# Determination of the Chemical Composition of Lithium Niobate Powders

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}; LN) crystals with the Czochralski method [1], synthesizing stoichiometric LN single crystals is still a state-of-the-art matter: The reason behind this is the fact that a Z-cut of a stoichiometric grown crystal costs around 12 times more than one possessing a congruent chemical composition [2]. Compared to this version of the material, while comprehensively studied [3] and well exploited technologically [4,5,6], powders are tacitly considered easier and far less expensive to synthesize. LN powders (LNPws) have served in the past only as survey materials, for example, in the prediction of the nonlinear second order optical capabilities of unavailable single crystals by applying the Kurtz-Perry method in the powdered version [7,8]. Nevertheless, recent developments in LNPws are certainly attracting the attention of scientists and engineers who seek to exploit their potential use in a wide range of applications that span from the construction industry to nonlinear optics.

_{mn}are preserved. Our work arises from noticing that at least one of the two linear equations that describe the CC of LN single crystals by polarized Raman Spectroscopy measurements [16,17] is not accurate for the case of powders. Hence, it is necessary to properly characterize LNPws, starting by unambiguously determining their CC. Most of the reports found in the literature are only devoted to LN single crystals, where optical and non-optical methods can be found [16,17,18]. Some of the non-optical methods might also be applied to powders; however, in some cases they would not be accessible to everyone, like neutron diffraction methods, and might also give rise to discrepancies like in cases determining the LN CC by measuring the Curie temperature T

_{C}. Since temperature is a scalar quantity (light propagates and interacts with matter in vector-like form), it would be permissible to expect a single description of the LN CC in terms of T

_{C}that serves for both large single crystals and powders. Interestingly, this is not the case: the systematic measurement of lower T

_{C}values (about 10 °C) for LNPws compared to equivalent single crystals has already been addressed and the reason behind this remains unexplained [18].

^{−1}, as given by Schlarb et al. [16] and Malovichko et al. [17], can be done on stoichiometric (ST) and congruent (CG) lithium niobate single-crystal wafers, according to the provider [2]. Likewise, this serves to calibrate this assembled system and to confidently state that the aforementioned linear equation does not describe LNPws. Then, with a commercially available system, we observed that the linear relationship remains between the CC of LNPws and the linewidth (Γ) of the same Raman mode (876 cm

^{−1}), under which in simpler circumstances the polarization state of light at the excitation and detection stages would be disregarded. In accordance to References [16,17,18,19], the accurate determination of the CC of LNPws is proposed by means of a linear fit in terms of the calculated Γ from non-polarized Raman spectra. Yet, the main contribution of this work is based on an a priori probing of the formed phases from 11 different synthesized samples by analysis of X-ray diffraction (XRD) experimental data, while relying on the existent information in the phase diagram that describes the pure LN phase along with its surrounding secondary phases (Figure 1). In this way the linear relationship obtained for the averaged Nb content in the crystallites $\langle {c}_{Nb}\rangle $, in terms of Γ, is affixed to two known or expected values of $\langle {c}_{Nb}\rangle $ for the two edges that delimit the pure ferroelectric phase: The boundary with phase LiNb

_{3}O

_{8}on one side (Nb excess) and the boundary with phase Li

_{3}NbO

_{4}on the other (Li excess).

_{g}), by means of UV-vis Diffuse Reflectance (DR), is also used for this purpose. Differential Thermal Analysis (DTA) is utilized as a verification technique for specific samples and a fourth empirical equation that describes the CC in terms of the Curie temperature is obtained this way. Scanning Electron Microscopy (SEM) is utilized to verify that the particle size distributions do not vary drastically from one sample to another.

## 2. Materials and Methods

#### 2.1. Synthesis

_{2}CO

_{3}) and niobium pentoxide (Nb

_{2}O

_{5}), from Alpha Aesar, were used as starting reagents in a 1:1 molar ratio. The respective masses of the precursors were determined such that 1 g of lithium niobate (LiNbO

_{3}; LN) was produced from the following balanced chemical equation:

^{−4}g) while keeping the mass of the other precursor constant, in both cases with respect to the masses measured for sample LN-STm (see Appendix A for table). In this way, 10 more samples were synthesized and labeled as LN + 1%LiP, LN + 1%NbP, LN + 2%LiP, and so on up to LN + 5%NbP (P stands for precursor). It must be clarified that the percentages that appear on these labels are not in terms of the ion species solely, but in terms of the whole mass of the precursors that contain them.

#### 2.2. X-Ray Diffraction

_{3}O

_{8}and Li

_{3}NbO

_{4}, ICSD-2921 and ICSD-75264 from The Inorganic Crystal Structure Database were used, respectively [25]. The archives were then inserted, along with the experimental data, and Rietveld analysis in “Automatic Mode” was executed, followed by iterative executions in “Semi-automatic Mode,” in which different “Profile Parameters” were allowed to vary until satisfactory indexes of agreement were obtained. The averaged crystallite size was also calculated by Rietveld refinement, following instructions from the Size/Strain Analysis section; a single lanthanum hexaboride (LaB

_{6}) crystal was used in this case as the standard sample, analyzed with the ICSD-194636 card.

