Fe3O4 Interfaces from DFT Results

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ScienceDirect Procedia Materials Science 9 (2015) 612 – 618

International Congress of Science and Technology of Metallurgy and Materials, SAM – CONAMET 2014

Charge difference calculation in Fe/Fe3O4 interfaces from DFT results Diego Tozinia, Mariano Fortia,b,*, Pablo Garganoa,b, P. R. Alonsoa,b, G. H. Rubiolo a,b,c a

Instituto Sabato, Universidad Nacional de San Martín - CNEA, Avda. General Paz 1499, B1650KNA, San Martín, Buenos Aires, Argentina. Comisión Nacional de Energía Atómica. Gerencia Materiales. Centro Atómico Constituyentes. Avenida General Paz 1499 (B1650KNA) San Martín, Buenos Aires, Argentina. c Consejo Nacional de Investigaciones Científicas y Tecnológicas, Avda Rivadavia 1917, C1033AAJ, Ciudad Autónoma de Buenos Aires, Argentina

b

Abstract In industrial applications, the mechanical stability of surface oxides formed from metal alloys is a key concern in the determination of component susceptibility to different deterioration mechanisms. In particular, the Fe/Fe3O4 system that is treated in this work is of great interest for many applications. A complete description of the chemical bonds between the metal substrate and the surface oxide may provide vital information. Charge density of the metal/oxide interface is obtained from DFT calculations, as well as for the free surfaces involved. A homemade computer program was implemented to calculate charge redistribution between the constituting surfaces and iron / magnetite interfaces. This analysis makes it possible to identify the interaction between surface iron as the key to understand interfacial adhesion. These results correlate to previous adhesion studies. © Published by Elsevier Ltd. This © 2015 2015The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of SAM– CONAMET 2014. Peer-review under responsibility of the Scientific Committee of SAM–CONAMET 2014 Keywords:DFT; Charge difference; Adhesion

1. Introduction In the frame of the analysis of susceptibility of metal alloys to corrosion, integrity of oxide layers that grow on metallic surfaces must be taken into account as a relevant feature. Mechanical defects on the oxide layer can behave

* Corresponding author. Tel.: +54-11-67727832; fax: +54-11-67727362.. E-mail address:[email protected]

2211-8128 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of SAM–CONAMET 2014 doi:10.1016/j.mspro.2015.05.037

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as starters for localized corrosion mechanisms; or chipping and peeling of oxide layers formed from generalized corrosion in a particular component can produce erosion in another component within the system or deposition of foreign particles. The study of mechanical integrity has been increased in the last decades. Schütze et al. (2005, 2009) have classified the possible oxide scale failure mechanisms based on the stress conditions of the oxide film and the crack orientation relative to the metal/oxide interface. The same authors summarized the breaking criteria in each case. In this frame, Fe / Fe3O4is of great technological interest due to the variety of applications of iron alloys. ). Magnetite, or a material Magnetite (Fe3O4) is a ferrimagnetic oxide with an inverse espinel structure ( with similar structure and composition, grows as the inner layer on iron surface in an oxidizing media, as observed by Davenport et al. (2000), Toney et al. (1997) and Yi (2004). It is thus relevant from a technological point of view to know the properties of this interface. In particular, topology of charge distribution can help in the identification of adhesion mechanisms and prediction of failure modes. The analysis of charge differences is used to measure charge redistribution between a reference system and the one of interest and there are found in literature several approaches. Bader analysis implemented by Sanville et al. (2007) assigns an atomic charge by integration of charge density in a zone determined through topological considerations. It is thus possible to estimate atomic charge gain or loss. Another usual analysis method is Charge Density Difference (CDD), which takes the difference between charge densities of the system of interest and a reference one and plots charge redistribution due to chemical bonds. Siegel et al. (2002 a, b) implemented this method to explain interfaces properties from Density Functional Theory (DFT) calculations and used topological arguments to find failure modes in metal-metal and metal-oxide interfaces. Another application was made by Teng et al. (2012) who used CDD to study charge redistribution generated by an adsorbate on an aluminium substrate. 2. Method Ground state charge densities were calculated using DFT from Hohenberg and Kohn (1964) and Kohn and Sham (1965) as implemented in the VASP package described by Hafner (2007, 2008). Ion – electron interactions were treated with augmented plane waves (PAW) developed by Vanderbilt (1990). Plane wave expansions were taken to cut off energy of 500 eV. Exchange and correlation interactions were treated through the generalized gradient approximation in the Perdew et al. (1996) interpretation (GGA-PBE). Integrations in the Brillouin zone were performed in a Monkhorst and Pack (1976) grid. Tetrahedron method with Blöch (Blöchl et al. (1994)) corrections was used for electronic occupation functions. 2.1. Bulk calculations Pure iron block, pure magnetite block and joined blocks to form the interface were relaxed to obtain total ) structure was obtained by relaxing internal degrees of freedom. Oxygen ions energies. Magnetite ( form an fcc lattice where iron ions occupy octahedral and tetrahedral interstices, in such way that (001) planes alternate in Fe and FeO2 compositions. Iron ions thus form sublattices that are ferrimagnetically ordered between each other as pointed out by Rowan et al. (2009) and Zhang and Satpathy (1991). Lattice parameters were obtained after fitting total energy values as a function of volume through Birch-Murnaghan type equations of state after Birch (1947, 1938). The Monkhorst-Pack grid was 7×7×7 for oxide and 15×15×15 for Fe (bcc), in order to ensure a convergence within 0.1 meV. 2.2. Interface calculations Davenport et al. (2000) experimentally obtained the orientation relations between oxide and metallic substrate as ) as it is shown in Fig. 2. This orientation takes advantage of the Fe (001) || Ox (001) and Fe (100) || Ox ( similarity between interatomic distances in [110] direction in Fe (bcc) and [100] direction in the oxide. Interface distance cannot be experimentally measured, but Forti et al. (2013) used DFT calculations to obtain its equilibrium value and the adhesion energy for the possible different conditions of composition of the layers in the interface and relative stacking between oxide and metallic substrate (Table 1). These authors considered a ferromagnetic coupling

