Trapping and Tunneling of Hydrogen, Deuterium and Oxygen in Niobium

Abstract

We investigate isolated O-H and O-D pairs trapped in BCC Nb using a machine-learning interatomic potential (MLIP) trained to density-functional theory (DFT). The MLIP enables large-supercell analysis and identification of trapping sites within BCC Nb, as well as efficient mapping of three-dimensional (3D) potential-energy surfaces. In addition to the pair of tetrahedral``face'' sites previously identified based on DFT, we identify a lower-energy pair of ``edge'' trapping sites and confirm the stability of H and D at these trapping sites with DFT. We solve the Schr\"odinger equation for H and D in the 3D potential that surrounds the trapping sites. Solutions based on the static-lattice limit yield tunnel splittings in the range $J/h \in\{3-100\}$ GHz for both trapping sites.