A fully quantum mechanical calculation of the diffusivity of hydrogen in iron using the tight binding approximation and path integral theory

TL;DR

This paper introduces a fully quantum mechanical method combining tight binding and path integral theory to accurately calculate hydrogen diffusivity in iron, revealing quantum effects persist at higher temperatures than previously thought.

Contribution

It develops a novel quantum approach for hydrogen diffusion in iron, improving accuracy over classical and previous quantum methods, and provides new insights into temperature-dependent quantum effects.

Findings

Quantum effects in hydrogen diffusion persist at higher temperatures.

Quantum diffusivity is lower than classical predictions at low temperatures.

Results align better with experimental data than previous models.

Abstract

We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in bcc-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a new self consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. We also find results in better agreement compared to recent centroid molecular dynamics (CMD) calculations of the diffusivity which employed a classical interatomic potential rather than our quantum mechanical tight binding theory. In particular we find first that quantum effects persist to higher temperatures than previously thought, and conversely that the low temperature diffusivity is smaller than predicted in CMD calculations and larger than predicted by classical transition state theory. This will have impact on future modeling and simulation of hydrogen trapping and diffusion.