Enhanced Electrochemical Property of Li1.2−x Na x Mn0.54Ni0.13Co0.13O2 Cathode Material for the New Optoelectronic Devices

The Li-rich Mn-based oxide Li1.2Mn0.54Ni0.13Co0.13O2 has been extensively studied as a cathode material of the battery module for new optoelectronic devices. To improve and enhance the electrochemical performance, sodium doping is one of the effective approaches. According to the density functional theory of first-principles, the band gap, partial density of states, lithiation formation energy, electron density difference, and potential energy of electrons for Li1.2−x Na x Mn0.54Ni0.13Co0.13O2 were simulated with Materials Studio, Nanodcal, and Matlab. When the sodium doping amount x = 0.10 mol, simulations show that Li1.2−x Na x Mn0.54Ni0.13Co0.13O2 has a better conductivity. The potential maps of Li1.2−x Na x Mn0.54Ni0.13Co0.13O2 obtained in Matlab demonstrate that the potential barrier is lower and the rate capability is enhanced after sodium doping. Results of analyses and calculations agree with the experimental result of Chaofan Yang’s group. This theoretical method could be a great avenue for the investigation of the battery application of new optoelectronic devices. Also, our findings could give some theoretical guidance for the subsequent electrochemical performance study on doping in the field of lithium-ion batteries.


INTRODUCTION
The commercial lithium-ion batteries (LIBs) have many advantages, such as their energy saving, high energy density, good cycle performance, less pollution, no memory characteristics, and rechargeable property [1]. With the rapid development of new optoelectronic devices in recent decades, LIBs have been widely applied as the stationary energy storage of the electro-optical conversion devices. Nowadays, the actual specific capacity of conventional cathode materials, such as LiCoO 2 , LiMnO 2 , spinel LiMn 2 O 4 , ternary lithium nickel cobalt aluminum oxide, and olivine LiFePO 4 , is less than 160 mAh/g, but that of the anode is much higher. Commercialized cathode materials are not adequate to match the next-generation power battery. In addition, the percentage of the cathode's cost in the whole battery's cost is very high. To meet the needs of people, the low-cost cathode materials with higher energy density and discharge/charge rate capability are urgent to be explored.
The layered Li-rich Mn-based Ni-Co-Mn (NCM) ternary cathode material xLi 2 MnO 3 ·(1−x) LiMO 2 (0 < x < 1, M Ni, Co, Mn, Ni 1/2 Mn 1/2 , Ni 1/3 Mn 1/3 Co 1/3 ) has attracted extensive attention owing to its lower price and good performance. Its space group is R3m, and its layered structure is α-NaFeO 2 -type like LiCoO 2 ; their synthesis is always thought as formed by two phases: monoclinic Li 2 MnO 3 -layered and rhombohedral LiMO 2layered moieties [2]. However, their complex crystal structure has not yet been fully realized. It is known that Co is poisonous and expensive. In Li-rich Mn-based NCM, the percentage of Co is far lower than that of Mn; thus, with the advantages of low cost and high safety, this material is superior to the commonly used cathode material. Meanwhile, for the layered structural stability influenced by the Li 2 MnO 3 component, when its first charging voltage is higher than 4.5 V (vs Li + /Li), Li and O are removed together and its theoretical capacity is up to 377 mAh/g. Therefore, the layered Li-rich Mn-based NCM is a hot candidate for the new LIBs.
Recently  [3,4], and it is considered one of the most promising layered cathode materials for the new battery of optoelectronic devices and LIBs. Its discharge-specific capacity is higher than 250 mAh/g in the voltage range from 2.0 to 4.8 V at 0.1 C. Its precursors are made by sol-gel, solid phase, coprecipitation, combustion, spray pyrolysis, and molten salt synthesis [5]. However, the application of this material has trapped seriously in higher-power systems due to high first irreversible specific capacity, poor cycling stability, and low rate capability [6]. To improve the electrochemical performance of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 , many effective approaches, such as surface modification [7,8] and doping [9,10], had been employed experimentally. The cycling stability and the rate capacity can be dramatically improved by coating with the La-Co-O compound [7] . Since Cs doping can alleviate structural transition from layer to spinel, the Cs-doped Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 has a better rate capability, a higher initial Coulombic efficiency, and a restrained discharge voltage [10]. Yb doping [11], Na + and F − co-doping [12], and Mg 2+ and PO 4 3− dual doping [13] were taken to strengthen the electrochemical performance of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 . The K-doped Li 1.2 Mn 0.52 Ni 0.2 Co 0.08 O 2 has a higher Coulombic efficiency, a larger reversible discharging capacity, and a more well-defined layered structure, which are mainly ascribable to the accommodation of bigger metal ions K + enlarging Li layers to facilitate the diffusion of Li + and stabilize the structure [14]. Sodium doping in Li 1.2 Mn 0.54 Co 0.13 Ni 0. 13  In parallel with these experimental efforts, the density functional theory (DFT) based on first-principles [16][17][18][19]

