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Cobalt Spinel (111) Facets of Various Stoichiometry – DFT+U and Ab Initio Thermodynamic Investigations Filip Zasada, Joanna Grybo#, Witold Piskorz, and Zbigniew Sojka J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11869 • Publication Date (Web): 15 Jan 2018 Downloaded from http://pubs.acs.org on January 18, 2018

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The Journal of Physical Chemistry

Cobalt Spinel (111) Facets of Various Stoichiometry – DFT+U and ab initio Thermodynamic Investigations

AUTHOR NAMES Filip Zasada*, Joanna Gryboś, Witold Piskorz, and Zbigniew Sojka

Faculty of Chemistry, Jagiellonian University, ul. Gronostajowa 2, PL 30-387 Krakow *Corresponding Author: Filip Zasada, e-mail: [email protected], phone/fax number: +48 12 686 24 92

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ABSTRACT Combination of periodic, spin unrestricted DFT calculations and first principle thermodynamic modeling were used to evaluate the structure, and stability of nine different pristine and eight defected terminations of the (111) surface of cobalt spinel under various redox conditions (T, pO2). The surface redox state diagram of possible spinel (111) terminations in the wide stoichiometry range from Co2.62O4 to Co3O3.75 was constructed, and thoroughly discussed revealing that three regions of spinel surface redox behavior may be distinguished. The region of temperatures and pressures of typical catalytic processes (T ~200 °C to ~500 °C, pO2/p° ~0.001 to ~1) corresponds to energetically well separated stoichiometric (111)-S facet exposing both truncated tetrahedral CoT3c and octahedral CoO3c cations. They preserve their bulk-like divalent (qB = 1.29 |e|) and trivalent (qB = 1.45 |e|) state, respectively, in contrast to the spin state of CoO3c (S = 1, μ = 1.9 μB) comparing to diamagnetic bulk CoO6c. In more reducing conditions (T > 600 °C and pO2/p° < 0.0001) several terminations of different stoichiometry induced by formation of oxygen vacancies may coexist, providing a thermodynamic background for enhanced redox activity. Redox properties are associated with extended electronic and spin relaxations that entails several octahedral surface (Co O3c, qB = 1.29) and subsurface (CoO6c, qB = 0.01) cations which are reduced (ΔqB = –0.24 |e|, Δμ = 0.87 μB) upon oxygen release (formation of redox active ensemble). In the oxygen rich conditions (T < 200 °C and pO2/p° > 10) the oxidized (111)-O termination, exposing the CoT3c ions only, is the most stable, and with the rising oxygen pressure it becomes defected due to the presence of the cationic vacancies in the tetrahedral sites. The sub-stoichiometry (Co deficiency) of the (111)O surface is reflected in trivalent state of half of the surface CoT3c cations, which are characterized by larger charge (ΔqB = 0.15 |e|) and lower magnetization (Δμ = –0.7 μB) in line with (dz2,dz2-y2)4(dxy)1(dxz)1 configuration. The shape of the Co3O4 nanograins was modeled by means of Wulff construction for oxidizing, ambient and reducing redox conditions. It was


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shown that rhombicubooctahedral morphology is preserved regardless the oxygen chemical potential and the (111) termination is more abundant in oxygen rich environment.



1.Introduction Cobalt spinel belongs to the mixed semiconductor metal oxides and is well known for its excellent redox-tunable properties, which originate from the presence of both mobile electrons and movable oxygen ions. Co3O4 in its bare form and the bulk/surface doped derivatives are characterized by complex, yet well-defined structure and quite easily controlled morphology. For this reason, cobalt spinel has been explored for a large record of applications in various fields of scientific and technological interest. In particular, Co3O4 is an excellent redox catalyst for oxidation (CO,1 NH3,2, hydrocarbons,3 and oxygen evolution reaction4) and reduction (oxygen reduction reaction, ORR,5 reduction of N2O6,7) catalysis. Co3O4 was also reported as a promising sensor material8,9 and has received wide attention, as robust anode material for Li batteries owing its high theoretical capacity.10 Cobalt spinel performance in all those applications strongly depends on the structure, grain size and surface morphological features, which influence the nature of the active sites exposed by the Co3O4 samples.11,12,13 For example, it is reported that the {110} facets of Co3O4 nanocrystals have higher catalytic activity for CO oxidation than the {100} and {111}, because of the more abundant catalytically active octahedral Co3+ sites.14 Contrary, for the ORR reaction the predominant {111} and {100} surfaces exhibit higher catalytic activity, which has been explained by the fact that Co2+ exposed cations are relevant for this process.15 On the other hand, in the case of methane combustion, the catalytic performance of the Co3O4 is believed to be related with the surface energy.11 Recently, it has been shown that Co3O4 nanosheets exhibit enhanced acetone sensing properties comparing to nanorods or nanofibers. This fact has been assigned tentatively to high abundance of Co2+ on the (111) surface.16 The crystal plane structure of cobalt spinel electrode materials has also significant influence on the electrochemical properties, especially for the charging rate capability of Li-ions battery anodes.17 Yet, explanations for the observed experimental phenomena are often built on very 4 ACS Paragon Plus Environment

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simplified picture of cobalt spinel facets, produced by mere cut of the bulk structure without taking into account a possible presence of several terminations, and their reconstruction under various thermodynamic conditions. Indeed, redox environments may influence severely the structure and chemical state of catalytic surfaces leading to

reconstruction, vacancy

formation,18 or even dramatic interfacial phase transitions.19 Thus, without the control and understanding of surface molecular level structure and its dynamics sensible tuning of the spinel oxide systems for dedicated applications is very difficult to be successful. Inspection of the available experimental data reveals that a vast majority of Co3O4 catalytic materials regardless the preparation method are faceted predominantly on the (100) and (111) planes with a minor contribution of the (110) termination.20,21,22 The low energy (100) plane has been described in detail in the series of our recent papers devoted to its geometry, stability, electronic and magnetic structure, and catalytic activity.18,23,24 There are also several reports in literature about the (110) facet25,26, which is believed to be active, i.a., in low temperature CO oxidation.27 However, much less attention has been paid to the (111) surface, despite that it active in oxygen reduction reaction,15 exhibits the highest rate of charge/discharge capacity and the best performance as a Li battery anode, comparing to the other facets of Co3O4 nanograins.17 Furthermore the reported results are rather fragmentary and confined to arbitrary selected terminations only.28,29,30 Herein, we use DFT+U level of theory combined with the first principles thermodynamics for molecular modelling of the structure and stability of the number of possible truncations of the Co3O4 (111) surface in wide range of redox conditions and cobalt oxygen stoichiometries, induced by oxygen pressure and temperature.



