The Effect of Ni Doping on the Mechanical and Thermal Properties of Spinel-Type LiMn₂O₄: A Theoretical Study

Abstract

The development of lithium-ion batteries necessitates cathode materials that possess excellent mechanical and thermal properties in addition to electrochemical performance. As a prominent functional ceramic, the properties of spinel LiMn₂O₄ are governed by its atomic-level structure. This study systematically investigates the impact of Ni doping concentration on the mechanical and thermal properties of spinel LiNi_xMn_2−xO₄ via first-principles calculations combined with the bond valence model. The results suggest that when x = 0.25, the LiNi_xMn_2−xO₄ shows excellent mechanical properties, including a high bulk modulus and hardness, due to the favorable ratio of bond valence to bonds length in octahedra. Furthermore, this optimized composition shows a lower thermal expansion coefficient. Additionally, Ni doping concentration has a very minimal influence on the maximum tolerable temperature of the cathode material during rapid heating. Therefore, from the perspective of mechanical and thermal properties, this composition could be beneficial for improving the cycling life of the battery, since comparatively inferior mechanical properties and a higher thermal expansion coefficient make it prone to microcrack formation during charge–discharge cycles.

1. Introduction

Lithium-ion batteries have been widely used in fields such as smart mobile devices and new energy vehicles due to their characteristics of high energy density, long cycle life, low self-discharge rate, and environmental friendliness [1,2,3]. The current development focus of lithium-ion batteries is geared towards low cost and high energy density, while cathode materials with excellent performance are of paramount importance for the enhancement of battery performance.

In the spinel-type LiMn₂O₄ structure, unoccupied tetrahedra and octahedra are connected through edge- and face-sharing, forming Li⁺ ion diffusion channels that facilitate the reversible extraction and insertion of Li⁺ ions, making it suitable as a cathode material for lithium-ion batteries. Additionally, the spinel-type LiMn₂O₄ ceramic, characterized by its low cost, high operating voltage, and excellent thermal stability, has emerged as one of the most promising cathode materials for lithium-ion batteries. However, LiMn₂O₄ suffers from severe capacity fading during charge–discharge cycles, which hinders its commercial viability. On one hand, LiMn₂O₄ undergoes Jahn–Teller distortion, which blocks Li⁺ ion transport channels and consequently reduces specific capacity [4,5]. On the other hand, the disproportionation of Mn³⁺ results in the generation of Mn²⁺, which subsequently dissolves into the electrolyte [6,7]. Studies have demonstrated that doping can effectively suppress Jahn–Teller distortion and reduce manganese dissolution, thereby improving the performance of LiMn₂O₄. For instance, the Ni-doped LiNi_0.5Mn_1.5O₄ cathode material has garnered significant attention due to its ability to effectively increase the operating voltage and mitigate capacity fading [1].

Currently, studies on Ni-doped LiMn₂O₄ primarily focus on the electrochemical performance. However, Ni doping not only affects the electrochemical properties but also influences the mechanical, thermal, and thermomechanical properties. Previous studies indicate that particle cracking is frequently observed in cathode materials, which is considered one of the primary reasons for capacity fading and the eventual failure of lithium-ion batteries under high-voltage operation [8]. Moreover, such cracking has been detected in several cathode materials after prolonged cycling, which is recognized as a major degradation mechanism leading to capacity fading [9,10,11]. Therefore, not only the traditional electrochemical performance but also the mechanical and thermal properties should be considered in the investigation on lithium-ion battery cathode materials.

First-principles calculations have become an efficient method for investigating the mechanical properties of materials, including bulk modulus, and elastic constant [12,13]. Although first-principles calculations are advantageous for evaluating the mechanical properties of materials, it is difficult to analyze the underlying mechanisms affecting mechanical properties from a deep perspective, especially for complex spinel-type compounds. Recently, we have developed a novel approach, which combines first-principles calculations with the bond valence model (denoted as FP-BVM), to investigate the mechanical, thermal, and thermomechanical properties of spinel-type compounds from the perspective of chemical bonds [14,15,16,17,18]. This method is particularly suitable for investigating the composition-dependent properties of solid solutions with complex compositions and crystal structures, as it enables the calculation of chemical bonding characteristics formed by mixed anions or cations and effectively reveals the coupling effects between different chemical bonds.

