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Surface Structure and Morphology of M[CoM′]O4 (M = Mg, Zn, Fe, Co and M′ = Ni, Al, Mn, Co) Spinel NanocrystalsDFT+U and TEM Screening Investigations F. Zasada,* J. Gryboś, P. Indyka, W. Piskorz, J. Kaczmarczyk, and Z. Sojka Faculty of Chemistry, Jagiellonian University, Ulica Ingardena 3, 30-060 Krakow, Poland S Supporting Information *

ABSTRACT: Plane wave periodic GGA-PBE+U density functional theory calculations were used to study the structure, surface energy, and equilibrium shape of faceted nanocrystals for a series of cubic (Fd3m) 2−3 AB2O4 spinels with the following formula: Co[Co2]O4, Mg[Co2]O4, Zn[Co2]O4, Co[NiCo]O4, Co[MnCo]O4, Fe[FeCo]O4, and Co[Al2]O4. Their bulk geometries (lattice constants and oxygen u parameters) as well as electronic and magnetic properties were computed and compared with experimental data. All planes, (100), (110), and (111), exposed by the spinel nanocrystallites of equilibrium morphology were taken into account, and their atomic structure, reconstruction, and stabilization were elucidated and systematized in terms of the structural oxygen u parameter. The strongest relaxation of the A cations was observed for the (100) plane, whereas that for the B cations was on the (111) plane. By using the calculated surface energy values, the shapes of the spinel nanocrystallites were predicted by means of the Wulff construction and classified according to their shapes into singly and doubly truncated hexahedra (rhombicuboctahedra) and truncated octahedra. The results were compared with experimental TEM and STEM pictures, corroborated by image simulation.

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(denoted MT) exhibiting one-eight occupancy are filled by A cations.21 In the case of x = 1 (inverse spinels), the MT sites are hosting the M3+ cations, whereas the MO sites are occupied half-and-half by the M3+ and M2+ cations. Off-stoichiometric (partially inversed) spinels (A1−xBx)[B2−xAx]O4, with antisite B•A and A′B defects, exhibit x values in the range of 0 < x < 1.22 The spinel structure can be regarded as a versatile matrix, being able to accommodate a wide range of metal cations and oxidation states.23,24 In particular, cobalt spinel (Co3O4) and its derivatives containing Zn, Ni, Fe, Mg, Mn, or Al ions have received a great deal of theoretical and practical attention. They exhibit, for instance, high activity in the low-temperature decomposition of nitrous oxide.25−28 Mixed Co−Fe−Al spinels, with optical band gaps between 1.6 and 2.0 eV, generate strong p-type photocurrent for photoelectrochemical splitting of water, whereas ZnCo2O429 or CoMn2O430 have a good cycling capacity in the Li+ charge−discharge processes. Due to widespread applications, new methods for the preparation of Co3O4-based nanospinels of desirable morphologies such as nanospheres, nanocubes, nano-octahedra, or nanorods and -tubes have been developed31,32 using chemical vapor deposition,33 sol−gel,34 and hydrothermal methods.35−37 Although there is large number of experimental studies on mixed oxide spinels, computational investigations are still rather limited,22,38,39 especially those dealing with surface and

INTRODUCTION Owing to their clear-cut structure and high surface area, faceted nanocrystals (NC) provide excellent model systems for experimental and theoretical investigations into surface-related properties.1−4 By exposing well-defined crystallographic planes they allow for judicious investigations into structure−reactivity relationships under practical conditions.5−7 This assists in designing, for example, new catalytic materials of enhanced activity and selectivity by preferential growth of desired specific planes and enhancement of the active sites density. As a result, much effort has recently been devoted for development and characterization of functional and catalytic nanomaterials of fully tunable morphology, yet their routine engineering still remains a challenge.8−13 The 2−3 spinels (AB2O4) belong to the scientifically and technologically most attractive oxides, with a remarkable record of widespread applications in heterogeneous catalysis,4,14−16 energy storage and conversion,17,18 or sensor devices.19,20 Their performance is associated with particular electronic, magnetic, optical, and catalytic properties that stem from the intrinsic multivalence nature and coordination dichotomy of the constituent ions and strongly depend on both the bulk and the surface structures. The close-packed cubic Fd3m structure of the 2−3 spinels is characterized by divalent A (M2+) and trivalent B (M3+) cations distributed among the tetrahedral (8a) and the octahedral (16d) interstitials, depending on the degree of inversion x. For normal spinels, x = 0, the half-filled octahedral sites (denoted hereafter as MO) contain B cations, whereas tetrahedral sites © 2014 American Chemical Society

Received: April 16, 2014 Revised: July 29, 2014 Published: July 29, 2014 19085

dx.doi.org/10.1021/jp503737p | J. Phys. Chem. C 2014, 118, 19085−19097

The Journal of Physical Chemistry C

Article

directions, to obtain large supercells containing ca. 10 atomic layers with vacuum space of 20 Å. The stoichiometry of the bulk AB2O4 was preserved in the constructed slab models, and the same structure of the top and the bottom slab terminations was ascertained. Relaxation of the atomic positions in the four top layers was assumed to render forces acting upon the ions below 1 × 10−2 eV Å−1. The Wulffman program63 was used to predict the theoretical equilibrium shape (minimum surface energy convex polyhedra) of the investigated nanocrystals, according to the rule

morphology issues. Structural investigations into cation distribution in CoAl2O4,40 intrinsic defects in Fe-doped CoAl2O4, or off-stoichiometry in ZnCo2O4, CoNiCoO4, and Fe2CoO4 with regard to their electric conductivity and magnetic properties may serve here as notable examples.22,41,42 More recent noteworthy studies of the doping rules24 and the formation free energies43 were carried out for a large series of 2−3 spinels including cobalt derivatives. Owing to the present state of the art in computational chemistry, fairly accurate first-principles modeling of surface structure44,45 and theoretical predictions of the resultant morphology for faceted nanocrystals are made possible. By employing the Wulff construction along with the ab initio thermodynamics, the influence of chemical environment can also be taken into account.46 Such an approach has proved its excellent predictive and explanatory capabilities for titania,47 alumina,48 maghemite,49,50 or magnesia, for example, in dry and wet conditions.51 In this context, despite rich literature experimental reports on the morphology of spinels, reviewed recently elsewhere,4,52 no systematic atomic-level understanding of their surface structure and morphology in relation to the bulk composition, has emerged as yet. In the present work by means of periodic DFT+U calculations we investigated the surface structure, energetics, and morphology of bare and mixed cubic spinel nanocrystals of the following formula: Co[Co2]O4, Mg[Co2]O4, Zn[Co2]O4, Co[NiCo]O4, Co[MnCo]O4, Fe[FeCo]O4, and Co[Al2]O4. The results were compared with experimental TEM and STEM images, corroborated by image simulation, and discussed in terms of the oxygen u parameter.

where γhkl is the surface energy of the exposed (hkl) plane, and rhkl is the distance from the center of the nanocrystal to the hkl facet. The size effect on the stability of the cobalt spinel NCs was evaluated by means of the model used in our previous paper.10 For nanocrystals with a size in the range of 7−200 nm, the surface energy usually dominates the edge and corner contributions. For the investigated spinel NCs with dimensions around 50 nm (vide infra), they can safely be ignored. For the stress energy calculations, the volume compressive dilation caused by the surface energy was taken into account, and the validity of the Laplace−Young equation was assumed. The energy vs volume data were fitted to the Birch−Murnaghan equation of state (with the root-mean-square < 10−4). The compressibility of the bulk was calculated as a second derivative of the energy with respect to the cell volume at the equilibrium point.

