table 2. Chemical analysis of the pristine and selected delithiated commercial NMC442 samples. The nominal stoichiometry was calculated based on transition metals’ cations equal to 1 in composition (sum TM = 1).

Analyzed Elements		Pristine Specimen	Medium Degree Delithiated Specimen	High Degree Delithiated Specimen
ICP-OES and CGHE wt.%	Li	7.68 ± 0.16	5.33 ± 0.11	3.40 ± 0.07
	Ni	24.40 ± 0.37	24.37 ± 0.37	22.43 ± 0.34
	Mn	22.50 ± 0.41	23.30 ± 0.42	25.90 ± 0.47
	Co	10.10 ± 0.19	10.13 ± 0.19	9.75 ± 0.19
	O	33.60 ± 2.99	34 ± 3.0	33.7 ± 3.0
Molar ratio	Li/sum TM	1.11	0.76	0.48
	Ni/sum TM	0.42	0.41	0.38
	Mn/sum TM	0.41	0.42	0.46
	Co/sum TM	0.17	0.17	0.16
	O/sum TM	2.11	2.10	2.07
Nominal composition		Li1.11Ni0.42Mn0.41Co0.17O2.11	Li0.76Ni0.41Mn0.42Co0.17O2.10	Li0.48Ni0.38Mn0.46Co0.16O2.07

for pristine and two delithiated NMC442 materials. TM stands for transition metals. Stoichiometric compositions were calculated based on the assumption that the atomic sum of the transition metals is equal to 1 (TM = 1). The amount of Li per formula unit in medium- and high degree delithiation was 0.76 and 0.48, corresponding to state of charge 50% and 100% of NMC442 cells, respectively. The Li content showed a clear dependence on the degree of delithiation, as it decreased by more than a factor of two from the pristine sample to the high degree delithiated one. The content of the transition metal ions exhibited only small variations upon the degree of delithiation, which can be due to stoichiometric scattering between the samples combined with the level of uncertainty of the analysis method. The same effects can be observed in the molar ratios given in the table. Comparable results were found in a study by Ma et al. [10], in which the delithiation in NMC442 was achieved by applying different acid solutions, adjusting the Li content between x = 1.0 and x = 0.362, respectively.

3.2. XRD Results for Pristine and Chemically Delithiated Specimens

The measured XRD patterns of three specimens (pristine, medium-, and high degree delithiated) are shown in Figure 1, and the corresponding results from the Rietveld refinement are listed in

Table 3. Rietveld refinement for X-ray diffraction of the pristine NMC442 and chemically delithiated specimens Li_xNMC442, compared with reference [10,12].

Li Content x	Space Group	Lattice Parameters			Phase wt.%
		a (Å)	b (Å)	c (Å)
1.11	R$\stackrel{-}{3}$m	2.8769 (7)	-	14.2922 (0)	-
0.76	R$\stackrel{-}{3}$m	2.8606 (8)	-	14.2926 (7)	84.5
0.48	R$\stackrel{-}{3}$m	2.8562 (2)	-	14.2722 (5)	86.4
1.11	R$\stackrel{-}{3}$m	2.861		14.238	Ref. [11]
1.04	R$\stackrel{-}{3}$m	2.865		14.245
0.97	R$\stackrel{-}{3}$m	2.870		14.265
0.90	R$\stackrel{-}{3}$m	2.874		14.280
1	R$\stackrel{-}{3}$m	2.8694 (1)		14.266 (1)	Ref. [12]
0.94	R$\stackrel{-}{3}$m	2.8616 (3)		14.272 (2)
0.5	R$\stackrel{-}{3}$m	2.8280 (5)		14.456 (4)

. The initial structure of the pristine sample and main structure of the delithiated specimens are an O3 layered structure (space group R$\stackrel{-}{3}$m), which belongs to the α-NaFeO₂ structure type. However, after delithiation, small shoulders appeared near reflections (003), as shown in Figure 1b,c, which can be assigned to an O1 phase belonging to the trigonal structure P$\stackrel{-}{3}$m1. Comparing to delithiated NMC442 [10,12], the lattice parameters show a similar decrease. Lattice parameters c remain almost the same in this work, while reference [10,12] show an increased trend for the c parameters. The slight differences could be caused by the implement of different oxidizers for chemical delithiation.

