Oxygen–Ion Conductivity, Dielectric Properties and Spectroscopic Characterization of “Stuffed” Tm 2 (Ti 2 − x Tm x )O 7 − x /2 ( x = 0, 0.1, 0.18, 0.28, 0.74) Pyrochlores

: Tm 2 (Ti 2 − x Tm x )O 7 − x /2 ( x = 0, 0.1, 0.18, 0.28, 0.74) solid electrolytes have been investigated as potential electrolyte materials for solid oxygen fuel cells (SOFCs), operating in the medium temperature range (600–700 ◦ C). The design of new oxygen-conducting materials is of importance for their possible utilization in the solid oxide fuel cells. The oxygen–ion conductivity of the Tm 2 (Ti 2 − x Tm x )O 7 − x /2 ( x = 0, 0.1, 0.18, 0.28, 0.74) “stuffed” pyrochlores ceramics was investigated by electrochemical impedance spectroscopy (two-probe AC) in dry and wet air. The synthesis of precursors via co-precipitation and the precipitate decomposition temperature have been shown to be of key importance for obtaining dense and highly conductive ceramics. At ~770 ◦ C, the highest total conductivity, ~3.16 × 10 − 3 S/cm, is offered by Tm 2 Ti 2 O 7 . The conductivity of the ﬂuorite-like solid solution Tm 2 (Ti 2 − x Tm x )O 7 − x /2 ( x = 0.74) is an order of magnitude lower. However, for the ﬁrst time a proton contribution of ~5 × 10 − 5 S/cm at 600 ◦ C has been found in Tm 2 (Ti 2 − x Tm x )O 7 − x /2 ( x = 0.74) ﬂuorite. Until now, compositions with proton conductivity were not known for the intermediate and heavy rare earth titanates Ln 2 (Ti 2 − x Ln x )O 7 − x /2 ( Ln = Ho − Lu) systems. The use of X-ray diffraction (structural analysis with Rietveld reﬁnement), optical spectroscopy and dielectric permittivity data allowed us to follow structural disordering in the solid solution series with increasing thulium oxide content. High and low cooling rates have been shown to have different effects on the properties of the ceramics. Slow cooling initiates’ growth of ﬂuorite nanodomains in a pyrochlore matrix. The fabrication of such nanostructured dense composites is a promising direction in the synthesis of highly conductive solid electrolytes for SOFCs. We assume that high-temperature ﬁring of nanophase precursors helps to obtain lightly doped “stuffed” pyrochlores, which also provide the high oxygen–ion conductivity.

Thus, there are still significant discrepancies in the conductivity data reported for oxygen-ion conducting RE titanates prepared by different techniques, and the origin of the striking difference in properties between the Tm 2 Ti 2 O 7 single crystal and ceramics with the nominal composition Tm 2 Ti 2 O 7 remains unclear. In a study of oxygen-ion conducting ceramics and a single crystal with the composition La 10 W 2 O 21 and a fluorite-related structure [31], the ionic conductivity of the crystal was found to considerably exceed that of the ceramics. The conductivity of a hexagonal La 2 W 1+x O 6+3x (x~0.22) single crystal was reported to be lower than that of La 18 W 10 O 57 ceramics, having a similar composition and the same structure [32], but above 600 • C they had the same conduction mechanism: oxygen-ion transport. At the same time, below 600 • C the temperature behavior of conductivity for the single crystal changed sharply, and the activation energy for conduction increased to 2.17 eV [32].
In this paper, we report the properties of a series of Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) prepared via co-precipitation followed by high-temperature firing. The materials were characterized by impedance spectroscopy (oxygen-ion conductivity and dielectric properties) during both heating and cooling. Optical spectroscopy was used to follow the variation in the degree of structural order with Tm content on the Ti site. We make assumptions that account for the large spread in the conductivity data for Tm 2 (Ti 2−x Tm x )O 7−x/2 materials prepared by different methods and the difference in properties between the Tm 2 Ti 2 O 7 single crystal and ceramics with the same nominal composition.

