叠熵理论：从材料基因到材料性能

doi:10.11900/0412.1961.2024.00147

金属学报

2024, Vol. 60

Issue (10): 1379-1387 DOI: 10.11900/0412.1961.2024.00147

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叠熵理论：从材料基因到材料性能

廖名情¹, 王毅²(

), 王义³, 商顺利³, 刘梓葵³(

)

1 江苏科技大学材料科学与工程学院镇江 212100
2 西北工业大学凝固技术国家重点实验室西安 710072
3 Department of Materials Science and Engineering, the Pennsylvania State University, University Park, PA, 16802, USA

Zentropy Theory: Bridging Materials Gene to Materials Properties

LIAO Mingqing¹, WANG William Yi²(

), WANG Yi³, SHANG Shun-Li³, LIU Zi-Kui³(

)

1 School of Materials Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China
2 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China
3 Department of Materials Science and Engineering, the Pennsylvania State University, University Park, PA, 16802, USA

引用本文:

廖名情, 王毅, 王义, 商顺利, 刘梓葵. 叠熵理论：从材料基因到材料性能[J]. 金属学报, 2024, 60(10): 1379-1387.
Mingqing LIAO, William Yi WANG, Yi WANG, Shun-Li SHANG, Zi-Kui LIU. Zentropy Theory: Bridging Materials Gene to Materials Properties[J]. Acta Metall Sin, 2024, 60(10): 1379-1387.

全文: PDF(1381 KB) HTML

摘要:

熵是科学中一个非常重要的概念，从量子到天文，无处不在。基于统计力学，综合量子力学密度泛函理论和热力学，刘梓葵教授团队建立了关于系统总熵的理论：叠熵理论。该理论以Gibbs统计力学中的微观组态作为材料的基因，把密度泛函理论中的基态作为最基本的微观组态，通过基态的内部自由度遍历所有的微观组态。叠熵理论定义系统总熵为每个微观组态熵的加权平均再加上微观组态之间的Gibbs统计熵。本文系统介绍了叠熵理论的基础方程与原理，简单概述了叠熵理论的典型应用，包括磁性转变、铁电转变、热膨胀机制以及临界现象预测，并对叠熵理论从理论发展、软件生态构建、高通量计算以及与人工智能集成等方面进行了展望。

关键词 ：叠熵理论, 热力学, 材料基因工程, 热膨胀机制, 铁电转变温度, 有序-无序转变

Abstract：

Entropy is an important concept in science and is ubiquitous from quantum to astronomy. By integrating statistical mechanics, quantum mechanics, and thermodynamics, Professor Zi-Kui Liu proposed the zentropy theory, which stacks entropy over configurations. The zentropy theory takes the configurations in Gibbs' statistical mechanics of a given ensemble as the material gene with the ground state as the basic configuration and additional configurations ergodically derived from its internal degrees of freedom. In the zentropy theory, the total entropy of a system is defined as the weighted average of the entropy of each configuration plus the statistical entropy among all configurations. In this paper, the basic equations and principles of the zentropy theory are introduced, and their typical applications, including magnetic and ferroelectric transformations, thermal expansion mechanisms, and critical phenomenon prediction are outlined. Furthermore, a perspective on the development of this theory, software ecosystems, high-throughput computing, and integration with artificial intelligence is provided in this study.

Key words： zentropy theory thermodynamics materials genome engineering thermal expansion mechanism ferroelectric transition temperature order-disorder transition

收稿日期: 2024-05-08

ZTFLH:

O414

基金资助:江苏省自然科学基金项目(BK20230673);江苏省双创博士人才项目(JSSCBS20221270)

通讯作者: 王毅，wywang@nwpu.edu.cn，主要从事极端条件先进材料的材料基因工程&集成计算材料工程的研究;
刘梓葵，zxl15@psu.edu，主要从事材料热力学、动力学、晶体学以及材料基因组的研究

Corresponding author: WANG William Yi, professor, Tel: (029)88460294, E-mail: wywang@nwpu.edu.cn;
LIU Zi-Kui, professor, Tel: (814)8651934, E-mail: zxl15@psu.edu

作者简介: 廖名情，男，1992年生，博士

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https://www.ams.org.cn/CN/10.11900/0412.1961.2024.00147 或 https://www.ams.org.cn/CN/Y2024/V60/I10/1379

图1 多尺度熵示意图

图2 叠熵理论示意图

Property	Statistical mechanics	Zentropy framework
Entropy	$S = - k B ∑ k p k l n p k$	$S = ∑ k p k S k - k B ∑ k p k l n p k$
Free energy	$F = ∑ k p k E k + k B T ∑ k p k l n p k$	$F = ∑ k p k F k + k B T ∑ k p k l n p k$
Partition function	$Z = e x p (- F k B T) = ∑ k e x p (- E k k B T)$	$Z = e x p (- F k B T) = ∑ k e x p (- F k k B T)$
Probability	$p k = Z k Z = e x p (- E k - F k B T)$	$p k = Z k Z = e x p (- F k - F k B T)$

表1 叠熵理论框架与经典统计力学下热力学物理量的比较[41]

图3 不同微观组态0 K下的体积-能量曲线[30]

图4 不同压强下的温度-体积相图[45]

图5 PbTiO3各个组态概率随温度的变化[47]

图6 通过熵预测的Fe3Pt无序程度(fDoDS)随温度的变化[46]

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