Firing salts method for the synthesis of orthorhombic Gd2TiO5: experimental characterization supported by DFT first principles calculations

This work presents the synthesis by the new ‘firing salts method’ (FSM) of orthorhombic Gd 2 TiO 5 which requires only two hours at 1200 °C. X Ray Diffraction, High Resolution Transmission Electron Microscopy, Fourier Transform Infrared Spectroscopy and Raman spectroscopy characterized it. Electron microscopy shows particle size distribution between 50–500 nm with orthorhombic structure according to Rietveld analysis. Raman—infrared spectroscopies and first principles calculations indicate that the second order contribution to the spectra comes from the Ti-O5 interactions. First principles calculations (Density Functional Theory) were used as an aid for the interpretation of the experimental results to assign the normal modes to the bands on the Raman and IR spectra; it also provided an insight of the chemical reactivity of the synthesis.


Introduction
Rare Earth titanates are a wide family of compounds that depending on its chemical composition and Rare Earth (RE) elements, synthesize mainly in two stable different crystal structures: cubic pyrochlore RE 2 Ti 2 O 7 , or orthorhombic RE 2 TiO 5 .The Ti oxygen coordination has the most important contribution to the physical properties since the RE 3+ sublattice is almost the same in both systems.The pyrochlore structure occurs when the ionic radius ratio (R A /R Ti 1.2); it can be understood in terms of interpenetrated networks of TiO6 octahedra and RE2O chains of distorted cubes, a high ordered system with a cubic Fd-3m symmetry that belongs to the No. 227 space group.It has very interesting magnetic properties -frustrated magnetism [1]; and transport properties like ferroelectricity and fast ionic conductivity [2].When the chemical composition changes to a less ordered system like that of the RE 2 TiO 5 , it crystallizes in a stable orthorhombic structure with Pnma symmetry belonging to the No. 62 space group; where the RE 3+ cations occupy two 7-fold sites, forming a distorted cube because of one oxygen is missing in the polyhedral while the remaining oxygen atoms are slightly rearranged to compensate from their ideal cubic position [3].On the other hand, there are four Ti 4+ cations with five-fold oxygen coordination, giving rise to an offset square based pyramidal polyhedral.The orthorhombic RE 2 TiO 5 compound have no mixed occupancy in the different 4c Wyckoff symmetry sites [3][4][5].These changes allow them to have a wide range of important applications from high permeability dielectrics used in memory devices [6], biomedical applications [7], luminescence [8,9], nuclear reactor control rod materials or as a neutron absorber [3,10,11].
There are several methods for the synthesis of RE titanates.From the solid state reaction of the RE 2 O 3 and TiO 2 reagent materials, with thermal treatments between 1200 °C to 1500 °C and time intervals from 24 to 72 h with more than two intermediate annealing processes [3,4,12,13], or the wet chemistry methods besides the use of RE 2 O 3 as reagent material it is also employed RE(NO 3 ) 3 6H 2 O, citric acid as chelating agent, nitric acid (HNO 3 ) and different materials as titanium ions precursors as for example titanium metal (Ti°), titanium isopropoxide or tetrabutyl titanate.The thermal treatments are focused in two different steps: first, the gel formation with temperatures between 70 °C to 400 °C with time intervals between 1 to 18 h.The second step consists in the annealing of the solid obtained from the gel calcination with thermal treatments between 1100 °C to 1400 °Cwith time intervals between 6 to 24 h [8,9,13].As it could be seen, both synthesis methods use long thermal -high temperature treatments; additionally, the wet chemistry methodologies have water polluted with chemical reagents as a byproduct.In recent years, the need of cleaner and sustainable methodologies or the socalled green chemistry methods aim to avoid or diminish the waste reagents production after chemical reactions.The Molten Salts Method (MSM) is an alternative route for the synthesis of complex oxide materials which has been successfully tested for the formation of perovskite, sillenite and pyrochlore compounds [14][15][16][17][18][19] which also offers a high scalable material production.The synthesis process uses a mixture of convenient salts as a reaction media for the constituent metal oxide precursors that enhance time-saving formation process; therefore, the products achieved after the reaction are the complex oxide material and saline water [14].This method is quite effective for the RE titanates with pyrochlore structure [20], but for the orthorhombic RE 2 TiO 5 it is only after repeated grinding and heating processes that a pure orthorhombic phase is obtained; as in all the syntheses methods, the samples have the presence of the RE 2 Ti 2 O 7 (pyrochlore) impurity which affects the transport properties of the samples.This behavior can be explained in terms of the chemical reactivity for both materials: The rate of formation of the orthorhombic phase is twice the rate of TiO 2 consumption, so the pyrochlore phase is easily produced.Thus, for the solid-state reaction, for example, the synthesis of RE 2 TiO 5 goes thru several stages of heating and grinding of the form: The result usually is: In this work, the synthesis of Gd 2 TiO 5 is presented by a novel method where a mixture of salts (NaCl-KCl) and reactive oxides (Gd 2 O 3 and TiO 2 ) are heated way beyond the melting-sublimation point of the salts, and its experimental and theoretical characterization, to provide useful information to their plausible potential applications and for comparison with previous reported parameters assessed with different synthesis methodologies.The mixture of salts must be such that the difference between melting-sublimation and the reaction temperatures allows a broad thermalization that permits the completeness of the reaction before all salts get evaporated.
This work also explores the high temperature firing of the mixture salts by assessing the reaction kinetics.First principles calculations for the orthorhombic Gd 2 TiO 5 , the pyrochlore Gd 2 Ti 2 O 7 , the precursor oxides cubic Gd 2 O 3 , anatase TiO 2 and the individual crystalline materials (Gd hexagonal (hcp), Ti hexagonal (hcp) and the O 2 molecular crystal (tetragonal)) were performed to obtain the vibrational spectra of the titanates and precursor oxides, and their formation energies and reaction enthalpies.X-ray powder diffraction (XRD), Raman and Infrared (IR) spectroscopy, High Resolution Electron Microscopy (HREM) were performed to define the conditions of the orthorhombic formation.

