First-principles Study on Low Index Surface Structure Optimization and Surface Energy of LiMn2O4 Spinel Oxides

doi:10.6023/A21050213

Abstract

The first principles density functional calculation method was used to calculate the index of low surface properties of LiMn₂O₄ spinel. Comparing with the bulk phase structures of LiMn₂O₄ crystals calculated by generalized gradient approximation (GGA) and generalized gradient approximation+on-site coulombic (GGA+U), it is found that the lattice parameters are obviously larger when the effective U value for the d orbital of Mn. However, the structural parameters of charge order and Jahn-Teller distortion are not found in own calculation. The results show that the Li terminal surface energy is lower when the (001), (010) and (100) surfaces of LiMn₂O₄ spinel in the state of lacking Li. The surface energy of (110) Mn/O terminal is lower than that of Li/Mn/O terminal in the state of lacking Li. The surface energy of (111) is the lowest in the low index surfaces. The surface energy of (111) after surface reconstruction is as low as 0.270 J/m², which is the most stable section of spinel structure in this work. Considering antiferromagnetism, the surface energies of Mn/O terminal on (110) surface are lower than those of Li/Mn/O terminal, which Mn/O terminal surface energies are 1.050 J/m² in the [↑↑↓↓] magnetic order and 1.061 J/m² in [↑↓↑↓] magnetic order, respectively. The antiferromagnetic (110) surface is more stable in the spin configuration than in the magnetic order. We found that the structure of undercoordinated manganese ions on the surface are more stable by position exchange with the fully coordinated lithium ions by the observation of the surface reconstruction of (111). The Jahn-Teller effect is reduced when the average manganese oxidation state of the reconstructed surface is reduced. Except for (111) surface, the surface energies of other surfaces in the ferromagnetic state are similar to those in the antiferromagnetic state. Among them, the surface structures of (001)T3, (100)T1, (110)T1 and (111)T2 have the least surface energy among their own different surface terminals. This study provides theoretical calculation reference for understanding the capacity attenuation problem of LiMn₂O₄ materials and related experiments. It is also helpful to promote the research of high-performance lithium battery materials.

Key words: LiMn₂O₄ spinel oxide, first principle, Jahn-Teller effect, low exponent surface, surface reconstruction

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Yuan Lu, Jifen Wang, Huaqing Xie. First-principles Study on Low Index Surface Structure Optimization and Surface Energy of LiMn₂O₄ Spinel Oxides[J]. Acta Chimica Sinica, 2021, 79(8): 1058-1064.

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Fig. & Tab. 15

Figure1. LiMn2O4 cubic spinel structure, indicating the positions of atoms Li (green), Mn (magenta), and O (red)

Figure 2. Ternary phase diagram, indicating stable compound complex Li-Mn-O

化学式	平板混合物组分	锂锰氧化物基态能量∆G_f
Slab: Li₁₊_xMn₂O₄
Li₁₀Mn₁₆O₃₂	4.67LiMn₂O₄+2.67Li₂MnO₃+1.33Mn₃O₄	E_LiMn2O4= –47.17 eV
Li₁₈Mn₃₂O₆₄	12.67LiMn₂O₄+2.67Li₂MnO₃+1.33Mn₃O₄	E_Li2MnO3= –36.65 eV
Li₂₆Mn₄₈O₉₆	20.67LiMn₂O₄+2.67Li₂MnO₃+1.33Mn₃O₄	E_Mn3O4=–52.30 eV
Slab: LiMn₂₊_xO₄
Li₈Mn₂₀O₃₂	8LiMnO₂+4Mn₃O₄	E_Li10Mn16O32= –387.71 eV
Li₁₆Mn₃₆O₆₄	5.33LiMn₂O₄+5.33Li₂MnO₃+6.67Mn₃O₄	E_Li16Mn36O64= –795.80 eV
Li₂₄Mn₅₂O₉₆	13.33LiMn₂O₄+5.33Li₂MnO₃+6.67Mn₃O₄	E_Li24Mn52O96= –1172.98 eV

Table 1. Non-stoichiometric plate composition as summarized by three-phase diagram

LiMn₂O₄	实验值(nm)	GGA (nm)	GGA+U (nm)	GGA (nm)	GGA+U (nm)
a	0.8238^[27]	0.8146	0.8419	0.809^[12]	0.843^[12]
b	0.8238^[27]	0.8146	0.8419	0.809^[12]	0.843^[12]
c	0.8238^[27]	0.8146	0.8419	0.809^[12]	0.843^[12]

