硅酸盐学报

二次电池正极材料能带高通量计算与电化学特性关联分析

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梁叔全 ¹^,² , 郭珊 ¹ , 曹鑫鑫 ¹^,² , 马君剑 ¹ , 周江 ¹^,² , 方国赵 ¹^,²

硅酸盐学报 | 电化学储能材料计算与设计专题—研究论文 2025,53(7): 1786-1800

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硅酸盐学报 |电化学储能材料计算与设计专题—研究论文 2025 , 53 (7) : 1786 -1800

二次电池正极材料能带高通量计算与电化学特性关联分析

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梁叔全¹^,², 郭珊¹, 曹鑫鑫¹^,², 马君剑¹, 周江¹^,², 方国赵¹^,²

作者信息

^1．中南大学材料科学与工程学院，长沙 410083

^2．中南大学电子封装及先进功能材料湖南省重点实验室，长沙 410083

作者简介:

梁叔全（1962—），男，博士，教授。

High-throughput Calculation of Electron Band Structure and Correlation Analysis of Electrochemical Characteristics of Cathodes in Secondary Battery

Shuquan LIANG¹^,², Shan GUO¹, Xinxin CAO¹^,², Junjian MA¹, Jiang ZHOU¹^,², Guozhao FANG¹^,²

Affiliations

^1.School of Materials Science and Engineering, Central South University, Changsha 410083, China

^2.Key Laboratory of Electronic Packaging and Advanced Functional Materials of Hunan Province, Central South University, Changsha 410083, China

LIANG Shuquan (1962-), male, Ph.D., Professor. E-mail: lsq@csu.edu.cn

出版时间: 2025-07-20 doi: 10.14062/j.issn.0454-5648.20240779

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摘要

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在二次电池系统研究过程中，鉴于电子在电池系统中直接参与电化学反应，深入理解系统中的电子行为至关重要。在过去几十年里，Goodenough等通过引入过渡金属元素d轨道能级分裂，实现晶体局域配位场重建，建立起了一套二次电池的电子理论，为电池材料的结构性能调控提供了十分重要的指导。然而，这套理论涉及复杂的原子、分子轨道和轨道杂化理论，处理过程烦琐，且难以直观理解。众所周知，随着以密度泛函理论为基础的结构复杂材料第一性原理高通量量子晶体学计算科学和技术的不断发展，材料科学领域能够通过相关计算获取更多、更科学且更精确的材料电子结构和参数信息，包括Fermi能级、Fermi能级附近能带的准确结构、电子态密度（DOS）等。这些关键电子信息对于理解二次电池电极材料综合电化学行为将是非常有益的。本工作重点阐述了相关的第一性原理计算实现方法，并以钠离子电池用典型磷酸盐正极进行了高通量计算和相关的电化学实验结果分析。研究发现，基于3种典型磷酸盐化合物可靠的高通量计算，对综合电化学性能变化可以进行更深层次的解析。表明二次电池电极材料能带高通量计算结果与电极材料综合电化学性能间存在很强的关联性，这将为理解二次电池电极材料电化学行为提供一个新的视角。

关键词

二次电池 / 正极材料 / 第一性原理计算 / 能带结构 / Fermi能级

Abstract

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Introduction

Understanding electron behavior is crucial in secondary battery research, as electrons directly participate in electrochemical reactions. Over the past few decades, Goodenough and his co-workers developed an electron theory for secondary batteries, introducing the splitting of d-orbital energy levels in transition metals, which reconstructs the local crystal field. This theory has provided valuable insights for optimizing the structure and performance of battery materials. However, the theory is not easy to be handled and difficult to intuitively understand due to its reliance on complex atomic and molecular orbitals, as well as orbital hybridization theories. With the advancement of material science, particularly density functional theory (DFT) and first-principles high-throughput calculations in quantum crystallography, researchers can obtain more precise insights into electronic structures and key parameters, such as the Fermi energy levels, band structures near the Fermi level, electron state, and density of states (DOS). These electronic characteristics are vital for understanding the electrochemical performance of electrode materials in secondary battery. This study was to investigate the band structures of phosphate cathodes for sodium-ion batteries via the first-principles calculations in order to establish a qualitative and semi-quantitative correlation between electronic properties and electrochemical behavior.

Methods

Three typical phosphate compounds, i.e., β-NaVP₂O₇, Na₃V₂(PO₄)₂F₃ and Na₃V₂(PO₄)₃, were selected as model materials. Their crystal structures were obtained from the Inorganic Crystal Structure Database (ICSD) and optimized by the Vienna Ab initio Simulation Package (VASP) with the Perdew-Burke-Ernzerhof (PBE) functional and projector-augmented wave (PAW) pseudopotentials. The key computational parameters included a plane-wave cutoff energy of 520 eV and Monkhorst-Pack k-point grids of 4×3×3 for β-NaVP₂O₇, 3×3×2 for Na₃V₂(PO₄)₂F₃ and 2×3×3 for Na₃V₂(PO₄)₃. The convergence criteria were set at 10^-5 eV for energy and -0.01 eV/Å for forces. The band structures and density of states (DOS) were initially calculated using optimized structures for theoretically perfect crystals. However, since the actual sodium ion content in some phosphate cathodes deviates from the perfect crystal, the structural modifications were implemented. For Na₃V₂(PO₄)₃, the unit cell was doubled, and the number of sodium ions was adjusted according to symmetry rules to align with practical requirements. For Na₃V₂(PO₄)₂F₃, no unit cell expansion needed, but the number of sodium ions reduced based on symmetry considerations. For β-NaVP₂O₇, no sodium ion adjustments required. After these corrections, the band structures and DOS were recalculated. The electrochemical performance was further validated through galvanostatic charge/discharge tests at 0.2 C, with the specific capacities and cycling stability evaluated for 50 cycles.

