Elastic Mechanics Study of Layered $\mathrm{Li}({\mathrm{Ni}}_x{\mathrm{Mn}}_y{\mathrm{Co}}_z){\mathrm{O}}_2$

Understanding the elastic mechanical behavior of layered $\mathrm{Li}({\mathrm{Ni}}_x{\mathrm{Mn}}_y{\mathrm{Co}}_z){\mathrm{O}}_2$ (NMC) cathode materials is critical for developing strategies to address their prominent cracking issues and mitigate the mechanical degradation of the cathode of lithium-ion batteries (LIBs). So far, a systematic and in-depth investigation into the elastic mechanical properties of NMC materials is still lacking. Hence, both the isotropic and anisotropic mechanical properties, including elastic constants, Young’s modulus, shear modulus, bulk modulus, compressive modulus, linear compressibility, Poisson’s ratio, Pugh’s ratio, Cauchy pressure, and Kube’s log-Euclidean and universal elastic anisotropy indexes, of seven NMC materials with different compositions are systematically studied here through first-principles calculations. The bulk modulus is proved to be an isotropic mechanical quantity, and its proper relationship with the anisotropic linear compressibility is revealed. Then, we investigate how the isotropic and anisotropic mechanical properties of NMC materials can be tuned by the compositions of $\mathrm{Ni}$, $\mathrm{Mn}$, and $\mathrm{Co}$. It is found that the elastic moduli of NMC materials decrease as the $\mathrm{Ni}$ content increases, and $\mathrm{Mn}$ plays a positive role in not only enhancing the elastic moduli but also in reducing the mechanical anisotropy of NMC materials. Through a quantitative chemical bond analysis, we find that the reason for such a dependence of the elastic moduli on the transition metal (TM) compositions of NMC materials lies in the difference in the strengths of TM–O bonds, and the positive effect of $\mathrm{Mn}$ mainly stems from the contribution of the ionic bonding part of the $\mathrm{Mn}-\mathrm{O}$ bond due to the high average valence state (+4) of $\mathrm{Mn}$ ions; this highlights the benefits of doping with other high-valence-state ions for the promotion of the mechanical properties of NMC materials. Besides, the applicability, physical meaning, and proper use of Pugh’s ratio and the Cauchy pressure in metal-oxides like NMC materials, as well as their relations with Poisson’s ratio, are clarified. The analysis of the relative ductility and brittleness of NMC materials with different compositions via Pugh’s ratio and the isotropic Poisson's ratio reveals a negative correlation between the relative ductility and the magnitude of the modulus. Cauchy pressures of layered NMC materials are found to be directional, with an intralayer negative value but an interlayer positive value, which predicts the significant covalent bonding character of the TM–O bonds, but a nearly ionic dominated bonding character of the $\mathrm{Li}-\mathrm{O}$ bonds, and this qualitative result has been further proved by a quantitative chemical bond analysis. Furthermore, an in-depth investigation of the three-dimensional spatial distribution characteristics of anisotropic mechanical properties of NMC materials is conducted. It is found that, first, the distributions of directions of the extreme values of various anisotropic mechanical properties all exhibit an approximate trigonal symmetry to some extent; second, the anisotropy is most prominent in the $\{2\overline{1}0\}$ crystal plane family; third, the $(104)$ plane and $[\overline{4}\overline{8}1]$ direction are, respectively, prone to be the cleavage plane and cleavage direction, along which the microcracks and even mechanical failures may be susceptible to occur due to stress concentration. The findings presented in this study will provide guidance for the design and development of robust and reliable LIBs.

Popular Summary

The cracking and mechanical degradation of layered $\mathrm{Li}({\mathrm{Ni}}_x{\mathrm{Mn}}_y{\mathrm{Co}}_z){\mathrm{O}}_2$ (NMC) cathode materials is prominent in lithium ion batteries (LIBs) with high energy densities. Thus, the authors work toward an in-depth understanding of the mechanical behavior of NMC materials. Isotropic and anisotropic elastic mechanical properties are systematically assessed using ab initio calculations. As a result, a dual positive effect of manganese is discovered and understood via a quantitative chemical bond analysis. Moreover, the applicability, physical meaning, and proper use of Pugh's ratio and Cauchy pressure in metal-oxides like NMC materials, as well as their relations with oisson's ratio, are clarified. They report that relative ductility is negatively correlated with the magnitude of modulus, and Cauchy pressures are directional. Furthermore, in a study of 3D spatial distribution characteristics of the anisotropic mechanical properties, the most elastic anisotropic crystal planes and the potential cleavage plane are uncovered. These findings may guide the design and development of robust and reliable LIBs.

Figure 1

(a) Schematic representation of the composition distribution of various NMC materials studied in this work. (b) Top view and (c) side view (visualized by vesta [129]) of the crystal structure model for the supercell of $\mathrm{Li}({\mathrm{Ni}}_{0.5}{\mathrm{Mn}}_{0.3}{\mathrm{Co}}_{0.2}){\mathrm{O}}_2$ as a representative of the various NMC materials studied. Green, $\mathrm{Li}$; red, $\mathrm{O}$; silver, $\mathrm{Ni}$; purple, $\mathrm{Mn}$; blue, $\mathrm{Co}$. Note that for the convenience of viewing, the relative size of $\mathrm{O}$ ions and metal ions shown here are not consistent with their actual sizes.

Figure 2

Average mechanical properties of bulk NMC polycrystal. (a) Isotropic bulk moduli B, (b) isotropic shear moduli G, (c) isotropic Young’s moduli E, and (d) isotropic Poisson's ratio $\nu$ and Pugh’s ratio $R^P$. Subscripts V, R, and H denote the Voigt, Reuss, and Hill approximations, respectively.

Figure 3

3D spatial distribution of the anisotropic mechanical properties of bulk $\mathrm{NMC}532$ single crystal. (a) Directional Young’s modulus, (b) directional compressive modulus, (c) directional shear modulus in maximum values, (d) directional shear modulus in minimum values, (e) directional Poisson’s ratio in maximum values, and (f) directional Poisson’s ratio in minimum values. Distribution directions of maxima and minima can be, respectively, referred to as red and blue areas. Notably, the y-z plane here corresponds to $\varphi ={90}^{\circ }$, and thus, corresponds to the $(2\overline{1}0)$ crystal plane, and the six planes obtained by rotating the y-z plane around the z axis at the angles of $\varphi =k\times {60}^{\circ }(k=0,1,2,3,4,5)$ constitute the crystal planes of the $\{2\overline{1}0\}$ family. Visualization is completed by matlab with data processed by the vaspkit [137] tool. Data of directional compressive moduli were postprocessed by us based on data of directional linear compressibility obtained from vaspkit. The values of the moduli shown here are in GPa.

Figure 4

Maximum and minimum values of anisotropic (a) Young’s modulus and (c) shear modulus of bulk NMC single crystal. (b),(d) Assessment of their corresponding anisotropies by the custom-defined anisotropy parameters.

Figure 5

Universal elastic anisotropy index, $A^U$, and Kube’s log-Euclidean elastic anisotropy index, $A^L$, of bulk NMC single crystals.

Figure 6

$M-\mathrm{O}$ bond strengths in various NMC materials. (a) −IPCOHP average of each $M-\mathrm{O}$ bond species, (b) −IPCOHP overall average of all the $M-\mathrm{O}$ bonds, (c) ICOBI average of each $M-\mathrm{O}$ bond species, and (d) overall average covalent and ionic bond strengths of all the $M-\mathrm{O}$ bonds. $M$ = $\mathrm{Li},\mathrm{Ni},\mathrm{Mn},\mathrm{Co}$.