#### 2.3. Raman Spectroscopy

^{−1}of spectral resolution. With this equipment, the Raman spectra were collected in the range 100–1200 cm

^{−1}at room temperature and light incident on the normal component of the sample with a power of 3.4 mW; a Nikon 10 objective was used to focus the incoming light on a 1:5 mm spot. An intensity of approximately 11Wcm

^{−2}was delivered to the sample. The customized open-air Raman system consisted of an excitation beam output of a continuous wave diode laser at 638 nm wavelength with a power of 37 mW (Innovative photonic solution). The beam was linearly polarized from variable angle mounting and transmitted through a beam splitter to focus the excitation beam into the sample by an aspherized achromatic lens (NA = 0.5, Edmund optics). The excitation spot diameter measured at the focus point had a ~10 μm radius. The collected Raman scattered light from the sample through the aspheric lens and the beam splitter was focused by two silver coated mirrors and one bi-convex lens into a fiber Raman Stokes probe (InPhotonics) that was connected to a QE65 Raman Pro spectrometer (Ocean optics) for a Raman shift range detection between 250–3000 cm

^{−1}. In its use for the characterization of the powders, the light at λ = 638 nm was incident at razing angle with P = 10 mW. The Raman spectra were collected in the range 200–1200 cm

^{−1}at room temperature with a spectral resolution of 8 cm

^{−1}. In this case, a laser intensity of approximately 3 kWcm

^{−2}was delivered to the sample. Due to technical issues, most of the utilized experimental conditions were different from one Raman system to another—it is shown how this did not alter the obtained results, except for the detection mode which in both cases was fixed at the backscattering-detection mode (Figure 2).

#### 2.4. UV-Vis Diffuse Reflectances and Differential Thermal Analysis

_{2}O

_{3}) was chosen as the standard reference. Precautions were taken so that the approximations necessary to apply the Kubelka-Munk Theory were accomplished [27,28,29]. These approximations are, mainly speaking, a preparation of the sample being thick enough so that the measured reflectance does not change with further increasing of this parameter (avoidance of Fresnel reflection) and an averaged size of the particles being smaller than such thickness, but larger relative to the wavelength (scattering independent of the wavelength).

## 3. Results and Discussion

#### 3.1. X-Ray Diffraction

_{exp}) and their respective calculated patterns by means of Rietveld refinement (I

_{ref}) is also shown in the upper half of this figure; for the secondary phases LiNb

_{3}O

_{8}and Li

_{3}NbO

_{4}, ICSD-2921 and ICSD-75264 from The Inorganic Crystal Structure Database were used, respectively [25]. For all cases, this difference function tends to a common baseline, so that neither the formation of thermodynamically stable phases (other than LiNbO

_{3}, Li

_{3}NbO

_{4}, and LiNb

_{3}O

_{8}) nor the presence of one of the precursors in an interstitial fashion can be deduced, that is, without participating in the formation of one of the involved phases. As seen in this figure, most of the synthesized powders resulted in a pure ferroelectric LN phase, except for samples LN + 4%NbP and LN + 5%NbP (blue lines). Figure 4 and Table 1 have been added for a better visualization of this argument. A loss of Li equivalent to the loss of 5 mol % Li

_{2}CO

_{3}could be hastily addressed for the central sample LN-STm due to the calcination process. Nevertheless, this information can also be interpreted as having no loss of Li and thus the assumption of a non-ideal sensitivity for the XRD technique must be taken. In other words, a detection threshold of 5.0 mol % Li

_{2}CO

_{3}= 1.4 mol % Nb

_{2}O

_{5}exists for ‘seeing’ a secondary phase by the XRD analysis, combined with the structure refinement, done in this investigation. This assumption has been taken into account in this investigation, thus defining the boundaries that delimit the pure ferroelectric LN phase for samples LN-STm (Li excess) and LN+3%NbP (Nb excess). For the calculation of mol % equivalence between precursors, the values for the relative atomic masses of Li and Nb have been used as presented in the Periodic Table provided by the Royal Society of Chemistry [30].

_{2}O

_{5}. Hence, for future reference, we first propose the determination of $\langle {c}_{Nb}\rangle $ for LNPws in this CC range with the following equation:

_{cell}stands for the cell volume in (angstrom)

^{3}units, calculated by a standard structure refinement method. The 0.5 mol % uncertainty is determined by the sum of the uncertainty associated to the linear fitting (0.14 mol % Nb

_{2}O

_{5}) and half the longer step in the Nb precursor (0.53/2 = 0.27 mol % Nb

_{2}O

_{5}), both multiplied by the square root of the averaged goodness of fit factor for the six involved samples ($\sqrt{1.55}$). The uncertainty associated with the linear fitting has been determined following several calculations according to Baird [31].