Materials and methods
The firing salts synthesis process exploits the heath of sublimation of a mixture of salts to promote the formation of a higher temperature phase of rare earth titanates (RETiO 5 ) against the favored by the chemical reactivity one (RE 2 Ti 2 O 7 ).Reactive oxides, Gd 2 O 3 (Sigma-Aldrich > 99%) and TiO 2 (Sigma-Aldrich 99.99%) were mixed into stoichiometric proportion with an equimolar mixture of salts NaCl-KCl (Sigma-Aldrich 99.9%) with a total molar proportion of 7:1 between the salts and oxide powder reactants.The salts and precursors were grounded in an agate mortar into a fine homogeneous powder and heated at 1200 °C for 2 h, without a ramping heat rate in a something like a shocking thermal treatment and then quenched in air.The obtained product was washed and stirred in deionized water to dissolve the remaining unevaporated salts and filtered with a 0.22 μm pore nitrocellulose filter, to finally dry in air.
The x ray Diffraction (XRD) were measured at room temperature with a Bruker D8 diffractometer (Cu Kα radiation and a Ni filter) from 10°to 90°with steps of 0.02°in 2θ.Rietveld analysis of XRD pattern was carried out with the implementation of the MAUD software [21].SEM images were acquired with an ultra-high-resolution electron microscope JEOL JSM-7800F at 5 kV acceleration voltage with magnification of ×12,000 and ×50,000.High Resolution Transmission Electron Microscopy (HRTEM) images were acquired with a JEOL TEM-2010 FEG electron microscope with a 200 keV accelerating voltage and a point resolution of 0.19 nm.Measurements of the interplanar distance were performed in HRTEM images using the Fast Fourier Transform (FFT) in Digital Micrograph software from GATAN.Raman spectroscopy was measured with an Aseqinstruments Rm1 confocal Raman spectrometer.Fourier Transform Infrared Spectroscopy (FTIR) was measured in the range from 370 to 4000 cm −1 with a Bruker VERTEX 70 v FTIR spectrometer.

