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Trends in the Thermodynamic Stability of Ultrathin Supported Oxide Films Philipp N. Plessow,†,‡,§ Michal Bajdich,‡ Joshua Greene,† Aleksandra Vojvodic,‡ and Frank Abild-Pedersen*,‡ †

SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States ‡ SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States S Supporting Information *

ABSTRACT: The formation of thin oxide films on metal supports is an important phenomenon, especially in the context of strong metal support interaction (SMSI). Computational predictions of the stability of these films are hampered by their structural complexity and a varying lattice mismatch with different supports. In this study, we report a large combination of supports and ultrathin oxide films studied with density functional theory (DFT). Trends in stability are investigated through a descriptor-based analysis. Since the studied films are bound to the support exclusively through metal−metal interaction, the adsorption energy of the oxide-constituting metal atom can be expected to be a reasonable descriptor for the stability of the overlayers. If the same supercell is used for all supports, the overlayers experience different amounts of stress. Using supercells with small lattice mismatch for each system leads to significantly improved scaling relations for the stability of the overlayers. This approach works well for the studied systems and therefore allows the descriptor-based exploration of the thermodynamic stability of supported thin oxide layers.

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INTRODUCTION One of the major problems in heterogeneous catalysis is related to the loss of active surface area over time, and a significant effort has been focused on understanding the cause of catalyst deactivation.1 Strong metal support interaction (SMSI) is one important aspect of this, and it is driven mainly by the stability of metal supported thin oxide films. SMSI was discovered experimentally as a dramatic reduction in the ability of titaniasupported Pt-particles to adsorb CO when they were subjected to a reducing treatment (H2 gas).2,3 It was only later realized that this phenomenon is caused by the formation of thin TiOxfilm on the Pt-particles.4 Ultrahigh vacuum conditions are often also reducing enough to allow the formation of SMSI-layers as in the case of Pt/TiO2,5,6 Pd/TiO2,7,8 and Pt/Fe3O4.9−11 An experimentally more targeted approach toward the synthesis of thin oxide films is the deposition and growth of these films on metal surfaces. Apart from studying these films as models systems for SMSI states, supported ultrathin films of the metal-oxides display enhanced catalytic properties12,13 especially in the nanoscale regime14,15 and a potential for templategrowth applications.16 The number and complexity of these systems is overwhelming, and for a thorough review, we refer the reader to ref 16 and other reviews.14,17−19 Major challenges in modeling thin films are their variable composition and the © XXXX American Chemical Society

fact that lattice-mismatch with the underlying metal may lead to incommensurate overlayers or overlayers with very large unit cells.20 The computational (or any) prediction of the stability and structures of thin films may therefore seem elusive. In this work, we will introduce scaling relations widely employed in heterogeneous catalysis to thin films to obtain a simplified description of their energetics. Scaling relations relate adsorption energies of species such as AHx, with A = {C, N, S, and O} to the adsorption energy of A.21 Scaling relations also exist for transition states, and one can consequently describe the energetics of large catalytic reaction networks with few descriptors. This allows a drastic simplification in the comparison and optimization of catalysts.22−25 The existence of linear-scaling relations can be rationalized by the fact that adsorbates bind through the same atoms. The slope of the scaling relationship of adsorption energy versus descriptor can be explained by adsorbate−surface bond-order considerations. For highly oxidized films, such as TiO2/Pt(111)26 and VO2/ Pd(111),27 structures involving oxygen at the interphase have been proposed. The majority of thin oxide films with low Received: February 9, 2016 Revised: April 8, 2016

A

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typical values used for transition metals.15,42,51−53 All DFTcalculations have been carried out with Quantum Espresso54 using ultrasoft pseudopotentials.55 The energy cutoff for the plane wave expansion of wave function (density) was 500 eV (5000 eV). The k-point sampling was a Γ-centered (12 × 12 × 1)-grid for (1 × 1)-fcc(111) surfaces and correspondingly for larger supercells. Lattice constants were fixed at the computed bulk values. Comparable k-point sampling densities were used for ( n × n )-surface unit-cells that are not integer multiples of the (1 × 1)-cell. For the supporting metal, slabs with four surface layers, where the two lowest layers were kept fixed, were separated by 16 Å, and the dipole correction56 has been used to reduce the artificial interaction between slabs. Adsorption energies of metal atoms were calculated in the fcc site at θ = 1/ 4 coverage as a compromise between computational efficiency and adsorbate−adsorbate interactions. The metal coverage in the overlayers is generally in the range θ = 3/4 to 1. Spinpolarized calculations were performed within the row-wise antiferromagnetic (AFM) structure for the minimal (2 × 1)surface unit-cell known from FeO/Pt(111).40 Ferromagnetic (FM) structures were, without a specific spacial order, initialized with alternating positive and negative magnetic moments, giving a minimal total magnetic moment. To analyze the magnetic properties of FM and AFM supercells on equal footing and to be independent of local magnetic moments obtained from projectors, we discuss absolute magnetic moments per surface oxide atom, where ρα(r) and ρβ(r) are the densities of α and β spin.

oxygen content and, in particular those relevant for SMSI, bind through the oxide-metal to the underlying support metal.9−11,20,28−30 The general stacking sequence, for example, Pt−Ti−O in the various TiOx/Pt(111) films, implies that the energetics of such an oxide film on other metals can be described by the adsorption energies of Ti, and this is indeed what we found. A general difference between molecular adsorbates and an overlayer as a continuously periodic adsorbate is that the latter generally binds through more than one atom (at least one per unit cell). However, similar cases have also been reported for molecular adsorbate, where scaling relations have been shown to work for hydrocarbons31 and polyalcohols32 that bind through more than one atom. Adsorbate−adsorbate interaction generally plays a minor role in molecular scaling relations since adsorption is computed in the low-coverage limit. However, for overlayers as adsorbates, as with interfaces between bulk materials, artificial or real strain may occur since the support and overlayer generally do not have the same lattice constant. Again, similar problems have been dealt with for polydentate adsorbates,32 where ring-strain has been found to influence the adsorption energetics. For thin oxide films, the polarity of the unsupported layers and charge transfer between the overlayer and support is very important and plays a crucial role in stabilizing the otherwise polar surfaces.17 The same is true for molecular adsorbate, where, except for N2 and O2 and van-der Waals bound systems, all adsorbates (NO, CO, CH3, etc.) have a dipole moment. Another difference between thin oxide layers and molecular adsorbates may arise from chemical bonding. Most molecular scaling relations involve main group-elements, for example, C and CHx. It is a priori not clear that scaling relations between C and CHx can be found for Ti and TiOx as well. The article is organized as follows: in the first section, we will introduce the methods used to calculate the properties of the systems studied in this work. This includes computational details, thermodynamics, and choice of reference and an investigation into the role of lattice mismatch. After that, we will analyze trends in stability of the oxide films in terms of scaling relations. Lastly, we will discuss the thermodynamic stability of the thin films under different oxygen chemical potentials together with properties such as magnetism and charge transfer at the interface.

μ∝

∫UC dr 3|ρα (r) − ρβ (r)|

(1)

Bader charges57−59 are also always given per surface oxide atom, e.g., per oxide formular unit if the oxygen stoichiometry is reported as a fractional number as in TiO1.5. General Thermodynamics. For thin oxide layers (MOx) on a metal support 4 , there are generally two different situations determining the thermodynamic stability. In the case of SMSI, a bulk oxide (MOy) on which the nanoparticle is supported serves as a source for both the oxygen and the metal M constituting the metal-oxide layer. In relation to the surface of the nanoparticle, the bulk-oxide can be considered as a source of unlimited amounts of metal atoms M. One would therefore expect that, under thermodynamic control, the entire particle with a constant surface area Atotal will be covered. Consequently, the Gibbs free energy of the surface film can be expressed as

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METHODS It is generally accepted that DFT at the generalized-gradientapproximation (GGA) level of theory does not always provide an appropriate description of the electronic structure of bulk transition metal oxides, where DFT+U33,34 often gives an improved performance.35−39 The most transparent effect of DFT+U is that it often enforces a metal−insulator transition,33 which is in some cases the desired effect. Metal-supported thinoxide films cannot generally be strictly categorized as insulator or metal since the underlying support is certainly metallic. Conceptually, one may also regard them as oxygen-covered surface alloys. Thin oxide film can therefore in many cases a priori not be classified as a pure oxide or metal. In previous work, both DFT+U11,40−43 and GGA20,26,44−48 have been employed. We will mainly use PBE49,50 and discuss PBE+U results only for selected cases and if explicitly stated. We are mainly interested in testing what the effect of introducing the U parameter is, relative to PBE. Since it is in many cases not known, what an optimal value for U would be, we use U = 3 eV for all metals constituting the oxide layer as it is in the range of

Gform = A total ×

G UC − oxide − film A − oxide − film UC  (2)

γoxide − film

Here, GUC−oxide−film is the Gibbs free energy per unit cell (UC), and AUC−oxide−film is the corresponding surface area. The most stable film is in this case the film with the lowest surface free energy, γoxide−film. However, if a finite number of atoms is introduced, for example, through vapor deposition, the metal surface may only be partially covered. In this case, the total Gibbs free energy is given by Gform = ntotal(M ) × B

G UC − oxide − film n(M)

(3)

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The Journal of Physical Chemistry C Therefore, the most stable surface structure is the film with lowest free energy per metal atoms M of the oxide layer. We have in both cases implicitly assumed that an equilibrium with an oxygen source such as O2 in the gas phase is established and that the concentration of that species in the gas phase is constant. In our study, we are mainly interested in SMSI, and we therefore intend to use the transition metal oxides as references. Since formation energies of the bulk transition metal oxides are known experimentally,60,61 we computed the bulk metals (Fe, bcc; Ru,Os, hcp; else, fcc) and obtained the metal chemical potentials using the experimental formation energies as well as the oxygen chemical potential. We have always considered the most stable source of the metal M in the available data of MOy and bulk metal M. This circumvents error-prone DFT calculations of bulk metal oxides but has the disadvantage of having potentially less error-cancellation than comparing bulkoxides with surface-oxides. The oxygen chemical potential was derived from a H2 pressure of 1 bar at T = 800 K, close to experiments reported by Tauster2 and an assumed partial pressure of H2O of 10−5 bar. Relative to molecular oxygen at T 1 = 0 K, μO0 = 2 μO , the oxygen chemical potential is μO = −3.73 2 eV. This corresponds to an O2 partial pressure of 10−37 bar, which would be the decisive quantity of a UHV experiment. At these conditions, the most stable determined states of the transition metals are TiO2, MnO, Cr3O4, VO, Co(hcp), Ni(fcc), and Fe(bcc).

be generated by considering rotated ( n × n )-cells of either the support metal or the oxide-layer.40 A disadvantage of this approach is that the orientation of the films is changed and that a row-wise-AFM magnetic ordering can no longer be maintained. In order to assess the effect of lattice mismatch, we have generated supercells that cover a variety of lattice constants of the oxide overlayer (see Figure 1). All larger supercells

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RESULTS AND DISCUSSION Structural Models and Lattice Mismatch. Supported thin oxide films can have very complex structures. In the case of TiOx/Pt(111), structure and stoichiometry are furthermore very sensitive to experimental conditions.20,26,44−48 The structurally most simple thin film on fcc(111) metals is probably a MO-monolayer, which can be derived from the 111 polar plane of rocksalt. This structure has been observed for FeO9,10,40,41 and CoO43 and consists of a closed-packed layer of M covered by oxygen (θ = 1). With a hexagonal unit cell containing only one unit of metal and oxide, this film could form a commensurate overlayer on a closed-packed metal surfaces such as fcc(111) or hcp(001). While this may be the structure with the strongest interaction between rocksalt thin film and the support, it is unlikely that it will be stable on many different closed-packed metals surfaces due to their varying lattice constants. In the case of FeO/Pt(111) and CoO/ Au(111), incommensurate overlayers are formed.16,43 However, TiOx/Pt(111) films form overlayers with large unit-cells and complicated structures. This has also been explained as an adaption to the lattice mismatch, where small patches of TiOx are commensurate with the underlying support, and stress is released at the edges leading to zigzag and pin-wheel motifs.20 Apart from the orientation of the oxide-layer lattice relative to the support lattice, for a given combination of overlayer/ support, MOx/4 , the only structural variable is the optimal lattice constant of MOx. Within the technical limitation of periodic boundary conditions in the DFT-code, the most rigorous way of simulating this is creating sets of supercells containing varying amounts of overlayer on support, such as (1 × 1)/(1 × 1), (3 × 3)/(4 × 4), and so forth. Using this approach, one quickly generates supercells of intractable size, and it is certainly not feasible for the large number of overlayersupport combinations we will study. Additional structures can

Figure 1. Employed supercells for FeO/Pt(111). The unit cell is indicated, and small supercells have been repeated for better visualization.