In this paper, the FP-BVM method is used to simulate the mechanical, thermal, and thermomechanical properties of LiMn₂O₄ ceramics with different Ni doping concentration, namely LiNi_xMn_2−xO₄ (x = 0, 0.125, 0.25, 0.375, and 0.5), aiming to reveal the relationship among doping concentration, crystal structure, and properties from the perspective of chemical bonds. x = 0 and x = 0.5 are the two most extensively studied composition points, while intermediate doping concentrations have been relatively less explored. To identify a composition within the range of x = 0~0.5 that optimizes the mechanical and thermal properties, targeting improved mechanical and thermal stability in battery applications. Additionally, x = 0.5 represents a limiting composition in which all Mn³⁺ ions are converted to Mn⁴⁺. If compositions with x > 0.5 were selected, maintaining the charge balance within the stoichiometric LiNi_xMn_2−xO₄ spinel structure would be challenging. Therefore, a doping range of x = 0~0.5 was selected as the subject in this work. This study can guide the design of cathode materials with superior mechanical, thermal, and thermomechanical properties, thereby addressing the issue of battery capacity fading.

2. Theory and Methods

2.1. Crystal Structure Calculations

The calculations based on density functional theory were performed using the Materials Studio CASTEP version 2020 code [19]. The exchange-correlation potential was described within the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof [20]. The plane wave cutoff energy of 490 eV was set and the Brillouin zone (BZ) was sampled with a Monkhorst–Pack grid of 2 × 2 × 2. The geometries of configurations were optimized using the Broyden–Fletcher–Goldfarb–Shannon (BFGS) algorithm in the CASTEP package with convergence to 2 × 10⁻⁶ eV per atom. Spin polarization was included in the structural optimization of LiNi_xMn_2−xO₄. The initial spin polarization is 0.333 and 0.200 for Mn and Ni, respectively. And the initial magnetic moment is 5.000 and 2.000 uB for Mn and Ni, respectively. Specifically, the GGA + U approximation was employed to determine stable structures of LiNi_xMn_2−xO₄. The value of 4.46 eV, 5.04 eV, and 6.00 eV was used for Mn(III), Mn(IV), and Ni in LiNi_xMn_2−xO₄, respectively.

2.2. Mechanical Properties Calculations

After geometry optimization by first-principles calculations, the symmetry of LiNi_xMn_2−xO₄ supercell was reduced to P1. However, the structural parameters of the spinel-type structure with the symmetry of Fd3m, including the lattice constant and anion parameter, could be obtained. Based on the lattice constant and anion parameter, the Fd3m structure could be reconstructed [15,16].

A bond valence approach, founded on the reconstructed Fd3m structure, was employed to simulate the mechanical properties of spinel-type LiNi_xMn_2−xO₄. The bond valence (S_ij) between atom i and j can be calculated as follows [21]:

$$S_{ij}=\exp \left({\displaystyle \frac{d_0-d_{ij}}{b}}\right),$$

(1)

where S_ij is the bond valence, d_ij is the bond length between atom i and j, and b = 0.37 Å is a constant. The values of d₀ are 1.466, 1.732, 1.75, and 1.654 for Li–O, MnIII–O, MnIV–O, and Ni–O bond, respectively, which represent the nominal length of a bond of unit valence [22,23]. Then, the composition-weighted average bond valence (-S_AVE) can be calculated as follows [24]:

$$S_{\mathrm{AVE}}={\displaystyle \sum _i\left[X_i{\displaystyle \sum _j\left(Y_j{S}_{ij}\right)}\right]},$$

(2)

where X_i and Y_j are fraction of one type of cation and anion, respectively. For the LiNi_xMn_2−xO₄ unit cell, the weighted bond valence of bonds in its tetrahedral and octahedral sites is derived from their respective composition ratios. The bond force constant is simulated by the following [21]:

$$F_C={\displaystyle \frac{\beta {\left(\frac{8S_{ij}}{3}\right)}^{\frac{3}{2}}\left(\frac{1}{b}-\frac{2}{d_{ij}}\right)}{{d_{ij}}^2}},$$

(3)

where β = 23 nN Ų electrons⁻². Similarly, the composition-weighted average bond force constant for bonds in tetrahedra and octahedra is determined by weighing their values against the compositional ratio of LiNi_xMn_2−xO₄.