Materials and Methods
Precursors for the synthesis of Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) ceramics were prepared by co-precipitation. The starting materials used were Tm 2 O 3 (99.99%, TuO-1, purity standard TU 48-4-182-74, Moscow, Russia) and TiCl 4 (OSCh 12-3, TU-6-09-2118-77, Moscow, Russia). Tm 2 O 3 was dissolved in hydrochloric acid, and the titer of the solution was determined gravimetrically. The titanium-containing starting reagent used was TiCl 4 dissolved in concentrated hydrochloric acid. The titer of this solution was also determined gravimetrically. Co-precipitation from the thulium and titanium solutions in hydrochloric acid was performed at pH 11 using aqueous ammonia as a precipitant. The resultant precipitates were centrifuged and repeatedly washed with water. The precipitates were dried in a drying oven at 105 • C for 24 h and then decomposed at 650 • C for 2 h, following which the precursors were pressed at 140 MPa and fired at 1600 • C for 4 h. After the firing, the samples were furnace-cooled (2.2 • C/min). In addition, Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.28, 0.74) ceramics were prepared using slow cooling: the material was reheated to 1600 • C, slowly cooled at 3 • C/h to 1300 • C and then furnacecooled.
Absorption spectra of the materials were calculated from their diffuse reflectance spectra, measured on a TerraSpec 4 Hi-Res spectrophotometer (Malvern Panalytical, Malvern, UK) from 350 to 2500 nm (28,000 to 4000 cm -1 ) at a spectral resolution of 3 nm in the range 350 to 1000 nm and 6 nm in the rest of the spectrum. The response function of the spectrophotometer was taken into account at regular time intervals using a Labsphere certified Spectralon reflectance standard (Labsphere, Inc., North Sutton, USA). Absorption bands were fitted with a set of Gaussians using Origin version 8 (OriginLab Corp., Northampton, MA, USA). The estimate of the approximation accuracy is the coefficient of determinism R 2 .
Samples for impedance measurements had the form of disks 7.7 mm in diameter and 2.5 mm in thickness. Porous platinum coatings on their faces were used as electrodes. Oxygen-ion conductivity was determined by impedance measurements in dry air (for all samples) and wet air (for fluorite-like Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) only) in the range 255-771 • C (heating and cooling in about 50 • C steps with 2-h holding at each temperature) using a Novocontrol Alpha AN (Novocontrol Technologies GmbH and Co. KG, Montabaur, Germany) impedance meter. The frequency range was 0.1 Hz to 1 MHz, and the applied ac voltage amplitude was varied from 50 to 500 mV. XRD patterns were collected at room temperature with a Rigaku Smartlab SE X-ray diffractometer (Cu K α radiation, λ = 1.5418 Å, Bragg-reflection geometry, 40 kV, 50 mA) in continuous mode. The 2θ range was 10 • to 70 • , scan step 0.1 • , scan rate 5 • /min. Rietveld refinement determination was carried out using the SmartLab Studio II version 4.4 software. In some cases, X-ray diffraction patterns for the powder samples were collected at room temperature on a DRON-3M automatic diffractometer (Cu K α radiation, λ = 1.5418 Å, Bragg-reflection geometry, 35 kV, 28 mA) in the 2θ range of 10 • to 75 • (scan step of 0.1 • τ = 3 s).

Structure of the Solid Solutions Studied by XRD and Optical Spectroscopy
Ceramics 2023, 6, FOR PEER REVIEW 4 samples) and wet air (for fluorite-like Tm2(Ti2−xTmx)O7−x/2 (x = 0.74) only) in the range 255-771 °C (heating and cooling in about 50 °C steps with 2-h holding at each temperature) using a Novocontrol Alpha AN (Novocontrol Technologies GmbH and Co. KG, Montabaur, Germany) impedance meter. The frequency range was 0.1 Hz to 1 MHz, and the applied ac voltage amplitude was varied from 50 to 500 mV. XRD patterns were collected at room temperature with a Rigaku Smartlab SE X-ray diffractometer (Cu Kα radiation, λ = 1.5418 Å, Bragg-reflection geometry, 40 kV, 50 mA) in continuous mode. The 2θ range was 10° to 70°, scan step 0.1°, scan rate 5°/min. Rietveld refinement determination was carried out using the SmartLab Studio II version 4.4 software. In some cases, X-ray diffraction patterns for the powder samples were collected at room temperature on a DRON-3M automatic diffractometer (Cu Kα radiation, λ = 1.5418 Å, Bragg-reflection geometry, 35 kV, 28 mA) in the 2θ range of 10° to 75° (scan step of 0.1° τ = 3 s).
The microstructure of the ceramic samples was examined using scanning electron microscopy (SEM) on a JEOL JSM-6390LA (JEOL, Tokyo, Japan).   According to recent work [5,20], the broad isomorphism range of the pyrochlore structure observed in some titanate [20] and zirconate [5] systems does not exist in  It is worth noting that the unit-cell parameter increases with Tm content on the Ti site (RTi 4+ CN=6 = 0.605 Å; RTm 3+ CN=6 = 0.88 Å). No impurity phases were detected in the ceramics.

Structure of the Solid Solutions Studied by XRD and Optical Spectroscopy
According to recent work [5,20], the broad isomorphism range of the pyrochlore structure observed in some titanate [20] and zirconate [5] systems does not exist in shortrange order, and the materials contain nanodomains of related phases. Given this, in addition to conventional furnace cooling, we carried out controlled slow furnace cooling of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.28) sample, similar in nominal composition to the material having the highest conductivity in the thulium system: Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.268) prepared by solid-state reaction [20]. Using Rietveld refinement of structural parameters after rapid and slow cooling, we calculated the structure of the resultant ceramics in two models (Table 1): 1.
Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.28) as a mixture of two (pyrochlore + fluorite) phases.  Note that, in the case of the slowly cooled sample, the two-phase model ensures better results (all R-factors are smaller), whereas in the case of the rapidly cooled pyrochlore phase, none of the models is preferable. It is reasonable to assume that the size of the fluorite nanodomains in the pyrochlore matrix slightly increased during slow cooling.
A fluorite-like solid solution Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74), which may contain pyrochlore nanodomains (~2 nm) in the short-range order, as previously found for Yb 2 (Ti 2−x Yb x ) O 7−x/2 (x = (x = 0.67) by the TEM method [33], was cooled at different rates. In this case, the two-phase model (fluorite + pyrochlore) was also the best fit, regardless of the cooling rate.
According to the Rietveld refinement, the fluorite phase content reaches 87 and 93.5 wt.% for the slowly and rapidly cooled sample Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74), respectively (Table 1). Figure 2 shows the absorption spectra for samples of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) series of solid solutions obtained by conventional furnace cooling. The absorption spectra of the ceramics show broad, slightly structured bands due to transitions from the Tm 3+ 3 H 6 ground state to the 3 F 4 (5840 cm -1 ), 3 H 5 (8460), 3 H 4 (12700), 3 F 3 + 1 F 2 (14650) and 1 G 4 (21370) excited multiplets. With increasing Tm content on the Ti site, the structural flexibility of the Tm 2 (Ti 2−x Tm x )O 7−x/2 system leads to a pyrochlore-tofluorite phase transition, accompanied by marked disordering, which shows up in optical absorption spectra of the ceramics. The absorption bands of Tm 3+ become inhomogeneously broadened. To follow structural changes, we used the 3 H 6 → 3 H 5 transition, which can be thought of as supersensitive. Energy-level transitions meeting the selection rules ∆J ≤ 2, ∆L ≤ 2 and ∆S = 0 [34] (where ∆J, ∆L and ∆S are changes in the optical transition of the spin S orbital L and the total angular momentum of the momentum J, written according to the 2S+1 L J scheme) are thought to be supersensitive to the RE environment. The results obtained by decomposing the 3 H 6 → 3 H 5 band into two Gaussians are presented in Table 2. The center frequency of the band peaking near 8000 cm -1 gradually decreases as the Tm content of the Tm 2 (Ti 2−x Tm x )O 7−x/2 solid solutions increases to x = 0.28 and then rises sharply as the percentage of the fluorite phase in the ceramics increases. The full width at half maximum (FWHM) of this band gradually increases with Tm content. The position of the band peaking near 8800 cm -1 varies little with Tm content, whereas its FWHM gradually increases. The above data demonstrate that the absorption spectra of the solid solutions are sensitive to changes in their structure. In particular, the spectra of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28) materials indicate that, with increasing Tm content, their pyrochlore structure undergoes disordering, whereas the spectrum of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) ceramic corresponds to a fluorite derivative structure, with an additional absorption band at~28,000 cm -1 . The present results confirm that the supersensitive transitions in absorption spectra of Tm 3+ are structure-sensitive; i.e., they are influenced by structural disordering with increasing Tm content, but we failed to detect fluorite nanodomains in the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18) pyrochlore solid solutions by this spectroscopic technique.
