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

Ultralow compressible materials, which have high bulk modulus (K), are invaluable in extreme conditions due to their ability to undergo significant compression without structural failure. As large number of borides can be found with high K, this study develop 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 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 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 high K materials. Our computations suggest that Re3B2, Re2B3, W5VB4, and Re5CrB4 materials exhibit K > 300 GPa with negative formation energy and energy-above-hull less than 40 meV. Those materials are mechanically and dynamically stable based on the elastic constant calculations and the phonon dispersion.