COMPUTATIONAL DETAILS For all calculations density functional theory with Hubbardcorrected functionals (DFT+U) level of theory was employed as implemented in Vienna Ab Initio Simulations Package (VASP).53 We used the projector augmented plane wave (PAW)54 method for describing electron−ion interactions together with the generalized gradient GGA-PBE exchangefunctional.55 All calculations were performed using a standard Monkhorst−Pack56 grid (5 × 5 × 5 sampling mesh for bulk calculations and 3 × 3 × 2 for slab calculations) with a cutoff energy of 450 eV and a Methfessel−Paxton57 smearing with the σ parameter set to 0.1 eV. For solving, the Kohn−Sham SCF convergence energy change of 10−5 eV between two successive iterations was applied. To account for strong on-site Coulomb repulsion among the localized 3d electrons, the DFT+U level of theory with the Hubbard U58 parameter chosen uniquely for each oxidation state was used, for optimal reproduction of both the electronic (tested by band gap value, BG) and the geometrical (tested by lattice constant, a, and u parameter) structures. The lattice constants were determined by fitting computed total energies to Birch−Murnaghan’s equation of state,59 with all internal degrees of freedom fully relaxed. For surface energy modeling we considered three low-index, (100), (110), and (111), planes of cubic spinel with the largest interplanar spacing, as they are predicted to be the most stable, following the Bravais−Friedel−Donnay−Harker theory.60 Indeed, careful inspection of the available experimental data reveals that (100), (110), and (111) planes are exposed in a number of Co3O4-based oxide specimens prepared by various methods.61,62 Surface slab models (Figure S1, Supporting Information, SI) were constructed by cleaving the optimized bulk structures in the normal (100), (110), and (111)

EXPERIMENTAL DETAILS Spinel samples were synthesized with the use of the forced hydrolysis method with subsequent hydrothermal treatment of the precipitates in a Teflon-lined microwave autoclave (Ertec Magnum II) for 1 h at 180 °C and 30 atm (for more details, see the SI). All powders were characterized by measuring the N2− BET specific surface area SBET (Quantachrome Jr) and powder diffraction (Rigaku MiniFlex). The characterization results are summarized in Table S1 (SI). Transmission electron microscopy (TEM) measurements (bright-field and high-resolution TEM) were carried out using a Tecnai Osiris instrument (FEI) operating at 200 kV. Prior to TEM analysis, the samples were ultrasonically dispersed in methanol on a holey carbon film supported on a copper grid (400 mesh). The grid was dried for 45 min, and then surface contaminations were removed by plasma-cleaning (Solarus Gatan 950). HAADF-STEM images were recorded at 200 keV by means of a Hitachi HD2700 STEM microscope (for details see our previous paper64). The simulations of high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images were carried out using Quantitative TEM/STEM Simulations package (QSTEM).65 According to the experimental conditions, the Cs and Cc coefficients, equal to 1.1 mm and 1.74 mm, respectively, were used. Simulations were carried out for three angular ranges of the annular detector: 70−200, 0−40, and 40−70 mrad. The semiangle of the incident converged beam was set to 20 mrad. The specimen thickness was estimated on the basis of the 3D shape of the nanocrystals, and their diameters were derived from experimental images. The values of the mean-square thermal vibration of the Co and O atoms were set to 0.0052 Å.66

γhkl(n)/rhkl = constant, ∀ hkl

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19087

1.932

8.170 8.09074 0.2644 0.259074 1.973

1.933

1.951

a

The spinels are arranged by increasing u parameter.

Co−O: 1.982 Mn−O: 1.990

Co[Al2]O4 Mg[Co2]O4 Co[Co2]O4

8.162 8.08174 0.2641 0.264074 1.968 1.946 1.932 1.914 8.125 8.05076 0.2633

Zn[Co2]O4

8.161 8.08474 0.2638 0.263274 1.960 1.93564 1.932 1.92062 MO−O /Å

The calculated structural parameters are summarized in Table 2 along with the corresponding experimental values (the investigated spinels were arranged by increasing oxygen u parameter). Quick inspection of Table 2 shows that the PBE+U lattice constants and the bond distances are generally overestimated by about ∼0.5%. This effect, associated with inclusion of the Hubbard parameter, has been found previously in other GGA+U studies of oxide systems67,70 and is discussed in recent literature.42 The calculated oxygen u parameter is associated not only with the MT−O and MO−O bond lengths,71 but its value can also be used to predict an inverse vs normal spinel structure. Thus, for 2−3 spinels with zB > zA, if u > 0.2592, a normal configuration is assumed and the inverse if u < 0.2578.72 Among the investigated spinels, only for the Fe[CoFe]O4 system is u = 0.257, smaller than the critical value, implying its inverse structure. This, however, does not discard possible partial inversion in the case of the other spinels (see below). For each investigated mixed oxide, the calculated band gap and magnetization (for octahedral and tetrahedral ions) are collected in Table 3 and compared with the available experimental values. Co[Co2]O4. The optimized lattice constant of the Co3O4 spinel, a = 8.161 Å, and the u parameter of 0.2638 compare well with the experimental values of 8.082 Å and 0.2632, respectively. The calculated octahedral cobalt−oxygen and tetrahedral cobalt−oxygen bond lengths are equal to dCoO−O = 1.932 Å and dCoT−O = 1.960 Å, respectively, again in a good agreement with the experimental distances of 1.920 and 1.935 Å. Inclusion of the Hubbard parameter was found to be crucial for proper description of the cobalt−oxygen bond lengths. Without U the Co−O distance of 1.931 Å is longer than the CoT−O bond length (1.920 Å), contrary to XRD data. The crystal field splits the five degenerate atomic d orbitals into t2g and eg levels for the octahedral sites and into t2 and e levels for

1.9 1.979 Co−O: 1.932 Ni−O: 1.961

4.743

Co[NiCo]O4

ZnT

1.940

3.50

43

MT−O /Å

4.00

FeO

u

6.4

69

8.189 8.11575 0.2627

4.0

FeT

8.176 8.09074 0.2618 0.259074 1.954 1.962 1.963 1.913

43

a-Co[Al2]O4

NiO

68

Co[MnCo]O4

6.5

MnO

8.118 8.08073 0.2600

4.5

CoO

Fe[CoFe]O4

CoT

8.495 8.39042 0.2575 0.256077 1.921 1.904 Co−O: 1.977 Fe−O: 2.040 2.050

Table 2. Calculated Structural Parameters of the Investigated Spinels: Lattice Constant (a), Oxygen Parameter (u), and MT−O, MO−O Bond Lengths, along with the Corresponding Experimental Valuesa

Table 1. Employed Values of the Hubbard Parameter (eV)

