Elsevier

Corrosion Science

Volume 75, October 2013, Pages 248-255
Corrosion Science

A first-principles study of the diffusion of atomic oxygen in nickel

https://doi.org/10.1016/j.corsci.2013.06.006Get rights and content

Highlights

  • The diffusion process of atomic oxygen in nickel is modeled.

  • Density functional theory is used to calculate the activation energy of diffusion.

  • Oxygen diffusivities in nickel are estimated by a vacancy-mediated diffusion model.

  • The calculated diffusivities are compared with those observed experimentally.

Abstract

In this study, the coefficients of diffusion of oxygen in nickel-based alloys are determined by atomistically modeling the oxygen diffusion process using a vacancy-mediated diffusion model. Density functional theory is used to calculate the energy of the system. The activation barrier energy for the diffusion of atomic oxygen in nickel is quantified by determining the most favorable path, i.e., the minimum-energy path, for diffusion. Phonon analysis is performed using the direct force-constant method. The calculated pre-exponential factor for the lattice diffusion of oxygen in nickel is 5.45 × 10−7 m2/s and the activation energy is 158.65 kJ/mol.

Introduction

Nickel-based alloys such as Alloy 600 (Ni–16Cr–9Fe) are known to undergo intergranular stress corrosion cracking (IGSCC) in pressurized water reactor (PWR) primary water environments. The primary water stress corrosion cracking (PWSCC) of Alloy 600 and of the related weld metals Alloy 82 and Alloy 182 has become an increasing concern because cracks and leaks have been discovered at pressure boundaries in numerous PWRs of nuclear reactor systems, making them a threat to these systems. Microscopic observations have shown that oxygen plays a role in the PWSCC of nickel-based alloys, and Scott and Calvar have suggested an internal oxidation model for the process [1]. However, it was found that the value of oxygen diffusivity used in this model was several orders of magnitude greater than that known. Hence, for the model to be accurate, the correct value of the diffusivity must be used. In order to be able to do this, it is important to first understand the process of oxygen diffusion in nickel.

To this end, numerous experimental studies have been conducted to measure the coefficient of diffusion of oxygen in nickel [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. Barlow and Grundy [3], Goto et al. [4], and Lloyd and Martin [7], [8] used the internal oxidation method to measure the diffusivity of oxygen in nickel. In this method, the diffusivity of oxygen was determined indirectly on the basis of its measured permeability in nickel, because the permeability is a product of its solubility and diffusivity in nickel. All of these studies used the solubility data published by Seybolt [10]. However, the various diffusivity values reported in these studies were not in complete agreement; for instance, the solubility values reported by Seybolt showed a decrease with an increase in the temperature. This is in contrast to what is noticed in most metal–oxygen systems. Alcock and Brown used a thermogravimetric method to measure the diffusivity of oxygen in nickel [2]. They measured the change in the weight of nickel as a function of the oxygen partial pressure by controlling the composition of the CO2/CO mixture. On the basis of these measurements, the solubility of oxygen in nickel could be determined; an approximate diffusion coefficient was also determined indirectly by calculating the time required to reach equilibrium. However, the solubility values calculated by Alcock and Brown exhibited the same trend as that noticed in the data reported by Seybolt. An electrochemical method was also used to determine the diffusivity of oxygen in nickel [6], [9]. Park and Altstetter [9] employed a potentiometric method, which involved the use of yttria-stabilized zirconia as an oxygen-conducting solid electrolyte, to obtain more reliable data on the kinetics and the related thermodynamics of a nickel–oxygen solid solution. This method was advantageous in that it allowed the solubility and diffusivity of oxygen in nickel to be measured directly. In addition, the values obtained using this method showed an increase with an increase in the temperature.

As noted above, the previously reported data on the diffusivity of oxygen in nickel show large discrepancies; this is particularly true in the case of the activation energy values. These discrepancies arise from the use of different techniques to obtain the data. In addition, the complex modes of the diffusion mechanisms, the fact that the solubility of oxygen in nickel is extremely low, and the charge transfer reactions that take place between the oxygen and nickel atoms also contribute to the variations noticed.

For these reasons, several researchers have used atomistic calculations instead. Three studies using first principles to calculate the activation energy for the diffusion of oxygen in nickel have been reported [12], [13], [14], as has a study that used variable charge molecular dynamics (VCMD) for the same purpose and also to calculate the oxygen diffusion coefficient in nickel [15]. Megchiche et al. [12] and Kim et al. [13] used first principles calculational approach to investigate the diffusion of atomic oxygen in nickel metal. By determining the energetics of atomic oxygen interstitials in crystalline nickel, the diffusion of interstitial oxygen via a path between two octahedral sites that had an intermediate metastable tetrahedral site between them was evaluated. In addition, the effect of thermal expansion in nickel on the diffusion process was studied by varying the lattice constant. Young et al. [14] also used atomistic models of the diffusion of hydrogen and that of oxygen in nickel to calculate the coefficient of interstitial hydrogen diffusion; the calculated diffusivity was found to be in good agreement with the experimental data. However, they did not determine the coefficient of oxygen diffusion; instead, only the activation energy for oxygen diffusion in nickel was compared with the experimental data, while taking into consideration the interstitial and substitutional diffusion processes. Garruchet et al. [15] used variable charge molecular dynamics (VCMD) to study oxygen diffusivity in nickel. By using the electrostatic plus (ES+) model and the embedded-atom method (EAM) potential in the study, they were able to overcome the limitations associated with molecular dynamics—usually, empirical potentials are used in calculations related to charge-transfer reactions such as oxidation. Although the results obtained by them were less accurate that those of studies based on first principles, they evaluated the effect of temperature on the coefficients of interstitial and substitutional diffusion of oxygen in nickel. This had not been done in the studies based on first principles.