The results of the structural analysis of this work can be compared to the studies on the structural and electrochemical behavior of NMC111 [13] and NMC442 [10,12]. The data from X-ray and neutron diffraction on de- and re-intercalated NMC111 by Yin et al. [13] revealed the stability of the rhombohedral R$\stackrel{-}{3}$m structure in NMC111 down to a Li content of x < 0.3. Below this Li extraction level, the O1 phase with the trigonal structure P$\stackrel{-}{3}$m1 appeared.

Additional results were obtained from XRD investigations to determine the phases of the specimens after STA/MS measurement. Figure 2 shows the results of Rietveld refinement: (a) the pristine commercial NMC442 maintained the layered structure. Compared to the commercial NMC442’s structure before STA/MS measurement, the coalescence of the (006)/(012) and (018)/(110) reflections indicated an increase in the lattice parameter $a$ and a decrease in $c$. The lower intensity ratio of (003)/(104) implied a lower cation mixing after heat treatment up to 800 °C. (b) Three phases, namely a layered structure (space group R$\stackrel{-}{3}$m), spinel structure (space group Fd$\stackrel{-}{3}$m), and rock-salt structure (space group Fm$\stackrel{-}{3}$m), were found to be coexistent in the medium degree delithiated specimen. The previous chemical delithiation probably proceeded as an onion-like model, and the Li ions in core were not extracted, so the layered structure remained qualitatively similar to pristine powders. The intensity of the reflection (111)_spinel and (200)_rock-salt reflected the proportion of spinel and rock-salt structures, which were approximately 50% and 46%, respectively. (c) For the deep delithiated sample, spinel structure, and rock-salt structure were found, and the maximal reflection (003)_layered disappeared completely. The reflection (200)_rock-salt has a much higher intensity than (111)_spinel, indicating that rock-salt phase content increases. The formation of the rock-salt phase is directly proportional to the degree of delithiation, accompanied by release of oxygen.

3.3. Simultaneous Thermal Analysis (STA) and Gas Evolution Study

The heat flow signal and thermogravimetric analysis of the samples with compositions of Li_1.11Ni_0.42Mn_0.41Co_0.17O_2.11, Li_0.76Ni_0.41Mn_0.42Co_0.17O_2.10, and Li_0.48Ni_0.38Mn_0.46Co_0.16O_2.07, respectively, are shown in Figure 3. The mass loss increased significantly with the increasing degree of delithiation. However, the DTA signals (black curves) in Figure 3b,c for materials with different delithiation degrees are comparable and show similar sequence of multi-reactions. The red curves in Figure 3 are the derivatives of the DTA signal with respect to temperature, which indicate the heat flux changes. As shown in Figure 3a, the temperature derivative of the heat flux signal is flat, indicating no reaction taking place. Compared to the delithiated samples, the pristine sample was thermally stable up to high temperatures with a mass loss of only 0.2%. For the delithiated samples in Figure 3b,c, there were several peaks on the differential heat flux curve. For the medium degree delithiated sample, a sequence of reactions starting above 150 °C extended up to slightly below 700 °C, indicated by DTA peaks. The reactions at 300 °C and above 550 °C, marked the onset of oxygen release, where the phase transitions (Equation (1)) occurred. In Figure 4, the blue curves show oxygen concentration measured by an oxygen detector, and dash black curves are the differential of mass change rate. For the high degree delithiated sample, a comparable sequence of reactions could be observed. The reactions in both delithiated samples were accompanied by a partial mass loss which added up to about 3.5% in the medium delithiated sample and up to 7% in the highly delithiated sample.

