Contents lists available at ScienceDirect Intermetallics journal homepage: www.elsevier.com/locate/intermet A two-stage predicting model for γ′ solvus temperature of L1 2 -strengthened Co-base superalloys based on machine learning Jinxin Yu a,b,1 , Shun Guo b,1 , Yuechao Chen a , Jiajia Han a , Yong Lu a , Qingshan Jiang b , Cuiping Wang a,∗∗ , Xingjun Liu c,d,a,∗ a College of Materials and Fujian Provincial Key Laboratory of Materials Genome, Xiamen University, Xiamen, Fujian, 361000, PR China b Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong, 518000, PR China c State Key Laboratory of Advanced Welding and Joining, Harbin Institute of the Technology, Harbin, Heilongjiang, 150001, PR China d Institute of Materials Genome and Big Data, Harbin Institute of Technology, Shenzhen, Guangdong, 518000, PR China ARTICLE INFO Keywords: Machine-learning Co-base superalloy Modeling γ′ precipitates Solvus temperature Random forests ABSTRACT As one of the candidate materials of the next generation aircraft engines, L1 2 -strengthened Co-base superalloys have drawn lots of attentions. However, Co-base superalloys have some disadvantages, such as γ′ precipitates in the superalloys are metastable. Moreover, improving this superalloy through traditional experimental ap- proaches is extremely costly and inefficient. Thus, it is necessary to develop a new approach that could make rapid and accurate predictions of the properties of the L1 2 -strengthened Co-base superalloys. In this study, the γ′ solvus temperature, which is the basic property of L1 2 -strengthened Co-base superalloys, is predicted based on our two-stage approach. Firstly, the existence of the γ′ precipitates are predicted. And then, the solvus tem- peratures of the candidates which are predicted to have γ′ precipitates are calculated by our models. A new superalloy with high γ′ precipitates solvus temperature is designed successfully with the help of our approach. The time cost of this approach is less than that of the traditional experimental approach. This approach could also be used to discover L1 2 -strengthened Co-base superalloys with other desired properties. 1. Introduction Ni-base superalloys have been widely used in high-temperature and high-stress environments, such as aircraft engines and power generating gas turbines [1]. The microstructure of Ni-base superalloys is composed of a fcc matrix (γ) strengthened by γ′ precipitates, keeping these su- peralloys stable at elevated temperature [2]. To improve the engine efficiency, the working temperature of the engine needs to be higher. However, the melting point of Ni is only 1,455 °C which cannot meet the requirement of the development of next generation aircraft engines. The melting point of Co is 40 °C higher than that of the Ni, where a 10 °C increase in the working temperature of aircraft engines could be regarded as a significant improvement. Thus, Co is considered as a potential high-temperature alloy. However, traditional Co-base super- alloys are strengthened through carbide precipitates, and that would cause their strength to be low at elevated temperatures [3]. In 2006, Sato et al. discovered L1 2 -strengthened Co-base superalloys [4]. The newly reported CoeAleW alloys have a fcc matrix (γ) strengthened by γ′-Co 3 (Al,W) precipitates: their solidus temperatures and melting points were higher than those of Ni-base superalloys. However, γ′-Co 3 (Al,W) is metastable, which would not exists after heating at 900 °C for 2,000 h [5]. Aircraft engines are required to be capable of working regularly at high temperatures for over 150,000 h and their lifetime is directly related to the stability of the γ′ precipitates. Thus, increasing the stability of the γ′ precipitates of the alloy means that it would have longer lifetime, higher reliability, and better prop- erties [3]. Moreover, the γ-γ′ two phase range is of vital narrow, which makes the study of this alloy more difficult. As one of the most important evaluation indexes, much work has been done to improve the solvus temperature of the γ′ precipitates, which is considered as one of the characterizations on the stability of the γ′ precipitates. Bocchini et al. and others tried to stabilize the γ′- Co 3 (Al,W), broaden its two-phase region, and increase the solvus tem- perature of the γ′ precipitates by alloying with other elements [6–9]. The most effective element in improving the solvus temperatures of the γ′ precipitates is Ta, followed by Ti, Nb, W and Hf. Ni has been found https://doi.org/10.1016/j.intermet.2019.04.009 Received 18 February 2019; Received in revised form 21 March 2019; Accepted 7 April 2019 ∗ Corresponding author. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of the Technology, Harbin, Heilongjiang, 150001, PR China. ∗∗ Corresponding author. E-mail addresses: wangcp@xmu.edu.cn (C. Wang), lxj@xmu.edu.cn (X. Liu). 1 Jinxin Yu and Shun Guo contributed equally to this work. Intermetallics 110 (2019) 106466 0966-9795/ © 2019 Published by Elsevier Ltd. T