基于蒙特卡罗模拟的离子导体热力学与动力学特性

doi:10.19799/j.cnki.2095-4239.2022.0050

储能科学与技术 ›› 2022, Vol. 11 ›› Issue (3): 878-896.doi: 10.19799/j.cnki.2095-4239.2022.0050

• 储能新材料设计与先进表征专刊 • 上一篇下一篇

基于蒙特卡罗模拟的离子导体热力学与动力学特性

刘金平¹(), 蒲博伟¹, 邹喆乂², 李铭清¹, 丁昱清¹, 任元¹, 罗亚桥¹, 李杰³, 李亚捷¹, 王达¹, 何冰⁴, 施思齐^1,^5,⁶()

^1.上海大学材料科学与工程学院，上海 200444
^2.湘潭大学材料科学与工程学院，湖南湘潭 411105
^3.加州大学欧文分校物理与天文系，美国加州 92697
^4.上海大学计算机工程与科学学院
^5.上海大学材料基因组工程研究院，上海 200444
^6.之江实验室，浙江杭州 311100

收稿日期:2022-01-28 修回日期:2022-02-12 出版日期:2022-03-05 发布日期:2022-03-11
通讯作者: 施思齐 E-mail:506094182@qq.cm;sqshi@shu.edu.cn
作者简介:刘金平（1994—），男，硕士研究生，从事超离子导体离子输运特性的研究，E-mail：506094182@qq.cm；
基金资助:
国家自然科学基金面上项目(11874254);国家重点研发计划项目(2021YFB3802104);上海先进陶瓷结构设计与精密制造专业技术服务平台(20DZ2294000);之江实验室科研攻关项目(2021PE0AC02)

Investigating thermodynamic and kinetic properties of ionic conductors via Monte Carlo simulation

Jinping LIU¹(), Bowei PU¹, Zheyi ZOU², Mingqing LI¹, Yuqing DING¹, Yuan REN¹, Yaqiao LUO¹, Jie LI³, Yajie LI¹, Da WANG¹, Bing HE⁴, Siqi SHI^1,^5,⁶()

^1.School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China
^2.School of Materials Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, China
^3.Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
^4.School of Computer Engineering and Science, Shanghai University
^5.Materials Genome Institute, Shanghai University, Shanghai 200444, China
^6.Zhejiang Laboratory, Hangzhou 311100, Zhejiang, China

Received:2022-01-28 Revised:2022-02-12 Online:2022-03-05 Published:2022-03-11
Contact: Siqi SHI E-mail:506094182@qq.cm;sqshi@shu.edu.cn

摘要/Abstract

摘要：

基于概率统计理论的蒙特卡罗模拟(MC)在20世纪40年代由冯·诺伊曼等提出，其作为一种重要的数值计算方法，已被广泛应用于离子导体的热力学、动力学等性质的研究。然而，MC模拟在相关计算精度、模拟速度以及模拟流程自动化等方面，仍具有较大的提升空间。本文通过分析其在离子导体计算领域中哈密顿量的构建模式(如基于键价和计算或利用团簇展开将通过拟合代表性小尺寸晶胞第一性原理计算总能得到的近邻作用参数给出构型能量)以及结构演变方式(如基于单离子迁移模式假设的构型演变)，提炼出一套用于分析离子导体离子输运特性及相变特性的MC模拟范式，并给出与之相关的半自动化MC模拟程序，预测了石榴石结构离子导体的电导率与迁移离子占据率分别随锂离子浓度的变化趋势。为了更好地拓展MC模拟在离子导体研究中的应用，本文就其在包括正负极材料、电解质及其相关界面的电化学储能材料中的典型热力学与动力学计算案例进行了剖析，包括求解离子导体中的离子扩散问题、模拟迁移离子的分布特征与相关界面层的演变过程等。最后，展望了MC方法目前面临的挑战并给出可能的对策，包括：①精确地获取所有可能发生的事件(如单离子迁移与双离子协同迁移)及其描述(如哈密顿的计算)；②探寻高效算法以精确找到系统的演化轨迹；③精确获得MC模拟中对应的时间步长。

关键词: 蒙特卡罗模拟, 离子导体, 离子输运特性, 相变特性, 晶体生长

Abstract:

Monte Carlo (MC) simulation, on the basis of probability and statistics theory, was proposed by Von Neumann et al. in 1940s. As an important numerical method, MC simulation has been used to investigate thermodynamic and kinetic properties of ionic conductors. However, there exists a large improvable space for the MC simulation in the calculation accuracy, simulation efficiency and simulation process automation. In this work, through systematic analysis of the Hamiltonian model in MC simulation (For example, based on bond-valence theory or cluster expansion, the configuration energy is given by fitting the neighbors interaction parameters that can always be obtained by first principles calculations of representative small supercells) and the evolution model (For example, configuration evolution based on the assumption of single-ion jump mode) of material structure, a set of MC simulation paradigms for analyzing the ion transport and phase transition characteristics of ionic conductors are extracted, and the corresponding semi-automatic simulation codes are given which can be used for predicting the respective dependences of the ionic conductivity and the occupancy of the migrated ions in the garnet-structured ionic conductor with the lithium ion concentration. To expand the application of MC simulation in the research of ionic conductor, we further analyze its applications in the typical thermodynamic and kinetic properties calculations of electrochemical energy storage materials which includes anode and cathode materials, electrolytes and the related interfaces, including the ionic diffusion problems, the distribution characteristics of migrated ions and the evolution of related interface. Finally, the current challenges faced by MC methods are prospected and the possible solutions are presented, including: ① Accurately capturing all possible events (such as single-ion hop and two-ion cooperation hop) and their descriptions (such as the Hamiltonian calculations); ② Searching for efficient algorithm to accurately find the evolution trajectory of the system; ③ Accurately obtaining the corresponding actual time in the MC simulation.

Key words: Monte Carlo simulation, ionic conductors, ion transport properties, phase transition properties, crystal growth

中图分类号:

TB 34

刘金平, 蒲博伟, 邹喆乂, 李铭清, 丁昱清, 任元, 罗亚桥, 李杰, 李亚捷, 王达, 何冰, 施思齐. 基于蒙特卡罗模拟的离子导体热力学与动力学特性[J]. 储能科学与技术, 2022, 11(3): 878-896.

Jinping LIU, Bowei PU, Zheyi ZOU, Mingqing LI, Yuqing DING, Yuan REN, Yaqiao LUO, Jie LI, Yajie LI, Da WANG, Bing HE, Siqi SHI. Investigating thermodynamic and kinetic properties of ionic conductors via Monte Carlo simulation[J]. Energy Storage Science and Technology, 2022, 11(3): 878-896.

图/表 16

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基于蒙特卡罗模拟的离子导体热力学与动力学特性

Investigating thermodynamic and kinetic properties of ionic conductors via Monte Carlo simulation

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