Hydrogen Diffusion and Trapping in {\alpha}-Iron: The Role of Quantum and Anharmonic Fluctuations

TL;DR

This study explores hydrogen diffusion and trapping in { extalpha}-iron, emphasizing quantum and anharmonic effects, revealing deviations from classical models and quantifying quantum contributions to binding energies.

Contribution

It introduces a comprehensive analysis of quantum and anharmonic effects on hydrogen behavior in iron, combining theoretical and computational methods to quantify their impact.

Findings

Hydrogen diffusivity deviates from Arrhenius behavior at low temperatures.

Quantum fluctuations significantly influence hydrogen trapping energies.

Phonons inhibit hydrogen diffusivity at intermediate temperatures.

Abstract

We investigate the thermodynamics and kinetics of a hydrogen interstitial in magnetic {\alpha}-iron, taking account of the quantum fluctuations of the proton as well as the anharmonicities of lattice vibrations and hydrogen hopping. We show that the diffusivity of hydrogen in the lattice of BCC iron deviates strongly from an Arrhenius behavior at and below room temperature. We compare a quantum transition state theory to explicit ring polymer molecular dynamics in the calculation of diffusivity and we find that the role of phonons is to inhibit, not to enhance, diffusivity at intermediate temperatures in constrast to the usual polaron picture of hopping. We then address the trapping of hydrogen by a vacancy as a prototype lattice defect. By a sequence of steps in a thought experiment, each involving a thermodynamic integration, we are able to separate out the binding free energy of a proton to a defect into harmonic and anharmonic, and classical and quantum contributions. We find that about 30% of a typical binding free energy of hydrogen to a lattice defect in iron is accounted for by finite temperature effects and about half of these arise from quantum proton fluctuations. This has huge implications for the comparison between thermal desorption and permeation experiments and standard electronic structure theory. The implications are even greater for the interpretation of muon spin resonance experiments.