It is of interest to note that a defect fluorite structure and the structure of amorphous defect fluorite-like phases resulting from crystallization of pyrochlores were recently described in terms of short-range order using a weberite-based structural model (sp. gr. Ccmm), which ensured the best fit [16,17,35]. Most likely, the 28,000 cm -1 band observed in the spectrum of the fluorite phase is assignable to nanodomains with the weberite structure (sp. gr. Imma), which is also a fluorite derivative. In many systems where pyrochlores crystallize, there exist weberites as well. The stability of the B cations in the pyrochlore structure is important for its stabilization, e.g., in Ca 2−x Cd x Sb 2 O 7 and Ca 2−x Cd x Sb 2 O 6 F substituted calcium antimonates [36].  (Figure 3a-c). The Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.1) ceramic is more homogeneous. The particle size distribution is between 1 and 7 µm (Figure 3c). The grains are in the form of polyhedrons with 4-6 faces. Small crystallites up to 1 µm in size were observed on the ceramic surface. It is most likely that these are small particles of the micro-sized crystalline precursor that were not incorporated into the grain during crystallization, forming a fine-grained fraction. Figure 3d shows a fracture surface of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.28) ceramic. It can be seen that there is virtually no closed porosity in this ceramic.
The ceramic with the highest content of Tm 2 O 3 -Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) has a different microstructure (Figure 3d,f). Its grains are elongated in one direction, and there is no open porosity. It is evident that an unusual striated microstructure is preserved inside the grains (Figure 3f). The resulting ceramics have a density close to 100%.  Figure 5 shows temperature dependences of total and bulk conductivity, and Table 3 presents activation energies for conduction. The conductivity of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28) ceramics obeys the Arrhenius law in a wide temperature range, from 255 to 771 • C. It is also worth noting that, almost throughout the temperature range studied, the highest conductivity (3.16·10 −3 S/cm at 770 • C) is offered by the nominally stoichiometric pyrochlore phase Tm 2 Ti 2 O 7 (Table 3), like in previously studied ytterbium titanatebased ceramics [26]. Recently, a maximum oxygen-ion conductivity of~9.4 × 10 −2 S/cm at 800 • C has been achieved on 5 mol% Bi 2 O 3 doped ScSZ (Sc 2 O 3 doped ZrO 2 ) [37]. However, the introduction of Bi 2 O 3 oxide has its negative side associated with its easy reduction. With increasing Tm content, the activation energy for bulk conduction in the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18) solid solutions gradually rises from 0.946 to 1.071 eV (Table 3).     Figure 5c presents apparent grain-boundary conductivity (σ gb app ) data obtained directly from the impedance spectra, whereas Figure 5d presents specific grain-boundary conductivity σ gb sp = (C 1 /C 2 ) × σ gb app obtained with the C 1 /C 2 coefficient, where C 1 and C 2 are the capacitances of the grain bulk and grain-boundary components attained by the deconvolution of the impedance spectra using the following assumptions in the brick layer model [38][39][40][41][42]. This model relies on the following assumptions: (1) σ bulk > σ gb sp , (2) g (grain boundary thickness) << G (diameter of the grains) and (3) ε gb (the permittivity of the grain-boundary phase)~ε bulk (the permittivity of the grain interior phase). Note that it may require some revision based on new experimental data because there is solid evidence that, in some cases, grain boundary conductivity considerably exceeds bulk conductivity [43,44].  Figure 5b shows Arrhenius plots of bulk conductivity for the thulium series in comparison with data reported by Mullens et al. [20]. It is seen that, at the nominal composition Tm 2 Ti 2 O 7 , the difference in conductivity between the samples prepared in this study using co-precipitation and those prepared by solid-state reaction [20] is up to three orders of magnitude. The plot for fluorite-related Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) has a small break at 550 • C, like in the case of Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.67) prepared by solid-state reaction [20].