Density Functional Theory
DFT originates from the uniform electronic gas model, which is called the Thomas-Fermi model [16,20]. On the assumption of no interaction between electrons, the Schrödinger equation of the electron's motion is the wave equation shown in the following: Based on the distribution of free electrons' energy levels at absolute zero, the electron density ρ is shown in the following equation: Here, E F is the Fermi energy level, and the kinetic energy T e of a single electron is shown in the following equation: And the system's kinetic energy density is shown in the following equation: Considering the external field u(r) of the classical Coulombic interaction between nuclei and electrons, the total energy of the electron system can be obtained as shown in the following equation: The above equation shows the electronic systemic total energy is affected only by the electron density function r(r); hence, this theory of Thomas-Fermi model is called DFT. But this model could not be used directly. Then, Hohenberg and Kohn proposed the more exact density functional method (HK theorems) [17,21] considering the nonrelativistic, adiabatic, and single-electron approximations. In fact, the theoretical basis of DFT is HK theorems including the first theory and the second theory. According to HK theorems, when the particles' number is constant, the ground state of particles can be expressed by a variational function of energy function on the number density function of particles ρ(r), and the total energy E v [ρ(r)] relevant to external potential is shown in the following equation: , which is independent of the external field, V ne [ρ(r)] is the attraction potential between nuclei, T[ρ(r)] is the kinetic energy of noninteracting particle models, 1 2 ρ(r)ρ(r′) |r−r ′ | drdr ′ is the Coulombic repulsion, and E xc [ρ(r)] is the exchange-correlation energy functional.

Kohn-Sham Equation and Exchange-Correlation Functional
From the Kohn-Sham equation [22], ρ(r) and T [ρ(r)] can be solved as shown in the following Hamiltonian: is the Coulombic potential between electrons, and V xc [ρ(r)] is the exchange-correlation potential.
E xc [ρ(r)] is generally solved by the local density approximation (LDA) and the generalized gradients approximation (GGA) [23]. When the system's electron density in the space is not changed much, LDA is used to give more accurate results. Considering the uniformity of the electron density, GGA can get better energy features and more rigorous results than LDA. Now, GGA is one of the important thermotical methods employed by the first-principles and relevant researches of systemic properties. Under GGA, there are many kinds of exchange-correlation functionals, such as PW91 (Perdew-Wang) [24] and PBE (Perdew-Burke-Ernzerhof) [25]. With the development of computing power, theoretical investigation based on DFT is more and more important for the performance study of materials.

METHOD AND MODEL
Using the PW91 method with the PBE exchange-correlation functional and GGA, the electronic conductivity of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 was implemented by CAmbridge Serial Total Energy Package (CASTEP) of Materials Studio 8.0, which is the quantum mechanical procedure. The plane wave pseudopotential method was used in CASTEP. The Coulombic attraction potential, between the inner layer electrons around the nucleus and those of the outer layer [26], was described by the ultrasoft pseudopotential. A plane wave cutoff was set at 440 eV. To relax all structures [27], a 4 × 4 × 1 mesh of k-points in the Monkhorst-Pack scheme was taken. The self-consistency energy tolerance was 1 × 10 −6 eV. To obtain the local stable structure of the material, the structure geometry should be optimized; the maximum stress tolerance, the maximum displacement tolerance, and the average force on every atom were the same as those in our previous work [19]. And DFT calculations had been carried out with the virtual mixed atom method.  Table 1, all band gap values are listed. Figure 2 shows the relationship between the band gap and x. According to Figure 2, the band gap curve of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 has three inflection points at x 0.02 mol, x 0.07 mol, and x 0.12 mol, respectively, where the band gap has changed clearly. When x 0.02 mol, the band gap value begins to decrease; at x 0.07 mol, its value increases slightly, which may be ascribed to the expanding volume and disorder of Ni 2+ /Li + cation mixing, but from then on, it decreases continually. In other words, it basically decreases with increasing x until x 0.12 mol, which indicates sodium doping can effectively improve the conductivity of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 when 0.02 < x < 0.13 mol.
The sodium doping influence on the conductivity of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 was achieved by the PDOS, which can clearly describe the bonding and density of states near the Fermi level. Figure 3 shows its PDOS, respectively, when x 0, 0.01, 0.04, and 0.10 mol. The peak of the PDOS corresponds to the electron number at this energy level. The colored lines in Figure 3 represent the density of different orbital states. In Figure 3B, when x 0.01 mol, the PDOS peak is about 181 eV, which is subtly different from that of the pristine as shown in Figure 3A; when x 0.02 ∼ 0.03 mol, PDOS peaks have increased slowly; when x 0.04 mol (shown in Figure 3C), the PDOS peak at the Fermi level around 201 eV may be ascribed to the wider Li-O layers made by the bigger sodium atoms' substitution, and the conductivity of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 is getting better distinctly; when x 0.05 ∼ 0.14 mol, the PDOS peaks have not changed much. Figure 3D shows the PDOS peak is about 207 eV when x 0.10 mol; but when x 0.15 mol, the peak of the PDOS declines. Therefore, the right amount of sodium doping can multiply greatly the electrons near the Fermi level, and sodium doping should be within x 0.04 ∼ 0.14 mol.

