Synthesis and Characterization of Novel Nanoparticles of Lithium Aluminum Iodate LiAl(IO3)4, and DFT Calculations of the Crystal Structure and Physical Properties

Here we report on the non-hydrothermal aqueous synthesis and characterization of nanocrystalline lithium aluminum iodate, LiAl(IO3)4. Morphological and compositional analyses were carried out by using scanning electron microscopy (SEM) and energy-dispersive X-ray measurements (EDX). The optical and vibrational properties of LiAl(IO3)4 have been studied by UV-Vis and IR spectroscopy. LiAl(IO3)4 is found to crystallize in the non-centrosymmetric, monoclinic P21 space group, contrary to what was reported previously. Theoretical simulations and Rietveld refinements of crystal structure support this finding, together with the relatively high Second Harmonic Generation (SGH) response that was observed. Electronic band structure calculations show that LiAl(IO3)4 crystal has an indirect band gap Egap = 3.68 eV, in agreement with the experimental optical band gap Egap = 3.43(3) eV. The complex relative permittivity and the refraction index of LiAl(IO3)4 have also been calculated as a function of energy, as well as its elastic constants and mechanical parameters. LiAl(IO3)4 is found to be a very compressible and ductile material. Our findings imply that LiAl(IO3)4 is a promising material for optoelectronic and non -linear optical applications.


Introduction
Inorganic nanoparticles usually exhibit interesting magnetic, electrical, and optical properties, including non-linear optical (NLO) features. Many methods for the synthesis of inorganic nanoparticles exist, encompassing physical, chemical, and mechanical processes. The choice of the synthesis method is dictated by the structure that has to be obtained which, in turn, depends on the foreseen applications [1,2]. In fact, the nanoparticle size and size-distribution, the surface area, the chemical composition, as well as the purity, shape, and surface structure of the nanoparticles, play key roles in the resulting functional properties. Broadly speaking, synthesis methods can be subdivided into two categories: constructive methods and destructive methods. The former consists of the build-up of materials from single atoms to clusters and to nanoparticles, by methods including sol-gel [3,4], spinning [5], chemical vapor deposition [6], pyrolysis [7], and biosynthesis [8]. Conversely, in destructive methods, the reduction of bulk material to nanometric particles takes place through mechanical milling [9], nanolithography [10], laser ablation [11], sputtering [12], and thermal decomposition [13].
Hydrothermal and solvothermal synthesis methods are typically the most promising approaches for the preparation of metal iodate nanomaterials. These methods can be combined with microwave heating to improve the quality and the reproducibility of the final products [14].
In the first part of this work, we describe for the first time a simple and inexpensive chemical route for the preparation of pure nanocrystals of LiAl(IO 3 ) 4 , which is a novel and interesting material for optoelectronics and nonlinear optics. LiAl(IO 3 ) 4 nanocrystals have been synthetized using a soft-chemistry method, which takes advantage of the direct precipitation reaction between lithium iodate (LiIO 3 ) and aluminum nitrate nonahydrate (Al(NO 3 ) 3 ·9H 2 O) from highly concentrated water solutions, without hydrothermal conditions. To the best of our knowledge, this is one of the first examples of such a simple chemical route for the preparation of iodate nanoparticles. The morphology of the final product was inspected by electron microscopy, and the average size of particles was measured by X-ray diffraction, using Le Bail fir refinement and the Williamson-Hall method (W-H). UV-Vis and infrared spectra were also measured and discussed. Preliminary results dealing with a crude estimation of the SHG efficiency of LiAl(IO 3 ) 4 were also included after comparison of the emitted signals from two colloidal suspensions, the reference sample being LiNbO 3 nanocrystals of similar size. The optical band gap of LiAl(IO 3 ) 4 nanoparticles was measured experimentally by absorbance spectroscopy. The second part of the manuscript is devoted to the theoretical calculation of the structural model and physical properties of this new compound using the Density-Functional Theory (DFT).