calculations were carried out on slabs that consist only of two layers of unrelaxed Pt(111). The employed unit cells are (2 × 2)/(2 × 2), (6 × 6)/(7 × 7), ( 3 × 3 )R30°/(2 × 2), ( 7 × 7 )R19°/(3 × 3), ( 13 × 13 )R14°/(4 × 4), and (3 × 3)/( 13 × 13 )R14° (see Figure 1). Supercells with large lattice-mismatch such as (4 × 4)/(5 × 5), generally show a separation of the oxide film into patches that are commensurate with the surface. This is in line with reports on TiOx/Pt(111) and FeO/Pt(111) where such dislocation lines have been observed, and the stoichiometry at these lines usually deviates from that within the commensurate patches.20,42,46 In Figure 2, we plot the formation energy per MO-unit against the average M−M distance for rocksalt(111) TiO and FeO constructed from larger supercells discussed above. The apparent minima of both curves in Figure 2 is about 3.2 Å, in good agreement with the reported 3.1 Å on FeO/Pt(111).16 This result can be compared to varying lattice constant calculations of unsupported thin films (e.g., two-dimensional materials), which is expected to work best for weak interaction between oxide and support.29 The location of the minima for the corresponding energy curves of unsupported oxides agrees roughly for TiO, while for FeO the deviation at lattice constants C

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estimates for supported films. Since we will examine a large number of supported oxide films in this work, we have generally employed only two small supercells: (2 × 2)/(2 × 2) and ( 3 × 3 )R30°/(2 × 2). Using this approach, we can obtain an overlayer lattice constant within ±0.2 Å of 3.1 Å for all support metals except Ni. Therefore, these supercells are expected to provide enough flexibility to obtain formation energies at lattice constants sufficiently close to the optimum. In the epitaxial overlayers (2 × 2)/(2 × 2), the metal atoms of the oxide film were placed in the fcc-positions of the support. The oxygen atoms were placed in the fcc-positions with respect to the metal atoms of the oxide film. For the larger, nonepitaxial supercells, the positions are generally not as well defined. In the other important supercell ( 3 × 3 )R30°/(2 × 2), the metal atoms of the oxide film are roughly in fcc, fcc, and on-top positions. For the analysis in scaling relations, we have chosen the most stable supercell according to eq 3, e.g., we use the formation energy per overlayer-metal atom. This is because scaling relations that describe the bonding between the overlayer and support can be expected to work best if the energy per bonding adsorbed atom is used. Trends in Formation Free Energies: Scaling Relations. In order to investigate trends, we have studied the relationship between the formation of an oxide layer MOx and the adsorption energy of the corresponding metal atom M denoted as Ead(M). Since the oxide films investigated in this work bind exclusively through the metal atom, M, we expect this adsorption energy to be a valid descriptor for these systems and will follow a simple linear scaling relationship:21 G UC − oxide − film = γ ·Ead(M ) + ξ

(4)

Table 1 summarizes the scaling relations that we have obtained for all systems. Generally, the slope γ is about 0.4, which

Figure 2. (a) Potential energy (PBE) of unsupported TiO (red line) as a function of the norm of the hexagonal lattice vectors a,b. Supercell calculations for TiO/Pt(111) using two unrelaxed layers of Pt(111) are plotted as black squares for the corresponding lattice constants of the oxide film. For smaller super cells, we have additionally carried out calculations with four layers of Pt(111) of which two are fixed (pink crosses; this is the model used throughout the rest of the work). All calculations are carried out nonspin polarized. (b) Same calculations for FeO. All calculations were carried out spin-polarized, and the average absolute magnetic moment per Fe-atom is shown in blue both for the unsupported oxide (dots) and the supported oxide (squares). Furthermore, the total magnetic moment of the unsupported oxide is included, showing a perfect antiferromagnetic structure.

