Theory of Diffusion of Hydrogen Subjected to a Constant Force and Its Validation Analysis Using Molecular Dynamics

Abstract

Diffusion theories of hydrogen subjected to a constant force are studied and entablished. First, the Einstein relationship, which connects ensemble averages of mean displacement and mean square displacement to the diffusion coefficient, is derived via formulation of dynamics theory based on Langevin equation. Then, the jump theory based on the stochastic process is applied to the jumps of hydrogen in face-centered-cubic crystal and the diffusion coefficient is expressed in terms of the average of expectation value of the number of jumps. We clarify that both theories agree well with each other under some appropriate assumptions. Secondly, we show that these theories are validated by using a molecular dynamics simulation. The result of microscopic information such as displacement and the number of jumps obtained by the simulation is universally represented and a unique value of diffusion coefficient can be determined with comparing the theories and simulation.