*3.3. Discussion of the Mechanochemical Reaction Including Redox Processes*

Congruent LiNbO3 crystals are strongly Li deficient and can be described by the Li1−5*x*Nb1<sup>+</sup>*x*O3 formula, where x ≈ 0.01. The excess Nb ions occupy Li sites and are charge compensated by Li vacancies. The antisite NbLi ions may trap electrons, forming small polarons. Moreover, NbLi—NbNb pairs, consisting of an antisite and its regular nearest-neighbor along the ferroelectric c axis, are capable to form stable bipolarons (for a review see [33]). The strongly localized polaron/bipolaron models can evidently be applied for the redox processes in LN nanocrystals.

Already before the appearance of the LiNb3O8 phase the LN particles underwent partial reduction as a result of ball-milling. During reduction, oxygen gas and lithium oxide are formed, the latter leaving the sample only upon annealing treatments. This leads to the appearance of various polarons with elementary cell loss at the surface [33,34]

$$2\text{LiNbO}\_3 \rightarrow \text{Nb}\_{\text{Nb}}\,^{4+} + \text{Nb}\_{\text{Li}}\,^{4+} + \text{3O}\_{\text{O}}\,^{2\cdot} + 2\text{e}^{\cdot} + \text{Li}\_2\text{O}\uparrow + \text{O}\_2\uparrow\tag{2}$$

where the NbNb<sup>4</sup><sup>+</sup> + NbLi<sup>4</sup><sup>+</sup> pair makes a bipolaron. The remaining electrons may also form either a further bipolaron or two NbLi<sup>4</sup><sup>+</sup> polarons on pre-existing NbLi antisite defects in the congruent bulk. Their broad absorption bands near 500 nm and 760 nm and the disordered structure result in uniform gray color as observed for the as-ground samples (see Scheme 1 and reflection spectra in Figure 4a). In this stage the surface is disordered and consists of strongly subcongruent lithium niobate, while Li2O forms a different phase.

The structure of the particles consisting of a large number of grains can be understood to result from an interplay of disturbed ferroelectric surface fields. The grains may be assumed to be monodomain regions of LN pairwise attracted by the strong electric fields acting on most blank surfaces of this ferroelectric. Structural damage does not allow exact fitting of the attached surfaces, resulting also in crystallographic misorientation of the grains in touch. During ball milling, the particles constantly break up and recoalesce in different arrangements, while reduction may only proceed on surfaces where oxygen evaporation is possible for a sufficiently long period. Li2O segregation on such exposed grain surfaces may finally shield the electric fields and hamper further attachments with neighboring grains. During prolonged grinding, this may result in a structure where a large part of the Li2O phase is on the external surface of the particles.

Oxidation of the samples leads to the evaporation of the segregated Li2O phase and in parallel the disappearance of all polarons. The latter recovers the white color by reverting the reduction described by Equation (2) and promotes the formation of the LiNb3O8 phase according to Equation (1) whereby a further LN formula unit is used up:

$$\text{LiNbO}\_3 + \text{Nb}\_{\text{Nb}} \overset{4+}{\text{}} + \text{Nb}\_{\text{Li}} \overset{4+}{\text{}} + \text{3O}\_{\text{O}} \overset{2^\circ}{\text{}} + 2\text{e}^\circ + \text{O}\_2 \to \text{LiNb}\_3\text{O}\_8 \tag{3}$$

as observed by XRD, Raman and optical reflection measurements prominently for the oxidized samples. The LiNb3O8 phase may form an epitaxial layer on the LiNbO3 surface as described by Semiletov et al. [35].

In all other preparation stages various mixtures of bipolarons and polarons are present mainly absorbing in the blue-green and red range, respectively (Figure 4b). While the as-ground state has a balanced mixture, its direct reduction leads to a larger bipolaron portion (less reflection in the blue-green region, see the curve with lowest reflection in Figure 4b. The same reduction, if preceded by oxidation, reproduces only bipolarons but very few NbLi<sup>4</sup><sup>+</sup> polarons (high reflection only in the red region, see blue curve). Some additional structure observed near 350 nm and 670 nm in samples having an oxidizing step in their history might be attributed to absorption related to the LiNb3O8 phase. As shown by Sugak et al. [36] the coloration is formed near the crystal surface and its distribution depends on annealing temperature. Annealing is assumed to attack the exposed surface of the particles without essentially changing their deeper structure. It should be noted that the large formation enthalpy of oxygen vacancies in LN compared to that of similar defects of the cation sublattice prevents the diffusion of oxygen within the bulk, while diffusing cations may easily occupy the empty Li sites amply available in congruent LN (see [33] and references therein).

Reaction (2) is an equivalent version of Equation (2) in Sugak et al.'s paper, separately showing near-surface formation of polarons by Nb displacement to a Li site on the one hand, and electrons available for diffusion to more deeply situated antisites causing similar coloration on the other hand. This distinction, together with the overlooked fact that elementary cells are lost upon reduction, resolves the problems of Sugak et al. about unrealistic properties of coloration allegedly following from their Equation (2). In contrast to the opinion of Sugak et al., reduction-oxidation cycles are not completely reversible processes due to possible Li oxide loss especially at higher temperatures and in closely stoichiometric LiNbO3, the latter being also much more resistant to reduction. Thermal reduction was shown to increase off-stoichiometry which, in turn, leads to larger density [37,38], quantitatively supporting Equation (2). All this gives full support to the cationic model of coloration excluding any diffusion of oxygen in the bulk. A further argument for reaction (2) specifically in our case is the expected higher density of Li-poor grain kernels, taken into account that they are produced by mechanical pressing exerted by the vials.