Sample Preparation and Characterization
Reagents purchased from Sigma-Aldrich (Burlington, MA, USA), lithium iodate (LiIO 3 , 99.5%) and aluminum nitrate nonahydrate (Al(NO 3 ) 3 ·9H 2 O, 98%), were used without further purification. Powder X-ray diffraction patterns (XRD) of the final product were obtained at ambient conditions using a Panalytical EMPYREAN MALVERN (Malvern, UK) powder diffractometer (Cu Kα 1 , 40 mA, 30 kV) with a 0.01 • step size and an acquisition time of 6 s/step in the 17-85 • 2θ range. The homogeneity and chemical composition of the sample were investigated by Scanning Electron Microscopy (SEM) using a Tescan Vega (Brno -Kohoutovice, Czech Republic) electron microscope system attached to a Peltiercooled XFlashTM (Bruker AXS-Karlsruhe, Germany) silicon drift detector, model 410 M, for energy dispersive X-ray (EDX) analysis. Optical absorption spectra were recorded using a Jasco V-630 UV-Vis (Easton, MD, USA) spectrophotometer in the 190-1100 nm wavelength range. Infrared spectra (FTIR) were recorded on a Jasco FT/IR-4200 (Easton, MD, USA) setup between 1000 and 400 cm −1 using KBr pellets. Dynamic light scattering (DLS) measurements (Zetasizer Nano, Malvern Panalytical, Palaiseau, France) were used to assess the colloidal stability and aggregation state of the synthesized samples after re-dispersion in ethanol.

Ab-Initio Calculations
The performed ab-initio calculations were based on the DFT theory [39,40] to calculate the structural, electronic, mechanical, and linear optical properties, using the pseudopotential plane-wave (PP-PW) method as implemented in the Cambridge Sequential Total Energy Package (CASTEP) module of Material Studio [39]. The exchange correlation interaction was described by the generalized-gradient approximation (GGA), using the Perdew-Burke-Ernzerhof (PBE) parameterization [40], with a kinetic cut-off energy of 700 eV for the plane-wave expansions. The reciprocal space integration was performed using (6 10 6) k-point grids in the first Brillouin zone (BZ). The geometry optimization was performed using the Broyden-Fletcher-Golfard-Shannon (BFGS) algorithm. The ultra-soft pseudopotential was used within the following valence electronic configuration: Li: 1s 2 2s 1 ; O: 2s 2 2p 4 ; Al: 3p 1 4s 2 ; and I: 5s 2 5p 5 . For band structure calculations, in addition to the PBE functional we have implemented the nonlocal hybrid functional HSE06 (Heyd-Scuseria-Ernzerhof) [41], for a more precise determination of gap energy.

Synthesis and XRD Characterization
A white precipitate of nanoparticles of pure LiAl(IO 3 ) 4 was collected, after a few hours, from an aqueous solution of 4 mmol LiIO 3 and 1 mmol of Al(NO 3 ) 3 ·9H 2 O, dissolved in 3 mL of distilled water. The volume of water was kept to the minimum that allowed for the dissolution of the reagents, i.e., the solution was almost saturated. The reaction mixture was subsequently dried in an oven at 70 • C, until the water was completely evaporated. After drying, no residual reagents were found, implying a complete reaction. This was confirmed by EDX analysis (Figure 1), demonstrating the correct stoichiometry and the absence of residual reagents. Within the experimental error, EDX analyses of Al and I content by both weight percent and atomic percent agreed with the expected molar ratio of 1:4. Numerically, the measured Al and I contents were 19.97 at% and 80.03 at%, respectively. As no impurities were detected, the elementary analysis shown in Figure 1 Figure 3 shows the X-ray diffraction patterns of LiAl(IO 3 ) 4 nanoparticles. To the best of our knowledge, the only mention of LiAl(IO 3 ) 4 in the literature is in Ref. [42]. A hexagonal structure (space group P6 3 ) was proposed, with lattice constants a = 5.585 Å and c = 4.945 Å. This structure was derived from the structure of LiIO 3 , assuming that Li and Al atoms in LiAl(IO 3 ) 4 randomly occupy the atomic positions of Li in LiIO 3 with a 0.5 occupancy factor. However, this structure does not satisfy the stoichiometry of the compound and does not result in the density measured previously [42] and in this work. In addition, we found that a structure based on the P6 3 space group cannot properly index all the experimental XRD peaks, as demonstrated by the green ticks in Figure 3 for a hexagonal indexation. In fact, an indexation with the hexagonal structure led to a = 10.649 Å and c = 5.182 Å for the unit-cell parameter, with a being almost twice the value previously reported [42]. This suggests that the structure previously reported is not correct and that a lower symmetry structure is needed to account for all experimental diffraction peaks. We found that a monoclinic structure isomorphic to Co(IO 3 ) 2 (space group P2 1 ) can satisfactorily explain the XRD pattern measured for LiAl(IO 3 ) 4 [43]. This can be seen in Figure 3, where we show the result of a Rietveld refinement and the calculated positions of the different (hkl) reflections. Because of the small nanoparticle size and the significant FWHM of the XRD peaks, a full structural refinement is not yet allowed. Instead, we built a crystal structure based on Co(IO 3 ) 2 , assuming two independent positions for Co atoms: one occupied by Li atoms and the other by Al atoms. This structure was subsequently optimized by means of tn Table 1.  