#### Justification of the Assumption made in the X-Ray Diffraction Analysis

_{2}O

_{5}is deduced for the pure ferroelectric LN phase. In this investigation, the observed range goes from the ST point $\langle {c}_{Nb}\rangle =$ 50.0 mol % (sample LN-STm) to a near-CG point $\langle {c}_{Nb}\rangle =$ 53.0 − 1.4 = 51.6 mol % (sample LN + 3%NbP), that is $\Delta {c}_{pureLN}=$1.6 mol % Nb

_{2}O

_{5}. A direct explanation would not be found for an estimated range of 4.4 mol % Nb

_{2}O

_{5}if this assumption had not been taken. Secondly, under these circumstances it follows that, out of 11 synthesized samples, only samples LN-STm, LN + 1%NbP, LN + 2%NbP, and LN+3%NbP resulted to have a pure ferroelectric LN phase. It will be soon shown that, for all the performed studies, unmistakable linear relationships happen to exist among these samples and their corresponding experimental parameters (related to the CC); a striking, very sensitive, deviation from these trends is observed for all samples out of this range, in some cases even under the consideration only of neighbor samples such as LN + 1%LiP and LN + 4%NbP. Lastly, besides the well-known difficulties to produce single-phase ST LN at temperatures used in solid-state reactions (T ≥ 1200 C) [32,33], much ambiguity can be found in the literature concerning deviation from stoichiometry in the formation of LNPws at calcination temperatures near T = 850 °C. While only one work is found to report no loss of Li after two 16-hour reaction periods at 1120 °C [34], other authors have observed the loss of Li at 600–800 °C within at least three different investigations [33,35,36]. However, these methods of synthesis are very different from each other, except for those in the works published in 2006 (Liu et al.) [33] and 2008 (Liu et al.) [36], which are aqueous soft-chemistry methods. The deviation from stoichiometry tendency in the formation of LNPws through aqueous soft-chemistry methods, in comparison to non-aqueous (as in this investigation), has already been identified [37]. Besides, high-energy milling has previously been proposed as a method to prevent loss of Li, in contrast to Pechini’s method, sol-gel, and coprecipitation [21].

_{2}CO

_{3}not detected by XRD, but only identified after DTA and Infrared Spectroscopy; the LNPws were synthesized via mechanical alloying. They explained this observation by assuming that the number and size of the Li

_{2}CO

_{3}nanocrystals were sufficiently low and small to not being detected by XRD. Hence, the assumption taken of no loss of Li and the existence of a detection threshold of 1.4 mol % Nb

_{2}O

_{5}in XRD might have been justified with these lines. This detection threshold can be considered unique and expected to change according to different experimental variables and analysis tools, including spatial and temporal size of the step during the experiment, brand, and model of equipment utilized, as well as the software used for Rietveld refinement, among others.

#### 3.2. Raman Spectroscopy

^{−1}[16,17] was done by using the assembled Raman system (Figure 2a) on the aforementioned stoichiometric (ST) and congruent (CG) lithium niobate (LN) wafers. Even though the experimental conditions therein described were not exactly reproduced, this could be accomplished within the given absolute accuracy and, thus, calibration of this equipment could be done. At this instance, use of the equation for the Raman band located at 876 cm

^{−1}has been done [16,17]. A detailed description of the phonon branches of single crystal LN and their assignment can be found elsewhere [39,40]. No specifications regarding the resolution of the Raman bands or fitting techniques are given by Schlarb et al. [16] or Malovichko et al. [17], although these procedures are critical for achieving great accuracy in the determination of the LN CC [16,39,40,41]. Moreover, it is not clearly stated whether the complete linewidth (Γ), or just the halfwidth, is to be entered in this equation.

^{−1}and 578 cm

^{−1}(red and blue shifts), have already been identified and addressed to the overlapping of the LO and TO lattice vibrations [42,43,44]. Such an overlapping is clearly a drawback for band resolution and it might be the reason behind the discrepancy between predicted and measured values; interestingly, this is only relevant in single crystals of ST composition.

^{−1}, where the corresponding linear equation is used, and the Raman spectra are measured with the commercially available Raman system (Witec), which features recording of intensity in the range 0–200 cm

^{−1}. However, well defined linear trends can be seen for the calculated Raman halfwidths around the pure LN ferroelectric phase, but only for the case of the band at 876 cm

^{−1}as measured under non-polarized experimental conditions. For both situations (Witec and self-assembled systems), the trend is of an increasing halfwidth with decreasing Li content; surprisingly, despite the great differences between both experimental configurations and conditions (Figure 2), both trends are very similar. This feature can also be seen for the positions of the bands (x

_{c}), and it remains for the resultant values of the halfwidths divided by the positions (Γ/2x

_{c}). Figure 5b shows how this Γ/2x

_{c}parameter relates to the Nb content of the synthesized powders, as determined by XRD analysis. Given the similarity between the results obtained by both experimental configurations, this graph represents the average of such results. For sample LN-STm, the Raman spectra measured with the Witec system are shown in Figure 5a; these closely resemble those obtained in polycrystalline LN by Repelin et al. [40].

^{−1}) by means of a Gaussian fitting does not entail significant changes either, the following equations are proposed for the determination of $\langle {c}_{Nb}\rangle $ in LNPws:

_{i}stands for the FWHM in cm

^{−1}of the Raman band around 876 cm

^{−1}, resolved by linear fitting either using a Lorentzian or a Gaussian line shape, ${x}_{c}$ denotes the center of this Raman band. Normalization of the full Raman spectra precedes the linear fitting and, regardless of the line shape, enlargement around this band is suggested, extending it as much as possible (precise determination of the baseline) and applying a single or double-peak fitting, rather than performing a multi-peak fitting to the full Raman spectra. Like in the XRD analysis, the uncertainty is determined by summation over half the longer step in the Nb precursor (0.53/2 = 0.27 mol % Nb

_{2}O

_{5}), the uncertainty associated to the linear fitting (0.12 mol % Nb

_{2}O

_{5}(0.23 mol % Nb

_{2}O

_{5}) for the Lorentzian (Gaussian) case), and dividing by the square root of the averaged (five involved samples) reduced χ

^{2}fit factor obtained in the resolution of the band $\sqrt{0.9823}$ ($\sqrt{0.9866}$). Once more, the uncertainty associated to the linear fitting is determined following several calculations according to Baird [31].