Table 1. Scaling Relations [Slope γ, Coefficient of Determination R2, and Mean Absolute Error (MAE)] Resulting from a Linear Fit of Formation Energy versus Adsorption Energy of the Oxide-Forming Metal As Obtained from PBE and PBE+U Methods PBE

below 3 Å is significant. In general, this deviation is not unexpected since perfect agreement of the potential energy curves of unsupported and supported film would mean that the adhesion energy of the film is independent of the strain. Another complication is that the unsupported film may have significant structural differences. Even for TiO, for lattice constants above 3.3 Å one finds that the unsupported oxide film undergoes a structural transition, where the oxygen atom moves into one plane with the Ti-atoms therefore creating another minimum, despite having only two atoms in the unit cell. On the supported TiO-film, this is never the case, and the oxygen atoms stay consistently above the Ti-plane, which means that they are generally not in contact with the support metal as has been reported for related TiOx structures.20,46 We conclude that unsupported oxide films do not generally provide a quantitative estimate of the geometry and latticemismatch of supported films. Nevertheless, as the computational cost for computing unsupported films is negligible, the strain of the unsupported oxide film can still give useful

2

oxide

MAE

R

Ti2O3-k-phase V2O3-k-phase TiO-hex. VO-hex. CrO-hex. MnO-hex. FeO-hex. CoO-hex. NiO-hex.

0.08 0.04 0.13 0.11 0.09 0.06 0.05 0.05 0.14

0.93 0.99 0.93 0.92 0.85 0.91 0.96 0.95 0.82

PBE+U γ

MAE

R2

γ

0.25 0.53 0.43 0.47 0.58 0.36 0.46 0.40 0.62

0.11 0.06 0.06 0.02 0.03 0.10 0.21

0.92 0.97 0.92 0.90 0.86 0.79 0.66

0.65 0.76 0.70 0.18 0.21 0.71 0.71

suggests a bond-order of 0.4 relative to that of the isolated atom in an fcc-site. Slopes obtained with DFT+U are generally larger, with the exception of FeO and MnO which show only little variation in formation energies for different supports. Details of the structures and their scaling relations will be discussed below. Hexagonal MO Films on Closed-Packed Surfaces. We will now discuss the properties of the MO-rocksalt(111) overlayers based on the most stable supercell of (2 × 2)/(2 × 2) and ( 3 × 3 )R30°/(2 × 2). As one might expect, for support D

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and the more strongly binding transition metals. Most of the scaling correlation comes from the clear separation of these two groups as well as good correlation within the coinage metals. The variation within the strongly binding metal surfaces is generally smaller, and the correlation within these is weaker.62 The absolute magnetic moment has also been included in Figure 3. While TiO is generally nonmagnetic, FeO shows the reported row-wise-AFM ordering40 for the (2 × 2)/(2 × 2) supercell and ferromagnetic ordering for ( 3 × 3 )R30°/(2 × 2) with a magnetic moment that shows some variation between different supporting metals. As discussed in ref 40, the precise magnetic ordering has apparently a much smaller impact on the energetics compared to that of the strain. Stability of k-Phase M2O3 Structures on Closed-Packed Surfaces. A hexagonal structure first described by Kresse and co-workers for V2O3/Pd(111) (s-V2O3)29 and termed k-phase in the case of Ti2O3/Pt(111)63 has also been found for Ti2O3/ Au(111).64 A structural model is shown as an inset in Figure 4. Apart from the higher oxygen content, a main difference between this structure and the epitaxial continuation of closed-

metals with larger lattice constants (Au and Ag), the system is more stable in the dense unit cell, (2 × 2)/(2 × 2), as in TiO/ Au(111). Also, the overlayers CoO and NiO generally are more stable in this supercell. This is also true for supports with smaller lattice constants such as Pt, as in CoO/Pt(111). For the remaining cases, such as (TiO, FeO, CrO, VO, and MnO) on (Pd, Pt, Rh, Ir, Ru, and Os) the less dense unit cell, ( 3 × 3 )R30°/(2 × 2), is usually more stable. Two scaling relationship plots are presented in Figure 3, corresponding to the examples where we have explicitly examined the dependence of the stability on the lattice constants of the overlayer.

Figure 3. (a) Free energy of formation (PBE) of the TiOrocksalt(111) structure on various closed-packed surfaces (red squares) as a function of the adsorption energy of the Ti atom on these surfaces in the fcc-site. Only the most stable structure of the computed supercells is shown, as discussed in the main text. Absolute magnetic moments per Ti-atoms are shown as blue triangles. Ni and Cu have been excluded from the linear regression because of their small lattice constants. (b) The same for FeO-rocksalt(111).