The atomic positions obtained from DFT were assumed for the Rietveld refinement. They were fixed during the refinement; only the unit-cell parameters, background, and peak-shape parameters were used as fitting parameters. We obtained a = 10.579(4) Å, b = 5.183(2) Å, c = 10.701(4) Å, and β = 119.88(5) • . The goodness of the fit refinement parameters were R p = 10.41%, R wp = 14.28%, and χ 2 = 1.29. As illustrated in Figure 4, the Li 1+ and Al 3+ cations are coordinated to six O atoms and form slightly distorted octahedral units, which are connected by IO 3 triangular pyramids. This coordination for I 5+ ions is typical of metal iodates, being related to the existence of a lone pair of electrons of the I atom in the IO 3 molecule. In the proposed crystal structure, each octahedral unit is surrounded by six IO 3 groups. Regarding the nanoparticle size leading to the XRD peak-broadening, the Le Bail global fitting procedure was implemented by assuming a spherical morphology and the absence of any strain, and by considering the Lorentzian and Gaussian parts of the peak shape. The nanocrystal size thus derived at 22.7 nm is in good agreement with the value at ≈22.9 nm obtained by the Williamson-Hall method [44][45][46]. The atomic positions obtained from DFT were assumed for the Rietveld refinement. They were fixed during the refinement; only the unit-cell parameters, background, and peak-shape parameters were used as fitting parameters. We obtained = 10.579(4) Å,  Figure 4, the Li 1+ and Al 3+ cations are coordinated to six O atoms and form slightly distorted octahedral units, which are connected by IO3 triangular pyramids. This coordination for I 5+ ions is typical of metal iodates, being related to the existence of a lone pair of electrons of the I atom in the IO3 molecule. In the proposed crystal structure, each octahedral unit is surrounded by six IO3 groups. Regarding the nanoparticle size leading to the XRD peak-broadening, the Le Bail global fitting procedure was implemented by assuming a spherical morphology and the absence of any strain, and by considering the Lorentzian and Gaussian parts of the peak shape. The nanocrystal size thus derived at 22.7 nm is in good agreement with the value at ≈22.9 nm obtained by the Williamson-Hall method. [45][46][47].
As shown in the following discussion, according to our DFT calculations, the band gap of LiAl(IO3)4 is indirect. Thus, the value = 3.43(3) eV of the band gap wass estimated by extrapolating the linear part of the (αhν) 1/2 curve as a function of the incident phonon energy hν (α being the absorbance) in a Tauc plot (Figure 5b) [49]. The optical properties of the particles were explored using UV-Vis absorption spectroscopy. The absorption spectrum of LiAl(IO3)4 nanoparticles, as shown in Figure 5b, exhibits strong absorbance below 250 nm. An excitonic absorption peak is found at about 275 nm (eV), with an exciton binding energy = 1.08 eV. Finally, because of the non-centrosymmetric space group P21 derived above, SHG properties were expected for LiAl(IO3)4. To get a rapid insight of its SHG efficiency, a suspension was initially prepared at 1 g/L, after sonication of the raw powder in ethanol. After sedimentation for 10 h, drying and weighing of the larger aggregates that had settled down allowed an estimation of the final mass concentration at 0.7 g/L within the supernatant. The corresponding DLS size distribution in intensity is indicated in the inset of Figure 6. The mean size centered at ~255 nm, together with a relatively high PDI value at 0.22, indicated the presence of remaining aggregates whose hydrodynamic diameters were significantly larger than the 23 nm XRD crystallite size derived above. For comparison, a colloidal suspension of LiNbO3 nanocrystals, of mean DLS at 120 nm and small PDI value at 0.09, was also prepared at 1 g/L in ethanol. The corresponding mean XRD size at ~30 nm and the synthesis method are described elsewhere [50]. Both suspensions containing LiNbO3 and LiAl(IO3)4 nanocrystals of similar XRD mean size and mass concentration were prepared with the aim of obtaining a rapid comparison of their SHG conversion efficiencies from Second Harmonic (SH) spectroscopy, with the setup fully described in Ref. [51]. Here, for two excitation wavelengths arbitrarily fixed at 800 nm and 1064 nm, As shown in the following discussion, according to our DFT calculations, the band gap of LiAl(IO 3 ) 4 is indirect. Thus, the value E gap = 3.43(3) eV of the band gap wass estimated by extrapolating the linear part of the (αhν) 1/2 curve as a function of the incident phonon energy hν (α being the absorbance) in a Tauc plot (Figure 5b) [48].