_{Li}), which are compensated by their charge-compensating Li vacancies (V

_{Li}) [3,46]. Such a substitution mechanism imposes fundamental changes on the electronic structure, inducing in this way, variations in the macroscopic dielectric tensor of LN [16]. Yet, because in this substitution mechanism gradual Nb increments are proportional to the decreasing of Li, the variations of the dielectric tensor are expected to be linear, as far as the Nb-Li interchange is sufficiently small.

#### 3.3. UV-Vis Diffuse Reflectances and Differential Thermal Analysis

^{−1}or 15 cm

^{−1}) [48]. There is no point in using this equation to describe the CC of LNPws, since these terms (refractive index and absorption coefficient) make no sense when related to powders.

_{g}(Figure 6c). Equation (4) allows us to accurately determine the Nb content of a determined sample, in terms of E

_{g}(in eV units).

_{c}) of these distributions fall within a band 1 μm thick, centered at 2.6 μm, as shown in Figure 7.

_{C}, is in Celsius.

_{C}= 1181.56 °C (1153.41 °C for a ST (CG) powder); whereas, with the quadratic expression, it is of 1182.61 °C and 1153.01 °C, respectively. These values vary in no more than 0.1%. Regarding single crystals, a variation of 0.7% can be found for the Curie temperatures calculated for these CCs, by use of equations reported in two independent investigations [51,52]. Using the equation given by Bordui et al. [52], the calculated values are T

_{C}= 1206.47 °C (1149.83 °C) for the ST (CG) crystal. Thus, contrary to what was believed, not a unique description of the LN CC regardless of its version (powder or single crystal) can be formulated by DTA either. This observation of the T

_{C}being lower for ST LNPws, with respect to ST LN crystals, has been previously noticed [36], apart from the observations highlighted in the introduction. A straight explanation of this subtlety cannot be found nowadays in the literature. A classic theoretical development shows that the energy of the vibrations within the structure is the dominant contribution to the heat capacity—if the elastic response of a crystal is a linear function of the applied forces [53]. Thus, it is inferred that this might be explained under consideration of anharmonic crystal interactions, that is, phonon-phonon coupling. Still, further investigations on these matters are needed.

_{2}O

_{5}mol %. This is readily understood since even in the fabrication of large LN single crystals, melts of Nb

_{2}O

_{5}and another compound containing Li are used [3,20]. The equivalent equations in terms of $\langle {c}_{Li}\rangle $ are given in Appendix B.

#### 3.4. Grinding of a Single Crystal

_{2}O

_{5}), the structure refinement does not. This can be attributed to changes of the lattice parameter (lattice distortion) due to a variable local lattice strain frequently observed in nanocrystalline materials, induced by excess of volume at the grain boundaries [54]. Remarkably, our powdered single crystal differs from the synthesized powders in the averaged crystallite size: On the latter, a myriad of nanosized crystals (100–300 nm) form large particles of the order of 2–3 μm (see Figure 7c), while on the former it can be argued that crystallite size equals the particle size; actually, the applied Rietveld refinement for the calculation of the averaged crystallite size of the grinded crystal does not converge. These implications must be confirmed and scrutinized by further investigation. Lastly, since Equation (3) is strongly dependent on the XRD analysis (re-labeling of the samples in terms of their predicted CC), the Raman results shown in Table 2 demonstrate the reliability of our method.

## 4. Conclusions

_{3}) powders for example.

_{2}O

_{5}by three increasing steps of Nb content, and then dividing by 2 (0.53/2 = 0.27 mol % Nb

_{2}O

_{5}). The associated uncertainty to Equations (2)–(5) can be significantly reduced if a larger number of samples are synthesized in this range, which can be more easily achieved if larger quantities of powder are prepared. As an example, it is expected that by synthesizing approximately 10 g of powder, around 40 points would be available for analysis if the increasing step is fixed at 0.1% in the mass of the Nb precursor, resulting in a decrease in the overall uncertainties of about 50–80% (noticing that the uncertainty associated with the linear fitting would also be reduced significantly). Conclusively, although it is acknowledged that the proposed equations are not universal in the sense that they may only describe the CC of LNPws with specific physical properties (crystallite and particle dimensions), this work paves the way to furnish a general description and claims the attention of the community advocated to this field to broaden the present results. For a more general description, besides the synthesis of larger number of samples, the influence of other experimental factors and parameters such as the method of synthesis, the beam spot size, the intensity of light (Raman Spectroscopy), the averaged crystallite and particle size, and randomness, among others, should be considered in future investigations.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Sample | Nb_{2}O_{5} Mass (g) | Li_{2}CO_{3} Mass (g) | Sample | Nb_{2}O_{5} Mass (g) | Li_{2}CO_{3} Mass (g) |