Conductivity of the Solid Solutions Studied by Impedance Spectroscopy
Above 550 • C, the fluorite-like ceramics prepared by the methods in question differ little in activation energy for conduction, whereas between 300 and 500 • C there is a considerable difference. This means that the choice of the synthesis method plays an important role in the preparation of pyrochlores. It seems likely that, in the synthesis of these phases, good mixing of their constituent cations should be ensured. Powders and, accordingly, ceramics prepared by conventional solid-state reaction are typically slightly inhomogeneous [45].
The conductivity of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28) pyrochlores measured during heating differed insignificantly from that obtained during cooling. At the same time, in the case of the fluorite-related Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) material, there was a marked difference in both total and bulk conductivity ( Figure 6). The difference in temperature behavior is due to the inhomogeneity of the composite ceramics, which contain domains of one phase embedded in the matrix of another phase. In the above case, the fluorite phase was a matrix. Clearly, in the case of the samples prepared by the wet chemical method, which are more uniform in composition and microstructure, the highest oxygen-ion conductivity is offered by the composite pyrochlores, whereas the composite fluorites have much lower conductivity. Unlike Mullens et al. [20], we detected no high conductivity in the case of the fluorite-related solid solutions. Thus, the matrix of such a high-temperature composite should have a basic pyrochlore structure to obtain high conductivity. Conductivity depends on the change in occupancy of the 48f, 8a and 8b sites in the Tm 2 (Ti 2−x Tm x )O 7−x/2 system and is consistent with previous results [18,46,47]. The fluorite-based composite has substantially lower conductivity, in conflict with previously reported data [20]. Note that, in the Yb 2 (Ti 2−x Yb x )O 7−x/2 series [21], synthesized by the same group as the thulium series [20], also using solid-state reaction, the conductivity of pyrochlore Yb 2 Ti 2 O 7 ceramics was substantially higher than that of fluorite-related Yb 2 (Ti 2−x Yb x )O 7−x/2 (x = 0.67) ceramics, in full accord with previously reported conductivity data for such "stuffed" titanate series [19,[27][28][29], and in both cases the conductivity was extremely low.  Figure 7 presents bulk conductivity data for two Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.28) samples, after rapid and slow cooling. The conductivity of the slowly cooled sample is seen to slightly exceed that of the rapidly cooled sample. It is reasonable to assume growth of fluorite nanodomains in the pyrochlore matrix to an optimal size, which ensures higher conductivity of such an ultradense "composite."
Comparison of the bulk conductivity data obtained for the rapidly and slowly cooled Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.28) samples during heating and cooling (Figure 8) indicates Ceramics 2023, 6 960 that these samples have slightly different Arrhenius plots of conductivity. The conductivity of the slowly cooled sample exhibits different types of behavior during heating and cooling, which is typical of fluorite-related ceramics ( Figure 6). Note that, being more homogeneous, the ceramics prepared via co-precipitation behave as a uniform system. They have the smallest possible scatter in grain size and consist of more homogeneous grains, so they cool uniformly. It seems likely that ceramics prepared by solid-state reaction have a considerable scatter in grain size, and such systems typically cool nonuniformly. Considering the change in the slope of the temperature dependence of the conductivity of the fluorite-like Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) at 550 • C (Figure 5a-c), the conductivity of a slowly cooled sample was measured not only in dry but also in wet air. Figure 9a,b show the Arrhenius dependence of the bulk and total conductivity for rapidly cooled (in dry air) and slowly cooled (in dry and wet air) Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) fluorite, respectively. It can be seen that decreasing the cooling rate in the range of 1600-1300 • C does not affect the temperature dependence of the bulk conductivity of fluorite, but it is obvious that the bulk conductivity is higher in wet air than in dry air (Figure 9a, Table 3). Taking into account the almost 100% density of this ceramic (Figure 3f), we can identify the proton contribution to the conductivity, which was first discovered in the Ln 2 O 3 -TiO 2 (Ln = Dy -Lu) systems. The proton transfer number has a value of about 0.7 (inset Figure 9a) in the temperature range from 255 • C to 411 • C and drops to 0.1 at 670 • C. The calculation is made according to the work [48].