The rate of mass change and the O₂ concentration released from the samples as a function of temperature are shown in Figure 4. While the pristine sample showed no significant mass change and oxygen release, strong effects were visible for the delithiated samples. A strong fluctuation in the rate of mass change at around 300 °C triggered the onset of the first release of oxygen, leading to a significant peak in the O₂ concentration which overlapped with a smaller rate of mass change at 400 °C. The onset of a second O₂ concentration peak can be observed above 550 °C. While the sequence of mass change and oxygen release were comparable in both delithiated samples, the effects appear to be more strongly pronounced in the sample with the higher degree of delithiation. The first O₂ concentration peak of the sample with x = 0.48 was nearly doubled compared to the sample with x = 0.76. Furthermore, the oxygen release above 550 °C was strongly broadened and extended to temperatures above 750 °C.

With lower onset temperatures, faster rate of mass change, and larger amount of oxygen released, the delithiated samples show deteriorating thermally stability depending on the degree of delithiation. According to Equation (1) accompanied with further Li loss, this induced a phase transformation from the layered structure to spinel and finally to a rock-salt type phase. The following sequence of phase transitions took place [14] with increasing temperature:

$$\begin{gathered} {\mathrm{L}\mathrm{i}}_x\mathrm{T}\mathrm{M}{\mathrm{O}}_2\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}(R\stackrel{-}{3}m)\stackrel{\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}}{\Rightarrow }{\frac{x}{2}\mathrm{L}\mathrm{i}}_2\mathrm{O}+\mathrm{T}{\mathrm{M}}_3{\mathrm{O}}_4\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{l}(Fd\stackrel{-}{3}m)+\epsilon {\mathrm{O}}_2 \\ {\mathrm{T}\mathrm{M}}_3{\mathrm{O}}_4\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{l}(Fd\stackrel{-}{3}m)\stackrel{\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}}{\Rightarrow }\mathrm{T}\mathrm{M}\mathrm{O}\mathrm{r}\mathrm{o}\mathrm{c}\mathrm{k}-\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{t}\left(Fm3m\right)+\epsilon {\mathrm{O}}_2 \end{gathered}$$

(1)

The gas species released during the temperature rise were measured by the mass spectrometer (MS), and the results are presented as the function of temperature and volume percentage in Figure 5. During the beginning of the heating ramp of the pristine sample, small amounts of nitrogen and oxygen were observed, but both signals disappeared during heating and no further oxygen release could be observed. During the initial heating, the delithiated samples also showed small nitrogen signals. However, on further heating, there were two oxygen peaks detected in both of the delithiated samples. For Li_0.76NMC442, the first O₂ peak appeared with an onset temperature slightly below 300 °C, while the second peak appeared with an onset between 450 °C and 500 °C. In the Li_0.48NMC442 sample, the O₂ peaks appeared with a comparable thermal history. Qualitatively, this corresponded to the results of the measurements with the oxygen sensor shown in Figure 4. However, the small shifts in the onset and peak temperatures, respectively, can be explained by differences in the time constants and sensitivities of the two measurement methods.

Initially Ni²⁺ and Co³⁺ were the electrochemically active ions in the stoichiometric NMC442 positive electrode materials, and their oxidation states in the delithiated samples changed to Ni³⁺, Ni⁴⁺, and Co⁴⁺. Upon heating, oxygen vacancies formed in the structure, and the TM cations reduced to lower oxidation states in order to maintain the overall charge neutrality [7]. The thermal stability of the NMC442 materials was significantly affected by the amount of Ni³⁺ and Ni⁴⁺, which increased with the degree of delithiation.

3.4. Enthalpy Analysis for Pristine and Chemically Delithiated Samples

The enthalpies of drop solution are listed in Table 4, with the corresponding uncertainties and number of drops. Enthalpies of drop solution are 102.66 ± 1.15 kJ/mol, 99.57 ± 0.95 kJ/mol and 111.27 ± 1.52 kJ/mol for pristine, medium and high degree delithiated specimens, respectively. In Figure 6 the measured heat flow signal (in μV) is shown for the drops of pristine specimens. Masses of dropped specimens are given with corresponding calculated heat effect (in Joule) in parentheses.