2.Computational method 2.1. DFT parametrization: Tuning of the DFT parameters for cobalt spinel systems was described in detail in our recent papers devoted to cobalt spinel (100) surface redox stability, and catalytic activity.31,18,23 For all calculations we employed periodic, spin unrestricted DFT+U approach together with the PW9132 exchange-functional, conducted within projector augmented plane wave method as implemented in VASP code.33 We selected Hubbard parameter, U, value of 3.5 eV, which provide adequate description of both structural and electronic parameters, and reproduce correctly the formation enthalpy of cobalt spinel as well.34,35 For the Brilluone zone sampling the standard Monkhorst-Pack36 grid with 5×5×5 mesh for bulk calculations and 5×5×1 mesh for slab calculations were employed. The cutoff energy was set to 500 eV, and SCF convergence criterion of 1·10-6 eV was chosen. The atomic charges were calculated using the Bader population analysis.37 Good agreement between the calculated and experimental data (see Table S1 and Table S2, Supporting Information, SI) revealed that the calculation scheme was adequate for sensible modeling of the cobalt spinel structure and energetics. 2.2 Slab model of surface terminations: The surface (1×1) supercell slab models were obtained by cleavage of the bulk cubic unit cell (with the composition of Co24O32) in the normal [111] direction. For each termination the slab model was composed of oxide layer of about 9 to11 Å thickness (12 to 16 atomic layers) with a vacuum separation of 15 Å (see Figure S1, SI). The same geometry of the top and the bottom slab terminations was assured to minimize the dipole moment development in the supercells. The relaxation of the surface was restricted to the four top and the four bottom layers of the slab model, until the forces acting upon the ions were below 1·10-3 eV·Å-1. In our calculations we considered nine different pristine terminations of the (111) surface, and the most stable were further modified by introduction of cationic and anionic vacancies to evaluate the influence of point defects. 6 ACS Paragon Plus Environment

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2.3. First principles thermodynamics: The redox behavior of the cobalt spinel surface under various temperature and oxygen pressure conditions, was studied with employment of the first principles thermodynamics.38,39,40,41 In this scheme the free energy, γ, of the surface represented by the slab model containing NO oxygen and NCo cobalt atoms can be calculated as:

𝛾(𝑇, 𝑝 ) =

𝐺

(𝑇, 𝑝 , 𝑁 , 𝑁 ) −

In this equation G

and G

(𝑇, 𝑝 ) − 𝑁 −

𝐺

𝑁

𝜇 (𝑇, 𝑝 )

(eq. 1)

represent the free energy of the slab and the bulk (per one

formula unit) of the cobalt spinel, respectively. The surface area exposed by the slab is denoted as A, and 𝜇 (𝑇, 𝑝 ) is the chemical potential of dioxygen. Following our previous work and literature38,31 the Gibbs free energies of the bulk and the slab can be approximated as Gslab ≈ 𝐸

, and Gbulk ≈ 𝐸

, since the surface oscillations do not vary upon oxygen

adsorption/desorption in a significant way. The oxygen potential, μ (T, p ), in turn, can be divided into the T and p independent total energy component (including the zero vibrational point energy) of dioxygen, 𝐸

, and a ∆μ (T, p ) part that comprises all the T and p related

contributions: 𝜇 (𝑇, 𝑝 ) =

𝐸

+ ∆𝜇 (𝑇, 𝑝 )

(eq. 2)

The second term of eq. 2 is the sum of temperature (T) and pressure (pO2) dependent contributions: ∆𝜇 (𝑇, 𝑝 ) = 𝜇 (𝑇, 𝑝 ) + k𝑇ln

(eq. 3)

The combination of equations 1, 2 and 3, shows the functional dependence of the surface free energy on the temperature and partial pressure of the oxygen for the investigated slab models. The μ' (T, p ) term was computed by means of standard statistical thermodynamics as proposed by Hirano.42 The μO values were varied within the thresholds imposed by the 7 ACS Paragon Plus Environment


maximum value, ΔμO = 0.0, corresponding to the state when oxygen condense on the surface (oxygen rich conditions), and a minimum value, ΔμO = –2.4 eV, corresponding to decomposition of cobalt spinel into solid Co and gas phase oxygen (oxygen lean conditions).28,29


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3.Results and Discussion 3.1. Bulk cobalt spinel: Tricobalt tetraoxide (Co3O4), is a p-type semiconductor, characterized by the normal spinel structure (Fd-3m, space group 227), and the unit cell (Figure 1a) containing eight formula units with 56 ions (Co24O32) with the experimental lattice constant equal to 8.084 Å.43 The oxygen ions form a fcc close packed sublattice (marked red) with the tetrahedral sites in Wycoff position 8a (marked green), and the octahedral sites in Wycoff position 16d (marked blue). The divalent tetrahedral cobalt, (d7, e4t23 configuration, see Figure 1a1) and the trivalent octahedral cobalt (d6, t2g6eg0, Figure 1a2) cations are denoted hereafter as CoT and CoO, respectively. The lattice constant, a, and the oxygen parameter, u, determine the atomic positions within the unit cell, and thus the atomic bond distances and bond angles of spinel Co3O4. The theoretical lattice parameters of the Co3O4 spinel, optimized by means of Birch-Murnaghan equation of state,44 are equal to a = 8.149 Å and u = 0.2638. These values compare well with the experimental counterparts of 8.084 Å and 0.2632, respectively. 21 Deviation of the oxygen position from the optimal lattice position, 0.255, in bulk spinel materials results in a trigonal distortion of the oxygen octahedron along the [111] direction (see Figure 1a2). The calculated CoO−O and CoT−O bond lengths (dCoO-O = 1.932 Å and dCoT-O = 1.960 Å) are also in a good agreement with the experimental distances of 1.920 Å and 1.935 Å. The typical overestimation (by about ~0.5 %) of the lattice constant and bond lengths has been found previously in other GGA+U studies of oxide systems,45 and its nature has been discussed in the literature.46 The calculated magnetic moments, Bader charges and electronic Band Gap compares fairly well with previous calculations,29 and the experimental values47 (Table S1 and Table S2) revealing that both the applied model and the calculation scheme were adequate for sensible modeling of the cobalt spinel structure and energetics.



The equilibrium shape of a Co3O4 nanograin in typical ambient is presented in Figure 1b, revealing the predominant faceting by (100) and (111) planes with only a minor contribution of the (110) termination. A perspective view of the (3×3×3) element of a selected termination of the (111) plane with the evenly populated tetrahedral (green) and octahedral (navy blue) surface cations is shown in Figure 1c. The top view of the magnified central (1×1×1) element (Figure 1c1) reveals its diamond (α = 60°, β = 120°) shape with both types of exposed cobalt ions (tetrahedral green and octahedral navy blue) exhibiting a trifold coordination.

Figure 1: Cubic Co24O36 unit cell representing the bulk of the cobalt spinel with indication of the most important structural parameters (a) together with cobalt ions shown in tetrahedral (a1) and perturbed octahedral (a2) environment. Typical Co3O4 nanograin exposing low-index surfaces (b) and perspective view of the (111) surface (c) together with the top view of the (1×1×1) surface element showing its dimensions and surface ions arrangement (c1).