The mean absolute error (MAE) of most linear regressions is smaller than 0.1 eV which is similar or better than values reported for strongly bound adsorbates.21 However, since the variation in binding energies for the thin oxide films is usually smaller than that for adsorbates like C, CH, N, etc., a better measure of the quality of the scaling relationship is the R2 value. The R2 value is generally high, showing a strong correlation. In terms of binding energies, there are typically two groups of metals, the weakly binding coinage metals (Cu, Ag, and Au)

Figure 4. (a) Free energy of formation of the Ti2O3-k-phase64 structure on various (2 × 2)-closed-packed surfaces (red squares) as a function of the adsorption energy of the Ti atom on these surfaces in the fcc-site. Cu has been excluded from the linear regression because of its small lattice constant. The charge transfer from support to oxide based on Bader analysis is shown as blue triangles in units of the elementary charge. A negative charge transfer means that negative charge (electrons) is transferred from the support to the oxide layer. (b) The same for the V2O3-k-phase.29 E

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The Journal of Physical Chemistry C packed surfaces is the low density of the film. This leads to a larger flexibility of the structure, where compression/expansion of the lattice constant does not result in as strong a repulsion as for the rocksalt(111) structures. Instead, the M-O-M framework can respond by a rotation resulting in a straight M-O-Mbridge at large lattice constants and a M-O-M bridge where the oxygen atom is offset from the plane defined by the surface normal and the M−M direction at shorter lattice constants. This is illustrated for Pd and Au as a support in the insets of Figure 4. This can explain why linear scaling works very well for these structures, although only one supercell was explored. In Figure 4, we have also included the charge transfer between the support and oxide per the surface-oxide metal atom based on Bader analysis.57−59 For Ti2O3, we find transfer of electrons from the support to the oxide and the other way around for V2O3. In general, the amount of charge transfer roughly correlates with the descriptor, the adsorption energy of the metal atom, M, and consequently also with the formation free energy of the thin oxide film MOx. Stability, Magnetism, and Charge Transfer of Oxide Layers. We summarize our results on the thermodynamics of computed oxide films in Figure 5. It can be seen that for metal

Figure 5. Stability of supported oxide-surface layers based on PBE at μO = −3.73 eV, corresponding to very reducing conditions. Surface structures are abbreviated as follows: hex. and k-phase for the rocksalt(111)- and k-phase structure on either the fcc(111) or the hcp(001) structure, depending on the support-metal.

Figure 6. Stability of supported oxide-surface layers based on PBE: (a) illustration of μO, max and ΔμO for the stability of TiO on Pt(111). (b) μO, max below which overlayer MOx is stable with respect to the highest oxidized bulk metal-oxide MOy. (c) Range ΔμO, relative to μO, max, in which overlayer MOx is stable with respect to the bulk metal M and bulk metal-oxide MOy. Blank spaces mean that the overlayers are never stable.

oxides for which SMSI has been reported (TiOx and FeOx), we find relatively stable oxide layers for most reactive supports. Generally, coinage support-metals lead to the least stable oxide films. NiO and CoO are not stable on any of the supports. This is not too surprising since we investigate the stability at very low oxygen chemical potential. Since at these conditions, both Ni and Co are most stable as bulk metals, formation of the oxide films is not favorable. Even at higher oxygen chemical potentials that would lead to stable bulk oxides, the stoichiometry of these oxides (NiO and CoO) is the same as those of the oxide films. Therefore, the main driving force of SMSI, releasing oxygen from more oxygen-rich bulk oxides to form oxygen-poor surface oxides, is missing. Another way to analyze the stability of the overlayers is through the space in chemical potential in which they are stable. This is done in parts b and c of Figure 6. Part b shows the maximum oxygen chemical potential at which the

corresponding overlayer is stable with respect to the formation of a bulk oxide. Part c shows the range, ΔμO, in which the overlayer is stable not only with respect to the formation of bulk oxides but also with respect to the bulk metal. The meaning of μO,max and ΔμO is illustrated in part a of Figure 6. Most overlayers are predicted to be always thermodynamically unstable on the coinage metals. For example, FeO/Au(111) is predicted to be always less stable than either bulk Fe(bcc) or a bulk oxide of iron (FeO, Fe2O3, and Fe3O4). CoO is predicted to be unstable on all supports. The lower bound of the chemical potential of oxygen is important to judge whether the formation of a surface oxide from deposited metal atoms is more favorable than the formation of a bulk metal. Most F

