Ab Initio Investigation of Helium Interstitials in Y<sub>2</sub>Ti<sub>2</sub>O<sub>7</sub>: Kinetics and Bulk Moduli

Research Article

Ann Materials Sci Eng. 2015; 2(2): 1026.

Ab Initio Investigation of Helium Interstitials in Y2Ti2O7: Kinetics and Bulk Moduli

Danielson T¹* and Hin C1,2

¹Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, USA

²Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, USA

*Corresponding author: Danielson T, Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, 460 Turner St, Blacksburg, VA, 24060, USA

Received: November 06, 2015; Accepted: December 28, 2015; Published: December 30, 2015


Density functional theory has been used to investigate the migration barrier of a helium interstitial from one octahedral site to an adjacent octahedral site and the effects of octahedral helium interstitials on the bulk modulus of Y2Ti2O7. The interstitial is shown to travel through the tetrahedral location with an energetic barrier that can be largely attributed to the proximal location of the neighboring oxygen atom.

The bulk modulus has been investigated with up to three octahedral helium interstitials in Y2Ti2O7.

Keywords: Density Functional Theory; Nanostructured Ferritic Alloys; Irradiation; Defects


NFAs: Nanostructured Ferritic Alloys; NCs: Nanoclusters; DFT: Density Functional Theory; GGA: Generalized Gradient Approximation; CI-NEB: Climbing Image Nudged Elastic Band


The challenges opposing the efforts to develop materials systems for the next generation of fission reactors and future fusion reactors include; high neutron flux, high temperatures and pressures, corrosion and especially, embrittlement due to the transmutation product helium. Nanostructured ferritic alloys (NFAs) offer a promising solution to overcoming these challenges due to microstructural features such as a high stable dislocation density and a high number density of complex oxide nanoclusters (NCs) that serve to act as trapping sites for helium [1-4]. Despite experimental evidence of NCs acting as trapping sites, no concrete and complete theoretical understanding exists for the interaction of helium with the NCs and the resulting effects of its presence on the mechanical properties.

The migration barrier of helium in BCC iron is extremely low allowing helium to readily diffuse to preferential nucleation sites such as, dislocations, grain boundaries and voids [5-9]. Previous ab initio simulations have shown helium to have an attractive selfinteraction, making the formation of clusters favorable [5]. Likewise, the displacement cascade resulting from the kinetic energy transfer between an incident neutron and a constituent atom exacerbates the risk of growing bubbles as vacancies have been shown to stabilize the growth of helium bubbles [5,10,11]. Thus, a high concentration of vacancies coupled with the implantation of high-energy alpha particles promotes the risk of increased helium bubble formation. At high temperatures, helium bubbles become highly pressurized, resulting in damage to the surrounding lattice and potentially catastrophic cracking [12-15].

The complex oxide nanoclusters in NFAs exist in three main stoichiometric compositions; Y2Ti2O7, Y2O3 and Y2TiO5 [1]. Helium implanter transmission electron microscopy experiments carried out by Edmondson et al., have shown the effectiveness of NCs at trapping helium bubbles where the percentage of helium bubbles reaching grain boundaries is decreased by greater than 50% [9,16,17]. Similarly, due to the attractive self-interaction of helium, the bubbles trapped at the surface of NCs act as further trapping sites for helium diffusing through the matrix [15]. Thus, the trapping of helium at NCs has the potential to significantly mitigate the risk of helium embrittlement. Likewise, developing an understanding of the interactions of helium with the NCs and the effects of helium on their properties is of critical importance to further improving the ability to prevent helium embrittlement.

Further improvement of the prevention of helium embrittlement in candidate reactor materials relies heavily on the use of multiscale modeling that must be parameterized with large quantities of thermodynamic and kinetic information describing the matrix material, the oxide/matrix interface and the oxide [18-25]. Likewise, it is important to understand the changes that occur to the mechanical properties as a growing number of radiation induced defects, such as helium interstitials, are introduced.

Investigation of such quantities as the bulk modulus may help to understand why the oxides are well suited for trapping helium bubbles. Thus, this study deals with determining the migration barrier of helium in Y2Ti2O7 from the most stable interstitial site to an adjacent symmetry equivalent interstitial position and the effects of helium interstitials in Y2Ti2O7 on the bulk modulus.

Computational Methods

Density functional theory (DFT) as implemented by the VASP code [26-29] has been used in order to calculate the ground state properties of the migration path of helium and the bulk moduli of Y2Ti2O7 containing helium interstitials. One fully periodic unit cell has been used for each calculation where atoms are described by pseudopotentials generated with the projector-augmented wave method [30,31] and Brillouin zone integration is performed with a 4x4x4 k-point mesh. Due to the fact that DFT does not explicitly account for Van der Waals interactions, the ability of the pseudopotentials to accurately reproduce the interaction energy of a helium dimer at a variety of interatomic distances has been tested and compared to quantum Monte Carlo and configuration interaction simulations [32,33]. The generalized gradient approximation (GGA) from Perdew, Burke and Ernzerhoff (PBE) [34,35] best describes the behavior of the helium dimer. Thus, the GGA from PBE has been used to describe the exchange correlation effects where the semi-core 3p electrons and 4s and 4p electrons are treated as valence electrons for Ti and Y respectively.

In previous DFT calculations by Danielson and Hin [36,37] the four distinct helium interstitial positions in the Y2Ti2O7 unit cell and their relative stabilities have been determined. The interstitial positions (Figure 1) are the octahedral, tetrahedral, Y-Y and O-O configurations simply described as: