Charging behavior of ZnMn₂O₄ and LiMn₂O₄ in a zinc- and lithium-ion battery: an ab initio study

Under ambient conditions, ZMO crystallizes in a tetragonal structure with space group $I41/amd\,\left( {\# 141} \right).$ Mn³⁺ ions are in octahedral sites (Wyckoff atomic position 8d) while Zn²⁺ ions are in tetrahedral sites (4a), as shown in figure S2. After replacing Zn by Li in the ZMO structure, the formed TLMO structure also remains tetragonal. Thus, Li ions are in tetrahedral sites (4a) while Mn ions are in octahedral sites (8d). The TLMO compound is a mixed oxide in which Mn is in both +3 and +4 oxidation states: 50% of them are formed by active Jahn-Teller ions (Mn³⁺) and 50% formed by non-active Jahn-Teller ions (Mn⁴⁺), as schematically depicted in figure S2. This mixed configuration is also observed for the cubic and orthorhombic phases [31, 32].

After the structural optimization step, where the atomic positions were relaxed and lattice parameters were optimized, the electronic structures of TLMO and ZMO were obtained. Table 1 shows the results of the lattice parameters, Mn oxidation states, magnetic moments, and band gap calculations for the stoichiometric configurations. The lattice parameters are in very good agreement with the available experimental data. The Mn³⁺ ion has four unpaired $3d$ electrons while the Mn⁴⁺ has three unpaired $3d\,$electrons, therefore the magnetic moment of Mn³⁺ should be larger than the magnetic moment of the Mn⁴⁺ ion, as obtained by our calculations. The ZMO experimental band gap is very well described using $U = 6.0$ eV. To the best of our knowledge no experimental results regarding the band gaps of TLMO have been reported before. The TLMO exhibits a band gap of 0.89 eV and the ZMO a band gap of 1.83 eV. Therefore, TLMO has a higher ability to create electron-hole pairs under sunlight exposition than ZMO.

Table 1. Theoretical lattice parameters, Mn oxidation states, magnetic moments $\mu$, and band gaps of TLMO (tetragonal phase of LiMn₂O₄) and ZMO (ZnMn₂O₄) compounds. Available experimental data are also shown.

	$a\,$($\mathop A\limits^ \circ$)	$c\,$($\mathop A\limits^ \circ$)	Mn oxidation state	$\mu$ (${\mu _B}$)	gap (eV)
Theor.
ZMO	5.82	9.33	Mn3+	3.67	1.83
TLMO	5.77	9.08	Mn3+	3.64	0.89
			Mn4+	3.00
Expt.
ZMO	5.72 [33]	9.23 [33]		$\cong$4 [13]	1.86 [25–27]
TLMO	—	—		—	—

The TLMO and ZMO partial densities of states (PDOS) are shown in figure 1. The TLMO has two types of Mn ions in its structure (Mn³⁺ and Mn⁴⁺) while ZMO has only one (Mn³⁺). The crystals tetragonal symmetry splits the $3d$ states of the Mn³⁺ ion and the electronic configuration is given by $e_g^2$, $b_{2g}^1$, $a_{1g}^1$, $b_{1g}^0$ while in the Mn⁴⁺ ion the electronic configuration is given by $t_{2g}^3(e_g^2$ + $b_{2g}^1)$, $e_g^0(a_{1g}^0$ + $b_{1g}^0)$.