Results and discussion

High-throughput calculations can yield the more precise Fermi energies for the selected phosphate cathodes, with β-NaVP₂O₇ at 2.06 eV, Na₃V₂(PO₄)₂F₃ at 1.70 eV, and Na₃V₂(PO₄)₃ at 2.91 eV. Correspondingly, the bandgaps are determined to be 2.53 eV for β-NaVP₂O₇, 2.74 eV for Na₃V₂(PO₄)₂F₃, and 1.93 eV for Na₃V₂(PO₄)₃. These electronic parameters have a direct impact on the discharge voltages and conductivity of the materials. Note that β-NaVP₂O₇ with the minimum Fermi energy, achieves the maximum discharge voltage of 4.2 V, aligning with theoretical predictions that lower Fermi levels correspond to higher working voltages. Despite its relatively high Fermi level, Na₃V₂(PO₄)₃ maintains a stable 3.4 V platform due to its uniform energy band distribution near the Fermi level along the entire recommended band path, minimizing electron behavior changes and transition barriers. This uniform distribution facilitates consistent electron transport, resulting in an exceptional cycling stability with 99.4% capacity retention after 50 cycles. In contrast, β-NaVP₂O₇ and Na₃V₂(PO₄)₂F₃ exhibit non-uniform energy band distributions near the Fermi level, indicating multiple electron transition pathways that contribute to instable voltage plotforms. The discharge specific capacities of these materials are measured as 92.7 mA·h·g^-1 for β-NaVP₂O₇, 124 mA·h·g^-1 for Na₃V₂(PO₄)₂F₃ and 115.2 mA·h·g^-1 for Na₃V₂(PO₄)₃. A correlation between the integral of DOS near the Fermi level band and the discharge specific capacity of electrode materials occurs. Higher integrals of DOS for conductive electrons near the Fermi level correspond to greater discharge capacities, as demonstrated in the comparative analysis of these electrode materials.

Conclusions

This study established a correlation between high-throughput quantum crystallography calculations and electrochemical performance in sodium-ion battery cathodes. The Fermi levels directly affected discharge voltages, with lower Fermi levels corresponding to higher working voltages. A uniform band structure near the Fermi level over the whole recommended band path improved a cycling stability. The integral of the DOS near the Fermi level could be a critical factor determining the specific capacity of electrode materials. In addition, high-throughput calculations also revealed that structural imperfections, such as uncertain atomic occupancy in Na₃V₂(PO₄)₂F₃ and Na₃V₂(PO₄)₃, significantly could affect computational accuracy. The more precise Fermi energy values, band configurations, and DOS parameters were obtained via refining ion-occupancy corrections and implementing supercell expansions, providing deeper insights into fundamental electrochemical properties of these materials. These findings established a theoretical framework for designing next-generation battery materials via optimizing band structures for optimizing energy density and stability. This study could highlight a potential of high-throughput quantum crystallography calculations in predicting and improving electrochemical performance, thus offering a roadmap for the development of next-generation battery materials.

Key words

secondary battery / cathode materials / first-principles calculation / band structure / Fermi energy level

引用本文

梁叔全, 郭珊, 曹鑫鑫, 马君剑, 周江, 方国赵. 二次电池正极材料能带高通量计算与电化学特性关联分析. 硅酸盐学报, 2025 , 53 (7) : 1786 -1800 . DOI: 10.14062/j.issn.0454-5648.20240779

Shuquan LIANG, Shan GUO, Xinxin CAO, Junjian MA, Jiang ZHOU, Guozhao FANG. High-throughput Calculation of Electron Band Structure and Correlation Analysis of Electrochemical Characteristics of Cathodes in Secondary Battery[J]. Journal of the Chinese Ceramic Society, 2025 , 53 (7) : 1786 -1800 . DOI: 10.14062/j.issn.0454-5648.20240779

基金

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国家自然科学基金(51932011; 52272260)

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2025年第53卷第7期

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文章信息

doi: 10.14062/j.issn.0454-5648.20240779

接收时间：2024-12-11
首发时间：2026-10-21
出版时间：2025-07-20

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收稿日期：2024-12-11
修回日期：2025-01-10

基金

国家自然科学基金(51932011; 52272260)

作者信息

^1．中南大学材料科学与工程学院，长沙 410083

^2．中南大学电子封装及先进功能材料湖南省重点实验室，长沙 410083

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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