Vibrational and electronic peculiarities of NiTiO₃ nanostructures inferred from first principle calculations

Abstract

Structural, electronic and vibrational properties of nanostructured (NiTiO₃)_n clusters were calculated by numerical models based on DFT and semi-empirical quantum chemistry codes. The clusters were built by using the initial atomic positions of crystalline ilmenite, which were relaxed to ensure stable and energetically favourable geometries. For the electronic properties, the semi-empirical PM6 parameterisation method was used to evaluate the HOMO–LUMO energy differences versus nanocrystal sizes. The quantum confinement effect was induced with cluster size reduction. Theoretical UV-Vis absorption and Raman spectroscopy showed the drastic influence of the surface characteristics on the electronic and the vibrational properties of the nanoclusters. Theoretically, it was proved that powder NiTiO₃ exhibits a patchwork of the properties of the bulk ilmenite material, amorphous Ni–Ti–O structures and atoms located at the surface of the investigated cluster.

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Introduction

Photocatalytic processes have been intensively discussed and investigated in the last two decades, due to their potential applications in solving problems of waste in the environment or alternatively in creating new sources of energy.^1,2 For example, it can be mentioned that photocatalytic reactions contribute to the remediation of environmental pollution by the degradation of organic compounds or to the production of hydrogen by the dissociation of water for renewable energy.^3–9 These processes are based on photoinduced charge transfers caused by light sources (visible or UV) in the semiconducting oxides.

Beyond its applications in photovoltaic devices, titanium dioxide (TiO₂) is one of the most efficient materials for photocatalytic reactions and possesses the best performance, associated with its good stability, versatile applications, non-toxicity and low cost.^10–12 Photocatalytic reactions using TiO₂ under UV irradiation have been carried out to remove different types of impurities from wastewater.^13–16 The kinetics of the reactions are characterized by short relaxation times to achieve the complete removal of pollutants. However, the need for UV to induce the required charge transfer in the mentioned reactions limits the performance of TiO₂. Therefore, photocatalytic materials that operate under visible light irradiation are of interest, since the solar light spectrum can be exploited on a large scale to activate high performance photocatalytic reactions.

The perovskite-type oxides, such as tantalates and titanates, have recently attracted much attention, because of their high photocatalytic activities under UV irradiation and, more remarkably, under visible light.^17–19 These titanates, such as ATiO₃ (A = Ca, Bi, Pb, Fe, Co, Mn, Ni, Cu, and Zn) have been studied as functional inorganic materials with many applications as electrodes for solid oxide fuel cells, metal–air barriers, gas sensors, solid lubricants, and high-performance catalysts.^20–22 Among these materials, we consider the transition metal titanates, such as FeTiO₃, CoTiO₃, MnTiO₃, NiTiO₃, etc., that crystallize in the ilmenite structure under atmospheric pressure.^23–26 They are of particular interest due to their versatile electrical and magnetic properties, such as their antiferromagnetic behavior.^27,28 The related properties of several titanate oxides have been investigated experimentally and theoretically. FeTiO₃ is of interest as a natural mineral and a major source of titanium for the commercial production of TiO₂. The electronic, magnetic, structural and elastic properties of bulk FeTiO₃ have been computed using the density functional theory (DFT) formalism and ab initio calculations.^23–25 Within such approaches, the electronic ground-state properties and the charge transfer involved in FeTiO₃ were determined by the strong coupling of the structure with the charge distribution. The quantum-mechanical description of these features is very sensitive to the treatment of electronic exchange and correlation energies. This allows us to conclude that the metal titanates are strongly correlated systems and therefore the electron correlation part should be taken into account sufficiently.

The present work reports theoretical approaches to model the nanostructures and simulate the electronic and vibrational properties of NiTiO₃ nanoclusters. Comparative studies were also performed by using bulk crystal, with its infinite and periodic structure. Previous theoretical approaches developed by Xin et al.²⁹ were used to compute the electronic properties of the bulk and infinite NiTiO₃ system. However, to the best of our knowledge no particular models have been developed to compute and predict the physical properties of the NiTiO₃ nanostructures. The study of nanosized systems, with regard to the critical role of the specific active surface in physical phenomena, is of great interest. Particularly, because the interfaces between the active material and the surrounding media contribute critically to the efficiency of heterogeneous catalysis. However, developing theoretical models and numerical simulations to predict the electronic, optical, structural, vibrational and related properties of nanoparticles is a challenging task. The numerical approach presented here was partially used in our former studies devoted to functional semiconducting systems.^30–32 The nanostructures were built from their native bulk crystals with specified atomic positions as involved in defined space groups. Also, in this work, the modeling of bulk systems is of primary importance in developing the methodology for establishing the structural, vibrational and electronic properties of nanostructures. The quantum chemical calculations were based on first-principles calculations using the ultrasoft pseudopotential of the plane-wave within the DFT formalism. The generalized gradient approximation extended by Hubbard parameters was used to evaluate the electronic properties of the NiTiO₃ bulk crystal.

The original task in this work consisted of modeling the crystal structure at the nanoscale, including the relaxation of the outermost surface atoms with suitable treatment. The changes in their electronic and vibrational properties were accurately described as a function of the structural features of the investigated nanoclusters. Also the influence of the surface on the physical properties of the clusters was demonstrated. The simulation of electronic band structures clarified the charge transfer characteristics. This approach paves the way to elucidating the mechanisms behind the photocatalytic activity of the nanosized NiTiO₃ materials. The theoretical results are compared to the data obtained by experimental investigations of the relevant features of NiTiO₃ nanostructures.

Computational details and cluster building methodology

The crystal structures were computed for two different configurations of the material. One of them was considered to represent the bulk NiTiO₃ monocrystal crystallized in the ilmenite phase; i.e. space group R3̄ (no. 148).³³ The second was chosen to be a nanocrystalline cluster of varying size, possessing the ilmenite structure in the core. Therefore, the unit cell of ilmenite NiTiO₃ was built using the cell parameters a = b = 5.0289 Å, c = 13.7954 Å and the angular parameters α = β = 90° and γ = 120°. The positions of representative atoms within the unit cell are summarized in Table 1. The crystal structure of NiTiO₃ was built using the Materials Studio Program Package. The same simulation software was used to build the (NiTiO₃)_n nanostructures with diameters from 0.6 nm up to 2.6 nm, associated with clusters composed of (NiTiO₃)₂ and (NiTiO₃)₁₈₃ units, respectively. Consequently, all of the investigated nanocrystals exhibited spherical shapes and stoichiometric compositions. According to our previous work on other classes of nanocrystalline systems, dangling bonds were not specially saturated.³¹ The unit cell of the monocrystal and the morphology of the (NiTiO₃)₈₂ cluster are depicted in Fig. 1.

Table 1 Lattice parameters and atomic fractional coordinates of the NiTiO₃ crystal structures

Atom name	x/a	y/b	z/c
Ni	0	0	0.3499(1)
Ti	0	0	0.1441(1)
O	0.3263(7)	0.0214(10)	0.2430(3)
Cell parameters	a = b = 5.0289(1) Å, c = 13.7954(2) Å, α = β = 90°, γ = 120°
Space group	R3̄ (no. 148)

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Fig. 1 The unit cell of crystalline NiTiO₃ (left) and the unpassivated nanocrystalline structure made by the formula (NiTiO₃)₈₂ (right).

The electronic properties of the NiTiO₃ single crystal were calculated using the DFT methodology. The quantum chemical calculations were performed using the Cambridge Serial Total Energy Package (CASTEP);³⁴ i.e. the module of the Materials Studio Program. The CASTEP is based on the evaluation and analysis of the total energy inferred from the plane-wave pseudopotential method. The first task deals with the geometry optimisation of the investigated crystal structure, which is built and evaluated with respect to the total energy minimization within the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.³⁵ During the geometry optimisation procedure, the symmetry of the structure was frozen but the size of the unit cell was allowed to change. The convergence criteria for the optimization procedure were chosen as hereafter outlined. The convergence of the total energy during the geometry optimization procedure cannot be greater than 2 × 10⁻⁵ eV per atom, the force on the atom must be less than 0.01 eV Å⁻¹, the stress on the atom less than 0.02 GPa and the maximal atomic displacement no more than 5 × 10⁻⁴ Å. The electron exchange–correlation energy was treated within the framework of the generalized gradient approximation (GGA) using Perdew–Burke–Ernzerhof (PBE)³⁶ potential. To accelerate the computational runs, the ultrasoft pseudopotential formalism was used. In this frame, calculations were performed for Ti (3d² 4s²), Ni (3d⁸ 4s²) and O (2s² 2p⁴) electrons. The cut-off energy of the plane-wave basis set was chosen to be equal to 500 eV. The integration by numerical sampling for specific directions over the Brillouin zone (BZ) were carried out using the Monkhorst–Pack method with an 8 × 8 × 8 special k-point mesh. The total energy convergence criterion was assumed to be fulfilled when the self-consistent field (SCF) tolerance; i.e. equal to 10⁻⁵ eV per atom.

The electronic properties of the NiTiO₃ crystal were computed using the above-mentioned parameters, as specified for the geometry optimization procedure. The calculations were carried out in spin restricted as well as spin unrestricted procedures, applying the GGA/PBE potential and Heyd–Scuseria–Ernzerhof (HSE06) range-separated hybrid functional.^37,38 Hummer et al.³⁹ showed that the HSE06 functional yields the correct electronic band structure for the semiconductors of group-IV. Also the work of Śpiewak et al.⁴⁰ shows that the HSE06 potential may better reproduce the electronic properties of Ge single crystals with defects. Contrary to this, other works indicate that the range-separated functionals show improvements for strong charge transfer systems.^41,42 It is generally known that classical DFT potentials do not correctly reproduce far-nucleus asymptotic behaviour^43,44 and underestimate the excitation energies, notably for charge transfer processes.⁴⁵ The range-separated potentials lead to the partitioning of the total exchange energy into short-range and long-range contributions:

E_X = E^sr_X + E^lr_X. (1)

To improve the exchange functional, in terms of calculating the long-range electron–electron interactions using the HF exchange integral, the standard error function is used. The repulsion electron operator is also divided into short-range and long-range parts and can be defined for two electrons at the r_ij distance as:

where the α and β parameters define the exact exchange percentages between the short and long-range exchange functional. μ represents the weighting factor, which controls the separation between the short-range exchange functional and the long-range part of the HF exchange integral.

The Kohn–Sham equation was also solved using the GGA/PBE functional extended by the Hubbard parameters. The introduced methodology contributes to precise insights into the electronic properties of the material. The major drawback of all functionals lies in the underestimation of the calculated electronic band gap.⁴⁶ This is frequently encountered due to the approximate calculations of the electron self-interaction energies. Also, pure local density approximations (LDA),⁴⁷ generalized gradient approximations (GGA)⁴⁸ and even hybrid functionals^49–51 can lack precision in some instances, due to so-called “strongly correlated” systems.

One relevant solution for describing correlated electrons in solids concerns the Hubbard model,⁵² based on an extended LDA approach, also referred to as LDA + U. It decreases the electron self-interaction error by selectively adding an energy correction to localized electron states, such as d or f orbitals where the self-interaction is particularly large. To construct an appropriate functional, the LDA + U approach subdivides the charge density into two subsystems with delocalized and localized features. In the multiband Hubbard model the effective LDA + U energy functional is written as:

E_LDA+U = E_LDA + E_HF(n_μν) − E_dc(n_μν) (3)

where E_LDA denotes the standard LDA energy functional, E_HF is the Hartree–Fock (HF) functional, E_dc is the double counting term and n_μν is one particle density matrix. The HF part can be written as follows:where the U₁₃₂₄ terms represent the renormalized Coulomb integrals. In the LDA + U approach, the Kohn–Sham equation is supplemented by the non-local potential. On the other hand, the DFT/Hubbard method fails to compute the correct energy difference between systems with localized/correlated and delocalized/uncorrelated electronic states.⁵³ In such an approach, the LDA/GGA + U methodology has successfully been applied to compute the electronic properties of different ternary oxides, such as CuAlO₂,⁵⁴ CuAl₂O₄,⁵⁵ Pr₂Ti₂O₇ or Ce₂Ti₂O₇,⁵⁶ and MnFe₂O₄.⁵⁷ Based on the outlined theoretical framework, the influence of the Hubbard parameter U on the electronic properties of NiTiO₃ was investigated for the crystalline structure in bulk material or in nanosized clusters, taking into account the strong correlation of the d-orbital electrons.

In the present work, the electronic properties of the (NiTiO₃)_n nanoclusters were also calculated. To our knowledge, it is first time that nickel titanate nanostructures have been studied theoretically. The methodology requires two different calculation codes to perform the simulations and also to ensure their stability. Thus, the Gaussian09 and MOPAC (Molecular Orbital PACkage)⁵⁸ quantum chemistry programs were used. With regard to the size of the investigated clusters, semiempirical single point calculations were performed, applying the parameterized self-consistent restricted HF (SCF RHF) PM6 method.⁵⁹ The convergence of the SCF procedure was achieved with an energy uncertainty not greater than 10⁻⁶ hartrees and no more than 150 required iterations. Within such approaches, the electronic properties of two different cluster families were computed. The first one deals with (NiTiO₃)_n clusters possessing an ilmenite crystal structure without any reconstruction. The second considers the same clusters as specified previously, but their geometries were optimised according to the total energy minimization. The geometry of all clusters was specified in Cartesian coordinates with C1 symmetry. The gradient convergence tolerance was equal to 10⁻⁶ hartrees bohr⁻¹ using the quadratic approximation (QA) method,^60–62 updating the Hessian matrix during the optimization. The Hessian evaluation was performed to exclude the structures giving rise to negative frequency modes.

Results and discussion

Structure and electronic properties of bulk ilmenite NiTiO₃

The GGA/PBE functional was used to build the stable NiTiO₃ crystal geometry and to calculate the related physical responses. In the first step, the geometry optimization of the crystal structure was performed. The changes to the optimised atomic distances were less than 5% compared to the starting values from the defined crystallographic data. It is in agreement with the former report by Xin et al.²⁹ The noticed departures from these values could be attributed to the fact that the present calculations were performed at T = 0 K, whereas the experimental structural data measurements were generally performed at room temperature. Thus, the relatively low deviation between the optimized values and experimental structural data indicates that GGA/PBE is a suitable computational functional for the description of the structures of the NiTiO₃ crystal. Following the performed geometry optimization, one may conclude that the ilmenite NiTiO₃ structure appears as the layered organisation depicted in Fig. 2 (left-hand panel), where Ti and Ni atoms form the layers separated by oxygen atoms.

Fig. 2 Primitive unit cell of NiTiO₃ (left) and the corresponding reciprocal lattice (right) with the coordinates of the special points of the BZ: F (1/2, 1/2, 0); Γ (0, 0, 0); K (1/4, 1/4, 1/4) and Z (1/2, 1/2, 1/2).