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between iron atoms on both layers at the interface. Assuming the published value for interface distance, we constructed the interface model with two blocks involving atomic layers of both materials. Metallic substrate involves seven atomic layers, while oxide is modeled with eleven layers.

Fig. 1. Crystalline structure of magnetite. (a) inverse spinel (

) where planes alternate in composition. (b) Fe plane. (c) FeO2 plane.

Fig. 2. Interface model. (a) Supercell used for DFT calculations. (b) hollow stacking. (c) top stacking.

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Table 1. Interface distance d0 and adhesion energy Ȗ.





d0 Å

System

Ȗ Jm 2

Fe3O4 (= Fe) – hollow

1.93

1.3

Fe3O4 (= Fe) – top

1.04

2.2

Fe3O4 (= FeO2)

1.41

1.9

Since (001) oxide planes alternate different compositions, it can be chosen any of the two possible terminations in contact with the metal. For Fe termination, studied stackings are top, where iron tetrahedral lay on metallic iron atoms, and hollow stacking where iron atoms in the oxide lay on octahedral sites of the metal. Layer number on each block is enough to guarantee that the internal part of each of them has bulk properties. A compression of 4.3% in [100] and [010] oxide directions is performed in order to obtain coherency between blocks and simulate an infinite interface through periodic conditions. Finally, an 8 Å large gap is introduced to avoid interactions between contiguous images. A Monkhorst-Pack grid of 7×7×1 was used for surfaces and interfaces calculations. 2.3. Charge Density Difference – VODCA code. CDD can be calculated taking the superposition of non-interacting atoms (or isolated) as reference. This approximation is the easiest to apply since superposition can be obtained from the initial condition of the selfconsistency cycle in the code that implements the DFT. This strategy allows us to analyze atomic bonds but loses global redistributions of charge. Another suitable reference takes the superposition of isolated constitutional blocks, instead of isolated atoms. This approach makes it possible to appreciate global effects of interaction in surface redistribution due to the presence of the other block. In the present case blocks are the seven layers metal slab and the eleven layers oxide slab. For the direct calculation of CDD it is necessary to determine charge density of constituent blocks in the same real space points (FFT grid) where the whole system is determined. This requirement implies the calculation of isolated surface slabs and interface in the same supercell, with the same FFT grid. This calculation is not feasible since for isolated slabs in the same supercell a too large gap should be introduced, and a consequently too large number of plane waves should be involved. Computational cost prohibits such a calculation. A feasible alternative is implemented within the VODCA program (acronym of its spanish name: VASP Opere Densidades de Carga Ágilmente), able to overlap charge densities of surface blocks to make a direct comparison with the interface of interest. The VODCA code translates surface blocks and their charge densities to the position they occupy in the interface making use of translational and rotational operations. Finally, an interpolation by cubic splines in three dimensions is performed in order to determine the values for overlapping of charge densities in the points where the charge density has been calculated for the interface. The whole operation results in the sum of charge densities of free surfaces placed in the same supercell as the interface and reproducing its geometry to make possible the direct comparison. Mathematically:



term CDD = ȡint  ȡOxide + ȡ FeBCC



(1)

is charge density calculated for the interface, is charge density for the oxide in the corresponding where is charge density of BCC iron block. termination, and In order to valídate the method, we calculated the charge density of a BCC Fe unit cell using evaluation grids of several densities, and then VODCA was used to interpolate data to a denser grid. In all cases the relative error introduced by interpolation was less than 10-15, and was thus considered negligible. 3. Results It can be seen in Eq. (1) that a positive CDD implies charge gain and a negative CDD implies loss of electric charge. In general, charge gain is observed in the interface zone, and thus contributing to bonding between surfaces. Fig. 3 shows projected CDD values on planes of interest.

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Fig. 3. CDD contours in Fe (bcc)/Fe3O4 interfaces: (a) a) (100 (100) plane Fe (bcc) / Fe3O4(=Fe)-hollow, (b) (110) plane Fe (bcc) /Fe3O4(=Fe)-top. (c) plane Fe (bcc) / Fe3O4(=FeO2).

Color reference goes from white in the negative extreme and black in the positive extreme, with gray stating for zero difference. Gain zone extension varies in agreement with adhesion energy of the system. For the more stable interface, Fe (bcc)/Fe3O4(=Fe)-hollow, charge gain zone goes to the first atomic layer in the metal. Charge redistribution shows a tendency to increase from the tetrahedral iron on oxide surface towards the interface and the octahedral site in the metal, and at a lower rate from metallic iron ions close to the octahedral metallic site. In this way, iron ions on oxide surface partially fulfill the coordination with next nearest metallic iron atoms, as it is shown in Fig. 2(b). On the other hand, an inspection of results for the interface Fe (bcc)/Fe3O4 (= Fe) – top shows that charge redistribution is produced from tetrahedral oxide irons towards the interface zone, slightly modifying charge distribution on the last metallic layer. Besides, this stacking generates an unstable coordination of metallic iron atoms, contributing, together with the described redistribution of charge, to the low bonding of this interface. Finally, the interface Fe (bcc)/Fe3O4 (= FeO2) exhibits a charge redistribution from octahedral oxide iron atoms and metallic iron atoms. The remarkable difference with the other cases resides in the fact that major charge gain are located closer to the oxide surface than to the interface zone. Table 2. Bader analysis for atoms next to the surface. 'q/q is relative charge variation. Bader charge (e / Å3)

Bader volume (Å3)

