Adsorption of Water on the Fe3O4(111) Surface: Structures, Stabilities

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Adsorption of water on the FeO (111) surface: Structures, Stabilities, and Vibrational Properties studied by Density Functional Theory Xiaoke Li, and Joachim Paier J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10560 • Publication Date (Web): 21 Dec 2015 Downloaded from http://pubs.acs.org on December 26, 2015

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The Journal of Physical Chemistry

Adsorption of water on the Fe3O4 (111) surface: Structures, Stabilities, and Vibrational Properties studied by Density Functional Theory Xiaoke Li and Joachim Paier* Institut für Chemie, Humboldt-Universität zu Berlin, Unter Linden 6, 10099 Berlin, Germany

ABSTRACT: Majority of the theoretical work, that attempted to provide atomic level details on the adsorption of water at the Fe3O4(111) surface, is based on conventional density functionals, which suffer from shortcomings such as, e.g., self-interaction errors. In an effort to overcome these uncertainties in theoretical results, we use density functional theory (DFT) employing the Perdew, Burke, and Ernzerhof generalized-gradient corrected exchange-correlation functional augmented by a Hubbard-type U parameter. We test for robustness of these results by application of the Heyd, Scuseria, Ernzerhof hybrid functional. For the two relevant metal terminations (Feoct2 and Fetet1) having ambient conditions in mind, we determined the minimum energy adsorption structures up to relatively high water coverage, i.e., one, two, and three H2O molecules on the p(1×1) surface unit cells, respectively. Water adsorbs dissociatively and strongly exothermic on the Feoct2, whereas molecular adsorption occurs on the Fetet1 termination. Using D2O, two IR signals at 2720 and 2695 cm1

(typical of OD stretching modes) can be observed for a wide range of temperatures and at moderate

water vapor pressures. Our calculations reveal that these IR bands originate from a very stable water dimer-like species. However, at lower temperatures creation of larger aggregations, such as trimers, appears to be thermodynamically favorable.

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1. INTRODUCTION Atomic level understanding of the interaction of water with iron oxides, one of the most abundant metal oxides in the earth’s crust, is of great importance in many different fields, as e.g. in the catalysis research,1-2 the electro-,3-4 and the geochemistry.5-6 Although under most relevant conditions hematite (Fe2O3) represents the thermodynamically most stable iron oxide phase, under rather reducing conditions, i.e. at higher temperatures and lower oxygen partial pressures, magnetite (Fe3O4) is the prevailing phase.7-8 Also for other technologically relevant metal oxides, like TiO26, 9-12 and ZnO,13-14 much effort has been spent to elucidate atomic-level details in the hydration process of the oxide surfaces. At temperatures above the so-called Verwey insulator to metal transition at about 122 K,15 magnetite crystallizes in the cubic inverse spinel structure of space group 3 with an equilibrium lattice constant of 8.396 Å.16-17 The iron cations (Fe2+and Fe3+) are located in the interstitial sites of a closepacked face-centred cubic (fcc) sublattice, which is formed by the oxygen anions (O2−). With respect to coordination numbers, two different cation sites exist in the crystal: the first one (A site) is tetrahedrally coordinated by oxygen and occupied only by Fe3+ ions, and the second one (B) is octahedrally coordinated and occupied by an equal number of randomly distributed Fe2+ and Fe3+ ions. Thus, FeA3+[Fe2+Fe3+]BO4 is one way to indicate the multivalent character of iron in magnetite. Its bulk phase is a ferrimagnetic material, where local magnetic moments at FeA and FeB ions are antiparallel oriented. The natural growth facet of magnetite is a surface in [111] orientation.18-20 According to Tasker’s rules,21 six polar bulk terminations exist (cf. Figure 1), however, relaxation of the ions will minimize surface dipoles and therefore stabilize the surface.22-24 Along the [111] direction and caused by the (layered) crystal structure, terminating the surface by FeA and FeB sites is possible in two different ways for each termination, i.e., Fetet1, Fetet2 and Feoct1, Feoct2. We prefer the latter notation, as it is unambiguous and is therefore used throughout this work.

Figure 1. Sequence of atomic layers in a Fe3O4(111) surface slab (Feoct2 terminated) in ideal bulk structure. Color code used throughout this work: Feoct1, Feoct2 dark blue balls; Fetet1, Fetet2 light blue balls; oxygen small red balls. All figures were created using VESTA.25