Cell Volume and Lithiation Formation Energy
The volume and formation energy of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 were calculated. The volume data after doping indicate that x should be controlled at x < 0.11 mol. The volume is a little bigger at x 0.07 mol than that at x 0.06 mol; at x 0.08 mol, it decreases again; when x > 0.10 mol, the volume expansion is huge, which will lead to the structural instability. Due to the bigger sodium atom than the lithium atom, the interslab distance of the Li-O layer can be enlarged, and the diffusion ability of Li + in the crystal lattice is strengthened to enhance the conductivity of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 . More importantly, the proper sodium doping can stabilize the layered crystal structure.
It is very important to analyze the formation energy, which explicitly decides the difficulty of the lithiation/delithiation process. The greater the formation energy of metal oxide is, the higher the difficulty is for atoms to get free from the crystal lattice. The lithiation formation energy E is shown in the following equation: where E t is the supercell's total energy, E dl is the delithiation, and E dil is the supercell's energy after delithiation. In Figure 4, the energies in Eq. 8 are plotted to investigate the relationship between E and x. According to Figure 4, E has varied with x. When 0 < x < 0.09 mol, E decreases extremely, which indicates Li + can be deintercalated more easily and the cycling stability and rate capability of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 can be continually enhanced; when 0.09 < x < 0.12 mol, E remains stable; when x 0.10 mol, E is lowest and the rate capability is best; when x > 0.12 mol, E raises gradually. Therefore, the best doping amount x 0.10 mol.

Electron Density Difference
To analyze the electrons' distribution near local atoms, the electron density difference of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 was modulated. Compared with the pristine (Figure 5A), when 0 < x < 0.04 mol, the color of the electron cloud around atoms has not changed obviously and the coverage of the electron cloud is getting bigger slowly; in Figure 5B, the color of the electron cloud has changed much and the electron cloud's coverage is bigger significantly, which exhibit that the conductivity of Li 0.08 Na 0.04 Mn 0.54 Ni 0.13 Co 0.13 O 2 is better than that when x < 0.04 mol; when x 0.10 mol (Figure 5C), the color is orange and the coverage expands much, meaning that free electrons have increased enormously and its conductivity is far better than before; when x 0.11 mol (Figure 5D), the color of the electron cloud is the same as that of Li 1.1 Na 0.1 Mn 0.54 Ni 0.13 Co 0.13 O 2 ; when 0 < x < 0.14 mol, the coverage of the electron cloud is expanding continually until when x 0.14 mol; when x > 0.14 mol, the electron cloud's coverage has shrunk a little. Therefore, sodium doping can improve the conductivity of Li 1.2 Mn 0.54 Ni 0.13 Co 0.13 O 2 , and the excellent amount of sodium doping x 0.05-0.13 mol.

Potential Energy of Electrons
To study the rate capability after doping, the electrons' potential energy of Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 had been profiled. In a potential well, if electrons have lower potential energy and get the extra external energy, they can cross freely over the potential well. In Figure 6, the 3D potential energy map of Li 1.1 Na 0.1 Mn 0.54 Ni 0.13 Co 0.13 O 2 is shown. The different colors represent the potential energy change. In Figure 6, the taking turns of the potential barrier and well show Li 1. For the purpose of investigating the sodium doping influence on the potential energy well, diffusion paths were simulated. The 2D potential energy image of Li 1.1 Na 0.1 Mn 0.54 Ni 0.13 Co 0.13 O 2 is shown in Figure 7. Electrons will diffuse more facilely along the path marked with blue "*", which represents the minimum potential energy and can offer abundant channels to diffuse. And the energy barrier of Li + insertion/extraction is reduced in the crystal lattice. Therefore, electrons and Li + can be removed and migrated to other places almost without any energy barrier. In Figure 7, the potential energy of Li 1.1 Na 0.1 Mn 0.54 Ni 0.13 Co 0.13 O 2 is from 36 to 1 eV, and each marked path is not the same. According to the calculations of potential energy for Li 1.2−x Na x Mn 0.54 Ni 0.13 Co 0.13 O 2 , the minimum potential energy decreases with rising x, which     other approaches should be taken as well to further improve the energy density, reversible charge capacity, and cycling performance. Our calculations, analyses, and simulations based on DFT can provide some theoretical proposals for the doping study about the electrochemical performance, and these methods can contribute to the performance study of the battery module for new electro-optical conversion devices.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, and further inquiries can be directed to the corresponding author.