The bulk modulus (B) of LiNi_xMn_2−xO₄ can be simulated by bond valence models [24]:

$$B={\displaystyle \frac{B_{\mathrm{T}}+B_{\mathrm{M}}}{2}},$$

(4)

where B_T and B_M are bulk modulus of bonds in tetrahedra and octahedra, respectively, which can be expressed as follows [24]:

$$B_{\mathrm{T}}={\displaystyle \frac{F_C^{\mathrm{T}}}{3g_1{d}_{\mathrm{T}}}},$$

(5)

and

$$B_{\mathrm{M}}={\displaystyle \frac{F_C^{\mathrm{M}}}{3g_2{d}_{\mathrm{M}}}}.$$

(6)

Here, $F_C^{\mathrm{T}}$ and $F_C^{\mathrm{M}}$ denote the composition-weighted average bond force constants for the tetrahedral and octahedral sites, respectively, while d_T and d_M represent their corresponding bond lengths. The geometric factors g₁ and g₂ take values of 2.31 and 1, respectively [25].

According to the bond valence method, the hardness of µ-type chemical bonds (H_µ) is related to bond density (N_v^µ), bond length (d_ij,µ), and bond valence (S_ij,µ) [26,27]:

$$H_{\mu }=680.3\left({\displaystyle \frac{T{S}_{ij,\mu }^M}{d_{ij,\mu }^3}}\right)N_{\nu }^{\mu },$$

(7)

where T and M are the fitted constants, depending on the number of electrons in core of cation [27]. The values of T and M are provided in

Table 1. The value of T and M depending on the number of electrons in core of cation.

Number of Electrons in Core	T	M
0	0.67	1.8–2.0
2	0.60	1.73
10	0.54	1.64
18	0.49	1.57
28	0.60	1.50
36	0.49	1.57
46	0.67	1.43
54	0.49	1.57

. LiNi_xMn_2−xO₄ contains two distinct types of chemical bonds, located in tetrahedra and octahedra. Consequently, its hardness is determined by employing a geometric average model, weighted according to the respective bond contributions, as applied to multi-bond crystals [28]. The resulting expression for hardness follows:

$$H={\left(H_{\mathrm{T}}^{n_{\mathrm{T}}}\times H_{\mathrm{M}}^{n_{\mathrm{M}}}\right)}^{{\displaystyle \frac{1}{n_{\mathrm{T}}+n_{\mathrm{M}}}}},$$

(8)

where H_T and H_M are the hardness of bonds in tetrahedra and octahedra, respectively. n_T and n_M are the number of bonds in tetrahedra and octahedra, respectively.

Furthermore, the assessment of mechanical properties was not limited to the bulk modulus and hardness. The shear modulus (G), for instance, was acquired using Tian’s model [29]:

$$H=0.92{\left({\displaystyle \frac{G}{B}}\right)}^{1.137}{G}^{0.708}.$$

(9)

Additionally, Young’s modulus (E) and Poisson ratio (ν) can be estimated as follows:

$$E={\displaystyle \frac{9BG}{3B+G}},$$

(10)

and

$$v={\displaystyle \frac{3B-2G}{2\left(3B+G\right)}}.$$

(11)

2.3. Thermal Properties Calculations

The thermal expansion coefficient of bonds in tetrahedra (α_T) and octahedra (α_M) could be calculated as follows [30]:

$${\alpha }_{\mathrm{T}}={\displaystyle \frac{1.35k}{F_C^{\mathrm{T}}{d}_{\mathrm{T}}}},$$

(12)

$${\alpha }_{\mathrm{M}}={\displaystyle \frac{1.35k}{F_C^{\mathrm{M}}{d}_{\mathrm{M}}}},$$

(13)

where k is the Boltzmann constant. For spinel-type compounds, the thermal expansion coefficient of crystal (α) is as follows:

$$\alpha ={\displaystyle \frac{1}{4}}{\alpha }_{\mathrm{T}}+{\displaystyle \frac{3}{4}}{\alpha }_{\mathrm{M}},$$