Computational details
Computational calculations were performed within the Density Functional Theory (DFT) framework [22,23], as implemented in Quantum Espresso [24][25][26], under the generalized gradient approximation (GGA) with the Perdew-Burke-Ernserhof (PBE) exchange-correlation functional [27,28].The wave functions were expanded in a basis set through the Projector Augmented Wave pseudopotential method with cut-off energy of 1224 eV and a k-point sampling inside the first Brillouin zone constructed using the Monkhorst-Pack scheme with 8 × 8 × 8 grids [29], considering as valence electrons 4f 7 5d 1 6s 2 for gadolinium, 3s 2 4s 2 3p 6 3d 2 for titanium and 2s 2 2p 4 for oxygen.The equilibrium properties were obtained via the geometry optimization process in the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme, where system total energy and hydrostatic pressure were used as equilibrium parameters.The Gd 2 TiO 5 material were modeled with Pnma space group No. 62 symmetry with 2 gadolinium atoms in two independent Wyckoff sites (4c), 4 titanium atoms are in one independent Wyckoff position (4c) and 5 oxygen atoms in one independent Wyckoff site (4c), figure 1.For the Gd 2 TiO 5 geometry relaxation, the initial lattice parameters were measured experimentally from the Rietveld refinement.Although Gd and Ti have f and d electrons so the on-site and inter-site interaction should be considered, we only needed the energy differences to stablish energy trends between them.In this cases there was no need to consider the use of a Hubbard model or other approximations.

Results and discussion
The Rietveld refinement, figure 2, confirms the formation of the almost pure orthorhombic Gd 2 TiO 5 phase with lattice parameters a = 10.489Å, b = 3.761 Å and c = 11.321Å; in concordance with those previous reported values for the orthorhombic Gd 2 TiO 5 phase (table 1) [4,12,30], and with those calculated from the geometric optimization.According to the Rietveld results, the most distorted cation coordination is around the Gd1 site, because of the short interatomic Gd-O1 distance (1.794 Å), with a 30% difference between the 7-fold different oxygen ions while the Ti cation, tetrahedrally coordinated, have a maximal 10% difference between Ti-O2 compared against the different oxygen interatomic distances, as shown in table 1.
The 4% contribution of the Gd 2 Ti 2 O 7 pyrochlore phase on the x-ray diffractogram is an indication of the chemical reactivity of this phase over the Gd 2 TiO 5 one.This trend has been observed in a wide range of synthesis methods and thermodynamic conditions.Table 2 shows the energies DU, the reactive energy of the oxides ( ) DH 0 of both phases and the constituent atoms to calculate the cohesive energy ( ) E c and enthalpies of formation ( ) D H , r 0 in order to elucidate the role of the 'firing salts method' in the promotion of the orthorhombic Gd 2 TiO 5 phase compared against Gd 2 Ti 2 O 7 pyrochlore.
In terms of the cohesive energy, defined as the heat of sublimation of a solid into its constituents, given by: Where DU Gd TiO 2 5 and DU Gd Ti O 2 2 7 are the energies per atom of the crystals at equilibrium while U , Gd U Ti and U O2 are the energies of the isolated constituent atoms; the related results, shown in table 2, indicates that both phases are very stable with the pyrochlore one being a little more stable than the orthorombic one.However, a completely different trend happens with the heat of formation, calculated at equilibrium, given by the where 2 3 and DH , TiO 0 2 are the formation enthalpies of the orthorhombic, pyrochlore, gadolinium and titanium oxides at DFT equilibrium.Although the computed results in table 2 show that the heat of formation of the pyrochlore phase is 75% larger than the orthorhombic phase, the former requires less time and temperature than the later.This behavior can be explained in terms of the chemical reactivity for both materials: As already mentioned in the introduction, the rate of formation of the orthorhombic phase is twice the rate of TiO 2 consumption, so it has a rate of formation larger than the pyrochlore.
Therefore, it could be stated that solid state reaction and low temperature synthesis conditions promotes the formation of the pyrochlore phase, however, if the system is out of the thermodynamic equilibrium, the more stable structure is the Gd 2 TiO 5 .This is in concordance with the FSM that it is something like a shocking thermal treatment, where the reaction takes place at temperatures far away from the 660 °C melting temperature of the eutectic NaCl -KCl mixture.Therefore, the sublimation of the salt media increases drastically the heat of the reaction, promoting the twice formation rate of the Gd 2 TiO 5 , as it is confirmed experimentally, where the remaining Gd 2 Ti 2 O 7 phase comes from the highly formation stability of the compound.
According to the Rietveld analysis, the mean size of polycrystalline aggregates is 386 nm while scanning electron microscopy (figure 3) together with transmission electron microscopy, figure 4, suggests the presence of a dispersed size distribution of particles comprised between 50-500 nm of a well faceted morphology with a microstructure of the particles corresponding with orthorhombic crystal symmetry.The Fast Fourier transform (FFT) analysis of the HRTEM micrograph, figure 5, evidences the presence of three plane contributions ( ̅ ) 320 , ( ) 230 and ( ̅ ) 1 50 linked to the inter-planar distances 0.308 nm, 0.298 nm and 0.021 nm, respectively: all of them in good correlation with the orthorhombic No. 62 space group with zone axis [ ] 001 .This is an indication that the crystal growth and that the nucleation process occurs in the three principal lattice directions.
The profile of the particles allows to elucidate the characteristics related with the synthesis reaction.The 'firing salts method' requires high temperature (1200 °C) with a relative short-time calcination treatment, for the formation of the Gd 2 TiO 5 compound, with particle growth starting in the nanoscale regime.This behavior could be understood in terms of low solubility of Gd 2 O 3 in the molten chloride salts; this is assumed by the long thermal treatments necessary to the formation of Gd-based complexes synthesized by molten salt method [15,31].Therefore, the first reaction step involves the solubilization of the reagents to posteriorly initiate a slow nucleation process (at least 2 h), allowing the formation of faceted particles with orthorhombic geometry.
The experimental vibrational Raman and IR spectra together with the most representative calculated Raman -IR vibrational energies are shown at figure 6, and in table 3; it is noticed the good correlation between experimental (solid line) and computed DFT data (dashed lines).As it was established before for the A 2 TiO 5 ( A = Y, Dy, Tb, Gd, Sm, Nd, Pr) compounds, the main contribution bands are according to the irreducible 3 [32,33]; at which the strong Raman (B 2g −796 cm −1 ) and IR (B 1u −847 cm −1 ) bands are assigned to Ti-O2 stretching vibrational modes which is, according to the Rietveld refinement, the most asymmetric interatomic distance in the 5-fold Ti oxygen coordination.The 660 cm −1 (Raman-B2g) and 582 cm −1 (IR-B 3u ) are linked to the tetrahedral base Ti-O asymmetric stretching, while Raman (A g -B 3g ) and IR (A u -B u ) bands included from 300 to 500 cm −1 correspond to antisymmetric bending modes of the square planar Ti-O bonds.Below the 300 cm −1 regions, there are five Raman bands and one IR band; all of them related to the trivalent Gd cations with the narrowed B 3g (Raman − 247 cm −1 ) and B 3u (IR − 392 cm −1 ) being related to bending modes of the Gd1-O1 interatomic distance in the 7-fold coordination [32].
The width and intensity of the band at ∼596 cm −1 , not present in the calculated vibrational modes, figure 7, is a combination band from the Ti-O5 coordinated group as suggested by the correlation of the Ti-O5: C 4v point group to the D 2h factor group: ; since the direct product of the D 2h factor group is such that g xg = u xu = g, we have assigned it as a symmetric stretching Ti-O vibration with A g symmetry as the result of the most likely combination of two stretching Ti-O vibrations.