DFT expt DFT expt DFT expt DFT expt

RESULTS AND DISCUSSION

Bulk Properties. Bulk properties of the investigated cobalt spinels were computed and compared with the experimental data to verify the adequacy of the employed DFT approach. Since for the spinel bulk structure the lattice parameter, a, and the oxygen parameter, u, are required to completely determine the atomic positions within the unit cell, we selected these two quantities for validation purposes. We also analyzed the magnetic properties of the octahedral and tetrahedral ions to reveal their valence and spin states and, in conjunction with the u value, to attribute an inverse or normal configuration to each of the investigated spinels. To properly describe the electronic structure, we employed DFT+U with the PBE generalized gradient approximation. For the parent Co3O4, we scanned the U parameter, from 0 up to 7.0 eV with 0.5 eV steps, according to the method of Selloni67 with different values for CoT and CoO ions. The converged values of the effective U parameter were equal to 4.5 and 6.5 eV for Co3+ and Co2+, respectively. Following a literature survey, the Hubbard parameters for the other d-metals were assigned individually to reflect stronger onsite repulsion in more contracted 3d orbitals in higher oxidation states (Table 1).

a/Å

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Table 3. Calculated Electronic (band gap) and Magnetic (magnetic moment) Properties of the Investigated Spinelsa band gap X→X/eV magnetic moment/μB

a

Fe[CoFe]O4

Co[MnCo]O4

a-Co[Al2]O4

Co[NiCo]O4

Zn[Co2]O4

Co[Co2]O4

Mg[Co2]O4

Co[Al2]O4

DFT expt MT

2.9 2.778 Fe: 4.42

2.1 − Co: 2.71

1.82 1.9780 Co: 2.67

2.3 2.0981 Zn: 0.00

1.72 1.6582 Co: 2.69

1.91 − Mg: 0.00

1.65 1.6979 Co: 2.72

MO

Co: 1.01 Fe: 4.61

Mn: 3.85 Co: 0.02

1.66 1.6979 Co: 2.72 Al: 0.00 Co: 0.99 Al: 0.01

Ni: 1.01 Co: 0.01

Co: 0.00

Co: 0.01

Co:0.00

Al: 0.01

The spinels are arranged by increasing u parameter.

cubic symmetry of the ideal spinel lattice. Most of the experimental data indicate that Co ions occupy the tetrahedral interstitials, whereas Mn ions occupy the octahedral ones.85 Substitution of Mn3+ for Co3+ leads to an increase in the lattice parameter, due to the larger ionic radius of Mn3+. The valence states of the constituting ions following XPS86 and magnetic studies67,70 show the presence of the Mn3+, Co3+, and Co2+ ions. Thus, in our modeling we placed the tervalent Mn ions in half of the octahedral sites, and found a nice agreement between the theoretical and the experimental a values (8.080 vs 8.118 Å). Furthermore, the calculated magnetization is consistent with the fact that divalent Co2+ (e4t23) ions occupy MT sites, whereas the tervalent high-spin Mn3+ (t2g3eg1) and the low-spin Co3+ (t2g6eg0) ions are located in the MO sites. Fe[CoFe]O 4 . The cobalt ferrite, Fe[CoFe]O 4 , is a ferromagnetic inverse spinel with the Fe3+ ions occupying all tetrahedral sites and half of the octahedral ones, and the Co2+ cations are placed in the remaining octahedral interstitials. In this spinel, the inverse and normal configurations are very close in energy, so the choice of the right Hubbard parameter for iron and cobalt is of crucial importance to obtain satisfactory results, as previously discussed by O’Brien et al.43Both of the calculated a and u parameters are in agreement with their experimental counterparts (8.49 vs 8.39 Å and 0.2571 vs 0.2560). The magnetization for the octahedral cobalt (1.01 μB) stems from the low-spin t2g6eg1 configuration, in agreement with its divalent nature (Co2+, d7). The tervalent Fe ions in the MT and MO positions have a similar magnetization of about 4.5 μB, which can be assigned to the five unpaired electrons of high-spin configuration, t2g3eg2 (MO site) and e3t22 (MT site). Such results clearly define Fe[CoFe]O4 as an inverse spinel, in line with experimental observation. The calculated band gap (2.9 eV) compares well with the experimental value (2.7 eV). Co[Al2]O4. Co[Al2]O4 spinel is described as an normal spinel at low temperatures, whereas at high temperatures, part of the Co2+ and the Al3+ ions may interchange their positions (Co1−xAlx)[Al2−xCoxO4],40 leading to formation of Co′Al and Al•Co antisite defects (called hereafter off-stoichiometric aCo[Al2]O4). Our calculations confirm that the most stable bulk structure corresponds to the normal spinel. Indeed, placement of the trivalent cations in the octahedral sites is favored by the Madelung electrostatic energy. Comparison of the experimental structural parameters of CoAl2O4 and Co3O4 reveals an increase of the lattice constant and a decrease of the u parameter upon introduction of Al3+ cations. These effects led to the resultant slight modification of the M−O bond lengths in both the tetrahedral and the octahedral units by 0.013 and −0.008 Å, respectively. Owing to the presence of the divalent Co2+ ions in the tetrahedral positions, the magnetic properties of the parent Co3O4 spinel are preserved, and computational magnetic moments on Co2+ ions (2.72 μB) can be attributed to

the tetrahedral sites. Actually, each B site is distorted by the trigonal field with the unique axis along the [111] direction, leading to a D3d local symmetry, so the degeneracy of the t2g manifold is slightly removed (a1g + eg). The calculated magnetic moment (2.69 μB, see Table 3) for the divalent CoT ions is consistent their high spin e4t23 configuration, whereas for the trivalent CoO ions, the nil magnetic moment implies a closed shell CoIII(t2g6eg0) configuration. The calculated electronic X→ X band gap (1.72 eV) compares fairly well with previous calculations83 and the experimental value of 1.65 eV. Mg[Co2]O4 and Zn[Co2]O4. Analysis of the experimental XRD results revealed that introduction of magnesium into the cobalt spinel matrix does not change the lattice a and u parameters significantly,74 in line with the DFT results (see Table 2). The calculated value of u = 0.2641 > ucrit indicates a normal spinel structure, where Mg2+ ions are stabilized essentially in the tetrahedral 8a positions. This can be rationalized by the fact that the Co3+ cations exhibit a distinct preference toward octahedral sites, where their low-spin (t2g6eg0) configuration is favored by sizable crystal field stabilization energy. In line with this argumentation, all ions in Mg[Co2]O4 are diamagnetic (Table 3). The calculated band gap is slightly wider than those of the parent Co3O4 (1.91 vs 1.72 eV), again in nice agreement with the experimental value (1.81 eV). In accordance with the calculated value of u = 0.2633 and experimental observations,84 ZnCo2O4 exhibits a normal spinel structure, with the Zn2+ ions located in the tetrahedral sites. The calculated lattice parameter of 8.125 Å (vs experimental 8.050 Å) and the band gap are slightly overestimated (2.30 eV vs experimental 2.09 eV). Co[NiCo]O4 and Co[MnCo]O4. Co[NiCo]O4 is generally regarded to exhibit a spinel structure in which nickel occupies the octahedral interstitials, whereas cobalt ions are distributed over both octahedral and tetrahedral sites. This experimental constraint was taken into account by exchanging half of the octahedral cobalt ions with nickel, following the work of O’Brien et al.43 The calculated and experimental a (8.115 Å vs 8.189 Å) values remain in good mutual agreement. The tetrahedral Co2+ ions exhibit a magnetic moment of 2.67 μB, consistent with their divalent nature (e4t23), whereas octahedral Co3+ ions (t2g6eg0) are diamagnetic. Each nickel, in turn, bears one unpaired electron (1.0 μB) that originates from the Ni3+ low-spin configuration (t2g6eg1). The cobalt manganese spinel can adopt either an ideal cubic Fm3m or a body-centered tetragonal I41/amd structure, depending on the stoichiometry of the [Co2+]8a[Co3+2−xMn3+x]16dO4 system. For x lower than or equal to 1, the cubic form is expected, whereas for x in the range of 1−3, tetragonal phase is observed. This phenomenon is easily explained by the fact that the Mn3+ ions stabilized in the MO sites exhibit a strong Jahn−Teller effect, breaking the 19088