(14)

The thermal conductivity of LiNi_xMn_2−xO₄ is estimated according to the Slack model [31]:

$$\kappa =A{\displaystyle \frac{M\prime {\Theta }^3\delta }{{\gamma }^2{n}^{\frac{2}{3}}T}},$$

(15)

where M′ and δ³ are the average mass of atoms in the crystal and the volume per atom, respectively. γ is the Grüneisen parameter, which could be derived from Poisson’s ratio (v):

$$\gamma ={\displaystyle \frac{3}{2}}\left({\displaystyle \frac{1+\nu }{2-3\nu }}\right).$$

(16)

The Debye temperature is given by the following [32]:

$$\Theta ={\displaystyle \frac{h}{k}}{\left[{\displaystyle \frac{3n}{4\pi }}\left({\displaystyle \frac{N_{\mathrm{AV}}\rho }{M_m}}\right)\right]}^{{\displaystyle \frac{1}{3}}}{\nu }_m,$$

(17)

where k the Boltzmann’s constant, and N_AV the Avogadro constant. n, ρ, and M_m are the number of atoms in unit cell, the density, and the molecular weight of unit cell, respectively. v_m is the average sound velocity. Additionally, the parameter A is expressed as follows:

$$A={\displaystyle \frac{2.43\times {10}^{-8}}{1-\frac{0.514}{\gamma }+\frac{0.228}{{\gamma }^2}}}.$$

(18)

2.4. Thermomechanical Properties Calculations

The first thermal stress resistance factor (R) is used to describe the thermal resistance of materials for high rates of heat transfer, which can be expressed from flexural strength (σ_f), Poisson’s ratio (v), Young’s modulus (E), and the thermal expansion coefficient (α) [33]:

$$R={\displaystyle \frac{{\sigma }_f\left(1-\upsilon \right)}{E\alpha }}.$$

(19)

So, the maximum temperature difference in materials for high heat transfer rates is as follows [33]:

$$\Delta T_{\max }=RS,$$

(20)

where S is the shape factor, depending on the shape of the specimen. For infinite plates, S = 1.

3. Results

3.1. Crystal Structure of LiMn₂O₄ with Different Ni Doping Concentrations

The crystal structure of spinel was determined by Bragg, in which anions form a cubic close-packed sublattice (32e sites), and cations occupy one-eighth of the tetrahedral interstices (8a site) and one-half of the octahedral interstices (16d site) [34]. For spinel-type LiMn₂O₄, the 8a sites are occupied by Li⁺, the 16d sites by Mn³⁺ and Mn⁴⁺, and the 32e sites by O²⁻. When Ni²⁺ is doped, a Ni²⁺ ion replaces one Mn³⁺ ion at the 16d site, concurrently inducing the conversion of a neighboring Mn³⁺ ion to Mn⁴⁺ to maintain charge balance. An understanding of cation site preference in LiNi_xMn_2−xO₄ enables the efficient construction of a reasonable crystal structure model, which is a prerequisite for simulating material properties.

Table 2. The total energy of LiNi_xMn_2−xO₄ supercells with different configurations.

Composition	Configuration	Total Energy (eV)
x = 0	I	−19,640.174
	II	−19,639.554
x = 0.125	III	−23,553.408
	IV	−23,552.951
x = 0.25	III	−27,466.304
	IV	−27,466.086
x = 0.375	III	−31,379.451
	IV	−31,379.308
x = 0.5	III	−35,291.864

Configuration I denotes that Mn³⁺ and Mn⁴⁺ are distributed far away from each other. Configuration II denotes that Mn³⁺ and Mn⁴⁺ are distributed close to each other. Configuration III denotes that Ni²⁺ and Mn⁴⁺ are distributed close to each other. Configuration IV denotes that Ni²⁺ and Mn⁴⁺ are distributed far away to each other.

lists the total energies of LiNi_xMn_2−xO₄ with different configurations. The results indicate that in the crystal structure of LiMn₂O₄, the total energy of configuration I is lower than that of configuration II, suggesting that Mn³⁺ and Mn⁴⁺ ions prefer to distribute far away from each other within the crystal structure. Based on this finding, the supercells of LiNi_xMn_2−xO₄ with x = 0.125, 0.25, 0.375, and 0.5 were constructed with different configurations. The data in Table 2 shows that total energy of LiNi_xMn_2−xO₄ with configuration III is lower than that with configuration IV, implying that Ni²⁺ and Mn⁴⁺ ions are distributed close to each other, which may serve to prevent structural instability caused by localized charge inhomogeneity. Guided by the cation site preference, the crystal structure models of LiNi_xMn_2−xO₄ were constructed accordingly.