The electronic properties of the NiTiO₃ crystal were computed within the spin polarized approach for a primitive unit cell (see Fig. 2). The band structure calculations were performed in the k space within the BZ directions shown in Fig. 2 (right-hand panel). The DFT/HSE06 functional gives unsatisfactory results. The obtained energy gap is equal to 1.23 eV, whereas the experimental data are within 2.12–2.18 eV.^63–65 Also, the DFT/PBE functional was considered with and without the Hubbard approximation. The mentioned functional without the Hubbard approximation and in the spin polarized regime gives an energy gap equal to 0.77 eV for the NiTiO₃ crystal. This shows that using nonempirically tuned range-separated DFT methods results in a significant improvement over traditional GGA functionals but does not give good results for the studied crystal. The large discrepancies suggest the presence of strongly correlated electrons from the considered (Ti and Ni) ions, leading to the necessity to explore the Hubbard approximation in such systems. Within the approach based on the DFT/PBE potential, the electron density depicted in Fig. 3 also informs us about the covalent character of the O–Ti, O–Ni and Ti–Ni bonds. This behavior indicates the nature of the strongly correlated system and the necessity to develop the theoretical functional to reconcile the predicted electronic features with the experimental findings.

Fig. 3 Electron density projection in a selected plane of the NiTiO₃ ilmenite structure.

The functional modified by the Hubbard approximation uses parameters that can be chosen for Ti 3d and Ni 3d valence electrons in order to evaluate the energy band gap values. The influence of the chosen Hubbard parameter U on the obtained band gaps is demonstrated in the summary in Table 2. The correct evaluation of the electronic behaviour, in agreement with experimental findings, requires fixed Hubbard parameters at 3.5 eV and 4.5 eV for Ti 3d and Ni 3d electrons, respectively. Thus, the DFT/PBE + U method may provide a satisfactory qualitative electronic structure calculation with the correct choice of the Hubbard parameters. The electronic band structure computed with U_Ti = 3.5 eV and U_Ni = 4.5 eV is presented in Fig. 4. This plot indicates that the NiTiO₃ structure exhibits a direct semiconducting nature with an energy gap equal to 2.33 eV. Its spin polarized character is also included in the predicted electronic features. Thus, the top of the valence band is constituted by spin polarized alpha electrons while the bottom of the conduction band is composed of the beta state. In addition, the partial density of states depicted in Fig. 5 shows that the spin polarized alpha electrons with energies at the top of the valence band derive from the hybridization of Ni 3d and O 2p orbitals; while hybridization of the Ti 3d and Ni 3d states defines the electronic structure at the bottom of the conduction band, in agreement with the previous work of Salvador et al.⁶⁶

Table 2 Hubbard U parameter values for the Ti d and Ni d orbitals and the energy gap value calculated by the DFT/PBE + U methodology

Ti 3d	Ni 3d	Eg [eV]
0	0	0.77
2.5	2.5	1.75
3.5	4.5	2.33
4.5	3.5	1.94
4.5	4.5	2.46

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Fig. 4 Electron band structure calculated by the DFT/PBE functional within the Hubbard approximation U. The energy levels with spin polarized alpha electrons (black) and energy levels with a beta state (red) are shown.

Fig. 5 Electron density of state (DOS) calculated for the NiTiO₃ ilmenite structure by using the DFT/PBE functional augmented by the Hubbard approximation: polarized alpha electrons (top) and beta electrons (bottom).

The energy dispersion of the electronic states allows us to calculate the effective masses of charge carriers. The diagonal elements of the effective mass tensor for electrons and holes are calculated as the energy derivatives around the K point of the BZ, following the equations:

The effective mass of electrons and holes is determined by fitting the conduction and valence bands (see Fig. 4), respectively, to parabolic functions. One may see that the top of the valence band and bottom of the conduction band are symmetric around the K point of the BZ. In this case, the calculated effective masses of the electrons and holes are equal to m^*_e = 2.0986m_e and m^*_h = 0.6836m_e, with the same values in both the K–Z and K–Γ directions of the BZ. The relatively high values of the reported parameters suggest that the mobility of charges in the investigated NiTiO₃ single crystal is relatively low. This result is of particular importance for the very low electrical conductivity (10⁻⁹ S m⁻¹) achieved in NiTiO₃ at moderate temperatures up to 200 °C.⁶⁷ The performed calculations confirm that in the studied material the electrical conduction observed at temperatures below 700 K seems to be extrinsic, governed by impurities, interstitial sites, etc. It takes place via the small polaron hopping mechanism.⁶⁴