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three unpaired electrons occupying the t2 states. The calculated band gap of 1.69 eV remains in a good accordance with the experimental value of 1.65 eV. To obtain better correspondence with TEM observations (see below), we also considered partially inversed spinel (aCo[Al2]O4) with the stoichiometry Co0.75Al0.25[Al1.75Co0.25]O4. Such a ternary oxide is less stable in comparison to the normal Co[Al2]O4 structure (by 0.313 eV per unit cell), but actually it can be stabilized by increased configuration entropy. The calculated band gap and the lattice constants are comparable (1.65 vs 1.60 eV and 8.176 vs 8.170 Å). However, the oxygen u parameter is lower in the case of the off-stoichiometric configuration (0.2618 vs 0.2644), fitting much better the experimental value of 0.2600. The lowering of the u parameter is connected with exchanging of the larger Co2+ ions in the tetrahedral positions (rCo2+ = 0.58 Å) with much smaller Al3+ ions (rAl3+ = 0.39 Å), which strongly influences the MT−O/ MO−O bond lengths ratio. Analysis of the magnetic moments reveals that Al conserves its trivalent state (null magnetic moment), whereas the magnetization of 1.00 μB on octahedral cobalt stems from the low-spin t2g6eg1 configuration, in agreement with its divalent nature (Co2+, d7). Such partial inversion is important for proper reproduction of the experimental surface energies and the observed NCs morphologies (see below). In the case of other investigated spinels, slight inversion has also been reported for Co[MnCo]O485 and Fe[CoFe]O4,77 yet a good agreement between the predicted and observed shapes (see below) indicates that this effect has much less influence on the NCs morphology in comparison to that of the cobalt aluminate. Since structural, electronic, and magnetic parameters of the investigated spinels were reproduced correctly, the employed formalism and the used parametrization were adequate for quantum chemical modeling of surface structure and morphology. Surface Structure. For each investigated spinel we constructed stoichiometric (n-A[B2]O4) surface slab models for all considered terminations (Figure S1, SI). In the case of the (100) plane we used a slab composed of 11 oxide layers (8.01 Å) consisting of four coordinatively unsaturated 5-fold MO5c (with one missing oxygen ligand), two recessed, fully coordinated 4-fold MT4c, and two protruding 2-fold MT2c cations with two missing O ligands (Figure 1). On this facet there are two types of exposed oxygen ions: the 4-fold O4c species, preserving their bulk coordination, and truncated 3-fold O3c anions (with one bond to MT missing). In order to ensure the equivalence of both sides of the slab model and preserve the surface stoichiometry, one MT cation per unit cell was displaced from the upper to the lower plane of the slab, giving rise to the following surface composition {1MT2c, 4MO5c, 2MT4c, 6O3c, 2O4c} of the computational model used for the (100) plane. There are two principal types of terminations for the (110) spinel surface, often labeled as A and B in the literature.87 They were both modeled using slabs containing seven oxide layers with the thickness of 8.54 Å. The (110)-A plane (Figure 2) is terminated with the 4-fold octahedral (MO4c) and the 3-fold tetrahedral MT3c ions. The same trigonal coordination exhibits also the exposed oxygen anions (O3c). In order to ensure the proper stoichiometry and parity of the lower and upper planes, the (110)-A termination was adjusted by removing one CoT cation from both sides. The resultant computational model of the (110)-A plane exhibits the following composition {3MT3c, 4MO4c, 4O3c, 4O2c}. The (110)-B termination exhibits only 4-

Figure 1. Perspective view of the stoichiometric (100) spinel surface. Color coding: blue, octahedral cations; green, tetrahedral cations; red, oxygen anions. Side and top view of this termination are presented in the SI (Figure S2).

Figure 2. Perspective view of the stoichiometric (110)-A spinel termination. Color coding: blue, octahedral cations; green, tetrahedral cations; red, oxygen anions. Side and top view of this termination are presented in the SI (Figure S3).

fold MO4c cations and two types of 3-fold oxygen anions (with a MO or a MT neighbor missing). In the case of the (110)-B termination, more severe modifications involving depletion of two cobalt and four oxygen atoms were needed to meet the stoichiometry requirements. The resultant model of this termination consists of {4M3c, 2M3c, 8O3c} surface ions. Since our previous calculations predict that for all investigated spinels the 110-A termination is more stable than the 110-B plane (γ110‑A = 1.65 J/m2 and γ110‑B = 1.92 J/m2),64 we exclude the latter from further analysis. Thus, hereafter the (110) label refers to only the most stable (110)-A facet. The (111) plane was modeled using a slab comprising 13 layers (∼9.40 Å). Cleavage of the MTMO2O4 spinel across this plane can produce six conceivable nonequivalent terminations. The most stable (111) termination (Figure 3) with the smallest number of dangling bonds is characterized by strong undersaturation of four MO ions (reduced to 3-fold coordination MO3c), whereas in the case of four MT, only one O2− ligand is lost (MT3c). Among the exposed oxygen anions 3-fold O3c and 4-fold O4c species can be distinguished. In order to preserve the stoichiometry and equivalence of both planes of the slab, one MT ion was displaced from the upper into the lower plane, giving rise to the composition {4MT3c, 2MO3c, 10O3c, 6O4c} of the computational model for the (111) facet. 19089