Conclusion
Gd 2 TiO 5 was successfully synthesized with a minimum remnant pyrochlore phase by the firing salts method which requires less energy and time than typical solid-state reaction.The reduced reaction times produces growth grain sizes starting in the nanoscale region which favors high strength components, suitable for applications in nuclear reactor control rod materials or as neutron absorbers.DFT calculations supports the experimental results and clarify the origin of the second order Raman bands that indicates the phosphor behavior for luminescence centers.Also, the first principles calculations provide an insight of the formation process.The high scalable FSM of Gd 2 TiO 5 together with its characterization opens the research to RE-titanates and doped systems with many possible future applications.

Figure 1 .
Figure 1.Crystal structure of the Pnma Gd 2 TiO 5 material with the different oxygen labeled assigned coordinating the Gd and Ti cations.The structure was obtained with the Diamond Software from Crystal Impact version 3.0 T.M. .

Figure 4 .
Figure 4. Transmission electron micrograph from different regions of the Gd 2 TiO 5 synthesized compound.

Figure 6 .
Figure 6.Raman and FTIR spectra of the Gd 2 TiO 5 compound.The dotted lines are the calculated DFT vibrational contributions.

Figure 7 .
Figure 7.Comparison between DFT calculated and experimental IR and Raman active modes.

Table 2 .
Internal energy per atom ( ) DU and its constituents' atoms, cohesive energy (E c ) and enthalpy of formation (D H