The optical properties of the particles were explored using UV-Vis absorption spectroscopy. The absorption spectrum of LiAl(IO 3 ) 4 nanoparticles, as shown in Figure 5b, exhibits strong absorbance below 250 nm. An excitonic absorption peak is found at about 275 nm (eV), with an exciton binding energy E B = 1.08 eV.
Finally, because of the non-centrosymmetric space group P2 1 derived above, SHG properties were expected for LiAl(IO 3 ) 4 . To get a rapid insight of its SHG efficiency, a suspension was initially prepared at 1 g/L, after sonication of the raw powder in ethanol. After sedimentation for 10 h, drying and weighing of the larger aggregates that had settled down allowed an estimation of the final mass concentration at 0.7 g/L within the supernatant. The corresponding DLS size distribution in intensity is indicated in the inset of Figure 6. The mean size centered at~255 nm, together with a relatively high PDI value at 0.22, indicated the presence of remaining aggregates whose hydrodynamic diameters were significantly larger than the 23 nm XRD crystallite size derived above. For comparison, a colloidal suspension of LiNbO 3 nanocrystals, of mean DLS at 120 nm and small PDI value at 0.09, was also prepared at 1 g/L in ethanol. The corresponding mean XRD size at~30 nm and the synthesis method are described elsewhere [49]. Both suspensions containing LiNbO 3 and LiAl(IO 3 ) 4 nanocrystals of similar XRD mean size and mass concentration were prepared with the aim of obtaining a rapid comparison of their SHG conversion efficiencies from Second Harmonic (SH) spectroscopy, with the setup fully described in Ref. [50]. Here, for two excitation wavelengths arbitrarily fixed at 800 nm and 1064 nm, the scattered SH intensities are plotted in Figure 6 for the same experimental parameters in the excitation and detection arms. Interestingly, the SHG response of the LiAl(IO 3 ) 4 nanocrystal suspension was found to be above that of the reference LiNbO 3 material. At this stage, because of the partial aggregation state within the LiAl(IO 3 ) 4 nanocrystal suspension and the eventual presence of a broad size dispersion that would require further TEM imaging, a quantitative assessment of the orientation-averaged second-order susceptibility was difficult to achieve, although promising NLO performances were clearly demonstrated for the iodate modification.

Ab-Initio Calculations
Ab initio simulations were used to calculate the crystal structure of LiAl(IO 3 ) 4 . The structure was modeled starting from the isostructural Co(IO 3 ) 2 , in which the two independent cobalt atoms were substituted by Li and Al. Subsequently, we performed the optimization of the equilibrium geometry, determining atomic coordinates and lattice parameters. Forces (stresses) on atoms (lattice) were minimized using the Hellmann-Feynman theorem [51,52]. The calculated lattice parameters were a = 10.80(5) Å, b = 5.14(4) Å, c = 10.89(4) Å, and β = 119.00(3) • (V = 528.49(9) Å 3 ), which agreed within 1% with those we obtained from the refinements. The calculated atomic positions are summarized in Table 1. The molar mass of LiAl(IO 3 ) 4 was found to be 1467.07 g mol −1 , and it has two formula units per cell (Z = 2), with a density of ρ = 4.61 g cm −3 . From these calculations, we obtained information on the bond distances. The polyhedron corresponding to the iodate groups IO 3 − exhibited the expected trigonal-pyramidal symmetry, with four different iodine atoms. As can be seen in Table 2, each iodine atom is connected to three oxygen atoms by short bonds. The LiO 6 octahedral units are slightly distorted. The Li + cation is connected by three monodentate bonds with an average I-O length of 2.08 Å and with three additional iodate groups with an average I-O length of 2.14 Å (Figure 4). Similarly, AlO 6 units are also slightly distorted octahedral units connected to IO 3 pyramids in a similar way to LiO 6 .