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surface reconstruction, and the most significant displacements are associated with the cations. Generally, for all the spinels, the strongest relaxation of the MT cations was observed on the (100) plane, whereas for the MO cations it was on the (111) plane. In the case of the (100) and (110) terminations, the surface reconstruction is quite similar for all calculated spinels. For the (100) facet, the unsaturated MT2c ions move significantly inward (from −0.24 Å to −0.20 Å), whereas the MO5c ions remained almost intact (−0.06 Å < Δz < −0.04 Å). Those changes are accompanied by reduction of the MO5c−O3c and MT2c−O3c bond lengths, the latter one being much more pronounced (see Table 4 for details). In the case of the (110) plane, both the tetrahedral and the octahedral cations are shifted inwardly; however, these displacements are not sizable (from −0.11 to −0.05 Å and from −0.07 to −0.04 Å, for MT and MO, respectively). Contrary to the (100) plane, the shrinking of the MO−O and MT−O bonds is comparable. The situation is somehow different in the case of the (111) facet, where the tetrahedral MT3c cations behave similarly (with the z-shift from −0.14 Å to −0.17 Å) in all investigated spinels, yet the relaxation of the highly unsaturated MO3c is different. For Co[Co2]O4, Mg[Co2]O4, Zn[Co2]O4, and Co[NiCo]O4, the MO3c ions relax by moving along the z-axis from −0.020 to −0.026 Å. For Fe[CoFe]O4 and Co[MnCo]O4, this movement is more pronounced (−0.035 and −0.037 Å, respectively), and it is accompanied by significant MO3c−O3c bond length reduction (Δd = −0.158 and −0.156 Å, respectively). In the case of the normal Co[Al2]O4 spinel, an opposite effect is observed: the AlO3c cations are shifted toward the surface by −0.06 to −0.07 Å only, and in contrast with other spinels, those shifts were almost the same. The resultant contraction of the Al3cO−O3c bond length was quite small (ΔdAlO−O = −0.010 Å).

Figure 3. Perspective view of the stoichiometric (111) spinel plane. Color coding: blue, octahedral cations; green, tetrahedral cations; red, oxygen anions. Side and top view of this termination are presented in the SI (Figure S4).

Surface Relaxation. To investigate how the structure of the exposed planes relates to the spinel morphology, we relaxed their geometry and calculated the principal displacements of the undercoordinated ions along with the associated surface energy changes. The geometry optimization of all investigated spinel terminations gives rise to considerable lowering of the surface energy in comparison to the parent rigid structures (see Table S2 of the SI for details). The resultant surface reconstruction was significant only for the highly unsaturated surface ions and can be described as prevailing relaxation into the normal to the surface (z) direction, toward the bulk. The most pronounced shifts and bond distance changes are listed in Table 4 and indicated in Figures S2−S4 (SI). The collected data reveal that, upon optimization, the oxygen anions do not change their unit cell positions in a significant way (Δz < −0.03 Å). Thus, the face-centered cubic oxygen sublattice is almost intact during the

Table 4. Relaxation of the Undercoordinated Ions at the Spinel (100), (110) and (111) Planes Δz/Å Fe[CoFe]O4

Co[MnCo]O4

a-Co[Al2]O4

Co[NiCo]O4

Zn[Co2]O4

Co[Co2]O4

Mg[Co2]O4

Co[Al2]O4

Δd/Å

plane

A(M )

B(M )

O

M −O

MO−O

(100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (110) (111) (100) (110) (111)

−0.21 −0.05 −0.14 −0.19 −0.11 −0.17 −0.05 −0.05 −0.11 −0.24 −0.09 −0.14 −0.20 −0.05 −0.14 −0.22 −0.09 −0.15 −0.20 −0.11 −0.13 −0.22 −0.05 −0.14

−0.06 −0.06 −0.35 −0.04 −0.07 −0.37 −0.08 −0.09 −0.24 −0.06 −0.04 −0.23 −0.06 −0.06 −0.26 −0.05 −0.07 −0.25 −0.06 −0.05 −0.20 −0.06 −0.06 −0.07

−0.01 −0.02 −0.02 −0.02 −0.03 −0.03 −0.01 −0.02 −0.02 −0.01 −0.01 −0.01 −0.01 −0.02 −0.02 −0.01 −0.02 −0.03 −0.01 −0.01 −0.02 −0.01 −0.02 −0.03

−0.038 −0.029 −0.032 −0.012 −0.025 −0.091 −0.027 −0.031 −0.082 −0.025 −0.005 −0.058 −0.025 −0.013 −0.056 −0.048 −0.028 −0.105 −0.036 −0.036 −0.092 −0.071 −0.045 −0.078

−0.009 −0.011 −0.158 −0.019 −0.022 −0.146 −0.012 −0.018 −0.127 −0.004 −0.004 −0.077 −0.016 −0.009 −0.103 −0.014 −0.022 −0.090 −0.018 −0.024 −0.075 0.009 −0.011 −0.010

T

O

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Figure 4. HAADF-STEM pictures of (100), (110), and (111) cobalt spinel facets (a1, b1, and c1, respectively) with the imposed theoretically predicted facet atomic structures (a2, b2, c2: blue, cobalt; red, oxygen), together with the simulated images without (a3, b3, c3) and with noise (a4, b4, c4) added.

Table 5. DFT Surface Energies and Abundance (percentage contribution) of the Given Facet to the Overall Surface Area Calculated from the Corresponding Wulff Shapes (see below) (100)

(111)

A-(110)

B-(110)

spinel

γ /J m−2

abundance/%

γ /J m−2

abundance/%

γ /J m−2

abundance/%

Fe[CoFe]O4 Co[MnCo]O4 a-Co[Al2]O4 Co[NiCo]O4 Zn[Co2]O4 Co[Co2]O4 Mg[Co2]O4 Co[Al2]O4

1.0755 1.1654 1.321 1.2871 1.4846 1.4465 1.6402 1.1771

32.54 24.19 36.3 54.76 50.16 42.71 55.43 98.20

1.0157 1.0258 1.190 1.4182 1.5941 1.5018 1.8467 1.8686

67.46 75.81 63.7 38.25 42.98 47.71 35.79 1.80

1.4615 1.5557 1.645 1.6044 1.8129 1.6582 2.0304 1.6462

0.0 0.00 0.00 6.98 6.86 8.58 8.78 0.00

For the tetrahedral cations, the z-retraction follows the trend (100) > (111) ≫ (110); see Table 4. In case of the off-stoichiometric a-Co[Al2]O4 spinel, we observe two effects of the partial inversion. Replacement of the undersaturated octahedral aluminum ions by cobalt allows for better reconstruction of the (111) plane, reflected in a larger zshift (−0.25 vs −0.07 Å). On the other hand, tetrahedral AlT ions on the (100) surface exhibit the lowest z-shift among the all systems (−0.05 Å). As a result, the inversed aluminate cobaltite spinel has higher (100) surface energy and lower (111) surface energy than its normal counterpart. Taking the bare Co3O4 spinel as an example, the computed geometries of the relaxed (100), (110), and (111) terminations were used for simulation of the corresponding HAADF-STEM images and compared with experiment (Figure 4). The experimental HAADF-STEM images of the Co3O4 nanocrystals oriented along [100], [110] and [111] zone axes (obtained within near Scherzer focus conditions) are shown in parts a1, b1, and c1, respectively, of Figure 4. The corresponding DFT-predicted atomic structures for each plane are presented in the ball and stick representation (a2, b2, c2). They were used for simulation of the HAADF-STEM images without noise (a3, b3, c3) and with inclusion of the ∼40% noise (a4, b4, c4) to approach the experimental results. Along the [100] zone axis the experimental and simulated images (Figure 4a1,a4) can be associated directly with the atomic structure (Figure 4a2), even though the experimental image is a bit noisy. Bright spots are equivalent to the projected atomic columns, composed of the interlaced CoT, CoO, and O2− ions. Characteristic pattern with the 4-fold symmetry is also well-reproduced. The indicated an interplanar distance (d110 = 0.292 nm) corresponding to the (110) plane, in nice agreement with the calculated value.