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To investigate the alterations in ZMO and TLMO properties resulting from Li or Zn extraction, we constructed various structures with different concentrations of lithium or zinc (${\text{L}}{{\text{i}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$ and ${\text{Z}}{{\text{n}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$, $0 \unicode{x2A7D} x \unicode{x2A7D} 1$). Subsequently, we analyzed several material properties, including changes in volume, formation energy of intermediate phases, voltaic profile, redox processes, and electronic and ionic conductivity. Firstly, we analyzed how the lattice parameters and consequently the volume of the TLMO and ZMO behave during Li or Zn extraction. In the computational screening of electrode material, we consistently seek those that present the smallest possible volume change during the extraction/insertion of Li or Zn. Materials with zero or close to zero expansion/contraction during cycling have been widely studied for application in solid-state batteries [34, 35]. Figure S3 shows the variations of the lattice and volume parameters of the compounds throughout the Li or Zn extraction process. TLMO experienced a volume contraction of 5.8%, upon the complete removal of Li, which is an acceptable value to be applied as a cathode material in LIBs with soluble electrolytes. However, despite this minor contraction, TLMO could not be considered viable for use in solid-state batteries, where the electrolytes are solid and the tension (contraction/expansion) during cycling could potentially damage the battery. In turn, ZMO suffered a volume contraction of 12.5% when all Zn was removed. The host matrix is expected to undergo a more significant change in volume during the insertion/extraction of divalent ions compared to monovalent ions, as obtained by us in the case of Zn and Li in ZMO and TLMO, respectively.

Several strategies exist to mitigate changes in volume during battery cycling [34, 35]. One approach involves not extracting all the Li or Zn ions during the battery charging process. For instance, when only 75% of the Zn ions are extracted from the ZMO structure, the volume contracted by 9.6%, and with only 50% of Zn ions extraction, the contraction was 6.4%. In the case of the TLMO structure, extracting 75% of the Li ions resulted in a 4.8% volume contraction, while extracting 50% of the Li ions resulted in a 4.0% contraction. It should be noted that experimentally, not all Zn or Li ions are extracted from their respective host matrices. This is the reason why the theoretical specific capacity is higher than the experimental one. For example, experimentally only 0.8 Li per formula unit is extracted from the LMO cubic phase (80%), which corresponds to a specific capacity of $120$ mAh g⁻¹, whereas the theoretical specific capacity is estimated to be $\sim148\,$ mAh g⁻¹ with all lithium extracted.

After detailing the structural properties during battery charging, we shifted our focus to analyzing the voltage. To calculate the voltage, we only need to perform three independent first-principles calculations for each material, as described by equations (1) and (2). This approach implies that the average voltage of a material, TLMO for instance, can be straightforwardly derived from the results of DFT calculations performed on LiMn₂O₄, Mn₂O₄ (optimized TLMO fully delithiated), and metallic bcc lithium. Provided that the stable intermediate phases are known as a function of Li concentration, it is possible to employ them to compute a piecewise approximation of the voltage curve. However, the real challenge lies in determining which phases are thermodynamically stable during battery charging and what are their respective crystalline structures. The relevant quantity to determine the stable intermediate phases is the formation energy (${E_{f\,}}$), which is calculated in relation to the reference materials energies, as detailed in equations (3) and (4). For the sake of illustration, during delithiation process in TLMO, the formation energy of a ${\text{L}}{{\text{i}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$ phase is calculated from its total energy and the reference materials energies of ${\text{LiM}}{{\text{n}}_2}{{\text{O}}_4}$ and ${\text{M}}{{\text{n}}_2}{{\text{O}}_4}$. The formation energy for all ${\text{L}}{{\text{i}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$ phases, which are stable in comparison to the reference phases, lie on the lower convex hull in a plot of ${E_f}$ versus composition $x$ [36–38].

Ab initio calculations are not suitable for describing the stable intermediate phases that are formed during battery charging/discharging, due to the extensive number of possible lithium/vacancy orderings, preventing the energy evaluation of all configurations [37]. Generally, the intermediate phases are obtained by the cluster expansion technique [38–40]. However, as the conventional TLMO and ZMO cells have only four Li ions and four Zn ions, respectively, we accepted the challenge of verifying whether any intermediate phase is formed and what are the configuration of their crystalline structures.