Koyama et al. [15] investigated the electronic structure of delithiated NMC (positive cathode material) using first-principles calculations. They reported three oxidation reactions in Li_1-x[Ni_1/3Co_1/3Mn_1/3]O₂: 0 < x < 1/3 redox couple Ni^2+/3+, 1/3 < x < 2/3 redox couple Ni^3+/4+, and 2/3 < x < 1 redox couple Co^3+/4+. Kim and Chung [16] investigated the same composition and its delithiation procedure. They also reported the oxidation of Ni and Co ions. In contrast to Koyama et al. [15], they reported a Co^3+/4+ transition for 0 < x < 1. For the Ni oxidation, the experimental results were coincident with Koyama et al.’s calculations. Kim and Chung assumed that differences were caused by investigating particles that were in a non-equilibrious heterogeneous state, whereas Koyama et al. [15] assumed an equilibrious homogeneous state for the calculations.

Qiao et al. [17] analyzed the redox evolution in LiNi_0.5Mn_0.3Co_0.2O₂. Similar to [15,16], the oxidation of both Ni and Co ions was involved while charging up to 4.2 V, and Mn ions remained in the same oxidation status 4+. Further charging up to 4.5 V resulted in Co ion oxidation solely. At 4.5 V, the electrode surface contained approximately 20% of Ni²⁺.

In this work, the oxidation states of Ni and Co atoms in the pristine NMC442 sample are considered as 2+ and 3+, respectively. In delithiated samples, the oxidation states of Ni are simplified to a mixture of 2+ and 4+. As shown in Figure 7, the thermodynamic cycle for the calculation of the enthalpy of formation is based on binary oxides and oxygen. Since Co₂O₃ (Co³⁺), CoO₂ (Co⁴⁺), Ni₂O₃ (Ni³⁺), and NiO₂ (Ni⁴⁺) are unstable under normal conditions, the parameters of Li₂O (Li⁺), NiO (Ni²⁺), MnO₂ (Mn⁴⁺), and CoO (Co²⁺) are used according to [18,19]. Deviations α, β, γ, and δ from nominal NMC442 composition determined by ICP-OES and CGHE are also included in the thermodynamic cycle. With a thermodynamic cycle, the enthalpy of formation can be calculated from drop solution calorimetry (Equation (2)). A proper cycle (Figure 7) is as follows: Li-NMC (product) at room temperature $\stackrel{{∆}_{ds}H}{\to }$ dissolved Li-NMC at 974 K = dissolved binary oxides (educts) at 974 K $\stackrel{{∆}_{ds}H}{\leftarrow }$ educts at room temperature. As the dissolved state of the educts (in appropriate ratio) and the product is the same, the only remaining unknown to close the circle is the enthalpy of formation of the product at room temperature from the educts. Binary oxides are used to fulfill the composition conditions for Li, Ni, Mn, and Co. In the thermodynamic cycle, the remaining oxygen fraction ε, caused by the oxidation of Ni²⁺ and Co²⁺ ions, is included with an enthalpy increment derived by the integration of the specific heat capacity of oxygen. The oxygen enthalpy increment from room temperature to 974 K is calculated using Gibbs energy, obtained from SGTE data for pure elements [20]. The enthalpy of formation from elements is calculated using the enthalpies of formation of Li-NMC from Equation (2) and of the binary oxides from the literature (Table 4).

For Li_1-xNi_0.4Mn_0.4Co_0.2O₂ specimens, the equations for enthalpy of formation from oxides and elements are summarized in Equations (2) and (3), respectively, as follows:

$$\begin{array}{l}{∆}_f{H}_{{Li}_{1-x}{Ni}_{0.4}{Mn}_{0.4}{Co}_{0.2}{O}_2}^{\theta ,oxide}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{1-x}{2}{\bullet ∆}_{ds}{H}_{\left({Li}_{2}O\right)}+0.4{\bullet ∆}_{ds}{H}_{\left(NiO\right)}+0.4{\bullet ∆}_{ds}{H}_{\left(Mn{O}_2\right)}+0.2\bullet {∆}_{ds}{H}_{\left(CoO\right)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\frac{0.1+0.5\bullet x}{2}{\int }_{298K}^{974K}{C}_p\left(O_2\right)dT-{∆}_{ds}{H}_{\left({Li}_{1-x}{Ni}_{0.4}{Mn}_{0.4}{Co}_{0.2}{O}_2\right)}\end{array}$$