From DFT calculations, we also determined the electronic band structure of LiAl(IO 3 ) 4 , as shown in Figure 7. We found that the material is an indirect semiconductor, with the top of the valence band at the Z point of the Brillouin zone and the bottom of the conduction band between B and D. The calculated band gap was E gap = 2.43(9) eV or E gap = 3.68 eV, as calculated by the GGA (PBE) or the HSE06 approach, respectively. The first value underestimated the band gap, a known fact fore PBE functionals, while the hybrid HSE06 functional provided excellent agreement with the calculations. While the band dispersion is well described by PBE, this functional as well as other widely used local functionals, fails in computing the gap value. Therefore, the scissor operator (i.e., the difference between the theoretical value and the most reliable band gap values) was used in this case, which finally gave the same value for the band gap as for HSE06: E gap = 3.68 eV. The features observed here, from the calculated PDOS of LiAl(IO 3 ) 4 , are in a good agreement with those of other non-transition metal iodates widely reported in the literature [23,[53][54][55][56][57]. Moreover, as we pointed out in our previous work, if there is no transition metal in the metal iodates, the valence band maxima (VBM) will mainly be dominated by the O 2p orbitals, and the conduction band minima (CBM) will mainly be dominated by the I 5p orbitals [57]. On the other hand, the partially filled d orbitals of transition metal will usually contribute to either the VBM or CBM, thus narrowing the band gap. Based on this fact, the non-transition metal iodates are usually expected to have a relatively large band gap, which can explain the large band gap found here in LiAl(IO 3 ) 4 . The value of the ℇ (0) static dielectric constant is about 5, on average. The dispersion curves of the complex refractive index = + , along the main crystallographic directions, are depicted in Figure 9b and show a strong anisotropy between the optical components that are parallel and perpendicular to the [010] direction, in the plane (010) and the direction perpendicular to it [010]. This implies that LiAl(IO3)4 is a birefringent material, one of the most desirable features for active NLO materials [59,60]. Based on the difference The value of the ε 1 (0) static dielectric constant is about 5, on average. The dispersion curves of the complex refractive index n = n + ik, along the main crystallographic directions, are depicted in Figure 9b and show a strong anisotropy between the optical components that are parallel and perpendicular to the [010] direction, in the plane (010) and the direction perpendicular to it [010]. This implies that LiAl(IO 3 ) 4 is a birefringent material, one of the most desirable features for active NLO materials [58,59]. Based on the difference between the refractive indices n 100 and n 010 (2.47 (2.26) and 2.22 (2.05) without/with scissor, respectively), the birefringence index of LiAl(IO 3 ) 4, is D n = 0.21. Note that zinc iodate (Zn(IO 3 ) 2 ) and lithium zinc iodate (LiZn(IO 3 ) 3 ), both crystallizing in the P2 1 space group, have similar birefringence indices at 0.33 and 0.29, respectively [23]. Incidentally, as LiAl(IO 3 ) 4 is colorless, its transparency in the visible domain makes it a potential candidate for quadratic NLO applications and radio communications, in the special case of frequency duplication [60].
Finally, we also computed the components C ij of the elastic tensor C of LiAl(IO 3 ) 4 , as listed in Table 3. As expected for a monoclinic structure [52], 13 independent values C ij exist for LiAl(IO 3 ) 4 . In order to be a considered as mechanically stable, a crystal structure at ambient pressure must fulfill the Born criterion, one of whose equivalent formulations is that the eigenvalues of the elastic tensor must all be positive [61]. The eigenvalues of the C tensor are shown in Table 4, and they are positive, confirming the stability of the structure.  The computed elastic coefficients are of the same order of magnitude as other NLO materials [62]. Elastic properties such as the bulk (B), shear (G), and Young's (E) moduli in the Voigt, Reuss, and Hill approximations, and the corresponding Poisson ratio P, were calculated and are summarized in Table 5. The calculated bulk modulus B of LiAl(IO 3 ) 4 was found to be 28.7-36.1 GPa, indicating that LiAl(IO 3 ) 4 is a fairly compressible material. The obtained bulk modulus is comparable to that of Co(IO 3 ) 2 (B = 29.8 GPa) and Zn(IO 3 ) 2 (B = 21.6 GPa), which are structurally related to LiAl(IO 3 ) 4 [25,43]. On the other hand, the obtained Poisson ratio is in the lower limits of the typical value for solids [63], and B/G is 1.17-126, suggesting that LiAl(IO 3 ) 4 is a brittle material [63].

Conclusions
We have reported a novel experimental approach for a facile and cost-effective synthesis of likely nontoxic LiAl(IO 3 ) 4 nanocrystals, having potentially high IR NLO performances as exogenous optical biomarkers. The method makes use of a soft-chemistry technique, resulting within a few hours in precipitated nanoparticles from almost saturated solutions of the reagents. No hydrothermal processing is needed. The synthesized samples have been characterized by X-ray diffraction, scanning electron microscopy, EDX, UV-Vis, FTIR,