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3.2. Terminations of the Co3O4 (111) plane: Contrary to (100) and (110) surfaces which expose only two different terminations each,25,31 the ionic layers stacking in the (111) direction is much more involved, and the Co3O4 lattice may be cleaved into six different surface terminations. They are presented in Figure 2, where the successive layers of the initial slab model (a) are removed exposing the resulting terminations (b-f).

Figure 2: Different surface terminations of (111) facet: (a) (111)-4CoT3c-4CoO3c, (b) (111)-16O3c-4CoT3c, (c) (111)-12O2c-4O3c, (d) (111)-12CoO3c, (e) (111)-12O2c-4O1c, and (f) (111)-4CoO3c-4CoT1c. Color coding as follows: Octahedral cobalt atoms (CoO): blue, tetrahedral cobalt atoms (CoT): purple, oxygen atoms: red.

The termination presented in Figure 2a exhibits four tricoordinated octahedral ions (denoted CoO3c, where 3c subscript indicates trifold coordination) and four tricoordinated tetrahedral CoT3c ions. Such cationic layer rests on the recessed anionic layer composed of twelve fully coordinated (O4c) and four coordinatively unsaturated (O3c) oxygen anions. Thus, this surface may be denoted as (111)-4CoT3c-4CoO3c. Removal of the most elevated octahedral cations leads 11 ACS Paragon Plus Environment


to the termination presented in Figure 2b, with four CoT3c cationic surface ions only, and all the exposed oxygens anions of the trifold coordination ((111)-16O3c-4CoT3c). Next, when the remaining tetrahedral cations are removed the resulting termination (Figure 2c) contains unsaturated oxygen anions exclusively (12O2c and 4O3c, (111)-12O2c-4O3c), and is placed on the beneath monolayer of the CoO6c cations. These layer becomes exposed in next possible metallic termination (111)-12CoO3c (Figure 2d) placed on the dense packed layer of O4c anions. In analogous way the subsequent termination (Figure 2e) were produced exposing twelve dicoordinated and four monocoordianted anions ((111)-12O2c-4O1c). The last possible termination (Figure 2f) is, in turn, of metallic character with monocoordianted tetrahedral and tricoordinated octahedral cobalt ions, (111)-4CoO3c-4CoT1c. The removal of highly exposed CoT1c gives back the first facet (see Figure 2a). In order to account for possible stoichiometry changes of the cobalt spinel surface the most stable parent terminations described above ((111)-4CoT3c-4CoO3c and (111)-16O3c-4CoT3c, see below Figure 4) were modified by successive removal of 1, 2 or 3 strongly unsaturated CoO3c cations (see Figure 3). The structures of the three resultant terminations, (111)-4CoT3c-3CoO3c, (111)-4CoT3c-2CoO3c, (111)-4CoT3c-1CoO3c, are presented in Figure 3b, 3c, and 3d, respectively. Specification of the composition for the all investigated slab models is shown in Table 1.

Figure 3: Interpolation structures between the (111)-4CoT3c-4CoO3c (a) and (111)-4CoT3c (e) ideal terminations, constructed by the subsequent removal of CoO3c cations leading to (111)-4CoT3c-3CoO3c (b), (111)-4CoT3c-2CoO3c (c), and (111)-4CoT3c-1CoO3c (d) terminations. Color coding as follows: exposed octahedral cobalt atoms (CoO):


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blue, Exposed tetrahedral cobalt atoms (CoT): purple, exposed oxygen atoms: red, bulk cobalt atoms: light grey, bulk oxygen atoms: dark grey.

Table 1: The characteristic of the slab models corresponding to possible terminations of (111) Co3O4 surface.

termination name

figure

slab model stoichiometry

Co/O ratio

composition

Cox-δO4

Co3Ox-δ

(111)-4CoT3c-4CoO3c 2a / 3a

Co52O64

Co3.250O4

Co3O3.692

0.8125

(111)-16O3c-4CoT3c

2b / 3e

Co44O64

Co2.750O4

Co3O4.363

0.7097

(111)-12O2c-4O3c

2c

Co62O96

Co2.583O4

Co3O4.645

0.6458

(111)-12CoO3c

2d

Co60O64

Co3.750O4

Co3O3.200

0.9375

(111)-12O2c-4O1c

2e

Co60O96

Co2.500O4

Co3O4.800

0.6250

(111)-4CoO3c-4CoT1c

2f

Co60O64

Co3.750O4

Co3O3.200

0.9375

(111)-4CoT3c-3CoO3c

3b

Co50O64

Co3.125O4

Co3O3.840

0.7812

(111)-4CoT3c-2CoO2c

3c

Co48O64

Co3.000O4

Co3O4.000

0.7500

(111)-4CoT3c-1CoO1c

3d

Co46O64

Co2.875O4

Co3O4.175

0.7187

3.3. Thermodynamic stability of the (111) terminations: To examine the stability of the all distinguished (111) surface terminations (after their relaxation) at various redox conditions (induced by different oxygen potential) we used the FPT modelling, and the results are collated in Figure 4. The variation of the Gibbs surface energy as a function of oxygen chemical potential, µO, for all considered terminations is presented in Figure 4a. The slopes of the γ(ΔμO) lines are directly related to the Co/O ratio in the given slab model (see equation 1), thus the surface free enthalpy behaves differently for slab models with different composition. For understoichiometric models (Co/O ratio less 0.75) it increases with ΔμO (more rapidly when Co/O diverge more from ideal 0.75 value), for stoichiometric slabs it is ΔμO independent whereas for over-stoichiometric (Co/O ratio more than 0.75) it decreases with oxygen chemical potential. The brief inspection of the plots reveals that in the oxygen chemical potential of interest, only 13 ACS Paragon Plus Environment


five of nine terminations are stable (constituting the bottom envelope of the plot). They are coded with color solid lines and correspond to stoichiometric ((111)-4CoT3c-2CoO3c), or slightly defected terminations of (111) Co3O4 surface ((111)-4CoT3c-4CoO3c, (111)-4CoT3c-3CoO3c, (111)-4CoT3c-1CoO3c, (111)-16O3c-4CoT3c), thus their slopes are not significant. For the remaining slab models ((111)-4CoO3c-4CoT1c, (111)-12CoO3c, (111)-12O2c4O3c, and (111)-12O2c-4O1c, dashed black and grey lines) surface free enthalpy strongly depends on the oxygen chemical potential. Such pronounced dependence is related to significant non-stoichiometry of the corresponding surface terminations. Two of them ((111)4CoO3c-4CoT1c and (111)-12CoO3c) are characterized by large excess of the Co cations (Co/O ratio of 0.9375 each), and their stability decrease rapidly with an increasing µO making them very unstable in more oxidizing conditions. However, even at strongly reducing O-lean environment they are less stable than the stoichiometric ((111)-4CoT3c-2CoO3c, O/Co = 0.750) and the slightly reduced terminations ((111)-4CoT3c-3CoO3c and (111)-4CoT3c-4CoO3c). Such instability may be associated to the significant surface dipole resulting from fully cationic monolayer exposed to the vacuum. Another two strongly non-stoichiometric terminations are, in turn, terminated only with the oxygen anions, thus their Co/O ratios are much lower than stoichiometric 0.750 value (0.648 for (111)-12O2c-4O3c and 0.625 for (111)-12O2c-4O1c)). This implies that their surface Gibbs energy falls rapidly with the oxygen potential. Yet, similarly to previous case even in strongly oxidizing (O-rich) circumstances these terminations are less stable than slightly oxidized (111)-16O3c-4CoT3c (Co/O = 0.7097) and (111)-4CoT3c-1CoO3c (Co/O = 0.7187) facets. Thus, these four terminations are excluded from further elucidations. The overall picture emerging from the analysis of Figure 4a, is in line with the previous results of Montoya et. al,28 where the highly polar terminations of the (111) Co3O4 surface are featured by high surface energies.