Nanocrystalline ilmenite NiTiO₃ clusters

Structural and electronic features. Structural and electronic properties of NiTiO₃ nanocrystals were investigated for nanoparticles made of the ilmenite bulk material. The investigated nanostructures possess a spherical shape with a variable number of (NiTiO₃)_n units, from n = 2 up to 183. The single point DFT/PBE and DFT/HSE06 calculations were performed for clusters with n from 2 up to 20, but the results did not show the correct behaviour of the energy difference between the highest unoccupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) versus the size of the cluster. It is known that the standard DFT scheme is not useful for finite-sized objects because the asymptotic potential, absent in the bulk material, plays a crucial role in the cluster energy due to the addition and removal of electrons. This leads to the calculated energy gaps for finite-sized objects often being much smaller than the real gaps.⁶⁸

Contrary to the results obtained by DFT, the PM6 semi-empirical methodology was successfully applied for such clusters, leading to the correct estimation of the energy gap in nanosized NiTiO₃. In Fig. 6, the computed energy differences ΔE_HOMO–LUMO versus the cluster sizes are depicted. The reported energy gap splitting as a function of the (NiTiO₃)_n units demonstrates the size induced quantum confinement effect. This is in agreement with the experimental report⁶⁹ on NiTiO₃ nanoparticles that give rise to a blue shift in the absorption spectra compared to the bulk material. The ΔE_HOMO–LUMO value reaches saturation for clusters comprising n ≥ 50 (NiTiO₃)_n units. The energy gap value for the large clusters saturates at 2.55 eV.

Fig. 6 Evaluation of the ΔE_HOMO–LUMO energy splitting versus number n of (NiTiO₃)_n units calculated by the PM6 methodology.

Using the PM6 model, UV-Vis absorption spectra were computed for selected clusters, namely (NiTiO₃)₂, (NiTiO₃)₈ and (NiTiO₃)₁₇. Large clusters were not considered due to the memory limitations of the computer system. The calculated spectra are presented in Fig. 7, along with the experimental data. A good agreement is demonstrated between the spectrum calculated by the PM6 model for the (NiTiO₃)₁₇ cluster and the measured one for the crystalline powder of NiTiO₃. Increasing the cluster diameter (unit number n = 2–17), the position of the A band (see Fig. 7 left-hand panel) shifts to the red spectral range. The band labelled B, with pronounced intensity for small clusters, undergoes a red shift and decreases notably in intensity with increasing cluster size. For the cluster (NiTiO₃)₁₇ with a diameter of 1.20 nm an additional broad peak C develops in the range 750–900 nm. The broad band in that spectral range was also demonstrated experimentally. The UV-Vis spectrum calculated for the bulk crystal NiTiO₃ by using the DFT/PBE + U functional (see Fig. 7, upper right-hand panel) did not match that obtained experimentally in the high wavelength range, where the C band is involved. This confirms that the surface effect in the experimental absorption spectrum of the NiTiO₃ powders plays a key role.

Fig. 7 UV-Vis absorption spectra calculated by the PM6 model for different clusters (left-hand panel), the spectrum calculated for the bulk crystal by using the DFT/PBE + U functional (upper right-hand panel) and the experimentally obtained data (lower right-hand panel).

The HOMO and LUMO orbitals, depicted in Fig. 8, for the investigated clusters (NiTiO₃)₂, (NiTiO₃)₈ and (NiTiO₃)₁₇, show their explicit separation and contribute to the low energy absorption spectra. The separation feature between HOMO and LUMO orbitals is not seen for the bulk NiTiO₃, where the valence and conduction bands are attributed to the orbitals expanded through the volume of the crystal. The observed details suggest that the separation of the HOMO and LUMO orbitals gives rise to B and C bands.

Fig. 8 HOMO and LUMO orbitals calculated by the PM6 model for the (NiTiO₃)₂, (NiTiO₃)₈ and (NiTiO₃)₁₇ clusters.

The comparison of the theoretical and the experimental UV-Vis absorption spectra of the (NiTiO₃)₁₇ nanocluster clearly indicates the interesting optical activity of the system in the UV and the visible range of the solar spectrum. A broad absorption edge situated at ∼410 nm is associated with O²⁻ → Ti⁴⁺ charge transfer transitions. The higher wavelength shoulder is associated with the crystal field splitting of NiTiO₃, giving rise to the Ni²⁺ → Ti⁴⁺ transitions.⁷⁰ Thus, for the nanosized NiTiO₃, the photoinduced charge transfers that are required for photocatalytic reactions may be ensured by several electronic transitions covering the UV and visible light range. These contribute to the efficient photocatalytic activity. Finally, it is worth noting that the resolved details on the theoretical absorption spectra are induced by calculations performed without any influence from the temperature on the structural relaxation of the NiTiO₃ clusters. The possibility of reconciling the shapes of the absorption bands between the theory and experiments may be realized through the electron–phonon interactions and the Franck–Condon rule for the optical transition probabilities, as was used in our previous work.⁷¹

Raman spectroscopy of nanocrystalline NiTiO₃. Taking into account the effect of electron–phonon interactions, the evaluation of the Raman spectra related to the selected clusters were performed using the PM6 approach. The Raman spectra were calculated using the standard procedure implemented in the Gaussian program package. The calculations were performed on two (NiTiO₃)₁₇ clusters. In one of these, the ilmenite crystal structure was frozen and the other system possessed a surface reconstructed using the geometry optimization procedure according to the total energy minimization criterion. The last cluster was characterized by a completely amorphous network. The experimental and calculated Raman spectra modeled for the (NiTiO₃)₁₇ nanoclusters and for the NiTiO₃ powder are depicted in Fig. 9.

