Uncovering the thermal expansion in high-entropy ceramics by machine learning

Understanding the fundamental mechanisms of thermal expansion in high-entropy ceramics is crucial for their structural applications under extreme conditions. Here, we propose a machine learning (ML)-driven approach to reveal the different underlying mechanisms that govern the thermal expansion in high-entropy carbides (HECs) and high-entropy diborides (HEBs). Molecular dynamics simulations based on the well-fitted neuroevolution potentials are used to effectively collect the coefficient of thermal expansion (CTE) data of HECs and HEBs, and features with three levels, including the atomic level, the monolithic level, and the high-entropy level, are simultaneously considered to achieve reliable ML training. Five descriptors within a Linear Regression model are derived as the optimal combination for the accurate CTE prediction in HECs, where lattice distortion and its variation under temperature are revealed to have the dominant influence on suppressing the thermal expansion of HECs by strengthening ionic bonding and alleviating anharmonic effects. Conversely, the optimal combination of descriptors for the precise CTE prediction in HEBs is exclusively linked to fundamental parameters at both atomic and monolithic levels, highlighting the cocktail effects in impacting CTEs of HEBs. This work proposes an efficient framework for mechanism revelation by ML to facilitate the rational design of high-entropy ceramics with desired properties.