Keywords: Nickel; Molecular Dynamics simulation; Oxygen diffusion in solids

Transcription

1 Defect and Diffusion Forum Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Numerical Studies of the Diffusion Processes and First Step Oxidation in Nickel-Oxygen Systems by Variable Charge Molecular Dynamics S. Garruchet 1,a, O. Politano 1,b, P. Arnoux 2,c, V. Vignal 1,d 1 ICB, UMR 5209CNRS, Université de Bourgogne, Dijon, France 2 DANS/DEN/DPC/SCCME/LECA, CEA Saclay, Gif-sur-yvette, France a sgarruch@u-bourgogne.fr, b politano@u-bourgogne.fr, c Patrick.ARNOUX@cea.fr, d vincent.vignal@u-bourgogne.fr Keywords: Nickel; Molecular Dynamics simulation; Oxygen diffusion in solids Abstract. Variable charge molecular dynamic simulations have been performed to study the diffusion mechanisms of oxygen atoms (O) in nickel (Ni) in the temperature range K and the very first steps of oxidation of monocrystalline nickel surfaces at 300 K and 950 K. The oxygen diffusivity can be well described by an Arrhenius law over the temperature range considered. The oxygen diffusion coefficient has been analysed and values of E a = 1.99 ev for the activation energy and D 0 = 39 cm 2.s -1 for the pre-exponential factor were obtained. The first steps growth of the oxide layer show that after the dissociative chemisorption of the oxygen molecules on nickel surface, the oxidation leads to an island growth mode as observed experimentally. Introduction Nickel and nickel based alloys will be used for numerous applications in 4th generation reactor because of their good mechanical properties on a wide variety of severe environments (corrosive, irradiative, high temperatures, ). Oxidation of nickel surfaces proceeds by cationic diffusion. In that sense, the governing parameter is the diffusion of nickel in the oxide scale and several approaches focused on the transport of species through the oxide layer [1]. However, it is also experimentally observed that some oxygen atoms are trapped within the metal. At high temperature, those atoms will diffuse and form internal oxide clusters in nanovoids within the metallic bulk [2]. Oxygen diffusion and solubility have been intensively studied experimentally in the second part of the last century. But there is still controversy on the value on oxygen solubility in nickel which allow us to express doubts about the result of previous studies (see [3,4] and reference therein for an insightful reviewing). That is why, one can notice a very large discrepancy between the activation energy for the diffusion of oxygen in nickel, which varied between 4.29 and 1.70 ev. Recently, new experimental studies [4] have shown that no oxygen diffusion appears in nickel bulk without the presence of vacancies. Moreover they observed the presence of voids in grain boundaries, which are due to clustered vacancies. Nickel oxide particles were observed in these voids, which tends to prove that the oxygen migrates in nickel with vacancies. However, experimental determination of oxygen diffusion in nickel is extremely difficult and is complicated by (i) the relatively low solubility of oxygen and the difficulty to determine it, (ii) the potential presence of oxide films or clusters, (iii) complication due to chemical reaction, and (iv) microstructural trapping. Thus reliable values for solubility and diffusivity of oxygen in solid nickel have not yet been unambiguously established in literature and to our knowledge, only a few numbers of theoretical investigations were dedicated to this topic [5]. For all these reasons we started an atomistic study of oxygen diffusion by variable charge molecular dynamics (VCMD). In the following, we investigate the diffusion of oxygen in solid nickel for temperatures in the range 950 to 1600 K. Then the first steps of nickel monocrystal oxidation were studied at 300 K for the three low-index surface orientations ((100), (110) and (111)). Finally, the temperature effect was discussed for the (100) surface. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-16/09/16,20:26:40)