γ /J m−2 1.9058 1.7507 1.9748 1.8917 2.1994 1.7507

abundance/% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

For the picture recorded along the [110] direction, the correspondence between the experimental picture and the atomic structure is much more involved (Figure 4b1,b2). In this projection, the atomic columns are constituted exclusively by the CoT, CoO, or O2− ions and are separated from each other by 1.93 Å (CoO−O), 1.81 Å (CoT−O), and 1.75 Å (CoT−CoO) (see Figure S5a, SI). Furthermore, a more in-depth insight into the spinel structure revealed that two types of CoO columns with different vertical interatomic distances (2.86 and 5.72 nm, called hereafter as A-CoO and B-CoT, respectively) can be distinguished (Figure S5b, SI). Since the intensity of the HAADF-STEM image depends on the scattering factor and the average atomic number of the projected atomic columns, at the applied imaging conditions and the thickness of the sample, the oxygen, CoT, and B-CoO columns of lower average vertical density are not visible. As a result, the bright spots in Figure 4b1 correspond to the A-CoO atomic columns. Indeed, the characteristic diamond pattern with the interspot distance of 4.95 Å and the acute angle of 70° agree very well with the DFTcalculated structure. The image simulation (Figure 4b3,b4, with and without noise included) fully confirms the interpretation of the observed image. The correspondence between the simulated and the experimental images is emphasized by the marked interplanar d111 distance of 0.484 nm (Figure 4b1,b4). In the case of the [111] orientation, similarly to [100], analysis of the experimental and the simulated images (Figure 4c) is again straightforward. The atomic columns observed in this projection are constituted by the interlaced CoT, CoO, and O ions, so they are all equivalent. The corresponding bright spots reproduce well the hexagonal pattern (Figure 4c1,c4) typical for this orientation. The interplanar distance for the (110) plane, equals to d110 = 0.292 nm, is in agreement with the Co3O4 structure. As a result, the remarkable agreement 19091



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trend breaks abruptly into two distinct regions at u = 0.262. For u < 0.262, 14-faceted polyhedra (Fe[CoFe]O4, Co[MnCo]O4, and a-Co[Al2]O4) were observed, whereas for u > 0.262, the shape changes into 26-faceted polyhedra (Co[NiCo]O4, Zn[Co2]O4, Co[Co2]O4, Mg[Co2]O4). On the basis of the calculated energies, the Wulff shapes can be constructed and next classified by means of a {100}− {110}−{111} morphodrom (the Gibbs triangle of crystal habits) of the faceted cubic spinels (Figure 6). It epitomizes the

between the theory and experiment justifies the adequacy of the adopted calculation scheme and the surface models as well. Next we calculated the relaxed surface energies for all terminations. The results are collected in Table 5. For the all computed structures, the surface energy increases in the sequence γ100 < γ111 < γ110, with the latter one being always dominant. The only exception was the inversed Fe[CoFe]O4 spinel, with γ111 < γ100 < γ110, exhibiting the lowest γ values for all terminations. Whereas, tetrahedral substitution enhances the surface energies, the octahedral one tends to decrease the γhkl values. Being inspired by the fact that the electrostatic Madelung energy of spinels depends critically on the oxygen parameter,21 we plotted the calculated γhkl values as a function of u to rationalize the obtained results in terms of simple structural tenets. The plot of γhkl versus u revealed the pronounced sensitivity of the surface energy on the oxygen parameter for the (111) plane (Figure 5a). For this face the energy rises

Figure 6. A {100}−{110}−{111} morphodrom of the faceted cubic (Fm3m) spinels (left panel) and projections of the calculated shapes along the [100], [110], and [111] zone axes, with the indicated characteristic angles (right panel).

morphology variations as a function of R1 = A100/(A100 + A111), R2 = A111/(A111 + A110), and R3 = A110/(A100 + A110), where Ahkl is the area of the particular hkl facet (Table 5). The corners of the triangle define the prime forms produced by one type of the facet only (hexahedron, octahedron, and rhombidodecahedron). The edges of the triangle correspond to the shapes constituted by two types of faces, whereas the inside of the triangle corresponds to polyhedra with three different planes exposed. For more detailed description of the {100}−{110}− {111} morphodrom, see the SI. The Wulff constructions for all the investigated spinels are presented in Figure 7. The upper panel corresponds to the structures without surface relaxation (rigid shapes). Since in all the investigated spinels the number of dangling bonds is the same, the relative surface energies of the rigid structures are quite similar, giving rise to the essentially similar doubly truncated (with {111} and {110} planes) hexahedron. Such NC shape with 26 facets are referred to as a rhombicubooctahedron, hereafter. Surface reconstruction leads to pronounced shape diversity (lower panel of Figure 7), which is confirmed experimentally (see below). It is significant only for the highly unsaturated surface ions and confined to the prevailing relaxation in the z-direction (Table 4). The Rn parameters for the equilibrium morphology of each spinel are collected in Table 6. Then, using the{100}−{110}− {111} morphodrom as a classification backbone, the calculated shapes can be divided into three groups. The rhombicuboctahedron shape can be attributed to Co[NiCo]O4, Zn[Co2]O4, Co[Co2]O4, and Mg[Co2]O4, with R1 ∈ ⟨0.472, 0.608⟩ and R2 ∈ ⟨0.803, 0.863⟩, placed in the region denoted by a (emphasized by orange shadowing) in Figure 6. Singly {100}truncated octahedra calculated for the Fe[CoFe]O4, Co[MnCo]O4, and a-Co[Al2]O4 spinels correspond to R1 ∈ ⟨0.242, 0.363⟩ and R2 = 1.0 and are marked by green shadowing (Figure 6b). Singly {111}-truncated hexahedron with only a minor abundance of the (111) plane (R1 = 0.98, R2

Figure 5. Surface energies (a), vertical relaxation Δz (b), and relative γ111/γ100 ratio (c) as a function of the u parameter.

monotonously, while for the other terminations the shallow minimum can be observed. Moreover, the surface energies of the (100) and (110) planes are less sensitive to variation of this parameter. Actually, there is a remarkable resemblance in the profiles of the (100) and (110) surface energy curves, with the (110) energy always being larger by about 15% than that of the (100) termination (see Figure 5a). The magnitude of the vertical relaxation of the unsaturated MO3c on the (111) surface, Δz, (Table 4), is related to the oxygen u parameter in the same way as γ111 (Figure 5b). A direct influence of the vertical relaxation on the γ111 value is even more clear while analyzing the plot γ111 vs Δz, which is evidently linear (Figure 5b, insert). For further analysis of the surface energies, the γ111/γ100 ratio was traced as a function of u (Figure 5c), and interestingly, the 19092



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Figure 7. Calculated Wulff shapes of the mixed cobalt spinels arranged in order of the increasing u parameter. The top row corresponds to the rigid surfaces, whereas the bottom row is the relaxed surfaces.