Fig. 9 Raman spectra for the (NiTiO₃)₁₇ nanoparticles calculated by the parametrised PM6 method as well as experimental spectrum.

For the cluster (NiTiO₃)₁₇ with a primarily ilmenite structure, the calculations show only a single mode at position C. The experimental Raman spectrum shows an intense band with a wavenumber position in agreement with the calculated value. The C band is also the most intense detail in the experimental Raman spectrum. The titanates, such as NiTiO₃, CoTiO₃ and Na₄TiO₄, possess hexacoordinated Ti–O–Ti groups and their Raman modes are associated with the main band, located at 705, 688, 737 cm⁻¹, respectively.^72–74 Therefore, it was established that the Ti–O–Ti stretching mode should appear in the vicinity of 700 cm⁻¹. For NiTiO₃, the band at 720 cm⁻¹ corresponds to the Ti–O–Ti vibration of the crystal structure.

The Raman bands named A, B and D, with relatively low intensities compared to the C band, are associated to the full optimization and relaxation of the nanocluster structures. This procedure, which leads to stable amorphous networks, ensures molecular bonding distortions, including changes to bond lengths and angles. Such structural changes modify the vibrational features and, as shown experimentally and theoretically, cause new Raman bands to appear. A superposition of the main Raman band (90%) for O–Ti–O stretching and the secondary bands (10%) related to the amorphous structure leads to a theoretical Raman spectrum that reproduces the features of the experimental one. The slight departures from the experimental band positions may be explained by the fact that anharmonic vibration terms were not considered in the calculation model. The main origin may be related to bond frequency distributions due to amorphization or the occurrence of vacancies or antisites contributing to the damping and frequency shifts of Raman modes.^75,76 In this frame, it was proved that the bands located at 617 and 690 cm⁻¹ originate from the stretching of Ti–O and bending of O–Ti–O bonds, while the contribution at 547 cm⁻¹ results from Ni–O bonds.⁶⁹

As illustrated from the theoretical analysis and the experimental Raman investigations, the organization of the powder material is fully accounted for in the analysis that has been carried out. The particle core brings the signature features of the infinite and bulk crystal, while the outermost particle surface accounts for the amorphous features. This is presumably due to the manifestation of surface states with the relaxation and reconstruction of the outermost particle layers.

Conclusions

The electronic, optical and vibrational properties of (NiTiO₃)_n nanostructures were investigated and compared to those of bulk ilmenite NiTiO₃. The investigated nanostructures possess a spherical shape with the number of (NiTiO₃)_n units modified from n = 2 up to 183. The PM6 semi-empirical methodology was able to provide a valuable estimation of the energy gap in nanosized NiTiO₃ structures. The value of the ΔE_HOMO–LUMO saturates at 2.55 eV for the clusters comprising at least n = 50 (NiTiO₃)_n units. The UV-Vis absorption spectra were calculated using the PM6 methodology for nanostructures and compared with those obtained experimentally. The obtained spectra confirm that the surface effects in NiTiO₃ powders contribute with additional band edges. The comparison of the theoretical and the experimental UV-Vis absorption spectra obtained for the (NiTiO₃)₁₇ nanocluster clearly indicates the promising optical activity of the system in the UV and the visible range of the solar spectrum. The NiTiO₃ nanoclusters also exhibit other relevant properties required for efficient photocatalysis.

The calculated Raman spectra for the NiTiO₃ clusters show the noticeable contribution of the surface to the vibrational properties. Among the features of the Raman spectra, those related to active modes of the ilmenite structure and those inferred from amorphous NiTiO₃ can be distinguished. The theoretical superposition of a Raman band that constitutes 90% of the band intensity, and is associated with the O–Ti–O stretching mode, and secondary less intense bands (10%), related to the amorphous structure, represents the main features of the experimental spectrum.

Finally, the present work points out the relevant optical properties of the NiTiO₃ clusters that allow them to harvest visible light for efficient photocatalytic reactions. However, the low mobility of charge carriers, demonstrated from the effective mass estimation, leaves open questions that can be solved using a doping procedure. This is a matter of current development.

Acknowledgements

Calculations have been carried out in Wroclaw Center for Networking and Supercomputing <http://www.wcss.wroc.pl> (Grant no. 171). The MATERIALS STUDIO package was used under POLAND COUNTRY-WIDE LICENSE. The authors acknowledge the financial support of Polonium program 31300 TA – 2014 for researchers’ mobility. Marco Ruiz acknowledges the doctoral school 3MPL and CONACyT-Mexico for the financial support.