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The temperature dependence of the Gibbs surface energy for the most stable terminations (constituting the bottom envelope in Figure 4a) is shown in Figure 4b, for typical catalytic oxygen pressure of pO2/p° = 0.1. Presented results show that in lower temperatures (corresponding to more oxidizing conditions) the most stable termination is (111)-16O3c4CoT3c, however at ~250 °C the (111)-4CoT3c-1CoO3c becomes preferred. As the temperature increases, the latter is replaced by the stoichiometric (111)-4CoT3c-2CoO3c plane at ~325 °C. The stoichiometric termination is the most stable one even at high temperatures (up to 800 °C). Both over-stoichiometric terminations ((111)-4CoT3c-3CoO3c and (111)-4CoT3c-4CoO3c) are unstable comparing to stoichiometric one, but their energetic stability is expected in highly reducing conditions corresponding to lower oxygen pressures (see below).

Figure 4: Surface energies (γ) for different terminations of the (111) facet of the cobalt spinel plotted against oxygen chemical potential (a) and temperature (for pO2 set to 0.1 atm.) (b). 2-dimensional, (T, pO2), plot (c) together with the projection of the lowest surface free energies onto the (T, pO2) plane (d).



The three dimensional plot (Figure 4c) summarizes the stabilities of the thermodynamically most preferred terminations as a function of T and pO2. At high pressures and low temperatures the oxidized terminations ((111)-16O3c-4CoT3c, red plane, and (111)-4CoT3c1CoO3c, yellow) are apparently more stable than the stoichiometric one (green). However,

because the differences in their surface energies are rather small near the crossing lines of the corresponding planes (Δγ < 0.05 J·m-2), they may simultaneously be present, in the T and pO2 regions along the border lines. In contrast, at high temperatures and low O2 pressures, the surface energy difference between the reduced (purple and blue planes) and the stoichiometric terminations is larger (Δγ > 0.15 J·m-2) due to the significant steepness of the former. This makes the reduced (111)-4CoT3c-4CoO3c plane the only present in highly reducing conditions defined by the high-temperature low-pressure corner of the 3D plot. The stability regions of the cobalt spinel of various stoichiometry, Co(2.750-3.250)O4, are more explicitly revealed in the surface phase diagram obtained by 2D projection of the bottom surface free energies onto the (T, pO2) plane (Figure 4d). This diagram shows three main thermodynamic regions of the redox stability of different terminations. In the most oxidizing conditions (low T and high pO2) the (111)-16O3c-4CoT3c is the most stable and upon moving to more reducing environment (T↑ or pO2↓) it is replaced by the (111)-4CoT3c-1CoO3c. However, the latter is quickly substituted by the stoichiometric (111)-4CoT3c-2CoO3c termination, with stability region extending over the wide range of temperatures and oxygen partial pressures, typical for most catalytic processes. Only in the region of high temperatures and low O2 pressures (top right corner, highly reducing conditions), the stoichiometric termination is suppressed by the more stable reduced (111)4CoT3c-3CoO3c and (111)-4CoT3c-4CoO3c planes. The (111)-4CoT3c-3CoO3c termination is stable in narrow stripe of T, pO2 values only, and in the most reducing conditions is replaced by the more reduced (111)-4CoT3c-2CoO3c facet. These considerations show that, neglecting the planes of very narrow regions of stability, three types of the (111) terminations dominate in the


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wide range of the thermodynamic conditions defined by the 3D plot. They differ in the number of the exposed 3-fold octahedral cobalt cations. One is strictly stoichiometric ((111)-4CoT3c2CoO3c; two CoO3c), one is reduced ((111)-4CoT3c-4CoO3c; four CoO3c) and one is oxidized ((111)-16O3c-4CoT3c; zero CoO3c). To make the notation of this terminations simpler, from now on they are denoted as (111)-S, (111)-R and (111)-O, see Table 2. Table 2: The most stable terminations of the Co3O4 (111) surface.

ionic composition

redox state label

(111)-4CoT3c-4CoO3c

(111)-R / reduced

(111)-16O3c-4CoT3c

(111)-S / stoichiometric

(111)-4CoT3c-2CoO2c

(111)-O / oxidized



3.4. Molecular and electronic structure of Co3O4 (111) terminations: The molecular electronic, and magnetic structures of the relaxed (111)-R, (111)-S and (111)-O terminations are shown in Figure 5. Top panels (a, b, c) present perspective views of the geometric arrangement of the constituting ions for this terminations, along with the corresponding magnified (1×1) surface elements. The latter show the atomic structure in more detail, revealing specific surface composition and coordination of the all surface ions. Bottom panels (a1, b1 c1) present the corresponding spin density distribution within the top atomic layers. The coordination of selected surface ions together with the bond lengths and the bond angles, altered by the surface reconstruction, are shown in Figure S2 in Supporting Information. The calculated Bader charges (qB) and the magnetic moments (μ) of the all surface ions are summarized in Table 3.

Figure 5: Perspective view of the relaxed cobalt spinel together with magnified (1×1×1) surface elements showing surface ion coordination for (111)-R (a), (111)-S (b) and (111)-O (c) relaxed terminations, and the corresponding spin density contours, (a1), (b1) and (c1), presented for top layers of matching slab models. Color coding: CoO blue; protruding CoT - purple; subsurface CoT - green; O - red.


