Pausing-time distribution of hydrogen diffusion in Gaussian distribution energy

Abstract

The pausing-time distribution of thermal diffusion of hydrogen is analytically shown in the Gaussian density of state. The pausing-time distribution exhibits a log-normal distribution. It has been shown that the pausing-time distribution follows approximately power law, i.e., t-1-α(t: pausing time). The diffusion coefficient of hydrogen is also obtained to be approximately τα-1 (τ: diffusion time). The value of α is the ratio of hydrogen temperature Tr to T2σ, in which T2σ, is a temperature corresponding to 2σ (σ: standard deviation). Finally, Brownian motion is shown to correspond to the case of σ = 0. The width of the energy distribution play an important role in hydrogen diffusion.