After geometric optimization, the crystal structure of LiNi_xMn_2−xO₄ undergoes a symmetry reduction from Fd3m to P1. By averaging the structure with the symmetry of P1, the structural parameters of the spinel-type structure, namely the lattice constant and anion parameter, can be obtained. The lattice constant was calculated from the volume of supercells:

$$a=V^{{\displaystyle \frac{1}{3}}},$$

(21)

where a is lattice constant, and V is the volume of supercell. The anion parameter (u) was determined from the average bond length of the chemical bonds in the tetrahedra and octahedra in the spinel-type structure [34]:

$$u={\displaystyle \frac{\frac{1}{2}{R}^{\prime }-\frac{11}{12}+{\left(\frac{11}{48}{R}^{\prime }-\frac{1}{18}\right)}^{\frac{1}{2}}}{2R^{\prime 2}-2}}$$

(22)

where R^′ = d_T/d_M. The calculation results are summarized in

Table 3. The calculated lattice parameters of LiNi_xMn_2−xO₄ as well as some experimental values [35,36]. Vm, d_T and d_M denote the volume of crystal, the average bond length in tetrahedra, and the average bond length in octahedra, respectively.

Composition	Vm (Å3)	a (Å)	aexp (Å)	dT (Å)	dM (Å)	u
x = 0	511.997	8.0000	8.238	1.8382	1.9406	0.3827
x = 0.125	513.643	8.0085		1.8423	1.9416	0.3828
x = 0.25	512.018	8.0001		1.8476	1.9356	0.3833
x = 0.375	513.578	8.0082		1.8499	1.9374	0.3834
x = 0.5	512.628	8.0033	8.277	1.8631	1.9285	0.3844

. The agreement between the calculated values in this work and the experimental results [35,36] demonstrates the reliability of the crystal structure modeling and geometry optimization.

The data show that the octahedral bond length exhibits an approximately decreasing trend with increasing Ni²⁺ doping concentration, while the tetrahedral bond length increases. As mentioned above, when Ni²⁺ doping occurs, a Ni²⁺ ion replaces one Mn³⁺ at the 16d site and simultaneously converts an adjacent Mn³⁺ to Mn⁴⁺. The ionic radius of the Ni²⁺ ion is larger than that of the Mn³⁺ ion, which tends to expand the bonds in octahedra. On the other hand, the conversion of Mn³⁺ to Mn⁴⁺ in the 16d sites causes a contraction due to the smaller ionic radius of Mn⁴⁺. The combined effect of both results in an approximately decreasing trend of bond length in octahedra with increasing Ni doping concentration. In the spinel-type structure, each anion at the 32e site is coordinated with three cations at the 16d sites and one cation at the 8a site. As Ni doping increases, more Mn³⁺ ions at the 16d sites are converted to Mn⁴⁺. Since Mn⁴⁺ has a higher valence state than Mn³⁺, it exerts a stronger electrostatic attraction on the O²⁻ ions. As a result, the O²⁻ ions are closed to the cations at the 16d sites and far away from the Li⁺ ions at the 8a sites, because of the stronger electrostatic attraction. Consequently, the bond length in tetrahedra increases with higher Ni doping concentrations. According to Formula (22), the shortening of chemical bonds in octahedra and the expansion of chemical bonds in tetrahedra lead to an increasing trend in the anion parameter with rising Ni doping concentration. Through adjustments in bond lengths within the tetrahedra and octahedra, the crystal lattice constant ultimately remains nearly constant, as shown in Table 3.