In this study, the coefficient of oxygen diffusion in nickel-based alloys is evaluated using first-principles calculations of the process of oxygen diffusion in pure nickel. First, the coefficient of interstitial diffusion of oxygen through the octahedral–tetrahedral–octahedral (O–T–O) sites is calculated. Then, the coefficient of substitutional diffusion of oxygen in nickel is calculated using a vacancy-mediated diffusion model, and the obtained value is compared with experimental data. The surface diffusivity of oxygen with respect to nickel is calculated using a similar method, and the obtained value is used to determine the grain boundary diffusivity of oxygen in nickel. The effective diffusivity of oxygen is also assessed and compared to its experimentally determined diffusivities in polycrystalline materials.

Section snippets

Interstitial diffusion of oxygen in nickel

The diffusion coefficient, D, is classically expressed byD=D0·e-Q/kTwhere D0 is the temperature-independent pre-exponential factor, Q is the activation energy for the diffusion process, and k is the Boltzmann constant. The Arrhenius plot of the diffusion equation allows the kinetic properties of the diffusing particles to be expressed readily in terms of the pre-exponential factor and the activation energy.

Wert and Zener [16], [17], [18] have proposed that the coefficients for interstitial and

Computational details

The first-principles calculations are performed using the plane-wave density functional theory (DFT) [29], [30] in its spin-polarized form [31]. This is done using the projector-augmented wave (PAW) potentials [32], [33] and the generalized gradient approximation (GGA) with the Perdew–Wang 91 (PW91) functional [34], [35], [36] as implemented in the Vienna ab initio simulation package (VASP) [37], [38].

The system used in the calculations is a 2 × 2 × 2 fcc nickel supercell having a lattice constant,

Interstitial diffusion of oxygen in nickel

The ground state energies and phonon frequencies of three different configurations are calculated. These three configurations are the following: (i) the oxygen atom is in an octahedral site (hereafter, referred to as “oct”), (ii) the oxygen atom is in a tetrahedral site (hereafter, referred to as “tet”), and (iii) the oxygen atom in a transition state (TS) between the octahedral state and tetrahedral states. In this study, the height of the activation barrier (ΔETS–oct) is assumed to be 0.74 eV.

Conclusions

Nickel-based alloys are known to undergo IGSCC in PWR primary water environments. It has been found that oxygen plays a role in the PWSCC of nickel-based alloys. Scott et al. used oxygen diffusivity data obtained using an internal oxidation model to explain the PWSCC of these alloys. However, most of the previous experimental studies that have attempted to determine the diffusivity of oxygen in nickel have considered only high temperatures (>1000 K). This is because of the dramatic decrease in

Acknowledgements

This work was financially supported by the R&D Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Ministry of Trade Industry and Energy (MOTIE). Partial support was also provided by the KIST Research Project (No. 2E23920) and by the Ministry of Science, ICT & Future Planning (MSIP) through the EU Framework Project (MMM@HPC).

References (54)

  • C.B. Alcock et al.

    Physicochemical factors in the dissolution of thoria in solid nickel

    Metal Science

    (1969)
  • R. Barlow et al.

    The determination of the diffusion constants of oxygen in nickel and α-iron by an internal oxidation method

    Journal of Materials Science

    (1969)
  • S. Goto et al.

    Internal oxidation of nickel alloys containing a small amount of chromium

    The Journal of the Japan Institute of Metals

    (1967)
  • R. Iacocca et al.

    The kinetics of intergranular oxygen penetration in nickel and its relevance to weldment cracking

    Metallurgical and Materials Transactions A

    (1988)
  • R.A. Kerr, Thesis, The Ohio State University,...
  • G. Lloyd et al.

    The diffusivity of oxygen in nickel determined by internal oxidation of dilute Ni–Be alloys

    Metal Science

    (1972)
  • G.J. Lloyd et al.

    The diffusivity of oxygen in nickel determined by internal oxidation of dilute Ni–Be alloys

    Metal Science

    (1973)
  • J.-W. Park et al.

    The diffusion and solubility of oxygen in solid nickel

    Metallurgical and Materials Transactions A

    (1987)
  • A.U. Seybolt, Dissertation, Yale University, New Haven, CT,...
  • S.P. Zholobov et al.

    Diffusion of oxygen in a metal in electron bombardment of the surface

    Soviet Physics Technical Physics

    (1971)
  • E.H. Megchiche et al.

    First-principles calculations of the diffusion of atomic oxygen in nickel: thermal expansion contribution

    Journal of Physics Condensed Matter

    (2007)
  • J.J. Kim et al.

    First-principles study of interstitial diffusion of oxygen in nickel chromium binary alloy

    Applied Physics Letters

    (2012)
  • G.A. Young, W.W. Wilkening, D.S. Morton, E. Richey, N. Lewis, The mechanism and modeling of intergranular stress...
  • C. Wert et al.

    Interstitial atomic diffusion coefficients

    Physical Review

    (1949)
  • C.A. Wert

    Diffusion coefficient of C in alpha-iron

    Physical Review

    (1950)
  • C. Zener

    Theory of diffusion

  • K. Heinola et al.

    Diffusion of hydrogen in bcc tungsten studied with first principle calculations

    Journal of Applied Physics

    (2010)
  • Cited by (0)

    View full text