Quantum and isotope effects on hydrogen diffusion, trapping and escape in iron

Anthony T Paxton,Ivaylo H Katzarov

doi:10.1016/j.actamat.2015.09.054

Abstract

We calculate the rate coefficient as a function of temperature for lattice diffusion of hydrogen and its isotopes in α-iron; and also for trapping and escape from a vacancy. We employ Monte-Carlo and molecular dynamics methods based around the Feynman path integral formulation of the quantum partition function. We find large quantum effects including tunnelling at low temperature and recrossing at high temperature due to the finite extent of the particle probability density. In particular these serve to increase the rate of trapping and to decrease the rate of escape at low temperature. Our results also show very clear non classical isotope effects.

Highlights

One of the largest known diffusivities in the solid state is that of hydrogen in a-iron [1,2]
In addition we are keenly interested in the mean residence time, t, of a proton trapped at a defect [6]; this is the inverse of the associated rate coefficient for jumping out of the trap
For the case of bulk, lattice diffusivity we find that the transmission coefficient reaches a plateau value of one for both H and D at 200 K and 300 K; at 500 K k takes values of about 0.6 in D and 0.7 in H at 20 ps but has not yet reached a plateau

Summary

Introduction

One of the largest known diffusivities in the solid state is that of hydrogen in a-iron [1,2]. In addition we are keenly interested in the mean residence time, t, of a proton trapped at a defect [6]; this is the inverse of the associated rate coefficient for jumping out of the trap In addressing these matters we arrive at some rather startling conclusions concerning the roles of tunnelling through the barrier and recrossing at the saddle point in the potential energy surface. Interatomic forces that are required for these procedures are obtained from a magnetic tight binding (TB) model of H in iron [10] This is not a severe approximation, since comparison with density functional theory (DFT) calculations shows good agreement in both concentrated and dilute limits [10]. We would expect quantum effects effectively to lower the activation barrier at low T, but to raise it at high T

Theory and results

Findings

Discussion

Conclusions