3.2. Mechanical Properties of LiMn₂O₄ with Different Ni Doping Concentrations

Based on the bond valence model, the bulk modulus and hardness of LiMn₂O₄ with different Ni doping concentrations were calculated and the data is listed in

Table 4. The calculated mechanical properties including bulk modulus (B), hardness (H), shear modulus (G), and Poisson’s ratio (v) of LiNi_xMn_2−xO₄.

Composition	B (GPa)	H (GPa)	G (GPa)	E (GPa)	v
x = 0	212	13.77	119	301	0.263
x = 0.125	208	13.53	117	295	0.263
x = 0.25	214	13.80	120	304	0.263
x = 0.375	205	13.38	115	291	0.264
x = 0.5	209	13.44	117	295	0.264

. The calculated values show good agreement with experimental data [37], confirming the reliability of the calculations. The data in Table 4 indicates that the bulk modulus and hardness of LiNi_xMn_2−xO₄ initially decrease, then increase, and subsequently decrease with the rise in Ni doping concentration. At a Ni doping concentration of x = 0.25, both the bulk modulus and hardness reach their maximum values, at 214 GPa and 13.80 GPa, respectively. Although the lattice constant of LiNi_xMn_2−xO₄ remains almost unchanged with varying Ni doping concentration, the structural units, namely the tetrahedra and octahedra, undergo significant changes, ultimately leading to variation in the properties of crystal. To investigate the influence of these structural units on the properties of crystal, the mechanical properties, including bulk modulus and hardness, of chemical bonds in both tetrahedra and octahedra were calculated based on bond valence models, as shown in Figure 1. The data reveal that the bulk modulus and hardness of chemical bonds in tetrahedra decrease with the rise in Ni doping concentration, while those of the chemical bonds in octahedra exhibit a trend of initial decrease, followed by an increase, and then a subsequent decrease.

The previous research indicates that for the bonds in the same coordination environment, the excellent bulk modulus and hardness can be achieved by increasing the value of the ratio of bond valence to bond length [15]. Then, the bond valence parameters, including bond valence and bond force constant, were calculated for bonds in tetrahedra and octahedra in LiNi_xMn_2−xO₄, as shown in Figure 2. According to the bond valence method, bond valence describes the uniform distribution of valence electrons along the chemical bond [21]. Consequently, bond valence strongly depends on both the bond length and the number of valence electrons in the atoms forming the chemical bond. For the chemical bonds in octahedra, by increasing the Ni doping concentration, the bond length shortening occurs while the number of valence electrons distributed along the chemical bond decreases. These opposing effects result in an irregular trend in the bond valence of the octahedral bonds, with a maximum value of 0.59 v.u. observed at a Ni doping concentration of x = 0.25. In contrast, the bond valence of the tetrahedral bonds shows a steady decreasing trend since the bond length in tetrahedra increases with the Ni doping concentration while the number of valence electrons distributed along the bond remains unchanged. The bond force constant exhibits the same trend as the bond valence due to the quasi-linear relationship between these two parameters [24]. Combined with the bond length trends, the ratio of bond valence to bond length for chemical bonds in both tetrahedra and octahedra were obtained, as shown in Figure 2c. As the bulk modulus and hardness of chemical bonds exhibit a positive correlation with the ratio of bond valence to bond length, the trends of these mechanical properties of chemical bonds with varying Ni doping concentrations follow the same pattern as the ratio of bond valence to bond length. In spinel-type compounds, the chemical bonds in octahedra contribute significantly more to the mechanical properties of the crystal than that in tetrahedra. Consequently, the trends of the bulk modulus and hardness of crystal with varying Ni doping concentrations closely follow those of the bonds in octahedra, namely, a pattern of initial decrease, followed by an increase, and then a further decrease. However, the magnitude of variation is more pronounced than that observed in the properties of bonds in octahedra alone, due to the additional influence of the bonds in tetrahedra.

Based on the bulk modulus and hardness calculated from the bond valence model, the mechanical properties of crystal, such as shear modulus, Young’s modulus, and Poisson’s ratio, were calculated. The data in Table 4 suggests that composition with a Ni doping concentration of x = 0.25 (LiNi_0.25Mn_1.75O₄) exhibits the best mechanical properties, followed by LiMn₂O₄. This is attributed to the great ratio of bond valence to bond length in octahedra. From a perspective of mechanical properties, these two compositions may enhance the cycling stability of batteries when used as cathode materials.