Figure 2 shows the results of the formation energies as a function of Li or Zn concentration. Among all configurations, the structures that correspond to the lowest energies in the DFT calculations are shown. The results for the ZMO formation energies show that no intermediate phases are formed during Zn extraction, since the energies are all above 0 eV. On the other hand, TLMO presents a stable intermediate phase at $x = 0.5$ (${\text{L}}{{\text{i}}_{0.5}}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$). This is the only phase that lies on the lower convex hull of ${E_f}$ versus composition $x$. A zoom of the convex hull can be observed in figure S4, where one can better perceive the formation of the intermediate phase. The TLMO follows the same pattern presented by the cubic and orthorhombic structures [41, 42], that is, a single stable intermediate phase is observed for $x = 0.5$. It is worth mentioning, however, that other solid phases can be formed at Li or Zn concentrations not considered by us. To analyze the intermediate phases formation for every possible concentration we would have to consider a supercell with more than 100 Li or Zn ions in the structure, which is an impractical task to be realized by DFT simulations.

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Once the convex hull construction is available, a piecewise voltage profile can be obtained from equations (1) and (2). The voltaic profile obtained for $0 \unicode{x2A7D} x \unicode{x2A7D} 1\,$ is shown in figure S5. The TLMO presented a potential window of 4.05–4.06 V and an average voltage of 4.05 V. There is no experimental average voltage for the tetragonal phase of the LMO, however, voltage is not expected to change significantly with phase. In our previous work, we showed that the average voltages of the cubic phase and the orthorhombic phase of LMO are practically the same [42]. In this way, we can use the experimental average voltage value of the cubic phase (4.1 V) [43, 44] to compare with our current results. Thus, the average voltage calculated by us agrees with the experimental data very well. The TLMO voltage step value corresponded to 10 mV, being lower than the steps applied for the orthorhombic (92 mV) and cubic (80 mV) phases [42]. The experimental value of the cubic phase voltage step corresponds to 100 mV [43, 44]. The average voltage for ZMO, in turn, does not exhibit a voltage step, since we did not find any stable intermediate phases for $0 \unicode{x2A7D} x \unicode{x2A7D} 1\,$ concentrations. The ZMO calculated charge voltage was $1.9$ V, which is overestimated when compared to the experimental value of about $1.5$ V [8]. The TLMO and ZMO obtained theoretical specific capacity values are, respectively, $148$ and 224 mAh g⁻¹.

The ionic mobility of Zn²⁺ or Li⁺ ions at the cathode is another important factor affecting electrochemical performance. Figure 3(a) shows the diffusion paths of Zn²⁺ and Li⁺ ions in the ZMO and TLMO structures, respectively, and figure 3(b)) shows the results of energy barriers for Zn and Li diffusion. During the ionic diffusion, all host atoms in ZMO and TLMO were held fixed, and the energy of each step was calculated separately in the diffusion path. The diffusion barrier height was calculated as the energy difference between the TS and initial state (IS) (barrier of one reactant) [45, 46]. The ZMO and TLMO structure was completely relaxed before diffusion barrier calculations. The energy barrier for Zn²⁺ diffusion in the ZMO was 1.30 eV, while for Li⁺ diffusion in the TLMO structure it was 0.98 eV. The lower value of the energy barrier for Li was already expected since monovalent ions are better diffused, i.e. suffer less electrostatic repulsion than the divalent ions. Therefore, our results show that the TLMO presents better ionic conductivity compared to ZMO.

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The PDOS modifications occurring during the extraction of Zn or Li, from ZMO and TLMO, respectively, are illustrated in figure S6. We chose to present only the Mn-$3d$ PDOS, since Mn is the only ion that participates in the redox process. The shapes of the e_g, b_2g, a_1g, b_1g (Mn³⁺), and e_g, t_2g (Mn⁴⁺) predominant orbitals, during Li or Zn extraction, remained similar to those corresponding to $\,x = 1\,$ concentration. Small changes are expected in electrical conductivity due to variations of the band gap width in both materials. Due to a much narrower bandgap, it is expected that TLMO exhibits better electrical conductivity than ZMO.