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The Journal of Physical Chemistry C overlayers are predicted to be stable over a range of μO, up to a few electron volts. For SMSI, the determined thermodynamics are a necessary criterion for the overlayer to form. It is important to realize that this need not be the case for the formation of the overlayer from deposited metal atoms. This is because the formation of a bulk metal, as the alternative to the surface oxide, may have a higher barrier and could therefore be kinetically hindered. Furthermore, for a finite number of metal atoms, the stability of a formed metal particle could still be significantly below the bulk limit. This may explain, why, for example, supported CoO thin films exist,43 although they are predicted to be unstable relative to bulk materials. We have depicted the magnitude of the absolute magnetic moment in Figure 7. Generally, FeO, MnO, and CrO are strongly magnetic and CoO and VO weakly magnetic. The kphase structures V2O3 and Ti2O3 as well as TiO and NiO are nonmagnetic.

cases when M = Ti, i.e., TiO(111) and Ti2O3, transfer of electrons occurs from support-metal to oxide. More often, electrons are transferred from oxide to metal. Therefore, Ti2O3 is the only oxide in our study, which clearly prefers to be less oxidized when placed on support-metal. This observation might also explain the origin of reduced slopes γ observed for this layer. The opposite transfer is largest for V2O3 and VO, where, according to Bader analysis, about 0.5 electrons per V are transferred to the supporting metal. Together with CrO, which also generally donates electrons to the support, V2O3 has the largest slopes, >0.5. The magnetic moment and charge transfer of the FeO overlayer at the PBE+U level is in agreement with previous reports (3.6 μB and 0.2−0.3e).40,41 Figures 9 and 10 show the stability and magnetism of supported thin films using PBE+U in analogy to the

Figure 9. Colormap of the stability of oxide-surface layers based on PBE+U with U = 3 eV at μO = −3.73 eV.

Figure 7. Colormap of the absolute magnetization (μB) of oxidesurface layers per oxide-metal atom based on PBE.

An analysis of the charge transfer (see Figure 8) between support and oxide based on Bader analysis shows that only for

Figure 10. Colormap of the absolute magnetization (μB) of oxidesurface layer oxide-metal atom based on PBE+U with U = 3 eV.

calculations using PBE (Figures 5 and 7). As one would expect, using DFT+U leads generally to larger magnetic moments (see Figure 10); however, trends observed with PBE are reproduced with PBE+U: FeO, MnO, and CrO show the strongest magnetism, and MnO, CrO, VO, and TiO form

Figure 8. Colormap of charge transfer from the support to the oxide based on PBE and Bader analysis in units of the elementary charge. A negative charge transfer means that negative charge (electrons) is transferred from the support to the oxide layer. G

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generally the most stable overlayers, while overlayers of any kind are least stable on the coinage metals.

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SUMMARY AND CONCLUSIONS We have investigated the stability of a large combination of oxide layers and support metals for three different types of oxide layers. All of the oxide layers, MOx, bind through the metal atom M to the support metal, 4 . On the basis of experience with molecular adsorbates, we therefore expected that the adsorption energy of M atoms on 4 could serve as a descriptor for the formation energy of MOx on the same support, 4 . We found that this is indeed generally the case and that one can find linear scaling relations between these quantities. This allows the descriptor-based prediction of the stability of overlayers on new materials. The most obvious source of deviation from these scaling relations is a support-specific lattice mismatch. We found the correlation in scaling relations to be generally much better, when the lattice mismatch has been reduced through careful choice of supercells. Although we use only a few structurally simple types of oxide layers, we find that SMSI is predicted where it has indeed been reported, e.g., surface oxides of Ti, Fe, and V. We hope that scaling relations will therefore find use in the prediction of the stability of surface oxides as they have in catalysis.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01404. DFT-computed data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: 650-926-2480. E-mail: [email protected]. Present Address §

P.N.P.: Institute of Catalysis Research and Technology (IKFT), Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the Office of Basic Energy Sciences of the U.S. Department of Energy to the SUNCAT Center for Interface Science and Catalysis at SLAC/Stanford is gratefully acknowledged. M.B. and A.V. would like to acknowledge the use of the computer time allocation for the “Computational search for highly efficient 2d & 3d nano-catalysts for water splitting” at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. M.B. and A.V. would also like to acknowledge the support from the project titled “Predictive Theory of Transition Metal Oxide Catalysis: DOE Materials Genome Project (DE-AC02-76SF00515)”.

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REFERENCES

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