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In the case of (111)-R surface (Figure 5a) the relaxation processes caused slight changes in the atomic structure of the tetrahedral CoT3c and octahedral CoO3c site. Comparing with the bulk the distance dCoT-O is shorten by ~0.081 Å, whereas dCoO-O is slightly elongated (by 0.023 Å, see Figure S2, Supporting Information). The Bader charge analysis showed that for the partial charges of the surface oxygen ions are nearly the same as in the bulk, and that they are all diamagnetic (O2– character, see Table 3). Analogous preservation of the oxidation state is observed in the case of tetrahedral CoT3c ions, which are characterized by qB = 1.28 |e| and the μ = 2.65 μB. However, whereas the bulk CoT4c cations experience highly symmetric Td local crystal field and the e4t23configuration, the surface CoT3c cations (with the C3v local symmetry) exhibit (dz2,dz2-y2)4(dxy)1 (dxz)1(dyz)1 configuration. Both configurations correspond to the same, S = 3/2, magnetic state. On the contrary, in the case of the surface octahedral cobalt cations, two (of four) are significantly reduced with respect to the bulk (ΔqB = –0.25 |e|). Similar changes are also observed for subsurface octahedral cations of full coordination (see Table 3, and Figure 5a1). Such changes in the atomic charges are reflected in the increase of the associated magnetic moments. The reduced surface CoO3c cations exhibit μ = 2.6 μB (S = 3/2), whereas for the subsurface CoO6c cations μ = 0.9 μB (S = 1/2). This indicates that over-stoichiometry of the slab model influences the oxidation states of the octahedral ions only, and they are formally reduced to Co2+. This fact is well illustrated by the spin density repartition (Figure 5a1), where all the surface CoO3c cobalt cations and some subsurface CoO6c cations exhibit clearly a nonzero spin density (marked blue). The non-zero magnetization observed for the octahedral ions can be accounted for by surface crystal field of the local C3v symmetry that give rise to the (dz2,dz24 1 1 1 y2) (dxy) (dxz) (dyz)

configuration with S = 3/2 state in the case of surface CoO3c sites (d7; Co2+),

whereas for the subsurface CoO6c sites, the local distorted octahedral symmetry (D3d) implies a (dxy)2(dxz)2(dyz)2(dz2)1 ≈ (t2g6eg1) configuration, resulting in the S = 1/2 state. The areal



concentration of the exposed ions is the following {0.035/Å 2 CoT3c(2+), 0.017/Å2 CoO3c(2+), 0.017/Å2 CoO3c(3+), 0.104/Å2 O4c, 0.035/Å2 O3c}. Considering the (111)-S surface (Figure 5b), the relaxation caused only slight modification in the atomic structure of the tetrahedral and octahedral sites. Comparing with the bulk, the dCoT-O distance is shortened (Δd = –0.181 Å), whereas the dCoO-O bond length is slightly elongated by 0.023 Å (see Figure S2, Supporting Information). The partial charges of the exposed oxygen ions, as well as the partial charges of the both types of the cobalt cations (Co T3c, and CoO3c) maintain the bulk values, (compare Table S2 and Table 3), hence the oxidation state remains constant contrary to the previous case of slightly reduced surface. The analysis of the magnetic moments reveals that for tetrahedral ions magnetic moment is conserved (similarly to the previous termination), but the magnetic structure of the surface CoO3c cations is significantly perturbed (see spin density contours in Figure 5b1). In contrast to bulk the CoO3c cations possess 2 unpaired electrons (μ = 1.9 μB), in line with the (dz2,dz2-y2)4(dxy)1(dxz)1 configuration of Co3+ (d6) in the C3v crystal field. The areal concentration of exposed ions is following {0.035/Å2 CoT3c(2+), 0.017/Å2 CoO3c(3+), 0.052/Å2 O4c, 0.087 Å2 O3c}. The relaxation of the (111)-O surface (Figure 5c) results in shortening of the surface dCoT-O distance ( = –0.181 Å). The only exposed ions are CoT3c cations and O3c anions with the areal concentration of 0.035/Å2, and 0.139 Å2, respectively. As the electronic and magnetic state of the oxygen sub-lattice is conserved (see Table 3) the (111)-O surface understoichiometry increases the partial charges of the cobalt ions. Contrary to over-stoichiometric (111)-R surface (Figure 5a), in this case the octahedral cations (now present only in the subsurface with full coordination, CoO6c) maintain their charge (qB = 1.45 corresponding to Co3+) and diamagnetic character (see Figure 5c1), whereas tetrahedral surface cobalt ions (CoT3c) are oxidized. Half of them exhibit higher Bader charge than their bulk counterparts (qB = 1.45 |e| vs. 1.30 |e|), and their magnetic moment is accordingly reduced (from μ = 2.6 μB to


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μ = 1.9 μB). This is in line with the (dz2,dz2-y2)4(dxy)1(dxz)1 configuration, (S = 1), of surface trivalent cobalt cation in the local C3v field.

Table 3: The calculated Bader charges (qB) and the magnetic moments (μ) of the ions constituting different terminations of the cobalt spinel (111) surface.

Site

(111)-R

(111)-S

(111)-O

CoT CoO O CoT CoO O CoT CoO O

qB / |e|

μ / µB

surface

bulk

surface

bulk

1.28 1.44 or 1.21 –0.98 1.29 1.45 –1.01 1.28 or 1.45 –0.98

1.29 1.45 or 1.20 –0.99 1.31 1.45 –1.02 1.29 –0.99

2.65 1.9 or 2.6 0.0 2.6 1.9 0.0 2.6 or 1.9 0.0

2.61 0.0 or 0.9 0.0 2.61 0.0 0.0 2.6 0.0



3.5. Surface oxidation and reduction via vacancy formation: Composition, and thereby the redox state, of the cobalt spinel surface may be controlled by generation of the anionic (VO; reduction) and cationic (VCoT and VCoO; oxidation) surface vacancies (intrafacial processes), as well as via oxygen deposition on the surface (suprafacial process). Due to the variety of possible oxygen adspecies and mechanistic complexity of their formation this issue is beyond the intended scope of this work, and will be addressed in detail in a separate paper. The reduced surfaces (Co/O > 0.75) can in principle be generated either by an excess of cobalt ions (like in (111)-R facet, Figure 5a) or via deficiency of oxygen anions. As it is discussed below (see Figure 7) in the reducing conditions, a preferable pathway of the cobalt surface reduction involves the formation of the oxygen vacancies. Therefore for discussion of the cationic and anionic vacancies only the (111)-S and (111)-O terminations shall be considered. Stoichiometric (111)-S: For the stoichiometric (111)-S surface, the cations of the lowest stability are obviously the protruding CoO3c. Removal of these species leads to the slightly oxidized (111)-O termination, which was already analyzed in detail (see Figure 5c). Extraction of the least stable O3c surface oxygen ions is an endothermic process, and the corresponding energy, E

, may be calculated with respect to O2 molecule in the usual way: 𝐸

=𝐸

+

𝐸

− 𝐸

(eq. 3)

In the case of the (111)–S facet there are two kinds of the surface oxygen anions, one connected to three CoO6c subsurface octahedral cations of full coordination (O3O), and an O2O,1T species linked to two CoO6c cations and one CoT3c cation. Thus, two kinds of the surface anionic vacancies, VO3O and VO2O,1T were modeled. Their formation energies were compared with the 𝐸

values for the vacancies stabilized in the first (VO(layer1)) and the second (VO(layer1)) sublayer,

see Table 4.


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Table 4: Formation energies of oxygen vacancies on the (111)–S termination with respect to gas phase O2 molecule.

