Exploiting Transformer-Based Networks and Boosting Algorithms for Ultralow Compressible Boride Design

Ultralow compressible materials, which have a high bulk modulus (K), are invaluable in extreme conditions due to their ability to undergo significant compression without structural failure. As a large number of borides can be found with high K, this study develops a computational framework to scan the vast chemical space to identify the ultralow compressible borides. Transformer-based networks are helpful to generate new chemical compositions due to their self-attention mechanism, scalability, and ability to capture long-range dependencies. First, we developed a transformer-based network to generate new binary and ternary boride compositions based on the known boride compositions. Next, we trained a hybrid model based on AdaBoost and Gradient Boosting algorithms with a mean absolute error (MAE) of 14.1 GPa to scan the high K borides. The CALYPSO code was used to find the possible structures for those materials. After predicting K for a broad chemical domain, we found that Re–B and W–B systems are promising ultralow compressible materials. We then performed density functional theory (DFT) calculations to investigate the stability of the high K materials. Our computations suggest that W3B2, W2B3, W5VB4, and Re5CrB4 materials exhibit K > 300 GPa with a negative formation energy and energy-above-hull less than 40 meV. These materials are mechanically and dynamically stable based on the elastic constant calculations and the phonon dispersion.