**1. Introduction**

Nowadays, more than 50 years after Ballman managed to grow large lithium niobate (LiNbO3; 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 [4–6], 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.

Cementation materials based on LN have been proposed as a way to improve the air quality of the environment by Artificial Photosynthesis; this is considered important for the reduction of global warming [9]. Regarding LNPws, we emphasize that not only would they be easier than single crystals to implement into cemented materials, but they would also probably enhance the intrinsic surface effects, which are the basis for an improvement of the lifetime of the carriers (photo-generated electrons and holes) involved in Artificial Photosynthesis [10]. Fe-doped LNPws also show, after a post-thermal treatment in a controlled reducing atmosphere, a rather strong ferromagnetic response at room temperature for a doping concentration of the order of 1% mol; this may be considered a first report of the manifestation of ferromagnetism in nanocrystalline LNPws within the regime of very low doping concentrations [11]. Yet in another application based on the powder-in-tube method, a novel fabrication process has been demonstrated for the realization of polarization-maintaining optical fibers [12]. Comprehension of the main mechanism behind this technology, and by looking at the LN mechanical properties [3], it can easily be seen that LNPws are, in principle, good candidates for the fabrication of this type of optical components. Also, possible tuning on the intensity of the Second Harmonic Generation (SHG) that arises from LN micro powders could be ascribed to a proper control of their chemical composition and grain size [13]. This could soon translate into major technical benefits given that neither a critical adjustment of the orientation or temperature in the material (phase matching condition) nor the accurate engineering of a microstructure (quasi-phase matching condition) are substantially needed when the SHG from disordered materials—such as LNPws—are exploited [14].

The performance of LNPws for most of their potentially attributable properties are expected to drastically depend upon their chemical composition (CC), like in the case of single-crystalline LN [3]. Indeed, it has been already demonstrated that size at the nanoscale does not affect the structural symmetry of single LN crystals and that nanosized LN single crystals (down to 5 nm) inherit the nonlinear optical properties from that of large or bulk single crystals [15]: Both the magnitude and the orientation nature of the nonlinear coefficient *dmn* 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 [16–18]. 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 *TC*. 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 *TC* that serves for both large single crystals and powders. Interestingly, this is not the case: the systematic measurement of lower *TC* values (about 10 ◦C) for LNPws compared to equivalent single crystals has already been addressed and the reason behind this remains unexplained [18].

In this investigation, a custom-made Raman system has been crafted to obtain control on the polarization state of the light at the excitation and detection stages. With this system, verification of the linear equation for the Raman active mode centered at 876 cm−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<sup>−</sup>1), under which in simpler circumstances the polarization state of light at the excitation and detection stages would be disregarded. In accordance to References [16–19], 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 *cNb* , in terms of Γ*,* is affixed to two known or expected values of *cNb* for the two edges that delimit the pure ferroelectric phase: The boundary with phase LiNb3O8 on one side (Nb excess) and the boundary with phase Li3NbO4 on the other (Li excess).

**Figure 1.** Schematic phase diagram of the Li2O-Nb2O5 pseudo binary system in the vicinity of LiNbO3—redrawn from the publications by Volk and Wöhlecke [3] and Hatano et al. [20].

The nanocrystalline LNPws are obtained by a mechanochemical-calcination route [21,22]. Gradual addition of Li or Nb has been systematically performed by increasing the mass percentage of a precursor containing the desired ion species. Quantification of secondary-phase percentages is carried out with structure refinement by a standard Rietveld method. An alternative linear equation to determine the CC is also given in terms of the calculated cell volumes by means of the same structure refinement. Additionally, linear fitting of the measured band gap energy (*Eg*), 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.
