Hydrogen-induced volume changes, dipole tensor, and elastic hydrogen-hydrogen interaction in a metallic glass

Hydrogen and its isotopes, absorbed in metals, induce local stress on the atomic structure, which generates a global expansion in proportion to the concentration of hydrogen. The dipole force tensor and its interaction with the stress fields give rise to an effective attractive nonlocal potential between hydrogen atoms---the elastic hydrogen-hydrogen interaction---which is a key quantity governing the phase transitions of hydrogen in metals. While the dipole tensor and the elastic interaction have been researched in crystalline materials, they remain experimentally unexplored in metallic glasses and it is unclear how these quantities are affected by the lack of point group symmetries. Here, we investigate both experimentally and theoretically the volume changes, the components of the force dipole tensor, and ultimately the elastic hydrogen-hydrogen interaction in the metallic glass ${\mathrm{V}}_{80}{\mathrm{Zr}}_{20}$. In situ neutron reflectometry was used to determine the deuterium-induced volume changes as a function of deuterium concentration. The one-dimensional volume expansion is found to change by more than 14% without any structural degradation, up to concentrations of one deuterium atom per metal atom. From the expansion, we determine that the out-of-plane component of the elastic dipole tensor is remarkably similar to a composition weighted sum of the ones found in crystalline vanadium and zirconium. Via ab initio calculations of both free and biaxially constrained expanded metallic structures, we determine that the trace of the dipole tensor varies with hydrogen concentration and is essentially invariant of global elastic boundary conditions. As a consequence, the elastic hydrogen-hydrogen interaction energy is found to be concentration-dependent as well, illustrating that the disordered nature of a metallic glass does not impede the mediation of the elastic attraction, but rather allows it to vary with hydrogen content.