2 514 Diffusion in Solids and Liquids V Computational method Our VCMD simulation code is based on the interaction scheme developed by Streitz and Mintmire [6] for aluminium-oxygen systems and extended by Zhou et al. for many other metals [7]. This technique has been successfully applied in many different studies involving a metal oxide systems such as oxidation processes [8-10] or the deformation behaviour of nanocrystalline systems with a dilute concentration of oxygen [11,12]. With this potential, the total energy of the crystal is divided into an electrostatic energy (Es) that is ion charge dependent and a non-electrostatic energy that is ion charge independent (embedded atom method (EAM) potential). The interaction potential (Es+) has been shown to efficiently describe the cohesive energy, structure, and elastic properties of both fcc Ni and B1 phase of NiO [13]. To increase the computational efficiency, a local chemical potential approach was also used [11]. Oxygen diffusion in nickel We studied systems of 2048 n vac nickel atoms with 1 oxygen and n vac nickel vacancies in the box. The box size was chosen large enough to have no influence on the calculation results. The simulated nickel samples were created for each temperature by using the lattice parameter a calculated with a = a 0 (1+ ), where a 0 = 3.52 Å is the lattice parameter at 0 K and the linear thermal expansion coefficient. The simulation box was cubic (L x = L y = L z ) and periodic boundary conditions were applied in the three directions. In order to obtain the temperature dependence of the lattice parameter (i.e. a), we performed preliminary molecular dynamics simulation in the NPT ensemble (constant number of particles, volume and pressure) on a perfect nickel crystal in the temperature range 800K-1600K with a zero pressure. This last led us to compute a linear thermal expansion coefficient of = K -1. The equations of motion are integrated with a time step δt = 1fs. The atomic charges are updated every VCMD step. The oxygen diffusion coefficient is obtained from the mean square displacements (MSD) using the Einstein relation [14]: 6Dt r(t) r(0) 2, where r(t) is the position of oxygen at time t. From the knowledge of the successive positions of oxygen atom r(t n )=r(ndt), the mean square displacement is then given by: r(t) r(0) 2 n max n r((n j) t) r( j t) 2 (n max n 1) (1) j 0 At each temperature, we equilibrate the system in the NVT ensemble during 0.1 nanoseconds. Then, the diffusion coefficient is computed from a running average during a sufficiently long run (typically 10 nanoseconds) to obtain accurate statistics (i.e. a sufficient oxygen jump number and a linear dependence of mean square displacement with time). By repeating the MSD calculations at different defect concentrations for each temperature, the linear dependence of the diffusion coefficient versus vacancy concentration can be produce. Moreover to compare diffusion coefficients for each temperature with those obtain experimentally, we need to determine the vacancies concentration in nickel metal at those temperature. To obtain those data, we used the thermodynamic calculation of Perusin [2] which is based on the approach adopted by Kraftmakher [15]. This approach relies on two approximations: the first one is that the formation entropy varies linearly with the temperature; the second one is that the formation enthalpy varies linearly with the square of temperature. With these two things, the oxygen diffusion coefficient can be extrapolated. The diffusion coefficients obtained with the present approach are compiled in Fig. 1 with results extracted from the literature. As expected, the diffusion coefficient follows an Arrhenius law, D = D 0 exp E a kb T (2) were D 0 is the pre-exponential factor, E a the activation energy, k b the Boltzmann constant and T the

3 Defect and Diffusion Forum Vols temperature. The pre-exponential factor, D 0, and the activation energy, E a, are directly evaluated by fitting the simulation results with the above formula. Our simulations gave a value of 39.2 cm 2 s -1 for D 0, and 1.99 ev for E a, which are in good agreement with those reported in the literature and compiled in Table 1. Fig. 1: Review of diffusivity of oxygen in solid nickel at high temperature from literature (solid line) and from our simulations. Dashed line is the fit of simulation points with equation (2). Reference (Method) Temperature range (K) D 0 (cm 2 s -1 ) E a (ev) Goto et al. [21] (internal oxidation) 1173 to Alcock et al. [20] (gravimetric) 1323 to Barlow et al. [23] (internal oxidation) 1073 to Kerr [19] (electrochemistry) 1273 to Lloyd et al. [22] (internal oxydation) 1273 to Park et al. [18] (potensiometric) 1123 to Megchiche et al. [3] (ab-initio) Present work (Molecular dynamics) 950 to Table 1: Pre-exponential factor and Activation energy obtained from this work, along with those obtained from other experimental and numerical approaches. As one can notice from Table 1, the activation energy obtained by our simulations is in better agreement with the results obtained by electrochemical techniques [16,17]. Those experimental works seem to be more reliable than the other ones because the determination of the oxygen diffusivity is independent of the value of oxygen solubility. On the contrary, other studies [18-21] used the value of oxygen solubility that decreases with increasing temperature [18] whose veracity is in doubt with the light of the recent study [16]. With this result, one can conclude that oxygen mainly diffuses in nickel via a vacancy migration mechanism.