One way to visualize the Mn redox processes, during the extraction of Li or Zn from the respective materials, is to separately analyze the evolution of the density of states of each Mn ion, as a function of the concentration variation of the extracted ions. Another simpler way is to analyze the magnetic moment of each Mn. As already discussed previously, the Mn³⁺ ion has four unpaired valence electrons ($3{d^4}$) while Mn⁴⁺ has three ($3{d^3}$), therefore the magnetic moment of the Mn³⁺ ion should be larger than the one of the Mn^4+. Accordingly, the oxidation states of the Mn ions may be identified by analyzing their magnetic moments. Following this line of reasoning, the Mn ions average oxidation state, at each concentration of Li or Zn, can be obtained to describe the redox processes. Tables S6 and S7 (SI) show the results of the oxidation process from Mn³⁺ to Mn⁴⁺ for ${\text{Z}}{{\text{n}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$ and ${\text{L}}{{\text{i}}_x}{\text{M}}{{\text{n}}_2}{{\text{O}}_4}$ during battery charging. For instance, for the TLMO, $x = 1$, there are 4 Mn³⁺ ions and 4 Mn⁴⁺ in the supercell: Mn average oxidation state = Mn^3.5+. However, during the delithiation process, some Mn³⁺ ions are oxidized to Mn⁴⁺. At $x = 0.75$, i.e. for ${\text{L}}{{\text{i}}_{0.75}}{\text{M}}{{\text{n}}_2}{{\text{O}}_4},\,$ there are 3 Mn³⁺ ions and 5 Mn⁴⁺ in the supercell: Mn average oxidation state = Mn^3.62+, while at $x = 0.5$ there are 2 Mn³⁺ ions and 6 Mn⁴⁺, leading to an average oxidation state = Mn^3.75+, and at $x\, = \,0.25$ there are only 1 Mn³⁺ ion and 7 Mn⁴⁺ in the supercell: Mn average oxidation state = Mn^3.87+. Finally, for the fully delithiated TLMO, at $x\, = \,0,\,$ only Mn⁴⁺ ions are found in the material, confirming the Mn total oxidation state from Mn³⁺ to Mn⁴⁺. ZMO follows the same trend of the oxidation process. The difference is that at $x = 1$, i.e. for ${\text{ZnM}}{{\text{n}}_2}{{\text{O}}_4}$, only Mn³⁺ ions exist in the material structure. During the Zn extraction process, some Mn³⁺ are oxidized to Mn⁴⁺. At $x = 0.75$ there are 6 Mn³⁺ ions and 2 Mn⁴⁺, leading to an average oxidation state = Mn^3.25+, whereas at $x = 0.5$ there are 4 Mn³⁺ ions and 4 Mn⁴⁺ in the supercell: average oxidation state = Mn^3.5+, and at $x = 0.25$ there are 2 Mn³⁺ ions and 6 Mn⁴⁺, giving rise to an average oxidation state = Mn^3.75+. Lastly, at $x = 0$ only Mn⁴⁺ ions are found in the host matrix.

Describing the redox process by analyzing the magnetic moments is very useful in the case of simple host structures such as TLMO and ZMO. However, many cathode materials that are actually investigated have complicated compositions, such as ${\text{LiN}}{{\text{i}}_{1/3}}{\text{C}}{{\text{o}}_{1/3}}{\text{M}}{{\text{n}}_{1/3}}{{\text{O}}_2}$ (NCM), ${\text{LiN}}{{\text{i}}_{0.8}}{\text{C}}{{\text{o}}_{0.15}}{\text{A}}{{\text{l}}_{0.05}}{{\text{O}}_2}$ (NCA), ${\text{LiN}}{{\text{i}}_x}{\text{F}}{{\text{e}}_y}{\text{A}}{{\text{l}}_z}{{\text{O}}_2}$ ($x + y + z\, = \,1$, $x = 0.8$, NFA), ${\text{LiN}}{{\text{i}}_{0.93}}{\text{A}}{{\text{l}}_{0.05}}{\text{T}}{{\text{i}}_{0.01}}{\text{M}}{{\text{g}}_{0.01}}{{\text{O}}_2}$ (NATM), and ${\text{LiN}}{{\text{i}}_{0.8}}{\text{F}}{{\text{e}}_{0.1}}{\text{M}}{{\text{n}}_{0.1}}{{\text{O}}_2}$ (NFM). In this case, the analysis of which of these ions participate in the redox process during battery charging/discharging is a complicated task and, therefore, requires a more precise technique.