3.3. Thermal Properties of LiMn₂O₄ with Different Ni Doping Concentration

Figure 3 shows the calculated thermal expansion coefficients of LiMn₂O₄ with different Ni doping concentration. The data indicates that the thermal expansion coefficient of the crystal exhibits an increasing trend with rising Ni doping concentration. To further analyze the reasons for this variation, the thermal expansion coefficients of chemical bonds in tetrahedra and octahedra were calculated as displayed in Figure 3. The thermal expansion coefficient of the chemical bonds in tetrahedra shows a significant increasing trend with higher Ni doping concentrations, rising by ~11.1%. In contrast, the thermal expansion coefficient of chemical bonds in octahedra fluctuates within the range of 4.75–4.97, with lower values observed at doping concentrations of x = 0 and x = 0.25.

It is well known that the thermal expansion of crystals is caused by anharmonic vibrations of the lattice. This process leads to changes in the equilibrium distance between ions within the crystal, which should overcome the binding forces between ions. Bond valence can describe the Coulombic forces of chemical bonds since it corresponds to the electrostatic flux between bonded atoms [26], which implies that chemical bonds with higher bond valence are more difficult to expand, resulting in lower thermal expansion coefficients. Therefore, greater bond valence indicates smaller thermal expansion coefficients for chemical bonds. As mentioned previously, with increasing Ni doping concentrations, the bond valence in tetrahedra decreases, while that in octahedra initially decreases, then increases, and subsequently decreases again, reaching a maximum at x = 0.25. Consequently, for LiNi_xMn_2−xO₄, the thermal expansion coefficient of bonds in tetrahedra increases with Ni doping, while that in octahedra reaches a minimum at x = 0.25.

In the spinel structure, the majority of cations occupy 16d sites, forming a continuous three-dimensional framework through the edge-sharing of these octahedra. Therefore, the bond lengths in octahedra directly determine the framework dimensions, and the thermal expansion of spinel-type crystals primarily depends on the thermal expansion characteristics of the chemical bonds in the octahedral coordination sites. For the LiNi_xMn_2−xO₄ system, the coefficient of thermal expansion for bonds in octahedra fluctuates within a narrow range, whereas that in tetrahedra varies significantly with changes in the Ni doping concentration. Thus, chemical bonds in tetrahedra have played a non-negligible role in the variation in the thermal expansion coefficient of crystal. Ultimately, under the combined influence of bonds both in tetrahedra and octahedra, the thermal expansion coefficient of crystal exhibits a slight upward trend. A larger coefficient of thermal expansion indicates more pronounced volume expansion of the battery during heating, making it prone to microcrack formation and related detrimental effects. From the perspective of the thermal expansion coefficient, when the Ni doping concentration is less than 0.25, the relatively small thermal expansion coefficient of LiNi_xMn_2−xO₄ is beneficial for enhancing the cycling life of the battery. Other thermal properties simulated in this work, including thermal conductivity and the Debye temperature, are summarized in

Table 5. The calculated thermal properties, including thermal conductivity (κ) and Debye temperature (Θ), of LiNi_xMn_2−xO₄.

Composition	κ (W/m·K)	Θ (K)
x = 0	20.4	793
x = 0.125	19.7	784
x = 0.25	20.5	795
x = 0.375	19.2	777
x = 0.5	19.4	780

.