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Based on the low energy electron diffraction (LEED) and scanning tunneling microscopy (STM) studies by Weiss and coworkers, who focused on thin films of Fe3O4(111) supported on Pt(111), the surface is terminated by a 1/4 monolayer (ML) of the Fetet1 ion over a hexagonal close packed oxygen layer.26-29 This agrees with earlier LEED studies by Somorjai and coworkers.30-31 However, results from a study employing high resolution electron energy loss spectroscopy (HREELS), infrared reflection absorption spectroscopy (IRAS), and temperature programmed desorption (TPD) using CO as a probe molecule were reconcilable with a termination of two iron atoms, consisting of a topmost 1/4 ML of Feoct2 and a 1/4 ML of Fetet1 directly underneath.32 With regard to theoretical work, this section does not intend to be exhaustive about previous density functional theory (DFT) studies on the Fe3O4(111) surface. Instead, we only mention three–in our opinion–representative works using LDA+U(4.0,4.5 eV),33 PBE+U(3.8,4.0 eV),34-35 as well as PW91+U(3.61eV)36 to calculate surface energies and stabilities of various terminations under varying chemical potentials of oxygen. Although different DFT-based approaches have been used, these studies agree on the fact that the Fetet1 and Feoct2 terminations are (i) comparably stable in terms of surface energy, (ii) the most stable ones for a wide range of chemical potentials of oxygen. A few studies on the adsorption of water on the Fe3O4(100) surface exist,37-39 however, in spite of the large body of work by Ranke and coworkers7, 29, 40-41 focusing on the (111) facet, there are still some open questions. Al-Shamery and coworkers investigated the adsorption structure of small water aggregations based on TPD as well as IR spectroscopy.41 Relying on the work by Joseph et al.,40 they conjectured that upon dissociative H2O adsorption, the OH− coordinates to a surface Fe ion, and the H+ binds to a neighboring surface O ion creating another hydroxyl group. This hypothesis naturally suggests the assignment of the two observed IR bands (2712 and 2691 cm-1)41 to respective vibrational modes of the aforementioned “water induced” OH groups. However, firm evidence has not been provided yet. In another recent work, Batista and coworkers studied the adsorption of water on an iron-terminated Fe3O4(111) surface by virtue of STM and DFT.42 For temperatures below 235 K, they interpret their STM images as a signature of intact water molecules as well as hydroxyl groups bound to the surface, whereas for temperatures between 235 and 245 K, results are interpreted in favor of complete dissociation of adwater. Consequently, for this temperature range, the authors claim that all water is converted into hydroxyl groups bound on top of the terminating Fe3+ cations.42 Relatively few theoretical studies on the adsorption of water on the Fe3O4(111) surface exist.19, 42-44 Importantly, as shown by Jiao and coworkers,34 12 atomic layers for the periodic slab model appear to be mandatory, because the ninth layer for the Fetet1 and the seventh layer for the Feoct2 termination play an important role in electron localization, which is coupled to ionic relaxation. However, the criterion of a large enough model, i.e. employing a slab with a sufficient number of layers, is only met in ref. 44. Unfortunately, due to technical issues described in this aforementioned work, no Hubbard-type U parameter to correct for some of the correlation effects in the Fe 3d states was employed. A systematic



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theoretical study on water adsorption treating both important metal terminations has not been accomplished so far. The present work addresses these issues and discusses novel results on the interaction between H2O molecules and the Fetet1- and Feoct2-terminated Fe3O4(111) surfaces using periodic DFT and superposition error free plane waves as a basis set. We present a detailed, comparative report on minimum energy structures, adsorption thermodynamics, as well as IR frequencies including isotope effects with increasing water coverage, i.e. one, two, and three H2O per primitive surface unit cell. This corresponds to water coverages of 3.2, 6.4, and 9.6 × 1014 cm-2, respectively.

2. COMPUTATIONAL DETAILS 2.1. Methods PBE+U electronic and ionic structure calculations. Calculations were performed using the projector-augmented-wave (PAW) method45-46 as implemented in the Vienna ab initio simulation package (VASP)47-48 using plane waves up to a kinetic energy of 800 eV. We take care of corrections for the onsite Coulomb correlation of Fe 3d orbitals via the (spin-polarized) DFT+U49-50 approach based on the Perdew-Burke-Ernzerhof (PBE)51 exchange-correlation functional, that is, PBE+U. The specific implementation of DFT+U used in this work follows Dudarev et al.52-53 An effective Hubbardtype U parameter of 3.8 eV was employed following previous LSDA54-55 as well as PBE-GGA34, 56 studies on Fe3O4 surfaces. This appears to be an optimal choice, because local magnetic moments of the octahedrally and tetrahedrally coordinated Fe ions in the bulk amount to 3.9 and −4.1 µB, respectively, which is in very good agreement with experiment (4.05 µB)57 and results reported in the literature.34, 36, 56 In addition, the lattice parameter obtained using an effective U of 3.8 eV and the PBE functional amounts to 8.508 Å (fit to Murnaghan’s equation of state; cf. Supplemental Information, SI)58 agrees reasonably well with experiment (8.396 Å).16-17 The calculated bulk modulus amounts to 172 GPa, which underestimates the observed value (181-186 GPa)17, 59 by 5%. The overestimation of the lattice constant together with the aforementioned underestimation of the bulk modulus is typical of GGA functionals applied to crystalline solids.60 The overestimation of lattice constants by a GGA approximation becomes usually even more pronounced within the DFT+U approach, as e.g., discussed by Bayer et al.61 We use the PAW potentials as released with VASP 5.2. The potential used to describe the electron-ion interaction in Fe comprises 14 valence electrons (Fe: [Mg] 3p6 3d7 4s1 as the atomic reference configuration). For oxygen 6 ([He] 2s2 2p4) valence electrons have been used. For the Fe3O4 bulk calculations a Γ-centered Monkhorst-Pack62 k mesh of a grid density of 8 × 8 × 8 was employed. Surface calculations (cf. section 2.2) employ a 5 × 5 × 1 k mesh. Electronic optimization was performed using an energy break criterion of 10-5 eV. Structural optimizations were performed until all forces acting on the relaxed atoms were better than 0.02 eV/Å. ACS Paragon Plus Environment

