The influence of grain size on the hydrogen diffusion in bcc Fe
Graphical abstract
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 -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 ) 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 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 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 and 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 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 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 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.
Section snippets
Calculation methodology
Most calculations are performed with the molecular statics technique (MS), driven by suitable EAM interatomic potentials for the Fe-H system [19], [20]. Electronic structure DFT calculations are also performed. The reason behind this parallel approach is to employ the EAM technique to probe for possible non trivial defect structures that may develop in the GB, whe check their consistency with the ab initio, and much more demanding in computing resources, DFT technique. It is worth emphiszing
Hydrogen interaction with the GB
The structure of the GB is illustrated in Fig. 2. In the situation depicted in Fig. 2, also three different zones are qualitatively indicated, namely, core (Zone I), transition (Zone II), and bulk (Zone III).
The GB consisting of zone I and zone II implies in a stripe of thickness Å. The stripe is a periodic assembly of atoms in the y and x directions with periodicity Å and Å respectively. The GB unit cells (see Fig. 1) have hence a volume .
To set up the
Diffusion coefficient in a sample with structure
In this section we describe and analyze the role played by the grain size in the diffusion process. As already mentioned, the grain size influences the volume fraction of the sample occupied by the GB, and thus also the density of trapping sites. These trapping sites, present in the GB, are responsible for delaying the diffusion, mainly in the direction across the GB where the diffusion process is in series with the bulk.
During and effective diffusion process in the material, H atoms are
Concluding remarks
In this work, we developed a diffusion model which takes into account diffusion in bulk as well as in the GB. The mechanism for the diffusion process in the GB distinguishes between the directions along the GB, or crossing through it. In the first case it must be considered as in parallel with the diffusion in the bulk while for crossing the GB the process is in series with bulk diffusion. In addition, the average grain size is incorporated to the model, and our results highlighted that it is
CRediT authorship contribution statement
Viviana P. Ramunni: Data curation, Formal analysis, Investigation, Validation, Visualization, Writing - original draft. Alejandro M.F. Rivas: Conceptualization, Methodology, Investigation, Data curation, Software, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We want to thanks Dr. R.C. Pasianot for comments on the manuscript. This work was partially financed by CONICET PIP: 11220170100021CO.
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