(2)

$${∆}_f{H}_{{Li}_a{Ni}_b{Mn}_c{Co}_d{O}_e}^{\theta ,elements}={∆}_f{H}_{{Li}_a{Ni}_b{Mn}_c{Co}_d{O}_e}^{\theta ,oxides}+\frac{a}{2}\bullet {∆}_f{H}_{\left({Li}_{2}O\right)}+b\bullet {∆}_f{H}_{\left(NiO\right)}+c\bullet {∆}_f{H}_{\left(Mn{O}_2\right)}+d\bullet {∆}_f{H}_{\left(CoO\right)}$$

(3)

Assuming x = 0.8 (Li_0.2Ni_0.4Mn_0.4Co_0.2O₂), Ni²⁺ ions are completely oxidized to Ni⁴⁺, leading to Li⁺_0.2Ni⁴⁺_0.4Mn⁴⁺_0.4Co³⁺_0.2O²⁻₂. When 0 < x < 0.8, Ni⁴⁺ will replace Ni²⁺ partially. When x > 0.8, Co³⁺ ions will partially be oxidized to Co⁴⁺. According to [19], the enthalpy of formation calculations are based solely on stable binary oxides Li₂O, NiO, MnO₂, and CoO. The change in the oxidation state of Ni and Co is thereby included in the enthalpy of formation from the stable oxides and oxygen. For example, the medium degree delithiated sample Li_0.76Ni_0.41Mn_0.42Co_0.17O_2.10, will be Li⁺_0.76Ni⁴⁺_0.12Ni²⁺_0.29Mn⁴⁺_0.42Co³⁺_0.17O²⁻_2.10^.. Equations (4) and (5) are corresponding calculations including the deviations α = 0.01, β = 0.02, γ = −0.03, and δ = 0.1 from nominal Li₁-NMC442 composition determined by ICP-OES and CGHE, as follows:

$$\begin{array}{l}{∆}_f{H}_{{Li}_{0.76}{Ni}_{0.41}{Mn}_{0.42}{Co}_{0.17}{O}_{2.10}}^{\theta ,oxide}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{0.76}{2}{\bullet ∆}_{ds}{H}_{\left({Li}_{2}O\right)}+0.41{\bullet ∆}_{ds}{H}_{\left(NiO\right)}+0.42{\bullet ∆}_{ds}{H}_{\left(Mn{O}_2\right)}+{0.17\bullet ∆}_{ds}{H}_{\left(CoO\right)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left[2.10-\left(\frac{0.76}{2}+0.41+0.42\bullet 2+0.17\right)\right]\bullet \frac{1}{2}\bullet {\int }_{298K}^{974K}{C}_p\left(O_2\right)dT\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-{∆}_{ds}{H}_{\left({Li}_{0.76}{Ni}_{0.41}{Mn}_{0.42}{Co}_{0.17}{O}_{2.10}\right)}\end{array}$$

(4)

$$\begin{array}{l}{∆}_f{H}_{{Li}_{0.76}{Ni}_{0.41}{Mn}_{0.42}{Co}_{0.17}{O}_{2.10}}^{\theta ,oxide}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\frac{0.76}{2}{\bullet ∆}_{ds}{H}_{\left({Li}_{2}O\right)}+0.41{\bullet ∆}_{ds}{H}_{\left(NiO\right)}+0.42{\bullet ∆}_{ds}{H}_{\left(Mn{O}_2\right)}+{0.17\bullet ∆}_{ds}{H}_{\left(CoO\right)}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left[2.10-\left(\frac{0.76}{2}+0.41+0.42\bullet 2+0.17\right)\right]\bullet \frac{1}{2}\bullet {\int }_{298K}^{974K}{C}_p\left(O_2\right)dT\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-{∆}_{ds}{H}_{\left({Li}_{0.76}{Ni}_{0.41}{Mn}_{0.42}{Co}_{0.17}{O}_{2.10}\right)}\end{array}$$

(5)

The enthalpies of formation from oxides and elements are shown in Figure 8 as a function of the Li content. The results of the present work are in good agreement with the experimental and ab initio calculated results by Masoumi et al. [18]. The further delithiated specimens have less negative enthalpy values, which is considered to be thermodynamically less stable: thermodynamic stability decreases with increasing delithiation.