VO2O,1T

VO3O

VO(layer1)

VO(layer2)

2·VO

1.43

1.72

1.31

1.29

2.77

Slab model stoichiometry

Co48O62

Co48O62

Co48O62

Co48O62

Co48O60

Co / O ratio

0.774

0.774

0.774

0.774

0.800

𝐸

/ eV

As it can be inferred from Table 4, removal of an oxygen atom to form the VO2O,1T vacancy requires the energy of E

= 1.43 eV. The resultant atomic configuration of the relaxed

surface ((111)-S-VO2O,1T) is shown in Figure 6a, where the vacancy position is indicated as a yellow cube. The formation of the VO2O,1T vacancy lowers the coordination of the adjacent surface cations, and influences significantly the bond lengths in the first coordination sphere of the created defect. The tetrahedral cobalt cations in the vicinity of the vacancy are less stabilized since their coordination numbers are reduced to two (CoT2c), and their bonds with the remaining oxygens are elongated by 0.12 Å. Similar effect of the Co–O bonds weakening (dCo-O = 0.07 Å) is observed for the truncated octahedral (pentacoordinated) CoO5c species. Such elongation of bonds leads to decreasing of the interactionic Co O5c–CoO5c and CoO5c–CoT2c distances by Δd = –0.21 Å and Δd = –0.11 Å, respectively. The presence of the VO2O,1T vacancy results in dramatic changes in the electronic and magnetic structure of the surrounding cations. The two electrons left by the elimination of an oxygen atom are localized on two of the subsurface octahedral CoO6c cations (2𝐶𝑜 × + 𝑂

,

→ 𝑉 ∙∙

,

+ 2𝐶𝑜

+

𝑂 ), as revealed

by the drop of their Bader charges from 1.46 |e| to 1.22 |e|, and concomitant increase of their magnetic moments from 0.0 μB to 0.87 μB. This effect is similar to the reduction of octahedral deeper lying cations observed for reduced (111)-R termination (Figure 5a1). The composition of the defected (111)-S-VO2O,1T surface and the areal concentration of the constituting surface



ions may be thus summarized as {0.026/Å2 CoT3c(2+), 0.009/Å2 CoT2c(2+), 0.017/Å2 CoO3c(3+), 0.017/Å2 CoO5c(2+), 0.052/Å2 O4c, 0.079 Å2 O3c}.

Figure 6. Lateral view of the relaxed spinel (111)–S terminations after the formation of the anionic vacancies: a) VO2O1T and b) VO3O. For the sake of clarity only the most important changes of bond lengths (l) or interatomic distances (d) are indicated explicitly. For  > 0 the distance is elongated, whereas  < 0 the distance becomes shorter, comparing with the structures without vacancies. Color coding CoO, blue; CoT, green; O, red; VO; yellow cube.

The formation of the VO3O vacancy (yellow cube, Figure 6b) is energetically more demanding (E

of 1.72 eV), and it also influences the interatomic distances in the vacancy

vicinity only. Since the extracted oxygen anion has the 3-fold C3v symmetry, the formation of the vacancy influence the positions of three adjacent truncated octahedral cobalt ions (Co O5c) in the similar way. Their bonds with remaining oxygens are longer than in parent, undefected (111)-S surface by 0.16 Å, and the CoO5c–CoO5c distances (see Figure 6b) are now shorter (ΔdCo–Co = –0.09 Å). Analysis of the magnetic and electronic structure of the (111)-S-VO3O surface reveals reduction of two subsurface cobalt cations (ΔqB = –0.24 |e|, Δμ = 0.87 μB). These results imply that, similarly to previously described (111)-S-VO2O,1T facet, the electrons left by the released O atom are accommodated by the fully coordinated CoO6c cations. The composition of the defected (111)-S-VO3O surface and the areal concentration of the constituting surface ions may be summarized as {0.034/Å2 CoT3c(2+), 0.017/Å2 CoO3c(3+), 0.025/Å2 CoO5c(2+), 0.052/Å2 O4c, 0.079 Å2 O3c}. As can be learned from Table 4, the calculated energies of the O-vacancies formation in the sublayer region are lower than that of the surface vacancies. This provides a 24 ACS Paragon Plus Environment

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thermodynamic driving force for migration of the surface oxygen vacancies towards the spinel bulk. In our modeling we considered also the presence of more involved defects, by taking into account presence of double vacancies (coexistence of VO2O,1T and V(1layer) defects), coded as 2VO in the Table 4. The calculated energies showed that such vacancies can be treated as virtually non-interacting, since the energy of the double vacancy formation (2.77 eV) is close to the sum of the single vacancy energies (1.43 eV + 1.31 eV = 2.74 eV). The results of the thermodynamic calculations for the different anion depleted (111)-S terminations are presented in Figure 7. The panel shows the surface free enthalpy as a function of temperature for oxygen pressures corresponding to (i) reduction conditions, pO2/p° = 10-8 (achievable, e.g., by pCO/pCO2 ~ 102.5 buffer), (ii) oxygen pressures of typical catalytic oxidation reactions (pO2/p° = 10-2), and (iii) strong oxidation conditions (pO2/p° = 104). For the sake of completeness we added also the energies of the (111)-R facet, slightly reduced by the excess of the CoO3c cations, and the (111)-O termination slightly oxidized by the CoO3c cations deficiency (vide supra).

Figure 7: Surface energy (Δγ) of the oxygen depleted (111)-S termination as a function of temperature for three different oxygen pO2/p° values: a) 1.0·10-8, b) 1.0·10-2, and c) 1.0·104. Minimum energy lines define the most stable terminations, whereas the intersection areas depict the transition regions.

In the lean oxygen conditions (Figure 7a), in the lowest temperatures (T < 100 °C) the bottom line corresponds to the CoO3c depleted (111)-O termination (red). The horizontal line of



the reference stoichiometric (111)-S termination (green) constitutes the bottom envelope of the plot in the T range of 80–400 °C, and then is crossed by that of the surface with V O2O,1T vacancy ((111)-S-VO2O,1T, blue). Two lines referring to the stability of the sublayer vacancies ((111)-SVO(layer1) – dashed dark grey and (111)-S-VO(layer2) – dotted light grey) are lying lower, thus their crossing with the reference bare surface line is shifted toward lower temperatures (about 375 °C and 390 °C, respectively). It accounts well for the thermodynamic incentive for diffusion of the surface formed VO vacancies into the bulk. The steep navy blue line corresponding to the double vacancy ((111)-S-2VO) becomes the lowest at T > 750 °C, indicating that above this threshold enhanced reduction of the cobalt spinel is thermodynamically favored. Taking into account that in the temperature windows 300 °C < T < 500 °C and T > 600 °C several terminations exhibits very close surface energies, therefore they may coexist defining regions of enhanced surface redox activities. Due to the higher formation energy of the VO3O vacancies, the (111)-S-VO3O facet (dashed orange line) does not appear even at elevated temperatures. The cobalt rich (111)R facet (violet) is less stable than oxygen depleted surfaces in whole considered temperature range. The overall diagram for oxygen pressures corresponding to typical conditions of catalytic oxidation processes is similar to the previous case (Figure 7b), but the crossings of the stability lines are shifted towards higher temperature by about 150 °C. The (111)-S surface in such conditions is the most stable in the temperature range of 200-575 °C, and in the higher temperatures the regions of single ((111)-S-VO2O,1T, (111)-S-VO(layer1), and (111)-S-VO(layer2)) and then double ((111)-S-2VO) vacancy stability appear subsequently. However, since the corresponding lines are quite close to each other the involved terminations may actually coexist in the region of 500–650 °C (enhanced redox activity window). As the temperature further increases (~800 °C) the double vacancies starts to dominate. Finally, for high oxygen pressure conditions (Figure 7c), in the whole range of the considered temperatures, only the (111)-O and (111)-S terminations delineate the bottom envelope of the plot with the crossing point at