LN+5%LiP | 0.8989 | 0.2622 | LN+1%NbP | 0.9079 | 0.2498 |

LN+4%LiP | 0.8988 | 0.2598 | LN+2%NbP | 0.9167 | 0.2496 |

LN+3%LiP | 0.8991 | 0.2574 | LN+3%NbP | 0.9259 | 0.2497 |

LN+2%LiP | 0.8990 | 0.2547 | LN+4%NbP | 0.9348 | 0.2498 |

LN+1%LiP | 0.8989 | 0.2523 | LN+5%NbP | 0.9438 | 0.2498 |

LN-STm | 0.8990 | 0.2498 |

## Appendix B

## References

- Ballman, A.A. Growth of Piezoelectric and Ferroelectric Materials by the Czochralski Technique. J. Am. Ceram. Soc.
**1965**, 48, 112–113. [Google Scholar] [CrossRef] - MTI Corporation, LiNbO3 & Doped. Available online: http://www.mtixtl.com/linbo3.aspx (accessed on 29 January 2019).
- Volk, T.; Wöhlecke, M. Point Defects in LiNbO
_{3}. In Springer Series in Materials Science. Lithium Niobate. Defects, Photorefraction and Ferroelectric Switching, 1rst ed.; Hull, R., Osgood, R.M., Jr., Parisi, J., Warlimont, H., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; Volume 115, pp. 9–50. ISBN 978-3-540-70765-3. [Google Scholar] - Weis, R.S.; Gayklord, T.K. Lithium Niobate. Summary of Physical Properties and Crystal Structure. Appl. Phys. A
**1985**, 37, 191–203. [Google Scholar] [CrossRef] - Luo, R.; Jiang, H.; Rogers, S.; Liang, H.; He, Y.; Lin, Q. On-chip second-harmonic generation and broadband parametric down-conversion in a lithium niobate microresonator. Opt. Exp.
**2017**, 25, 24531–24539. [Google Scholar] [CrossRef] [PubMed] - Pang, C.; Li, R.; Li, Z.; Dong, N.; Cheng, C.; Nie, W.; Bötger, R.; Zhou, S.; Wang, J.; Chen, F. Lithium Niobate Crystal with Embedded Au Nanoparticles: A New Saturable Absorber for Efficient Mode-Locking of Ultrafast Laser Pulses at 1µm. Adv. Opt. Mater.
**2018**, 6, 1800357. [Google Scholar] [CrossRef] - Kurtz, S.K.; Perry, T.T. A Powder Technique for the Evaluation of Nonlinear Optical Materials. J. Appl. Phys.
**1968**, 39, 3798–3812. [Google Scholar] [CrossRef] - Aramburu, I.; Ortega, J.; Folcia, C.L.; Etxebarria, J. Second harmonic generation by micropowders: A revision of the Kurtz-Perry method and its practical application. Appl. Phys. B: Lasers Opt.
**2014**, 116, 211–233. [Google Scholar] [CrossRef] - Nath, R.K.; Zain, M.F.M.; Kadhum, A.A.H. Artificial Photosynthesis using LiNbO
_{3}as Photocatalyst for Sustainable and Environmental Friendly Construction and Reduction of Global Warming: A Review. Catal. Rev. Sci. Eng.**2013**, 56, 175–186. [Google Scholar] [CrossRef] - Yang, W.C.; Rodriguez, B.J.; Gruverman, A.; Nemanich, R.J. Polarization-dependent electron affinity of LiNbO
_{3}surfaces. Appl. Phys. Lett.**2004**, 85, 2316–2318. [Google Scholar] [CrossRef] - Fierro-Ruíz, C.D.; Sánchez-Dena, O.; Cabral-Larquier, E.M.; Elizalde-Galindo, J.T.; Farías, R. Structural and Magnetic Behavior of Oxidized and Reduced Fe Doped LiNbO
_{3}Powders. Crystals**2018**, 8, 108. [Google Scholar] [CrossRef] - Kudinova, M.; Humbert, G.; Auguste, J.L.; Delaizir, G. Multimaterial polarization maintaining optical fibers fabricated with powder-in-tube technology. Opt. Mater. Express
**2017**, 10, 3780–3790. [Google Scholar] [CrossRef] - Sánchez-Dena, O.; García-Ramírez, E.V.; Fierro-Ruíz, C.D.; Vigueras-Santiago, E.; Farías, R.; Reyes-Esqueda, J.A. Effect of size and composition on the second harmonic generation from lithium niobate powders at different excitation wavelengths. Mater. Res. Express
**2017**, 4, 035022. [Google Scholar] [CrossRef] - Skipetrov, S.E. Disorder is the new order. Nature
**2004**, 432, 285–286. [Google Scholar] [CrossRef] - Knabe, B.; Buse, K.; Assenmacher, W.; Mader, W. Spontaneous polarization in ultrasmall lithium niobate nanocrystals revealed by second harmonic generation. Phys. Rev. B
**2012**, 86, 195428. [Google Scholar] [CrossRef] - Schlarb, U.; Klauer, S.; Wesselmann, M.; Betzler, K.; Wöhlecke, M. Determination of the Li/Nb ratio in Lithium Niobate by Means of Birefringence and Raman Measurements. Appl. Phys. A
**1993**, 56, 311–315. [Google Scholar] [CrossRef] - Malovichko, G.I.; Grachev, V.G.; Kokanyan, E.P.; Schirmer, O.F.; Betzler, K.; Gather, B.; Jermann, F.; Klauer, S.; Schlarb, U.; Wöhlecke, M. Characterization of stoichiometric LiNbO
_{3}grown from melts containing K_{2}O. Appl. Phys. A: Mater. Sci. Process.**1993**, 56, 103–108. [Google Scholar] [CrossRef] - Wöhlecke, M.; Corradi, G.; Betzler, K. Optical methods to characterise the composition and homogeneity of lithium niobate single crystals. Appl. Phys. B
