Ab initio and machine-learning study of surface energetics in Be12Ti

A comprehensive ab initio study of the surface energetics of the intermetallic compound Be12Ti was performed, focusing on 24 low-index crystallographic planes (hkl with maximal Miller index ≤ 3) and their non-equivalent surface terminations. To enable accurate calculation of surface energies for non-stoichiometric slabs, a machine-learning interatomic potential was developed and trained on energies and atomic forces obtained by ab initio. Surface-layer relaxations are found to be strongly termination dependent, exhibiting complex inward and outward atomic displacements. Surface energies are influenced more significantly by surface termination than by crystallographic orientation, particularly for low-index planes. Surfaces with maximum Miller index one display pronounced termination dependence, while higher-index surfaces exhibit smaller variations. For a fixed crystallographic orientation, the dependence of surface energy on surface termination follows an invariant trend: the minimum surface energy corresponds to titanium-terminated surfaces, whereas the surface energy increases as titanium atoms are located at greater distances from the surface plane. Wulff constructions demonstrate that equilibrium crystal and void shapes are highly sensitive to termination-dependent surface energies. This work presents a high-throughput framework for surface modeling in multicomponent compounds based on machine-learning interatomic potentials. The approach establishes the groundwork for subsequent assessment of tritium retention at Be12Ti surfaces, which is an essential step toward quantifying tritium inventories in neutron multiplier components of fusion reactors.