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~550 °C. These considerations indicate that for obtaining a stoichiometric cobalt spinel with a nanooctahedral shape a calcination at 300 < T < 400 and 0.01 < p°/pO2 < 0.1 is recommended. Oxidized (111)-O: Oxidation of the (111)-O surface can conceivably be achieved by extraction of surface CoT3c cations. The relaxed surface after VCoT vacancy formation (green cube) is shown in Figure 8a, where the resultant O2c surface anions of lowered coordination are explicitly indicated. The geometrical rearrangement of the spinel structure is quite small, and the largest changes are observed for the O2c–CoO6c distances (dCo-O = 0.08 Å). The significant change in the Bader charges from 1.31 to 1.45, are consistent with an increase in the oxidation states of the surface CoT3c cations from Co2+ to Co3+. The oxidation is also reflected in drop of their magnetic moments from 2.7 B to 2.1 B, and corresponds to the (dxz,dyz)4(dxy)1(dz2)1(dx20 y2)

configuration of the trivalent d6 Co ion with two unpaired electrons (S = 1). The extraction

of the CoT3c cation is energetically demanding (𝐸

= 3.4 eV, against metallic cobalt phase),

so such disorder is not favored (see below, Figure 9).

Figure 8. Lateral view of the relaxed spinel (111)–O terminations after the formation of the cationic tetrahedral VCoT (a) and anionic VO3O (b) and VO2O1T (c) vacancies. Color coding CoO, blue; CoT, green; spinel O, red; VCo, green cube VO, yellow cube.



Upon formation of oxygen vacancies the (111)-O termination may be progressively reduced, via formation of two types of defects, VO3O and VO2O,1T, analogously to the previously described (111)-S facet. The resultant atomic configuration of the relaxed (111)-O-VO2O,1T and (111)-O-VO3O surfaces is presented in Figures 8b and 8c, respectively. As it can be inferred from Table 5, removal of an oxygen atom to form a VO2O,1T vacancy requires the energy expenditure of E

= 1.21 eV. Formation of the VO2O,1T vacancy influences the coordination

and position of the adjacent ions only, leading to an appearance of dicoordinated Co T2c and pentacoordianted CoO5c cations. The cobalt-oxygen bonds within the first coordination sphere of the vacancy are longer than in the parent (111)-O surface by 0.09 Å (dCoO-O), and by 0.12 Å (dCoT-O), as shown in Figure 8b. The composition of the defected (111)-S-VO2O,1T surface and the areal concentration of the constituting surface ions may be summarized as {0.026/Å 2 CoT3c(2+), 0.009/Å2 CoT2c(2+), 0.017/Å2 CoO5c(3+), 0.052/Å2 O4c, 0.079 Å2 O3c}. Formation of the VO3O on (111)-O termination is energetically more demanding (E of 1.28 eV). Oxygen extraction influences the positions of three adjacent truncated octahedral cobalt ions (CoO5c) in the similar way due to the local C3v symmetry (Figure 8c). The CoO5cO3c bonds are longer than in the parent (111)-O surface by 0.08 Å, and the composition of the defected (111)-S-VO3O surface is the following {0.034/Å2 CoT3c(2+), 0.025/Å2 CoO5c(3+), 0.052/Å2 O4c, 0.079 Å2 O3c}. As expected, the corresponding energies of vacancies formation are smaller than the analogous values for the (111)-S termination (cf. Table 4 and Table 5). Indeed, in the case of the (111)-O termination part of the surface CoT ions is oxidized lowering the Fermi level, which favors accommodation of two electrons left by the released oxygen. In line with previously described reduction of the (111)-S surface, we considered the model with two coexisting vacancies (VO2O,1T and VO(layer2)). The calculated energy of the double vacancy formation


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(2.38 eV) is close to the sum of the single vacancy energies (1.21 + 1.15 = 2.36), indicating again a small mutual interaction.

Table 5: Formation energies of oxygen vacancies on the (111)–O termination with respect to gas phase O2 molecule.

VO2O,1T

VO3O

VO(layer1)

VO(layer2)

2·VO

E / eV

1.21

1.28

1.16

1.15

2.38

Slab model composition

Co44O62

Co44O62

Co44O62

Co44O62

Co42O60

Co/O ratio

0.710

0.710

0.710

0.710

0.733

The results of the thermodynamic modeling for the defected (111)-O termination are presented in Figure 9, for the three different oxygen pressures (pO2/p° = 10-8, pO2/p° = 10-2 and pO2/p° = 104). In the low pressure regime (Figure 9a) the (111)-O termination (red solid line) is the most stable until ~250 °C, then upon oxygen release it is transformed into the (111)-OVO2O,1T surface (blue line). In the 225 °C–450 °C range the vacancy stabilization in the bulk is expected, as implied by the dashed grey line. The second vacancy appears around ~450 °C, and above this temperature the (111)-O-2VO facet is the most stable (navy blue line). As shown by Figure 9a, the region of an enhanced surface redox activity is shifted toward lower temperatures (200 °C < T < 500 °C) comparing to the (111)-S surface (see Figure 7). The orange dashed line corresponding to the cationic vacancies indicate that the cation depleted (111)-O-VCoT termination is highly disfavored in the whole range of the investigated temperatures (similarly to the octahedral cationic vacancy, dashed yellow line). Upon passing to higher oxygen pressures (Figure 9b), stability of the (111)-O facet extends to higher temperatures (450 °C at pO2/p° = 10-2), and finally at high oxygen pressure it becomes the most stable in nearly the whole investigated temperature range (Figure 9c).



Figure 9: Surface energy (Δγ) of the oxygen depleted (111)-16O3c-4CoT3c termination as a function of temperature for three different oxygen pO2/p° values: a) 1.0·10-8, b) 1.0·10-2, and c) 1.0·104. Minimum energy lines define the most stable terminations, whereas the intersection areas depict the transition regions.