Table 6. Calculated Rn Parameters for the Equilibrium Morphology of the Investigated Spinels spinel

R1

R2

R3

Fe[CoFe]O4 Co[MnCo]O4 a-Co[Al2]O4 Co[NiCo]O4 Zn[Co2]O4 Co[Co2]O4 Mg[Co2]O4 Co[Al2]O4

0.325 0.242 0.363 0.589 0.538 0.472 0.608 0.982

1.000 1.000 1.000 0.846 0.863 0.848 0.803 1.000

0.000 0.000 0.000 0.113 0.120 0.167 0.137 0.000

the most informative [110] direction. As implied by the right panel in Figure 6, the remaining orientations are less helpful for shape retrieving. Fortunately, a preliminary inspection of the TEM images revealed that crystallites are oriented mainly along the diagnostic [110] direction. Comparison of the calculated Wulff shapes with the experimental TEM morphologies is shown in Figure 8 for the spinels with the rhombicuboctahedral NC shape. The actual shape of the synthesized spinels is a matter of thermodynamic, kinetic, and space confinement issues. However, for a meaningful comparison with the theoretical morphologies, only those not perturbed significantly by the surroundings with nearly equilibrium shapes were taken into consideration. Representative nanocrystallites for the all investigated spinels were selected from the larger population. A typical survey TEM picture is shown in Figure 8a for Zn[Co2]O4, as an example. As it can be seen, the synthesized spinels exhibit exclusively nanocrystals with the exposed {111}, {110}, and {100} facets. At higher magnifications, more accurate fitting of the theoretical Wulff shapes to the observed crystallites is more reliable, as shown in Figure 8b−d for the Mg[Co2]O4 (b), Co[Co2]O4 (c), and Co[NiCo]O4 (d) crystallites in the [110] orientation. The presence of octagons with 145° angles together with the absence of hexagons with the 110° angles univocally confirms the rhombicuboctahedral shape of the observed nanocrystals, in nice agreement with the theoretical predictions.

= 1.00) was predicted for Co[Al2]O4 (Figure 6c, blue shadowing). To compare the theoretical shapes with the morphologies of the investigated spinels, extensive TEM observations were performed. Despite the fact that the synthesized nanocrystals are not of perfect shape, owing to the constancy of the interfacial angles (Steno law), the inclinations of the malformed planes are the same as for the perfect crystals, so they may be used for reliable assignment of the faceting. First, we performed detailed analysis of the Wulff shape projections along the [100], [110], and [111] axes (Figure 6, right panel). Together with the indicated diagnostic angles (see SI), they allow for straightforward distinguishing between the rhombicuboctahedral (4 × 125° and 4 × 145°) and the truncated octahedral shapes (4 × 125° and 2 × 110°) for the grains projection along

Figure 8. TEM pictures of Zn[Co2]O4 (a), Mg[Co2]O4 (b), Co[Co2]O4 (c), and Co[NiCo]O4 (d). 19093



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mixed cobalt spinels, the abundance of the (110) faces is always low (below 9%), despite previous claims.4,52 Size Effect. To examine the size−shape relationship, the overall energy of the parent Co3O4 nanocrystals, ENC = Ebulk + Esurface, was plotted as a function of the grain size (expressed as the logarithm of the diameter of an equivalent cube with the same volume), for the rhombicuboctahedral, rhombidecahedral, octahedral, and hexahedral morphologies (Figure 10). In the

Contrary to the mixed cobalt spinels described above (Co[NiCo]O4, Zn[Co2]O4, Co[Co2]O4, and Mg[Co2]O4), in the case of the Co[Al2]O4, Co[MnCo]O4, and Fe[CoFe]O4 samples, survey TEM pictures revealed predominant hexagonal projections of the spinel NCs. Detailed pictures along two zone axes, [100] (Figure 9a,b), and [110] (Figure 9c−g), show that

Figure 10. Size dependence of the overall energy per ion of the Co3O4 nanocrystals with the rhombicuboctahedral, rhombidecahedral, octahedral, and hexahedral morphologies, together with the energy excess with respect to the equilibrium rhombicuboctahedral shape (inset).

case of very small grains (d < 10 Å), the influence of shape is quite large, strongly disfavoring the octahedral grains. It can be attributed mainly to the enhanced surface area to volume ratio (A/V = 7.35) in comparison to hexahedral, rhombidecahedral, and rhombicuboctahedral shapes (A/V = 6.00, 5.36, and 5.23, respectively). Even though the {110} termination exhibits the largest surface energy (Table 4), a favorable A/V ratio for the rhombidodecahedron makes the total energy only slightly larger than for the optimal rhombicuboctahedra. The total energy normalized to the number of ions (∼grain size) converges to the bulk energy density with increasing size, since the surface energy has a gradually vanishing contribution. Yet, the plot of the total energy of the grains as a function of the size relative to the total energy of the NC with the equilibrium shape revealed that as the crystallites grow the equilibrium shape is increasingly preferred due to concomitant development of the surface component (see inset in Figure 10). It provides a thermodynamic driving force that favors the experimentally observed spinel nanocrystals to assume the equilibrium shapes (Figures 8 and 9), if only the kinetic and confinement constraints are negligible.

Figure 9. TEM pictures of truncated octahedrons observed along the (100) direction: (a) Fe[CoFe]O4 (adapted from ref 88) and (b) Co[Al2]O4. TO shapes observed along the (110) direction: (c) Fe[CoFe]O4, (d) Co[MnCo]O4, (e) Co[MnCo]O4 (adopted from ref 86), and (f, g) Co[Al2]O4.

the spinel nanocrystallites assume truncated octahedral shapes. This can be inferred from the 110° and 125° angles observed for the [110] oriented crystals (see also Figure 6). For the cobalt aluminate an excellent agreement with the crystal shape predicted for a-Co[Al2]O4, distinctly different from that of Co[Al2]O4, confirms partial inversion (x = 0.25) of this spinel (Figures 7 and 9f,g), unraveling its pronounced shape sensitivity. Generally, the humidity has a minor influence on the morphology of the spinel nanocrystals, since the energetics of all the exposed planes is affected by the adsorbed water molecules to a proportional extent. This point has been discussed in detail elsewhere.46 The overall shape of spinel NC is preserved, but in the wet environment the abundance of the (111) plane slightly increases at the expense of (100) and (110) terminations. Once the polyhedral shapes of the spinel nanocrystals are determined, one can easily calculate the fractional abundance, theoretical total surface area, and surface concentration of the exposed cations from the surface area of the exposed planes (Table S3, SI). Such data are useful for calculation of turnover frequencies in catalysis or for establishing quantitative relationships between the preparation conditions and the profusion of the specific crystallographic facets that are most active. Remarkably, regardless the nature of the alien metal in the

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CONCLUSIONS Combining periodic DFT+U calculations and TEM/STEM studies, the three most stable, (100), (110), and (111), planes exposed by faceted mixed cobalt spinel nanocrystals were examined in detail. The structure of each termination was confirmed by atomic-resolution STEM imaging corroborated by computer simulation of the obtained pictures. The calculated surface energies together with the Wulff construction demonstrate that it is possible to predict accurately the equilibrium polyhedral morphologies of cobalt spinel nano19094