4 516 Diffusion in Solids and Liquids V First step oxidation Bulk sample was created using the lattice parameter a calculated with a = a 0 (1+ ) for the different temperature (see section above for more detail). The two surfaces were generated by increasing the x direction of the simulation box. The system with surfaces was equilibrated in the NVT ensemble during 0.1 nanoseconds. We started the oxidation by introducing O 2 molecules, in the vacuum slab, with random velocities chosen from a Maxwell-Boltzmann distribution. A velocity rescaling technique was applied to maintain the whole Ni-O system at the required temperature. More detail on the simulation procedure can be found in [8,9]. Oxidation kinetics. The oxidation of the three low-index nickel surfaces ((100), (110) and (111)) was investigated. All the slab of nickel contained approximately 500 atoms with an exposed surface around 250 Å 2, depending on the surface orientation. Fig. 2 represents the three kinetics curves which correspond to the number of oxygen atoms into the oxide layer as a function of time. Fig. 2: Oxidation kinetics for the 3 surface orientations at 300 K. These curves represent the total number of O atoms uptake in the oxide layer versus time. The 3 insets are side and top views of the (111) sample. Three stages are observed: (1) dissociative chemisorption, (2) oxide island nucleation and (3) oxide island growth. The atoms belonging to the oxide layer are defined as those with the x position between the outermost nickel atoms and the innermost oxygen atom in the oxide. The kinetic curves behaviours are the same for the three surfaces and they can be divided into three different stages. First, no oxygen atoms are incorporated into the oxide layer. Then numerous oxygen atoms are integrated in the layer in a short time. Finally, the numbers of oxygen atoms included in the oxide layer follow a linear law. The thickness of oxide layer versus time represented in Fig. 3 can also be divided in three steps: The first one, with no oxide layer on the nickel surface, the second one with a strong increase of the thickness and the third one in which the oxide layer thickness seems to reach a plateau.

5 Defect and Diffusion Forum Vols With these kinetic curves and the insets in Fig. 2, these three stages can be accurately described. The first step can be called dissociative chemisorpstion. It corresponds to the dissociation of the O 2 molecules on the surface followed by the chemisorption of oxygen atoms (picture (1) in Fig. 2). The second one begins when a sufficient coverage of the surface is reached. Then we observe a rapid nucleation of nickel oxide island (picture (2) in Fig. 2). The stage 3 is the lateral growth of the oxide island (picture (3) in Fig. 2), which explains why the oxide thickness reaches a plateau. So we have observed that the first step of nickel oxidation is based on the nucleation and the growth of an oxide island, which is in good agreement with the experimental studies [22,23]. We can notice that the surface orientation has no effect on the step (2) and (3) of oxidation. On the other hand, the surface orientation influence the number of oxygen atoms that must be chemisorbed before the oxide island apparition. Fig. 3: Oxidation kinetics for the three surface orientations ((100), (110) and (100)) at 300 K. These curves represent the thickness of oxide layer versus time. The 3 numbers are equivalent to those in Fig. 2. The inset shows the temperature effect on the (100) oxidation kinetic. The inset in figure 3 shows the kinetic curves for the surface (100) at 300 K and 950 K. As for the surface orientation, it can be observed that the temperature have almost no effect on stage (2) and (3), but it decrease the time of step (1) due to thermal agitation and allow a faster nucleation of the oxide surface. These might be related to the difference of surface energy between (100), (110) and (111) surfaces [24-26]. Theses studies are in progress and will be the subject of a forthcoming article in the near future. Conclusion We have developed VCMD simulation of the diffusion processes of O in Ni and the first steps of nickel oxidation. We have been able to compute the oxygen diffusion coefficient in the temperature range 300K K. The study of the first steps of oxidation allows us to obtain the kinetics for the 3 low index orientations. We clearly characterized an island growth mode for the oxide on nickel surface.