3.4. Thermomechanical Properties of LiMn₂O₄ with Different Ni Doping Concentrations

When side reactions in a battery generate substantial heat, the thermal shock resistance of the cathode material should be taken into consideration. The first thermal stress resistance factor (R) can characterize the maximum temperature change under high heat transfer rates. Based on experimental results from other spinel-type ceramics, for which the values of flexural strength are usually in the range of 70–250 [38], the strength of LiNi_xMn_2−xO₄ was assumed as 200 MPa to calculate the first thermal stress resistance factor in this work. Figure 4 shows the first thermal stress resistance factor of LiMn₂O₄ with different Ni doping concentrations. The results indicate that the first thermal stress resistance factor remains nearly constant, at approximately 80, and is largely independent of the Ni doping concentration. According to Equation (19), the first thermal stress resistance factor is influenced by the thermal expansion coefficient, the fracture strength, Poisson’s ratio, and Young’s modulus. The fracture strength is an assumed value and is independent of composition; Poisson’s ratio is only slightly influenced by composition (as shown in Table 4). Therefore, Young’s modulus and the thermal expansion coefficient become the primary factors affecting the thermal shock resistance factor. With increasing Ni doping content, Young’s modulus initially decreases, then increases, and subsequently decreases again, while the thermal expansion coefficient exhibits an opposite trend to that of Young’s modulus. The opposing effects of these two factors result in the thermal shock resistance factor remaining nearly constant. This implies that the Ni doping concentration has a very minimal influence on the maximum tolerable temperature of the cathode material during rapid heating.

Upon investigating the effects of composition-dependent Ni doping concentration on the mechanical and thermal properties of LiNi_xMn_2−xO₄, a comprehensive understanding of the properties of LiNi_xMn_2−xO₄ can be obtained, enabling the assessment of cathode materials from the perspectives of mechanical and thermal properties. Figure 5 shows the mechanical and thermal properties of LiNi_xMn_2−xO₄ in the radar chart. The mechanical and thermal properties of LiNi_xMn_2−xO₄ were normalized against their respective maximum values. Consequently, all parameters were scaled between zero and one for comparison. The radar chart indicates that the composition with a Ni doping concentration of x = 0.25 exhibits the optimal combination of mechanical and thermal properties, which shows great mechanical properties and a low thermal expansion coefficient, followed by the composition with a Ni doping concentration of x = 0.

As electrode materials, the electrochemical performance of LiNi_xMn_2−xO₄ is undoubtedly critical. However, their mechanical and thermal properties cannot be overlooked. Poor mechanical and thermal properties can easily lead to particle cracking, generating fresh surfaces that accelerate side reactions and heat generation, thereby reducing the cycle life of battery. Especially in high-energy-density batteries, superior mechanical and thermal properties become even more critical. For the LiNi_xMn_2−xO₄ ceramic, LiNi_0.5Mn_1.5O₄ exhibits superior electrochemical performance, since all Mn³⁺ ions are oxidized to Mn⁴⁺ at this Ni doping concentration, eliminating the Mn³⁺ disproportionation reaction and thereby improving its electrochemical behavior. Nevertheless, from a mechanical and thermal perspective, the comparatively inferior mechanical properties and higher thermal expansion coefficient make it prone to microcrack formation during charge–discharge cycles, consequently impairing the cycling life battery. Alternatively, the composition with a Ni doping concentration of x = 0.25 could be considered. On one hand, Ni doping can mitigate the Mn³⁺ disproportionation reaction to some extent. On the other hand, this composition offers the best mechanical properties and the lowest thermal expansion coefficient, which may help improve the cycling life of the battery.

4. Conclusions

In this work, the influence of Ni doping concentration on the mechanical and thermal properties of LiMn₂O₄ was revealed by first-principles calculations combined with bond valence models. The results indicated that Mn³⁺ and Mn⁴⁺ ions prefer to distribute far away from each other within the crystal structure of LiNi_xMn_2−xO₄, and Ni²⁺ and Mn⁴⁺ ions are distributed close to each other, which may serve to prevent the structural instability caused by localized charge inhomogeneity. The composition with a Ni doping concentration of x = 0.25 (LiNi_0.25Mn_1.75O₄) exhibits the best mechanical properties, which is attributed to the great ratio of bond valence to bond length in octahedra. When the Ni doping concentration is less than 0.25, the relatively small thermal expansion coefficient of LiNi_xMn_2−xO₄ is beneficial for enhancing the cycling life of the battery. Additionally, the Ni doping concentration has a very minimal influence on the first thermal stress resistance factor. From the perspective of the mechanical and thermal properties, LiNi_xMn_2−xO₄ may enhance the cycling stability of batteries when used as cathode materials, followed by LiMn₂O₄. This study elucidates the influence of Ni doping concentration on the mechanical and thermal properties of LiMn₂O₄ electrode materials from a bonding perspective, thereby optimizing electrode performance through mechanical and thermal enhancement and providing a new strategy for electrode material design.