Table 2. Experimental and computational lattice parameters a, b and c values of LiMn2O4 spinel

Figure 3. (001) Surface and (010) surface structure, atomic structure of spinel LiMn2O4(001) surface: T1: Asymmetric Li- and Mn/O-terminal Li8Mn16O32 surface (eight layers); T2: Li8Mn16O32 surface (nine layers) of symmetrical Li terminal; T3: symmetrical Li terminal, non-stoichiometric Li10Mn16O32 surface (nine layers). Li (green), Mn (magenta) and O (red)

Terminated	Atomic structure	Top view
Li terminated
	T1
Mn/O terminated
	T2

Table 3. Surface structure and top view of LiMn2O4(100)

Figure 4. (110) Surface structure diagram: (a) Mn/O terminal Li8Mn16O32 surface (five layers); (b) Li/Mn/O terminal Li8Mn16O32 surface (five layers). Li (green), Mn (magenta), and O (red)

Figure 5. Atomic structure of spinel LiMn2O4(111) surface: (a) asymmetric Li/Mn/O and Li/O terminal Li24Mn48O96 surface; (b) Li24Mn48O96 with symmetrical equivalent Li/Mn/O terminal; (c) Non-stoichiometric laminae Li24Mn52O96 with 4Mn atoms added in the bottom layer. Surface Li (green), Mn (magenta) and O (red)

Figure 6. Atomic structure diagram of reconstructed (111) surface of LiMn2O4 T1: (a) surface of Li8Mn16O32 reconstructed at the top surface (T1-1); (b) Li16Mn32O64 surface (T1-2); (c) Li24Mn48O96 surface (T1-3)

Figure 7. Atomic structure diagram of (111) LiMn2O4 T2 and T3 surfaces reconstructed from upper and lower surfaces: (a) Li16Mn32O64 surface (T2-1); (b) Li24Mn48O96 surface (T2-2); (c) Li16Mn36O64 surface (T3-1); (d) Li24Mn52O96 Surface (T3-2)

Surface structure		Surface energy (FM)	Surface energy (AFM)	Literature reference
(001)	T1	0.598	0.628	0.860^[36]
	T2	0.600	0.626	0.840^[36]
	T3	0.597	0.615	0.720^[36]
(100)	T1	0.606	0.654	0.870^[12]
(100)	T2	1.127	1.195	1.280^[12]
(110)	T1	1.026	1.050	1.410^[12]
(110)	T2	1.971	1.969	1.760^[12]
(010)	T1	0.599	0.668	1.300^[12]
	T2	0.603	0.667	0.960^[12]
	T3	0.651	0.644	N/A
(111)	T1	1.005	1.299	1.290^[11]
	T2	0.812	0.896	0.850^[11]
	T3	1.458	1.588	N/A

Table 4. The surface energies of LiMn2O4 in the low index directions of (100), (010), (001), (110) and (111) are calculated using GGA+U (unit: J/m2)

Figure 8. Surface energy diagrams of LiMn2O4(001) and LiMn2O4(010)

Terminated	Surface energy	Fu^[39]	Benedek^[11]
Li terminated	0.654	0.40	0.58
Mn/O terminated	1.195	0.90	0.98

Table 5. surface energy scale for LiMn2O4(100) (unit: J/m2)

Terminated	Total energy	Surface energy [↑↑↓↓]	Surface energy [↑↓↑↓]
Mn/O terminated	–364.243 eV	1.050	1.061
Li/Mn/O terminated	–352.375 eV	1.969	1.998

Table 6. Surface energy scale for LiMn2O4(110) (unit: J/m2)

Figure 9. The surface energy of the DFT with the increase of plate thickness was calculated: (a) unconstructed (111) surface energy of T1, T2 and T3; (b) reconstructed surface energy (T1R, T2R and T3R)

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LiMn₂O₄尖晶石氧化物的低指数表面结构优化及表面能的第一性原理研究

First-principles Study on Low Index Surface Structure Optimization and Surface Energy of LiMn₂O₄ Spinel Oxides

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LiMn2O4尖晶石氧化物的低指数表面结构优化及表面能的第一性原理研究