6 518 Diffusion in Solids and Liquids V Acknowledgement We would like to thank P. Vashishta, A. Nakano and R. Kalia for fruitful discussions, the CRI- CCUB (Dijon) and the CINES (Montpellier) for allowing us to access their computer facilities. References [1] S. Chevalier, F. Desserrey, J.P. Larpin: Oxid. Met. Vol. 64 (2005), p [2] S. Perusin: PhD thesis INP Toulouse ( (2004). [3] S Garruchet, O. Politano, P. Arnoux and V. Vignal: submitted to Solid State Commun. (2009). [4] S. Perusin, D. Monceau and E. Andrieu: J. Electron. Chem. Soc. Vol. 152 (2005), p. E [5] E. H. Megchiche, M. Amarouche and C. Mijoule: J. Phys.: Condens. Matter. Vol. 19 (2007), p [6] F.H. Streitz and J.W. Mintmire: Phys. Rev. B Vol. 50 (1994), p [7] X.W. Zhou, R.A. Johnson and H.N.G. Wadley: Phys. Rev. B Vol. 69 (2004), p [8] A. Hasnaoui, O. Politano, J. M. Salazar, and G. Aral: Phys. Rev. B Vol. 73 (2006), p [9] A. Hasnaoui, O. Politano, J. M. Salazar, G. Aral, R. K. Kalia, A. Nakano and P. Vashishta: Surf. Sci. Vol. 579 (2005), p. 47. [10] SKRS. Sankaranarayanan, S. Ramanathan: Phys. Rev. B Vol. 78 (2008), p [11] A. Elsener, O. Politano, P. M. Derlet and H. Van Swygenhoven: Modelling Simul. Mater. Sci. Eng. Vol. 16 (2008), p [12] A. Elsener, O. Politano, P. M. Derlet and H. Van Swygenhoven: Acta Mater. Vol. 57 (2009), p [13] X.W. Zhou and H.N.G. Wadley: J. Phys. Condens. Matter. Vol. 17 (2005), p [14] A. Einstein: Ann. Phys. Vol. 17 (1905), p [15] Y. Kraftmakher: Physics Reports Vol. 229 (1998), p. 79. [16] J.-H. Park and C.J. Altstetter: Metall. Trans. A, Vol. 18 (1987), p. 4. [17] R.A. Kerr: M. S. Thesis, The Ohio State University, Colombus, OH, (1972). [18] C.B. Alcock and P.B. Brown: Met. Sci. J. Vol. 3 (1969), p [19] S. Goto, K. Nomaki and S. Koda: J. Japan Inst. Met. Vol. 31 (1967), p [20] G.J. Lloyd and J.W. Martin: Met. Sci. J. Vol. 6 (1972), p. 7. [21] R. Barlow and P.J. Grundy: Met. Sci. J. Vol. 3 (1969), p [22] P.H. Holloway and J. B. Hudson: Surface Science Vol. 43 (1974), p [23] P.H. Holloway and J. B. Hudson: Surface Science Vol. 43 (1974), p.141. [24] J.M. Salazar, O. Politano, S. Garruchet, A. Sanfeld and A. Steinchen: Phil. Mag. A Vol. 84 (2004), p [25] O. Politano, S. Garruchet and J.M. Salazar: Mat. Sci. Eng. A Vol (2004), p [26] S. Garruchet, O. Politano, J.M. Salazar, A. Hasnaoui and T. Montesin: Appl. Surf. Sci. Vol. 252 (2006), p