To summarize the obtained results in a concise way, projection of the most stable terminations on the (T , pO2)-plane is shown in Figure 10. The presented diagram covers a wide range of spinel non-stoichiometry resulting both from anionic (Co3O4-δ ; 0 > δ > 0.25) and cationic (Co3δO4

; 0 > δ > 0.38) disorders. The largest area in the center corresponds to the stoichiometric

(Co3O4) (111)-S termination exposing both the truncated octahedral CoO3c(3+) and tetrahedral CoT3c(2+) cations. The more oxidizing conditions are dominated by the large region of the (111)O termination stability (red plane, Co2.75O4) with the depleted CoO3c cations. Formation of the tetrahedral cationic vacancies (yellow region, Co2.62O4) takes place only at low temperatures (T < 200 °C) and very high oxygen pressures (pO2/p° > 104). In the upper right part of the diagram (lower pO2 and higher T) the anion depleted terminations are the most stable. Their stoichiometries correspond to Co3O3.875 ((111)-S-VO2O,1T, blue), and then to Co3O3.75 ((111)-S2VO, navy blue). Noting the structure compatibility of the (111) planes of Co3O4 and CoO,48 the (111)-S-2VO region can be associated with onset of the topotactic reduction of (111) surface of cobalt spinel. The dashed lines shows the stability borders of the close lying terminations which defines the regions of the enhanced redox activity of the cobalt spinel (111) surface. In comparison to the most abundant (100) plane31 the (p, T) borders of the enhanced redox activity and of the surface stability (reduction to CoO) are shifted toward more reducing conditions. 30 ACS Paragon Plus Environment

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This implies that the octahedral nanograins are more reluctant to reduction than the cubic Co3O4, and therfore are expected to be less reactive in the Mars van Krevelen processes.

Figure 10: Redox state diagram diagram of the surface free energies versus T and pO2 for the (111) terminations of Co3O4 depleted of oxygen anions and cobalt cations.



3.6. Redox environment versus shape of Co3O4 nanograins: To account for the influence of the redox environment on the cobalt spinel nanocrystals morphology we constructed Wulff shapes of cobalt spinel nanograins at various oxygen chemical potential (oxidizing, ambient and reducing conditions defined on Figure 11). In our modelling we considered low index (100), (110) and (111) planes observed in most of the cobalt spinel nanosamples. For the (100) and (110) surfaces we used the calculated surface free enthalpies (see Table 6) reported previously by us31 and by Montoya et al., respectively.28 The results show that regardless the redox conditions the overall rhombicubooctahedral shape, exposing all three surfaces, is essentially preserved, with the dominant abundance of the (100) facet (green). The closer inspection (see percentage exposure of surfaces in Table 6) reveals that oxygen rich environment favors the (111) facet (red). In ambient redox conditions, this plane lowers its contribution at the expense of (100) facet. Upon moving to more reducing conditions the further decrease of the (111) termination abundance is expected, however in this case it occurs at the expense of the (110) termination (blue). These results shows that cobalt spinel nanograins exhibit fairly good morphological stability (preserving rhombicubooctahedral shape) in the wide range of pO2, T conditions providing a stable model system for catalytic studies. It should be noted however, that in more detailed studies the contribution of the (111) facet to the overall surface area changes from 45 % to 23 % upon passing from oxidizing to reducing environment. This may be reflected in changes in the performance of the Co3O4 nanograins where the (111) facet plays a crucial role such as methane oxidation.11


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Figure 11: The cobalt spinel Wulff shapes constructed for oxidizing, ambient and reducing conditions.

Table 6: The surface free enthalpies (γ) used for cobalt spinel nanograins morphology modelling in different redox environments together with percentage abundance of corresponding surfaces. Surface

Thermodynamic Conditions μO2 / eV ; T / C ; pO2 / atm

(100) γ / J·m-2 abundance

facet

0.0 ; 25 ; 0.01 Oxidizing

-2.8 ; 700 ; 0.01 Reducing

facet

facet

1.47 (110)-B

40 % 1.34

1.41 45 %

1.65 (110)-S

52 %

1.51 (111)-S

10 %

1.25

40 %

1.43 (110)-A

55 %

ACS Paragon Plus Environment

1.46 (111)-2V

26 %

33

γ / J·m-2 abundance

(111)-O 15 %

(100)-S

(100)-S2VO

(111)

γ / J·m-2 abundance

1.27 (100)-O

-1.4 ; 350 ; 0.01 Ambient

(110)

23 %


CONCLUSION Comprehensive examination of all conceivable terminations of the cobalt spinel (111) surface with anionic and cationic vacancies, allowed for construction of a surface redox state diagram in a wide range of Co3O4 stoichiometry (Co2.62O4 to Co3O3.75). It was shown that the stoichiometric, (111)-S, surface exposing both octahedral CoO3c trivalent and tetrahedral CoT3c divalent cations is the most stable in the temperatures and pressures typical for the catalytic processes (T ~200 °C to ~500 °C, pO2/p° ~0.001 to ~1). In more reducing conditions (T > 600 °C and pO2/p° < 0.0001) an enhanced redox activity of the stoichiometric (111)-S termination is expected, which is related to reversible formation of oxygen surface vacancies and their diffusion toward the bulk. In oxygen rich conditions (T < 200 °C and pO2/p° > 10) the (111)-O termination, exposing tetrahedral CoT3c (divalent and trivalent) ions only, is the most stable, and with the rising oxygen pressure it becomes defected due to the presence of the cationic vacancies in the tetrahedral sites. Thorough analysis of the magnetic and electronic structure revealed that the excess of the CoT3c cations (over-stoichiometry) influences the oxidation states of both surface and bulk octahedral cobalt ions, whereas, the sub-stoichiometry leads to oxidation of the surface CoT3c cations only. The electrons left upon oxygen release are accommodated on CoO3c (for (111)-S) or CoT3c (for (111)-O) surface cobalt cations. Cobalt nanograin morphology regardless the redox conditions assume a rhombicubooctahedral shape, where the (111) termination is more abundant in oxygen rich environment.


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AUTHOR INFORMATION Corresponding Author *[email protected], telephone number: +48 12 663 20 73

AUTHOR CONTRIBUTIONS The manuscript was written through contributions of all authors.

SUPPORTING INFORMATION 1.Comparison of calculated and theoretical properties of Co3O4; 2.Slab models representing most stable (111) surface terminations; 3.Coordination environment of exposed ions on (111) terminations; This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT This work was supported by the Iuventus Plus project of the Polish Ministry of Science and Higher Education (Grant No. IP2015-088774).

ABBREVIATIONS (111)-S; bare stoichiometric cobalt spinel termination, (111)-O; oxidized cobalt spinel termination, (111)-R; reduced cobalt spinel termination, CoO; cobalt in octahedral site, CoT; cobalt in tetrahedral site, DFT+U; Density Functional Theory with Hubbard corrected functionals, GGA; generalized gradient approximation, ΔGr; reaction free enthalpy, SI; Supporting Information, FPT; First Principles Thermodynamics, oxygen reduction reaction, ORR; qB; Bader charge, VO; oxygen vacancy, VCo cobalt vacancy, γ; Surface Energy, μ; magnetization, ΔμO; Oxygen Chemical Potential,



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