Atomic-scale simulation of the thermodiffusion of hydrogen in palladium

Abstract

We report molecular-dynamics simulations of Pd:H to elucidate transport properties, with special focus placed on determining the temperature dependence of the heat of transport Q*. Simulation results are analyzed using the Green-Kubo approach. It is found that Q* describing the thermodiffusion of hydrogen increases linearly with temperature. By contrast, the reduced heat of transport Q*′=Q*−h2, with h2 the partial enthalpy of hydrogen, is approximately temperature independent. By computing separately the potential, kinetic, and virial contributions to Q*, it is possible to understand key features of the thermodiffusion process. In particular, the sum of the kinetic and potential energy of hydrogen atoms is increased above that of an average hydrogen atom by an amount comparable to the migration energy during a successful hop. However, the virial term in the energy flux is less than what would be expected based on the average local stress contribution due to the hydrogen atoms. Detailed calculations show that the relevant component of the stress tensor due to a hopping hydrogen atom exhibits a minimum at the transition state. Hence, while Q* has significant positive contributions due to the excited nature of the hopping hydrogen atom, the reduced heat of transport Q*′ can still be negative. The results here present important insight into the failure of simple kinetic theories of thermodiffusion, and provide a new perspective that can be tested on other systems.