Pushing the limits of atomistic simulations towards ultra-high temperature: A machine-learning force field for ZrB2

Determining thermal and physical quantities across a broad temperature domain, especially up to the ultra-high temperature region, is a formidable theoretical and experimental challenge. At the same time it is essential for understanding the performance of ultra-high temperature ceramic (UHTC) materials. Here we present the development of a machine-learning force field for ZrB2, one of the primary members of the UHTC family with a complex bonding structure. The force field exhibits chemistry accuracy for both energies and forces and can reproduce structural, elastic and phonon properties, including thermal expansion and thermal transport. A thorough comparison with available empirical potentials shows that our force field outperforms the competitors with the merits of high accuracy and great versatility. Most importantly, its effectiveness is extended from room temperature to the ultra-high temperature region (up to ???2500 K), where measurements are very difficult, costly and some time impossible. Our work demonstrates that machine-learning force fields (MLFF) can be used for simulations of materials in a harsh environment, where no experimental tools are available, but crucial for a number of engineering applications, such as in aerospace, aviation and nuclear