X-ray absorption spectroscopy (XAS) is a powerful experimental technique for detailed information on the electronic structure and its connection to oxidation state and crystalline environment, and hence is an ideal tool for mapping the redox process in battery materials. The XAS spectrum can be separated into x-ray absorption near-edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) spectroscopy. The local atomic environment around the absorbing redox ion can be determined by EXAFS, while XANES can be used to identify the valence state [47, 48]. Computer simulations have become a very effective method for visualizing XANES spectra. Currently, ab initio calculations are being used to describe the redox process of various cathode materials [47, 49–51]. In particular, the WIEN2k code has been used to calculate the transition metal K-edge XANES spectrum with high precision [47, 49, 51]. From the analysis of this edge, it is possible to characterize the redox process (oxidation/reduction) and the changes in the electronic properties of the material during battery charge/discharge.

In the present work, we used the WIEN2k code to calculate the Mn K-edge XANES spectrum during battery charging. The theoretical spectrum, calculated for the $x = 1$ concentration of Li or Zn, in the respective TLMO and ZMO compounds, is shown in figure 4(a)). In all calculations, the core-hole effect was taken into account, that is, one electron was removed from the 1 s orbital of the Mn ion and placed at the bottom of the conduction band that approximately corresponds to the final state of the x-ray absorption process. These calculations were performed in a supercell containing 112 atoms (2 × 2 × 1). Except for the pre-edge, which includes electric dipole-forbidden transition of a 1 s electron to an unoccupied 3d orbital, the Mn K-edge XANES spectrum was generated by dipole-allowed transitions from the 1 s electron of Mn to the empty bands above the Fermi energy. The peaks above the pre-edge region are attributed to the dipole-allowed $1s\, \to \,4p$ transition. Both the pre-edge region and the other main peaks of the Mn K-edge spectrum in the TLMO are shifted to higher energies when compared to the Mn K-edge spectrum in the ZMO. This is because the average valence of Mn in TLMO is 3.5+ while the average valence in ZMO is 3+. The higher the valence, the more shifted towards higher energies the spectrum will be.

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The theoretical Mn K-edge XANES spectra for TLMO and ZMO, calculated for the concentrations of Li or Zn at $x = 1,\,x = 0.5,\,{\text{and}}\,x = 0$, are illustrated in figure 4(b)). In general, the spectra are similar, both being shifted to higher energies during the extraction of Li or Zn due to the increase of the Mn oxidation state. The absorption edge shift indicates that the amount of Mn⁴⁺ ions increase as Li or Zn is extracted. This means that Mn³⁺ ions are being oxidized to Mn⁴⁺, precisely as it was predicted by analyzing the oxidation process via the magnetic moment of Mn. Mn⁴⁺ are more strongly bonded to the oxygen atoms and require more energy to be excited and this fact causes the shift of the absorption edge to higher energies.

To show that the results presented here accurately describe the Mn K-edge XANES spectra, we compare in figure 4(c) the obtained results for the $x = 1$ concentration with experimental data available in the literature [18]. As the XANES spectra determined by WIEN2k are calculated for a much lower energy range than that considered in the experiment [47, 49, 51], we have two options: to adjust the experimental energy range to the theoretical one or to adjust the theoretical energy range to the experimental one, and we chose the first option. Despite this adjustment, the band shapes must be equivalent if the theoretical results provide a good representation of the experimental data. Figure 4(c) shows that our results for the Mn K-edge XANES spectra align well with the experimental ones for $x = 1$. All main peaks determined theoretically are in concordance with those observed experimentally. This fact demonstrates that the electronic structures of the materials have been accurately calculated.