Diffusion theories of hydrogen subjected to a constant force were studied. Firstly, the Einstein relationship connecting ensemble averages of mean displacement and mean-square displacement to the diffusion coefficient, was derived via a formulation of dynamical theory based upon the Langevin equation. Jump theory based upon the stochastic process was then applied to jumps of hydrogen in a face-centered cubic crystal, and the diffusion coefficient was expressed in terms of the average of the expectation value of the number of jumps. It was confirmed that both theories agreed with each other under appropriate conditions. Secondly, it was shown that these theories were validated by using molecular dynamics simulation.

Theory of Diffusion of Hydrogen Subjected to a Constant Force and Its Validation Analysis using Molecular Dynamics. Masaie, T., Doi, Y., Nakatani, A.: Transactions of the Japan Society of Mechanical Engineers A, 2010, 76[761], 52-61