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Materials Genome Initiative Center of SJTU made significant progress in modeling and predicting volume effects in binary substitutional metallic solid solutions

SEPT 8,2022   

Recently, the team of Materials Genome Initiative Center led by Professor Hong Wang from the School of Materials Science and Engineering, Shanghai Jiao Tong University published online in the top international journal in the field of metal materials, Acta Materialia, the latest research results on the volume effects of binary substitutional metallic solid solutions (BSMSS) modeling and prediction by machine learning (ML), entitled “Machine-learning prediction of Vegard's law factor and volume size factor for binary substitutional metallic solid solutions”.

    Yuanxun Zhou, a PhD student at Shanghai Jiao Tong University, is the first author of the paper, and Prof. Hong Wang and Prof. Lanting Zhang are the co-corresponding authors of the paper. In this study, ML methods were applied to develop a proxy general ML model for predicting the Vegard's law factor (VLF) and volume size factor (SF) of BSMSS.

    The bulk effect of BSMSS can be characterized by VLF and SF. SF is involved in the calculation of many physical, chemical and mechanical properties of alloys, especially in the calculation of solid solution hardening and diffusion of metallic impurities, while VLF is a key parameter for calculating lattice parameters of BSMSS, intermetallic and high entropy alloys. However, due to the complex interactions between alloy atoms, a rigorous general model to accurately describe the bulk effects of alloys for accurate prediction has long been lacking. With the development of materials genetic engineering in recent years, ML methods have been widely used in materials science with some success. Inspired by it, this study introduced the ML method for modeling and compares it with the commonly used first-principles calculations.

Figure 1. Screenshot of paper publication

    After collecting the VLF and SF data of BSMSS reported in the relevant literature, a descriptor subset containing 182 initial descriptors was first obtained by descriptor (input to the model) construction. Then a working framework for descriptor/model combination selection was constructed based on the eight conventional ML models and symbolic regression (SR) algorithms commonly used today as shown in Figure 2. The best conventional ML model can be selected by the routine 1 and the SR algorithm by the routine 2 to obtain new descriptors. It was shown that among the eight conventional ML models, the Laplacian kernel-based ridge regression model has the best performance (top right corner of Figure 2). In the routine 2, 7,500 composite new descriptors based on the initial descriptors of the dataset were obtained by SR, and a best descriptor was selected based on the prediction accuracy and descriptor length. Compared with the best model in routine 1, this new descriptor gives a relatively simple display resolution expression, which greatly improves the interpretability of the model. We can then decompose it into a two-dimensional descriptor and make a structural distribution plot (bottom right of Figure 2). Compared with density functional theory calculations, ML has a superior prediction accuracy and can give reasonable results for systems for which no experimental results are currently available.

Figure 2. ML model building framework. Selection routine 1 is based on common traditional ML models, and selection routine 2 is based on SR, which can be used to obtain descriptor parameters with physical interpretability.

    The prediction of alloy volume effect is crucial in alloy design, such as high entropy alloy, solid solution strengthening, mismatch degree, etc. Traditionally, the theories on volume effect such as Hume-Rothery's law and Vegard's law are semi-empirical models based on some experimental observations, and it has been difficult to obtain an accurate general model utilizing strict physical reasoning. In this study, ML algorithm was introduced for the first time to develop the corresponding general model, which solved the problem of inaccurate prediction of lattice constants and unclear influence factors of classical binary alloys in metallurgy. It provides important insights and new approaches for exploring the establishment of a general model for predicting the volume effect of binary substitutional metallic solid solutions and related theoretical studies.

    This work was supported by the National Key Research and Development Program of China (2021YFB3702303 and 2017YFB0701900) and the Major Science and Technology Project of Yunnan Province “Genetic Engineering of Rare and Precious Metal Materials in Yunnan Province (Phase One 2020)” (202002AB080001-1).

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