**1996**, 63, 323–330. [Google Scholar] [CrossRef] - Zhang, Y.; Guilbert, L.; Bourson, P.; Polgár, K.; Fontana, M.D. Characterization of short-range heterogeneities in sub-congruent lithium niobate by micro-Raman spectroscopy. J. Phys. Condens. Matter
**2006**, 18, 957–963. [Google Scholar] [CrossRef] - Hatano, H.; Liu, Y.; Kitamura, K. Growth and Photorefractive Properties of Stoichiometric LiNbO
_{3}and LiTaO_{3}. In Photorefractive Materials and Their Applications 2, 1st ed.; Günter, P., Huignard, J.P., Eds.; Springer Series in Optical Sciences: New York, NY, USA, 2007; pp. 127–164. [Google Scholar] - Kong, L.B.; Chang, T.S.; Ma, J.; Boey, F. Progress in synthesis of ferroelectric ceramic materials via high-energy mechanochemical technique. Prog. Mater. Sci.
**2008**, 53, 207–322. [Google Scholar] [CrossRef] - Suryanarayana, C. Mechanical alloying and milling. Prog. Mater. Sci.
**2001**, 46, 1–184. [Google Scholar] [CrossRef] - Crystallographic Open Database, Information for card entry 2101175. Available online: http://www.crystallography.net/cod/2101175.html (accessed on 29 January 2019).
- Degen, T.; Sadki, M.; Bron, E.; König, U.; Nènert, W. The HighScore suite. Powder Diffr.
**2014**, 29, S13–S18. [Google Scholar] [CrossRef] [Green Version] - FIZ Karlsruhe ICSD, ICDS- Inorganic Crystal Structure Database. Available online: www2.fiz-karlsruhe.de/icsd_home.html (accessed on 29 January 2019).
- Porto, S.P.S.; Krishnan, R.S. Raman Effect of Corundum. J. Chem. Phys.
**1967**, 47, 1009–1011. [Google Scholar] [CrossRef] - Kubelka, P. New Contributions to the Optics of Intensely Light-Scattering Materials. Part I. J. Opt. Soc. Am.
**1948**, 38, 448–457. [Google Scholar] [CrossRef] - Kubelka, P. New Contributions to the Optics of Intensely Light-Scattering Materials. Part II: Nonhomogeneous Layers. J. Opt. Soc. Am.
**1954**, 44, 330–335. [Google Scholar] [CrossRef] - Torrent, J.; Barrón, V. Diffuse Reflectance Spectroscopy. In Methods of Soil Analysis Part5—Mineralogical Methods, 1st ed.; Ulery, A.L., Drees, R., Eds.; Soil Science Society of America: Wisconsin, WI, USA, 2008; pp. 367–385. [Google Scholar]
- The Royal Society of Chemistry, Periodic Table. Available online: http://www.rsc.org/periodic-table (accessed on 29 January 2019).
- Baird, D.C. Experimentation: An Introduction to Measurement Theory and Experiemtn Design, 3rd ed.; Prentice-Hall: Englewood Cliffs, NJ, USA, 1995; pp. 129–133. [Google Scholar]
- Kalinnikov, V.T.; Gromov, O.G.; Kunshina, G.B.; Kuz’min, A.P.; Lokshin, E.P.; Ivanenko, V.I. Preparation of LiTaO
_{3}, LiNbO_{3}, and NaNbO_{3}from Peroxide Solutions. Inorg. Mater.**2004**, 40, 411–414. [Google Scholar] [CrossRef] - Liu, M.; Xue, D.; Luo, C. Wet chemical synthesis of pure LiNbO
_{3}powders from simple niobium oxide Nb_{2}O_{5}. J. Alloys Compd.**2006**, 426, 118–122. [Google Scholar] [CrossRef] - Scott, B.A.; Burns, G. Determination of Stoichiometry Variations in LiNbO
_{3}and LiTaO_{3}by Raman Powder Spectroscopy. J. Am. Ceram. Soc.**1972**, 55, 225–230. [Google Scholar] [CrossRef] - Liu, M.; Xue, D. An efficient approach for the direct synthesis of lithium niobate powders. Solid State Ionics
