Elsevier

Journal of Nuclear Materials

Volume 496, 1 December 2017, Pages 157-162
Journal of Nuclear Materials

Stability and kinetics of helium interstitials in boron carbide from first principles

https://doi.org/10.1016/j.jnucmat.2017.09.020Get rights and content

Abstract

When boron carbide is used in nuclear reactors as a neutron absorber, helium concentrations on the order of a few atomic percent can be attained. It is thus of primary importance to know the distribution and kinetics of helium atoms in boron carbide. In spite of a variety is of experimental works devoted to the characterization of the microstructure and He bubbles in boron carbide irradiated in reactor, there is a serious lack of knowledge concerning the basic mechanisms governing helium kinetics. This study is devoted to the stability and mobility of helium interstitial atoms in carbon rich boron carbide. The lowest energy He insertion sites were screened through density functional theory and the most probable migration paths and energy barriers were investigated using the nudged elastic bands (NEB) approach. The results suggest that in a wide range of temperatures He interstitials undergo 2D diffusion confined between two 111 planes. The onset of 3D diffusion is expected, according to our calculations, with an activation energy close to 2 eV.

Our result is in qualitative agreement with the observation of flat bubbles with 111 orientation, although a quantitative comparison with He diffusion data is hindered by discrepancies and microstructure issues in available experimental results.

Introduction

Due to boron high neutron absorption cross section, boron carbide is used in shutdown and control rods of various types of nuclear reactors; moreover, due to the absence of a resonance region in the neutron absorption cross section, it is the best candidate for control rods of fast breeder reactors. The nuclear reaction taking place when neutrons are absorbed by the 10B isotope leads to the productions of large quantities of helium and lithium. In most cases the lifetime of the rods is limited by the swelling and microcracking occurring in the material, in particular due to the accumulation of helium bubbles [1].

Flat He bubbles preferentially oriented in the 111 planes in irradiated boron carbide were reported already in the early seventies [2], [3]. A transition from flat to equiaxed bubbles was reported at temperatures around 1500° C [4]. Other works reported spherical bubbles [5], [6], [7] even at relatively low temperature, probably due to different irradiation and annealing conditions. In the following decades additional works provided further evidence for 111-oriented flat bubbles, with a more refined quantitative analysis of bubbles sizes as a function of temperature and discussed the conditions in which they are expected [8], [9], [10]. The earliest studies did not observe bubbles at grain boundaries [2], and concluded that He diffusion was accelerated along them, but this was due to open porosity of the samples. In more recent works He bubbles were detected at grain boundaries and it was then considered that He is trapped there [11], [10]. Whether single He atoms also tend to segregate and get trapped at grain boundaries, or trapping occurs only for He clusters above a given threshold size, is not clearly understood yet.

It is clear that, in order to establish more reliable models for He clustering and release from boron carbide under irradiation, reliable data on diffusion activation energy are desirable. Diffusion of He in boron carbide has first been discussed by Clayton [12] in the framework of He release from B4C specimens irradiated in reactor at room temperature: with strong assumptions concerning the spatial distribution of He, a diffusion activation energy of 1.26 ± 0.13 eV has been estimated. However, considering the results of later works on dose dependences and bubbles formation, one would rather suppose that a large portion of He was trapped in grain boundaries and the measured activation energy might be associated with the release of single He atoms from trapped bubbles. More involved diffusion models [13] considered indeed both He diffusion in the matrix and He detrapping from so called “accumulation centers”, it is however unclear which are the activation energy values used. The activation energy given by Clayton was used in another model of He release [14], but the diffusion prefactor was significantly reduced in order to reproduce experimental results.

In this paper we investigate the elementary diffusion mechanisms and activation energy for interstitial He atoms from first principles calculations based on density functional theory. We focus mainly on the B4C stoichiometry —using the B11C-CBC structure described later— but, for the sake of comparison, the boron richer B12-CBC configuration was also tackled.

We predict the relative stability of substitutional and interstitial He insertion sites and find minimum energy paths between the most stable ones. The paper is organised as follows: section 2 is devoted to the technical details of our approach; section 3 is subdivided in subsection 3.1, which describes the stability of insertion sites, subsection 3.2 which discusses the diffusion mechanisms, and subsection 3.3 on the role of the electronic charge density. In section 4 we discuss the results in connection with experimental results. The main results are summarized in the final section 5.

Section snippets

Model structures and methods

Boron carbide has a rhombohedral crystalline structure, which is maintained in a large range of stoichiometry [15]. Here we focus mainly on the carbon rich side, with stoichiometry B4C for which we assume the structure shown in Fig. 1, B11C-CBC, where B11C icosahedra are connected by CBC chains. The latter structure is considered to be the most stable structure for this stoichiometry [16]; however some disorder, at least in the placement of the icosahedral carbon, is expected [15], [17].

In

Stability

In the B11C-CBC structure eleven insertion sites can be found which are non-equivalent by symmetry (see Fig. 2). Table 1 presents the results of vacancy formation energies, He incorporation and solution energies in these eleven insertion sites.

Solution energies are quite large. Vacancy formation energies on equatorial and polar sites are also very large. One can notice that two incorporation energies are negative; further investigations showed that, in those two cases, the substitutional He has

Discussion

The picture suggested by our results supports the idea that the formation of He flat bubbles aligned along the 111 direction, observed experimentally, might be favored by a two-dimensional He diffusion regime. Indeed we find that migration energies for a 2D diffusion are lower than the ones for a 3D motion of helium.

However, it is clear that a kinetic model able to give quantitative results would need several parameters in order to lead to a sensible comparison with experiments. In

Summary

The results previously presented concerning the energy of the interstitial and substitutional helium defects lead to the first conclusion that icosahedra are not concerned at all in the insertion of helium, at least in thermodynamical equilibrium. Indeed creating a vacancy on one of the icosahedral sites is quite expensive (between 4.2 and 5.6 eV) and inserting a helium atom inside an icosahedron costs 7.23 eV. The migration of helium in boron carbide then only concerns the inter-icosahedra

Acknowledgements

Kevin Gillet is gratefully acknowledged for pointing out the instability of vacancies and substitutional He on equatorial sites. This work was granted access to the HPC resources of TGCC and CINES under the allocation 2016A0010906018 made by GENCI.

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