Table 4. Enthalpy of drop solution, enthalpy of formation from the oxides, and from the elements of the investigated specimens and of binary oxides from the literature.

Nominal Stoichiometry	Enthalpy of Drop Solution (kJ/mol)	Enthalpy of Formation from Oxides (kJ/mol)	Enthalpy of Formation from Elements (kJ/(mol of Formula)
Li1.11Ni0.42Mn0.41Co0.17O2.11	102.66 ± 1.15 (8)	−82.23 ± 1.78	−769.20 ± 1.85
LiNi0.4Mn0.4Co0.2O2	98.86 ± 1.09 (18) e	−75.35 ± 1.65 e	−726.59 ± 1.72 e
Li0.76Ni0.41Mn0.42Co0.17O2.10	99.57 ± 0.95 (12)	−60.24 ± 1.39	−645.39 ± 1.47
Li0.48Ni0.38Mn0.46Co0.16O2.07	111.27 ± 1.52 (11)	−54.23 ± 1.70	−566.95 ± 1.77
Li2O	−93.02 ± 2.24 a,b		−597.935 ± 0.334 c
NiO	35.73 ± 0.95 (8) a		−239.743 ± 0.543 c
MnO2	128.92 ± 0.91 (11) d		−521.493 ± 0.836 c

The uncertainties are given behind the symbol ±, which is two standard deviations from the mean for enthalpy of the drop solution and the propagated uncertainties for enthalpy of formation. The number of experiments is given in parentheses. ^a [19] ^b [21] ^c [22] ^d [23] ^e [18].

Table 4. Enthalpy of drop solution, enthalpy of formation from the oxides, and from the elements of the investigated specimens and of binary oxides from the literature.

Nominal Stoichiometry	Enthalpy of Drop Solution (kJ/mol)	Enthalpy of Formation from Oxides (kJ/mol)	Enthalpy of Formation from Elements (kJ/(mol of Formula)
Li1.11Ni0.42Mn0.41Co0.17O2.11	102.66 ± 1.15 (8)	−82.23 ± 1.78	−769.20 ± 1.85
LiNi0.4Mn0.4Co0.2O2	98.86 ± 1.09 (18) e	−75.35 ± 1.65 e	−726.59 ± 1.72 e
Li0.76Ni0.41Mn0.42Co0.17O2.10	99.57 ± 0.95 (12)	−60.24 ± 1.39	−645.39 ± 1.47
Li0.48Ni0.38Mn0.46Co0.16O2.07	111.27 ± 1.52 (11)	−54.23 ± 1.70	−566.95 ± 1.77
Li2O	−93.02 ± 2.24 a,b		−597.935 ± 0.334 c
NiO	35.73 ± 0.95 (8) a		−239.743 ± 0.543 c
MnO2	128.92 ± 0.91 (11) d		−521.493 ± 0.836 c

The uncertainties are given behind the symbol ±, which is two standard deviations from the mean for enthalpy of the drop solution and the propagated uncertainties for enthalpy of formation. The number of experiments is given in parentheses. ^a [19] ^b [21] ^c [22] ^d [23] ^e [18].

4. Conclusions

Different delithiated specimens were obtained by using (NH₄)₂S₂O₈ oxidizer via chemical delithiation. The initial rhombohedral phase of the pristine NMC442 sample is stable upon delithiation at room temperature. Phase transitions accompanied with oxygen release were observed during heating in the temperature range from 25 to 800 °C. The onset temperatures of the oxygen concentration peaks indicate the starting of the phase transformations from the layered structure to the spinel and then to the rock-salt structure. Furthermore, a sequence of thermal effects was detected by the STA. Enthalpies of formation from oxides and enthalpies of formation from elements were calculated based on the measured enthalpies of drop solution in sodium molybdate, showing decreasing thermodynamic stabilities with the increasing degree of delithiation with a nearly linear relationship.