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(2) Gallino, F.; Di Valentin, C.; Pacchioni, G.; Chiesa, M.; Giamello, E. Nitrogen Impurity States in Polycrystalline ZnO. A Combined EPR and Theoretical Study. J. Mater. Chem. 2010, 20, 689−697. (3) Chizallet, C.; Costentin, G.; Lauron-Pernot, H.; Krafft, J.-M.; Che, M.; Delbecq, F.; Sautet, P. Assignment of Photoluminescence Spectra of MgO Powders: TD-DFT Cluster Calculations Combined to Experiments. Part I: Structure Effects on Dehydroxylated Surfaces. J. Phys. Chem. C 2008, 112, 16629−16637. (4) Xie, X.; Shen, W. Morphology Control of Cobalt Oxide Nanocrystals for Promoting their Catalytic Performance. Nanoscale 2009, 1, 50−60. (5) Mao, Y.; Park, T. J.; Zhang, F.; Zhou, H.; Wong, S. S. Environmentally Friendly Methodologies of Nanostructure Synthesis. Small 2007, 3, 1122−1139. (6) Cushing, B. L.; Kolesnichenko, V. L.; O’Connor, C. J. Recent Advances in the Liquid-Phase Syntheses of Inorganic Nanoparticles. Chem. Rev. 2004, 104, 3893−3946. (7) Qi, K.; Yang, J.; Fu, J.; Wang, G.; Zhu, L.; Liu, G.; Zheng, W. Morphology-Controllable ZnO Rings: Ionic Liquid Assisted Hydrothermal Synthesis, Growth Mechanism and Photoluminescence Properties. CrystEngComm 2013, 15, 6729−6735. (8) Pacholski, C.; Kornowski, A.; Weller, H. Self-Assembly of ZnO: From Nanodots to Nanorods. Angew. Chem., Int. Ed. 2002, 41, 1188− 1191. (9) Wang, L. B.; Song, L. X.; Dang, Z.; Chen, J.; Yang, J.; Zeng, J. Controlled Growth and Magnetic Properties of α-Fe2O3 Nanocrystals: Octahedra, Cuboctahedra and Truncated Cubes. CrystEngComm 2012, 14 (10), 21 3355−3358. (10) Geng, B.; Zhan, F.; Fang, C.; Yu, N. A Facile Coordination Compound Precursor Route to Controlled Synthesis of Co3O4 Nanostructures and Their Room-Temperature Gas Sensing Properties. J. Mater. Chem. 2008, 18, 4977−4984. (11) Piskorz, W.; Gryboś, J.; Zasada, F.; Zapała, P.; Cristol, S.; Paul, J.-F.; Sojka, Z. Periodic DFT Study of the Tetragonal ZrO2 Nanocrystals: Equilibrium Morphology Modeling and Atomistic Surface Hydration Thermodynamics. J. Phys. Chem. C 2012, 116, 19307−19320. (12) Dong, Y. M.; He, K.; Yin, L.; Zhang, A. M. A Facile Route to Controlled Synthesis of Co3O4 Nanoparticles and Their Environmental Catalytic Properties. Nanotechnology 2007, 18, 435602−1− 435602−6. (13) Polarz, S. Shape Matters: Anisotropy of the Morphology of Inorganic Colloidal ParticlesSynthesis and Function. Adv. Funct. Mater. 2011, 21, 3214−3230. (14) Yoshino, H.; Ohnishi, C. H.; Hosokawa, S.; Wada, K.; Inoue, M. Optimized Synthesis Method for K/Co3O4 Catalyst towards Direct Decomposition of N2O. J. Mater. Sci. 2011, 46, 797−805. (15) Wilczkowska, E.; Krawczyk, K.; Petryk, J.; Sobczak, J. W.; Kaszkur, Z. Direct Nitrous Oxide Decomposition With a Cobalt Oxide Catalyst. Appl. Catal. A: Gen. 2010, 389, 165−172. (16) Amrousse, R.; Tsutsumi, A.; Bachar, A.; Lahcene, D. N2O Catalytic Decomposition over Nano-Sized Particles of Co-Substituted Fe3O4 Substrates. Appl. Catal. A: Gen. 2013, 450, 253−260. (17) Li, W. Y.; Xu, L. N.; Chen, J. Co3O4 Nanomaterials in LithiumIon Batteries and Gas Sensors. Adv. Funct. Mater. 2005, 15, 851−857. (18) Woodhouse, M.; Herman, G. S.; Parkinson, B. A. Combinatorial Approach to Identification of Catalysts for the Photoelectrolysis of Water. Chem. Mater. 2005, 17, 4318−4324. (19) Wang, G. X.; Liu, H.; Horvat, J.; Wang, B.; Qiao, S. Z.; Park, J.; Ahn, H. Highly Ordered Mesoporous Cobalt Oxide Nanostructures: Synthesis, Characterisation, Magnetic Properties, and Applications for Electrochemical Energy Devices. Chem.−Eur. J. 2010, 16, 11020− 11027. (20) Fu, L.; Liu, Z.; Liu, Y.; Han, B.; Hu, P.; Cao, L.; Zhu, D. Beaded Cobalt Oxide Nanoparticles Along Carbon Nanotubes: Towards More Highly Integrated Electronic Devices. Adv. Mater. 2005, 17, 217−218. (21) Smith, W. L.; Hobson, A. D. The Structure of Cobalt Oxide, Co3O4. Acta Crystallogr. B 1973, 29, 362−364.

crystals that are in an excellent agreement with experimental TEM results. Regardless of the nature of the alien metal in the mixed cobalt spinels, the abundance of the (110) faces is always low (below 9%). The oxygen u parameter allowed for simple rationalization of the energies of the relaxed facets in a concise way. The predicted shapes of the spinel nanocrystals were quantified and categorized into singly and doubly truncated hexahedra (rhombicuboctahedra) and truncated octahedra using a {100}−{110}−{111} Gibbs triangle of crystal habits for the cubic spinels. As far as we know, this paper is the first attempt to explain the shape of faceted mixed cobalt spinel nanocrystals in a systematic way by means of ab initio calculations combined directly with experiment.

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ASSOCIATED CONTENT

S Supporting Information *

(1) DFT calculationslab models for spinel planes, (2) synthesis and characterization of spinel samples, (3) spinel surface reconstruction, (4) HAADF-STEM images interpretation, (5) surface energetics of rigid and relaxed terminations of spinel crystallites, (6) the {100}−{110}−{111} morphodrom of the faceted cubic spinels, (7) projections of the spinel equilibrium shapesdiagnostic angles, and (8) the surface concentration of the exposed cations for investigated spinel systems. This material is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +48 12 663 20 73. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Iuventus Plus project of the Polish Ministry of Science and Higher Education (Grant No. 0633/IP3/2011/71). The research was carried out with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Programme (contract no. POIG.02.01.00-12-023/08). Z.S. dedicates this paper to Andreas Schramm from Berlin on the occasion of his 60th anniversary.

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ABBREVIATIONS USED BG, band gap; DFT+U, density functional theory with Hubbard-corrected functionals; GGA, generalized gradient aproximation; HAADF, high-angle annular dark-field; NC, nanocrystals; SI, Supporting Information; STEM, scanning transmission electron microscopy; TEM, transmission electron microscopy.

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REFERENCES

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