The influence of grain size on the hydrogen diffusion in bcc Fe

Highlights

• We find Hydrogen interstitial sites in a sigma 5 Fe grain boundary.

• The jumps and migration energies between the interstitial sites are calculated.

• The density of interstitial sites depends on the grain size.

• Diffusion along or across the grain boundary are respectively in parallel or in series with the bulk.

• The smaller the grain size the slower the diffusion.

Abstract

This work studies the diffusion of Hydrogen (H) in bcc Fe, containing a high-angle symmetric tilt grain boundary (GB), as a function of both the temperature and the average grain size. For this purpose, we propose a microscopic effective model which includes diffusion in bulk and in the GB. The model distinguishes between diffusion along the GB, in parallel with the bulk, while diffusion through the GB is to be considered in series. The bounding and migration energies of the H interstitial sites are derived through an extensive study of H atoms dissolved in a high-angle symmetric tilt GB. This is undertaken in the framework of a set of classical interatomic potentials, and partially from Density Functional Theory (DFT) calculations, in order to check the consistency of equilibrium atomic structures. We find that preferential trapping sites for H in the GB delay the H migration, thus enhancing its solubility. The derived H diffusion coefficients are in agreement with experimental evidence, however various kinds of GBs are present in real samples. In addition, we see that at high temperature, H diffusion does not depend on the grain size, as similar results than in bulk are found. In contrast, at room temperatures (290 K) and nano-sized grains (100 nm) the effective diffusion can slow down up to two orders of magnitude.

Introduction

The behavior of Hydrogen impurities in metals is a topic of great relevance regarding key technological applications such as fusion reactor technology, H storage for purification or as cell batteries, and H gas as a secondary energy carrier [1], [2].

Hydrogen can greatly change the mechanical properties of structural metals and alloys, thereby causing failure [3], [4]. In particular, H diffusion and segregation in Fe and Fe alloys is considerably important because it leads to engineering problems of embrittlement and degradation of high-strength steels, reactor materials, etc. It is a very common impurity in iron-based materials which is incorporated into the material during production and service and exhibits a high mobility within the bulk phase. It has further been shown that microstructural defects in the material such as vacancies, dislocations, and grain boundaries can trap hydrogen impurities [5], [6], [7], [8].

Key aspects for understanding these phenomena are H diffusion, the interaction of H with microstructure defects, and the subsequent solubility. The latter is relatively low in bulk bcc Fe, however, point-defects and extended defects such as dislocations and grain boundaries provide interstitial sites that are much more energetically favorable for H precipitation than the classical tetrahedral sites in bulk.

Several studies were recently performed, employing different modeling strategies, in order to better understand the H behavior in materials. Noticeably,

A path-integral quantum dynamics approach for H diffusion in the bulk of iron is reported in [9]. Also, Cheng et al. [10] found that nuclear quantum effects change the diffusion coefficient of H in bulk $\alpha$-Fe at room temperature. The H embritlemet in Ni grain bundaries has been also studied in [11]. However, because of the lack of experimental observations, the detailed mechanism of H diffusivity are not yet fully understood.

It is important to investigate the key role played by the GB in the overall diffusion process, as it can delay or accelerate H mobility [12]. The experimental work of Oudriss et al. [13] dealt with grain size effects for H diffusion in pure nickel. For crystalline Fe, diffusion coefficients were shown to be different for single crystals or for poly-crystals [14]. Indeed, it was shown that below 270 K, H exhibits a lower effective diffusion in non-deformed poly-crystalline Fe (with a grain size of 17 $\mu m$) than in single crystal Fe. The smaller the grain size, the larger the proportion of GB; it is therefore logically expected that the diffusion process significantly depend on the grain size. Despite its great relevance, to the author’s knowledge, this topic has been extensively addressed in the literature.

In the present work, we develop a grain-size dependent microscopic model for H diffusion. The model is then applied for H diffusion in bcc Fe containing a $\mathrm{\Sigma }5$ GB structure.

The grain size, characterized by the average grain length, influences the volume fraction of the sample being occupied by the GB, and thus consequently influences the density of trapping sites. These trapping sites are responsible for delaying the diffusion, mainly in the direction across the GB where the diffusion process is in series with the diffusion process in bulk. In this way, we describe and analyze the role played by the grain size in the diffusion process.

This investigation involves a careful examination of the microscopic processes concerning H migration mechanisms in the $\mathrm{\Sigma }5$ GB. In particular, numerical calculations based on both semi-empirical interatomic potential formalism based on the embedded atom method (EAM), and DFT, are used to study H trapping sites and the possible migration paths in the above GB, deemed to be pertinent to the experimental observations.

The H trapping sites and migration paths are exploited in our diffusion model, which considers diffusion processes through both the GB and in bulk. With this aim, our model adequately takes into account the different diffusion directions according to GB orientation. The model also reveals the relevance of each process, as a function of the average grain size, which is related to the number trapping sites of each type.

The diffusion process is then studied as a function of both temperature and grain size.

It is important to highlight that our calculations are in agreement with the available experimental data from Ref. [14], [15] for both average grain sizes $L=17\mathrm{\mu }m$ and $L=0.3\mathit{mm}$ respectively, although various kinds of GBs are present in real samples.

In addition, we observe that at high temperature, grain size does not influence the H diffusion coefficients obtaining similar results than in bulk. However, at room temperatures (290 K), and for nano-size grains (100 nm), the diffusion coefficients can slow down up to two orders of magnitude due to GB diffusion.

The work is organized as follows:

In Section 2, we describe in details the methodology we follow in this work, in particular how the studied $\mathrm{\Sigma }5$ GB structure is constructed. The latter is taken as a prototype to model H trapping in Fe.

An extensive study of the H interaction with the GB is then performed in Section 3, where the migration barriers are calculated in order to evaluate the effective diffusion coefficients. We investigate the strength of trapping for H at various interstitial sites, in complement to a previous study [16].

…and found that within the $\mathrm{\Sigma }5$ GB interstitial sites close to the interface region are energetically more favorable for H atoms than the tetrahedral site in the bulk of bcc Fe. Present EAM and DFT calculations revealed around 10 distinctive interstitial sites within the $\mathrm{\Sigma }5$ GB-core.

In Section 4 we propose a model for the estimation of H diffusion, as a function of temperature and grain size. Finally, in the closing Section 5, conclusions and discussions are drawn from our results. An Appendix section is devoted to describe the grain size influence in the distribution of interstitials.