**2006**, 177, 275–280. [Google Scholar] [CrossRef] - Liu, M.; Xue, D.; Li, K. Soft-chemistry synthesis of LiNbO
_{3}crystallites. J. Alloys Compd.**2008**, 449, 28–31. [Google Scholar] [CrossRef] - Nyman, M.; Anderson, T.M.; Provencio, P.P. Comparison of Aqueous and Non-aqueous Soft-Chemical Syntheses of Lithium Niobate and Lithium Tantalate Powders. Cryst. Growth Des.
**2009**, 9, 1036–1040. [Google Scholar] [CrossRef] - De Figueiredo, R.S.; Messaia, A.; Hernandes, A.C.; Sombra, A.S.B. Piezoelectric lithium niobate obtained by mechanical alloying. J. Mater. Sci. Lett.
**1998**, 17, 449–451. [Google Scholar] [CrossRef] - Pezzotti, G. Raman spectroscopy of piezoelectrics. J. Appl. Phys.
**2013**, 113, 211301. [Google Scholar] [CrossRef] - Repelin, Y.; Husson, E.; Bennani, F.; Proust, C. Raman spectroscopy of lithium niobate and lithium tantalite. Force field calculations. J. Phys. Chem. Solids
**1999**, 60, 819–825. [Google Scholar] [CrossRef] - Thermo Fisher Scientific, Application Note: Curve Fitting in Raman and IR Spectroscopy. Available online: https://www.thermofisher.com/search/results?query=Curve%20Fitting%20in%20Raman&focusarea=Search%20All (accessed on 29 January 2019).
- Tuschel, D. The Effect of Microscope Objectives on the Raman Spectra of Crystals. Spectroscopy
**2017**, 32, 14–23. [Google Scholar] - Maïmounatou, B.; Mohamadou, B.; Erasmus, R. Experimental and theoretical directional dependence of optical polar phonons in the LiNbO
_{3}single crystal: New and complete assignment of the normal mode frequencies. Phys. Status Solidi B**2016**, 253, 573–582. [Google Scholar] [CrossRef] - Yang, X.; Lang, G.; Li, B.; Wang, H. Raman Spectra and Directional Dispersion in LiNbO
_{3}and LiTaO_{3}. Phys. Status Solidi B**1987**, 142, 287–300. [Google Scholar] [CrossRef] - Balanevskaya, A.É.; Pyatigorskaya, L.I.; Shapiro, Z.I.; Margolin, L.N.; Bovina, E.A. Determination of the composition of LiNbO
_{3}specimens by Raman spectroscopy. J. Appl. Spectrosc.**1983**, 38, 491–493. [Google Scholar] [CrossRef] - Kovács, L.; Kocsor, L.; Szaller, Z.; Hajdara, I.; Dravecz, G.; Lengyel, K.; Corradi, G. Lattice Site of Rare-Earth Ions in Stoichiometric Lithium Niobate Probed by OH
^{−}Vibrational Spectroscopy. Crystals**2017**, 7, 230. [Google Scholar] [CrossRef] - Redfield, D.; Burke, W.J. Optical absorption edge of LiNbO
_{3}. J. Appl. Phys.**1974**, 45, 4566–4571. [Google Scholar] [CrossRef] - Kovács, L.; Ruschhaupt, G.; Polgár, K.; Corradi, G.; Wöhlecke, M. Composition dependence of the ultraviolet absorption edge in lithium niobate. Appl. Phys. Lett.
**1997**, 70, 2801–2803. [Google Scholar] [CrossRef] - Thierfelder, C.; Sanna, S.; Schindlmayr, A.; Schmidt, W.G. Do we know the band gap of lithium niobate? Phys. Satus Solidi C
**2010**, 7, 362–365. [Google Scholar] [CrossRef] - Devonshire, A.F. Theory of ferroelectrics. Adv. Phys.
**1954**, 3, 85–130. [Google Scholar] [CrossRef] - O’Bryan, H.M.; Gallagher, P.K.; Brandle, C.D. Congruent Composition and Li-Rich Phase Boundary of LiNbO
_{3}. J. Am. Ceram. Soc.**1985**, 68, 493–496. [Google Scholar] [CrossRef] - Bordui, P.F.; Norwood, R.G.; Jundt, D.H.; Fejer, M.M. Preparation and characterization of off-congruent lithium niobate crystals. J. Appl. Phys.
**1992**, 71, 875–879. [Google Scholar] [CrossRef] - Kittel, C. Introduction to Solid State Physics, 7th ed.; John Wiley & Sons: New York, NY, USA, 1996; pp. 99–130. [Google Scholar]
- Quin, W.; Nagase, T.; Umakoshi, Y.; Szpunar, J.A. Relationship between microstrain and lattice parameter change in nanocrystalline materials. Philos. Mag. Lett.
**2008**, 88, 169–179. [Google Scholar] [CrossRef] - Iyi, N.; Kitamura, K.; Izumi, F.; Yamamoto, J.K.; Hayashi, T.; Asano, H.; Kimura, S. Comparative study of defect structures in lithium niobate with different compositions. J. Sol. State Chem.
**1992**, 101, 340–352. [Google Scholar] [CrossRef]