Notes and references

1. L. Linsebigler, G. Lu and J. T. Yates Jr, Chem. Rev., 1995, 95, 735.
2. K. Nakata and A. Fujishima, J. Photochem. Photobiol., C, 2012, 13, 169.
3. S. Bagwasi, B. Tian, J. Zhang and M. Nasir, Chem. Eng. J., 2013, 217, 108.
4. C. L. Torres-Martinez, R. Kho, O. I. Mian and R. K. Mehra, J. Colloid Interface Sci., 2001, 240, 525.
5. A. Di Paola, E. García-López, G. Marcì and L. Palmisano, J. Hazard. Mater., 2012, 211–212, 3.
6. Y. Liu, G. Su, B. Zhang, G. Jiang and B. Yan, Analyst, 2011, 136, 872.
7. D. Deng, S. T. Martin and S. Ramanathan, Nanoscale, 2010, 2, 2685.
8. M. M. Khin, A. Sreekumaran Nair, V. Jagadeesh Babu, R. Murugan and S. Ramakrishna, Energy Environ. Sci., 2012, 5, 8075.
9. K. Ariga, S. Ishihara, H. Abe, M. Lia and J. P. Hill, J. Mater. Chem., 2012, 22, 2369.
10. X. B. Chen, L. Liu, P. Y. Yu and S. S. Mao, Science, 2011, 331, 746.
11. J. Thomas, K. P. Kumar and S. Mathew, Sci. Technol. Adv. Mater., 2011, 3, 59.
12. X. J. Xu, X. S. Fang, T. Y. Zhai, H. B. Zeng, B. D. Liu, X. Y. Hu, Y. Bando and D. Golberg, Small, 2011, 7, 445.
13. M. A. Lazar, S. Varghese and S. S. Nair, Catalysts, 2012, 2, 572.
14. K. Hashimoto, H. Irie and A. Fuhjishima, Jpn. J. Appl. Phys., 2005, 44, 8269.
15. S. M. Gupta and M. Tripathi, Chin. Sci. Bull., 2011, 56, 1639.
16. Y. Ruzmanova, M. Ustundas, M. Stoller and A. Chianese, Chem. Eng. Transac., 2013, 32, 2233.
17. W. F. Yao, X. H. Xu, H. Wang, J. T. Zhou, X. N. Yang, Y. Zhang, S. Shang and B. B. Huang, Appl. Catal., B, 2004, 52, 109.
18. J. Kim, D. W. Hwang, H. G. Kim, S. W. Bae, S. M. Ji and J. S. Lee, Chem. Commun., 2002, 2488.
19. H. G. Kim, D. W. Hwang and J. S. Lee, J. Am. Chem. Soc., 2004, 126, 8912.
20. A. Navrotsky, Chem. Mater., 1998, 10, 2787.
21. D. M. Giaquinta and H.-C. zur Loye, Chem. Mater., 1994, 6, 365.
22. J. M. Neil, A. Navrotsky and O. J. Kleppa, Inorg. Chem., 1971, 10, 2076.
23. N. C. Wilson, J. Muscat, D. Mkhonto, P. E. Ngoepe and N. M. Harrison, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 71, 075202.
24. N. C. Wilson, S. P. Russo, J. Muscat and N. M. Harrison, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 024110.
25. S. W. Chen, M. J. Huang, P. A. Lin, H. T. Jeng, J. M. Lee, S. C. Haw, S. A. Chen, H. J. Lin, K. T. Lu, D. P. Chen, S. X. Dou, X. L. Wang and J. M. Chen, Appl. Phys. Lett., 2013, 102, 042107.
26. F. J. Craig, Phys. Rev. Lett., 2008, 100, 167203.
27. P. B. Fabritchnyi, M. V. Korolenko, M. I. Afanasov, M. Danot and E. Janod, Solid State Commun., 2003, 125, 341.
28. P. B. Fabritchnyi, A. Wattiaux, M. V. Korolenko, M. I. Afanasov and C. Delmas, Solid State Commun., 2009, 149, 1535.
29. C. Xin, Y. Wang, Y. Sui, Y. Wang, X. Wang, K. Zhao, Z. Liu, B. Li and X. Liu, J. Alloys Compd., 2014, 613, 401.
30. M. Makowska-Janusik and A. Kassiba, Functional Nanostructures and Nanocomposites – Numerical Modeling Approach and Experiment, in Handbook of Computational Chemistry, ed. J. Leszczynski, Springer, 2012.
31. M. Makowska-Janusik, O. Gladii, A. Kassiba, J. Boucle and N. Herlin-Boime, J. Phys. Chem. C, 2014, 118, 6009.
32. H. Melhem, P. Simon, J. Wang, C. Di Bin, B. Ratier, Y. Leconte, N. Herlin-Boime, M. Makowska-Janusik, A. Kassiba and J. Boucle, Sol. Energy Mater. Sol. Cells, 2013, 117, 624.
33. P. S. Anjana and M. T. Sebastian, J. Am. Ceram. Soc., 2006, 89, 2114.
34. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Payne, Z. Kristallogr., 2005, 220, 567.
35. B. G. Pfrommer, M. Cate, S. G. Louie and M. L. Cohen, J. Comput. Phys., 1997, 131, 233.
36. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
37. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207.
38. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2006, 124, 219906.
39. K. Hummer, J. Harl and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 115205.
40. P. Śpiewak, J. Vanhellemont and K. J. Kurzydłowski, J. Appl. Phys., 2011, 110, 063534.
41. M. E. Foster and B. M. Wong, J. Chem. Theory Comput., 2012, 8, 2682.
42. B. W. Wong, M. Piacenza and F. D. Sala, Phys. Chem. Chem. Phys., 2009, 11, 4498.
43. C. O. Almbladh and A. C. Pedroza, Phys. Rev. A, 1984, 29, 2322.
44. M. Levy, J. P. Perdew and V. Sahni, Phys. Rev. A, 1984, 30, 2745.
45. A. Dreuw, J. L. Weisman and M. Head-Gordon, J. Chem. Phys., 2003, 119, 2943.
46. M. S. Hybertsen and S. G. Louie, Phys. Rev. B: Condens. Matter Mater. Phys., 1986, 34, 5390.
47. W. Kohn and L. J. Sham, Phys. Rev. A, 1965, 140, 1133.
48. D. C. Langreth and J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1980, 21, 5469.
49. P. J. Stephenset, F. J. Devlin, C. F. Chabalowski and M. J. Frisch, J. Phys. Chem., 1994, 98, 11623.
50. J. P. Perdew, M. Ernzerhof and K. Burke, J. Chem. Phys., 1996, 105, 9982.
51. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207.
52. V. I. Anisimov, J. Zaanen and O. K. Andersen, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 44, 943.
53. A. Jain, G. Hautier, S. P. Ong, C. J. Moore, C. C. Fischer, K. A. Persson and G. Ceder, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 84, 045115.
54. R. Laskowski, N. E. Christensen, P. Blaha and B. Palanivel, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 165209.
55. Q. J. Liu and Z. T. Liu, Appl. Phys. Lett., 2011, 99, 091902.
56. A. Sayede, R. Khenata, A. Chahed and O. Benhelal, J. Appl. Phys., 2013, 113, 173501.
57. J. R. Huang and C. Cheng, J. Appl. Phys., 2013, 113, 033912.
58. MOPAC2012: Stewart, J. J. P. Stewart Computational Chemistry, Colorado Springs: CO, http://OpenMOPAC.net.
59. J. J. P. Stewart, J. Mol. Model., 2007, 13, 1173.
60. J. Baker, J. Comput. Chem., 1986, 7, 385.
61. T. Helgaker, Chem. Phys. Lett., 1991, 182, 503.
62. P. Culot, G. Dive, V. H. Nguyen and J. M. Ghuysen, Theor. Chim. Acta, 1992, 82, 189.
63. Y. Qu, W. Zhou, Z. Ren, S. Du, X. Meng, G. Tian, K. Pan, G. Wanga and H. Fu, J. Mater. Chem., 2012, 22, 16471.
64. R. S. Singh, T. H. Ansari, R. A. Singh and B. M. Wanklyn, Mater. Chem. Phys., 1995, 40, 173.
65. J.-L. Wang, Y.-Q. Li, Y.-J. Byon, S.-G. Mei and G.-L. Zhang, Powder Technol., 2013, 235, 303.
66. P. Salvador, C. Gutierrez and J. B. Goodenough, Appl. Phys. Lett., 1982, 40, 188.
67. S. Yuvaraj, V. D. Nithya, K. Saiadali Fathima, C. Sanjeeviraja, G. Kalai Selvan, S. Arumugam and R. Kalai Selvan, Mater. Res. Bull., 2013, 48, 1110.
68. T. Stein, H. Eisenberg, L. Kronik and R. Baer, Phys. Rev. Lett., 2010, 105, 266802.
69. R. Vijayalakshmi and V. Rajendran, E-J. Chem., 2012, 9, 282.
70. K. P. Lopes, L. S. Cavalcante, A. Z. Simoes, J. A. Varela, E. Longo and E. R. Leite, J. Alloys Compd., 2009, 468, 327.
71. A. Kassiba, M. Makowska-Janusik, J. Boucle, J. F. Bardeau, A. Bulou and N. Herlin-Boime, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 155317.
72. Y. Su and M. L. Balmer, J. Phys. Chem. B, 2000, 104, 8160; G. Busca, G. Ramis, J. M. Gallardo Amcres, V. Sanchez Escribano and P. Piaggio, J. Chem. Soc., Faraday Trans., 1994, 90, 3181.
73. F. X. Llabrés i Xamena, A. Damin, S. Bordiga and A. Zecchina, Chem. Commun., 2003, 1514.
74. M. I. Baraton, G. Busca, M. C. Prieto, G. Ricchiardi and V. Sanchez Escribano, J. Solid State Chem., 1994, 112, 9.
75. B. A. Scott and G. Burns, J. Am. Ceram. Soc., 1972, 55, 225.
76. J. B. Bellam, M. A. Ruiz-Preciado, M. Edely, J. Szade, A. Jouanneaux and A. Kassiba, RSC Adv., 2015, 5, 10551.

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