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Vibrational frequencies use central differences for the force derivative to calculate the (partial) Hessian matrix (cf. section 2.2) employing atomic displacements of ±0.015 Å. Hybrid functional calculations. In addition to PBE+U(3.8), adsorption energies required for thermodynamic stabilities (cf. sec. 3.4) were computed using the Heyd, Scuseria, Ernzerhof hybrid functional63 (HSE). This functional uses 25% Fock and 75% PBE exchange energy as the mixing ratio similar to the PBE0 hybrid functional64 and a screening parameter of 0.207 Å-1. Energy and force calculations employ a Fourier grid for the Fock exchange related routines determined by 9/4 times the cutoff used to expand the orbitals (PRECFOCK = normal). This protocol was extensively tested and has been shown to result in accurate energies and forces.65-67 To optimize the bulk lattice constant, a Γcentered 4 × 4 × 4 Monkhorst-Pack k mesh was used, and the surface slab calculations employ a k mesh of 2 × 2 × 1 grid density. This ensured k-point convergence in the hybrid functional results. To test for the influence of van der Waals dispersion-type of interactions on adsorption energies, we estimated this energy contribution by adding the semiempirical C6/R6 term following Grimme (DFT+D2) to energies and forces.68-69 Standard van der Waals C6 and R0 parameters as provided by Grimme were employed for Fe, O, and H atoms (cf. Table 1). Functional specific global scaling factors for the dispersion contribution of 0.75 and 0.60 were employed in PBE+U(3.8) and HSE calculations, respectively. For more extensive assessments and discussions on the global scaling factors, we refer to references 66 and 70. Table 1. C6 parameters (J nm6 mol-1) and van der Waals radii, R0 (pm), used in this work (as provided by Grimme68). Fe O H

C6 10.80 0.70 0.14

R0 156.2 134.2 100.1

2.2. Models The conventional unit cell for the bulk crystal used comprises 56 atoms (Fe24O32). The surface unit cells cut in [111] orientation are primitive (1×1) cells with respect to the oxygen plane with a cell vector of length (PBE+U(3.8): 601.6 pm; HSE: 594.8 pm) with a0 being the equilibrium bulk √2 lattice constant. Slab models use 12 atomic layers corresponding to a composition of Fe12O16 (cf. Figure 2). Periodically repeated images are separated by a vacuum layer of 10 Å. Spurious dipoledipole interactions between periodic images are compensated by the approach suggested by Makov and Payne71 as implemented in the VASP code. For the optimization of ionic positions, four atomic layers at the bottom of the slab are kept frozen in bulk positions (= asymmetric slab). Normal mode analysis uses the optimized slab involving adwater as well as four topmost surface layers, needed in the calculation of the partial Hessian. This means that the contribution from the remaining eight layers below the surface layers are not included in the



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calculation of harmonic frequencies. However, this contribution is supposed to largely cancel out in the calculation of adsorption energies.

Figure 2. Slab models for the clean and optimized a) Feoct2 and b) Fetet1 terminated Fe3O4(111) surfaces. See Figure 1 for the color code.

2.3. Thermodynamics The adsorption of water on the Feoct2 and Fetet1 terminated Fe3O4(111) surfaces is described by the following equation

Fe O 111/ n H O ⇄ Fe O 111, nH O!/

(1)

with n = 1, 2, and 3. The corresponding adsorption free energy, ∆Gads, is defined as &

&

:

∆#$%& ' ∆#$%& (, ), * + , ' #-./0 1 2#&345 * ∙ 789 ;, &

&

(2)

:

with #-./0 , #&345 , 789 as the free energies of the adsorption complex, the clean surface, and the chemical potential of water in the gas phase. The enthalpy for solids is approximated as the sum of the DFT electronic energy and the zero-point vibrational energy (ZPVE) using harmonic frequencies. As commonly applied,72 the volume work (pV) in solids is neglected:

+ & '

Adsorption of Water on the Fe3O4(111) Surface: Structures, Stabilities

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