**Figure 2.**Scheme of the experimental configurations used for the acquisition of Raman spectra: (

**a**) Custom-made featuring both configurations, polarized and non-polarized; (

**b**) commercially available featuring only non-polarized measurements. From left to right: RP—Raman probe, F—filter, M—mirror, L—lens, P—polarizer, BS—beam splitter, AL—aspheric lens, PS—powdered sample, S—spectrometer, O—objective.

**Figure 3.**XRD results: (

**a**) Experimental pattern of sample LN-STm and, for all samples, the differences between experimental and their respective calculated patterns with Rietveld refinement. The central sample, LN-STm, is distinguished from the rest by the solid line; (

**b**) cell volume as a function of mol % Nb precursor. The edges of the ferroelectric pure LN phase are represented by the vertical dashed lines.

**Figure 4.**X-ray diffraction patterns close to the boundaries of the pure ferroelectric LN phase: (

**a**) Under the assumption of no loss of Li, sample LN-STm is on the excess of the Li boundary; (

**b**) sample LN + 3%NbP is on the excess of Nb boundary.

**Figure 5.**Results obtained by Raman Spectroscopy: (

**a**) Non-polarized Raman spectra of the central sample LN-STm, obtained with the commercially available Raman system; (

**b**) Linear trend upon which Equation (3) is based for the case of band resolution with a Lorentzian fit, averaged calculated data from those obtained by two distinct Raman systems.

**Figure 6.**Graphics derived from analysis of the data obtained by UV-vis Diffuse Reflectance measurements: (

**a**) Normalized Kubelka-Munk or remission functions in terms of the energy of the light in eV units; (

**b**) Demonstration of the determination of the onset for sample LN-STm (assuming a direct interband transition) to determine the fundamental band gap energy; (

**c**) Fundamental band gap energy as a function of mol % Nb precursor.

**Figure 7.**Information derived from SEM: (

**a**) and (

**b**) Micrograph and particle size distribution for sample LN-STm, respectively; (

**c**) Centers of the particle size distributions obtained for four randomly-chosen samples.

**Figure 8.**Thermometric results: (

**a**) Curie temperatures as a function of mol % Nb precursor; (

**b**) Obtained curves for samples within the pure LN phase. The Curie temperatures are determined by extrapolation of the departure from the baseline.

**Table 1.**Phase percentages present in the synthesized samples, along with the calculated cell volumes and relevant agreement indices of the refinement process.

Sample | % LiNbO3 | % Li3NbO4 | % LiNb3O8 | Cell Volume $({\dot{\mathit{A}}}^{3})$ | Weighted R Profile | Goodness of Fit |
---|---|---|---|---|---|---|

LN+5%LiP | 99.9 | 0.1 | 0 | 318.0820 | 5.82 | 2.03 |

LN+4%LiP | 100 | 0 | 0 | 318.1917 | 5.24 | 1.48 |

LN+3%LiP | 100 | 0 | 0 | 318.1732 | 5.58 | 1.50 |

LN+2%LiP | 100 | 0 | 0 | 318.1546 | 5.60 | 1.49 |

LN+1%LiP | 100 | 0 | 0 | 318.0787 | 5.70 | 1.52 |

LN-STm | 100 | 0 | 0 | 318.1374 | 5.71 | 1.57 |

LN+1%NbP | 100 | 0 | 0 | 318.1930 | 5.52 | 1.55 |

LN+2%NbP | 100 | 0 | 0 | 318.3095 | 5.71 | 1.53 |

LN+3%NbP | 100 | 0 | 0 | 318.3149 | 5.54 | 1.65 |

LN+4%NbP | 98.2 | 0 | 1.8 | 318.3566 | 5.54 | 1.51 |

LN+5%NbP | 97.8 | 0 | 2.2 | 318.2735 | 5.54 | 1.57 |

Experimental Technique | Measured Parameter | Associated Error Parameter | Equation Utilized | Nb Content (mol % Nb_{2}O_{5}) |
---|---|---|---|---|

XRD + Rietveld refinement | Cell volume: 317.9234 A° | Goodness of Fit: 1.8756 | (2) | 48.2 |

Raman Spectroscopy | Γ/x_{c}: 45.3038cm^{−1}/873.9676 cm^{−1} | Reduced χ^{(2)}: 4.70 ϗ 10^{−6} | (3), Lorentz fit | 50.2 |

Γ/x_{c}: 21.8202cm^{−1}/874.1964 cm^{−1} | Reduced χ^{(2)}: 8.38 ϗ 10^{−6} | (3), Gaussian fit | 50.1 |

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**MDPI and ACS Style**

Sánchez-Dena, O.; Villagómez, C.J.; Fierro-Ruíz, C.D.; Padilla-Robles, A.S.; Farías, R.; Vigueras-Santiago, E.; Hernández-López, S.; Reyes-Esqueda, J.-A.
Determination of the Chemical Composition of Lithium Niobate Powders. *Crystals* **2019**, *9*, 340.
https://doi.org/10.3390/cryst9070340

**AMA Style**

Sánchez-Dena O, Villagómez CJ, Fierro-Ruíz CD, Padilla-Robles AS, Farías R, Vigueras-Santiago E, Hernández-López S, Reyes-Esqueda J-A.
Determination of the Chemical Composition of Lithium Niobate Powders. *Crystals*. 2019; 9(7):340.
https://doi.org/10.3390/cryst9070340

**Chicago/Turabian Style**

Sánchez-Dena, Oswaldo, Carlos J. Villagómez, César D. Fierro-Ruíz, Artemio S. Padilla-Robles, Rurik Farías, Enrique Vigueras-Santiago, Susana Hernández-López, and Jorge-Alejandro Reyes-Esqueda.
2019. "Determination of the Chemical Composition of Lithium Niobate Powders" *Crystals* 9, no. 7: 340.
https://doi.org/10.3390/cryst9070340