Surf

Interf

'q/q

Surf

interf

'V/V

Fe – Met

7.95

7.83

-0.02

36.6

13.2

-0.64

Fe – tetra

6.98

7.41

0.06

81.2

11.5

-0.86

Fe-Met

7.95

8.00

0.01

36.6

17.49

-0.52

Fe-tetra

6.98

7.02

0.01

81.2

14.87

-0.82

Atom

Fe (bcc) / Fe3O4(=Fe)-hollow

Fe (bcc) / Fe3O4(=Fe)-top

Fe (bcc) /Fe3O4(=FeO2) Fe-Met

7.95

7.77

-0.02

36.6

11.6

-0.68

Fe-Octa

6.34

6.69

0.06

20.3

7.9

-0.61

O

7.16

7.24

0.01

31.5

11.5

-0.63

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Results of a Bader analysis (Table 2), as implemented by Henkelman et al. (2006) and Tang et al. (2009), supports our comments. Change in Bader volume between surface and interface states is large since in the first one the lack of coordination extends atomic volume. A comparison of interfaces with Fe termination for the oxide shows that hollow configuration has the lowest atomic volumes. This is in agreement with the observation that bonding zone is farther from the oxide surface in top stacking than in hollow stacking. A charge transfer is observed from metallic atoms to oxide atoms in Fe (bcc)/Fe3O4(=Fe)-hollow and Fe (bcc) /Fe3O4(=FeO2) configurations, while in the Fe (bcc) /Fe3O4(=Fe)-top configuration both metal and oxide gain charge. This can be due to a decrease in charge in the surface of both oxide and metal, redistributed to the interface. 4. Conclusions CDD method was applied to the analysis of iron/magnetite interfaces, with geometrical and orientation parameters taken from the literature. Charge redistribution results show that interaction among iron atoms in the metal and in the oxide is the relevant one to understand bonds between surfaces. Adhesion is mainly influenced by charge transfer between iron sites in the oxide and iron sites in the metal. This observation is supported by Bader analysis. Acknowledgements This work has been performed at the Gerencia Materiales, CAC – CNEA. We thank ANPCyT for the grant PICT-2011-1861. Calculations were done at the High Performance Computing Center at Centro Atómico Constituyentes, Comisión Nacional de Energía Atómica. VESTA programme by Momma and Izumi (2011) was used for visualization of structures. References Birch, F., (1938). The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan’s Theory of Finite Strain. Journal of Applied Physics 9, pp 279. Birch, F., (1947). Finite Elastic Strain of Cubic Crystals. Physical Review. Blöchl, P.E., Jepsen, O., Andersen, K., (1994). Improved tetrahedron method far Brilleuin-zane integratians. Physical Review 49. Davenport, A.J., Oblonsky, L.J., Ryan, M.P., Toney, M.F., (2000). The Structure of the Passive Film That Forms on Iron in Aqueous Environments. Journal of The Electrochemical Society 147, pp 2162. Forti, M.D., Alonso, P., Gargano, P., Rubiolo, G.H., (2013). ENERGÍA DE ADHESIÓN DE LA INTERFASE Fe(BCC)/MAGNETITA EN LA APROXIMACIÓN DFT. In: 13er Congreso Internacional En Ciencia y Tecnologia de Metalurgia y Materiales 2013. Puerto Iguazu, Misiones, Argentina. Hafner, J., (2007). Materials simulations using VASP—a quantum perspective to materials science. Computer Physics Communications 177, pp 6–13. Hafner, J., (2008). Ab-initio simulations of materials using VASP: Density-functional theory and beyond. Journal of Computational Chemistry 29, pp 2044–2078. Henkelman, G., Arnaldsson, A., Jonsson, H., (2006). A fast and robust algorithm for Bader decomposition of charge density. Computational Materials Science 36, pp 354–360. Hohenberg, P., Kohn, W., (1964). Inhomogeneous electron gas. Phys. Rev 136, pp B864–B871. Kohn, W., Sham, L.J., (1965). Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review 140, pp A1133–A1138. Momma, K., Izumi, F., (2011). VESTA: a Three-Dimensional Visualization System for Electronic and Structural Analysis pp 3–23. Monkhorst, H., Pack, J., (1976). Special points for Brillouin-zone integrations. Physical Review B 13, pp 5188–5192. Perdew, J., Burke, K., Ernzerhof, M., (1996). Generalized Gradient Approximation Made Simple. Physical review letters 77, pp 3865–3868. Rowan, A., Patterson, C., Gasparov, L., (2009). Hybrid density functional theory applied to magnetite: Crystal structure, charge order, and phonons. Physical Review B 79, pp 1–18. Sanville, E., Kenny, S.D., Smith, R., Henkelman, G., (2007). Improved Grid-Based Algorithm for Bader Charge Allocation. Journal of Computational Chemistry 28. Schütze, M., (2005). Modelling oxide scale fracture. Materials at High Temperatures 22, pp 147–154. Schütze, M., Tortorelli, P.F., Wright, I.G., (2009). Development of a Comprehensive Oxide Scale Failure Diagram. Oxidation of Metals 73, pp 389–418. Siegel, D., Hector, L., Adams, J., (2002)(a). Adhesion, atomic structure, and bonding at the Al(111)/Į-Al2O3(0001) interface: A first principles study. Physical Review B 65, pp 085415.

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