Computational methodology for analysis of the Soret effect in crystals: Application to hydrogen in palladium

Abstract

Different computational methodologies to compute thermodiffusion of hydrogen in palladium are explored. It is found that diffusion occurs rapidly enough to directly observe thermodiffusion in the presence of an applied temperature gradient. This provides an unequivocal result that hydrogen moves from low to high temperatures, corresponding to a negative value for the reduced heat of transport Q*′≈−0.3 eV, which can be used to validate other methods. Further simulations using the Green-Kubo formulae and a recently developed constrained-dynamics approach are found to be in agreement with direct simulation results. In particular, in each of the three methods used, the value of Q*′ is found to be in the range between −0.3 and −0.2 eV. We show how to correctly define and compute the partial-enthalpy term for hydrogen which is key to obtaining accurate results. The results provide important foundational and numerical validation for the constrained-dynamics approach. The advantage of the constrained-dynamics method is that it can be applied to thermodiffusion in materials where diffusion does not occur on a molecular-dynamics time scale. Finally, we show that the empirical potential predicts behavior that is not in agreement with experiment. In particular, experiments are reported to show hydrogen diffusing from high to low temperatures corresponding to a positive value for Q*′.