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随着高熵合金的兴起，多组元合金设计成为近期的研究热点。微结构模拟，如相场模拟等是多组元合金设计的重要手段。构建热力学函数是微结构模拟的核心问题。然而，随着合金组元数目的增加，热力学函数的复杂性指数增加，因此构建多组元热力学函数十分困难，是合金设计的瓶颈之一。
来自比利时天主教鲁汶大学的Nele Moelans教授领导的团队，通过引入张量补全这一数值方法，将多组元体系中复杂的高维热力学函数有效简化。他们以热力学函数的张量形式为基础，基于张量补全简化热力学函数的表达式，进而通过CALPHD相图计算等方法获得的有限数据集来确定函数的参数从而构建热力学函数。以Ag-Cu-Ni-Sn四元合金体系为例，他们建立了热力学函数并应用于相场模拟检验了该方法的有效性。结果表明，与未简化模型相比，该方法不仅结果准确且可以大幅降低计算量。此外，由于简化得到的热力学函数的参数数量仅与组元数目呈线性关系，因此可在不显著增加计算量的情况下将其拓展到包含更多组元体系中，用于模拟复杂体系的微结构演化模拟。该方法有望成为多组元合金设计的有利工具。该文近期发表于npj Computational Materials 6: 2 (2020)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。
Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction
Yuri Amorim Coutinho, Nico Vervliet, Lieven De Lathauwer & Nele Moelans
Multicomponent alloys show intricate microstructure evolution, providing materials engineers with a nearly inexhaustible variety of solutions to enhance material properties. Multicomponent microstructure evolution simulations are indispensable to exploit these opportunities. These simulations, however, require the handling of high-dimensional and prohibitively large data sets of thermodynamic quantities, of which the size grows exponentially with the number of elements in the alloy, making it virtually impossible to handle the effects of four or more elements. In this paper, we introduce the use of tensor completion for high-dimensional data sets in materials science as a general and elegant solution to this problem. We show that we can obtain an accurate representation of the composition dependence of high-dimensional thermodynamic quantities, and that the decomposed tensor representation can be evaluated very efficiently in microstructure simulations. This realization enables true multicomponent thermodynamic and microstructure modeling for alloy design.
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