Proton conductivity is only typical for fluorite Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74). The low density of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.67) ceramics synthesized by solid state synthesis in [20] can explain the significant deviation of its temperature dependence of bulk conductivity at temperatures below 550 • C (Figure 5b). The temperature dependence of the total conductivity in dry air is slightly different for a rapidly and slowly cooled sample (Figure 9b), and this difference is only associated with a change in the grain boundary conductivity of ceramics (Figure 9a,b).  Figure 10 shows temperature dependences of permittivity at low frequencies (0.5-250 Hz) for the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) "stuffed" solid solutions. Peaks in temperature dependences of permittivity may have various origins. In our case, such a peak was observed at the lowest frequency, 0.5 Hz, in the curves of the nominally stoichiometric and slightly substituted pyrochlores. Such effects can be due to (ferroelectric) phase transitions [49][50][51] and growth transitions in materials [23]. They can reflect oxidation and reduction processes in ceramics in the temperature range under study [52] and can be related to defects in the materials. In our case, the permittivity peak at a frequency of 0.5 Hz (Figure 10a) is characteristic of the nominally stoichiometric pyrochlore phase. Tm 2 Ti 2 O 7 pyrochlore shows a "floating" maximum in permittivity, due to oxygen vacancy relaxation in the range 600-700 • C (Figure 10a). Here all oxygen vacancies participate in the hopping mechanism of oxygen-ion conductivity, typical of oxygen-ion conductors. A similar peak was previously observed for Tm 2 Ti 2 O 7 [23] and was related to a defect fluorite, the formation of which always precedes the crystallization of pyrochlore [53].

Dielectric Properties of the Solid Solutions
As the Tm content of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) "stuffed" pyrochlores increases (Figure 10b-d), the temperature behavior of 0.5-Hz permittivity gradually changes: the peak in the curve disappears, and ε decreases. At the same time, the curves of the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.18, 0.28) samples (Figure 10c,d) exhibit some bimodality, which can be interpreted as evidence for coexistence of similar (pyrochlore and fluorite) structures in short-range order. Note that there is no bimodality in the temperature dependence of permittivity for the fluorite-related Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0.74) ceramic (Figure 10e).

Causes of the Difference in Conductivity between the Tm 2 (Ti 2−x Tm x )O 7−x/2 Ceramics Prepared via Coprecipitation and by Solid-State Reaction and Single Crystals with the Pyrochlore Structure
The conductivity of mixed oxides depends on extended defects as well, which can form during synthesis, e.g., if nanophase precursors are used [53]. An important role in the synthesis of high-temperature ceramics is played by the decomposition temperature of the precursor. For example, in a previous study where Tm 2 Ti 2 O 7 ceramics were prepared at 1670 • C [23], the co-precipitated precursor was decomposed at two temperatures: (1) below the crystallization exotherm in the DSC curve, at 650 • C, and (2) above the exothermic peak, at 740 • C. Note that, in the former case, the ceramic prepared subsequently at high temperature had a higher conductivity. In the case of a wrong choice of the precipitate decomposition temperature and duration [53], residual hydroxycarbonates in the co-precipitated mixture can lead to the formation of extended defects in the ceramic after high-temperature firing. Therefore, it is important to optimize nanophase precursor decomposition conditions in each particular case. For example, in the case of precursors prepared by hydroxide co-precipitation, the decomposition temperature should be~100-150 • C below the crystallization peak of the pyrochlore phase in the DSC curve, and the decomposition time should be rather long [53]. In a number of recent studies [53][54][55], the mechanism of the synthesis of RE titanates and hafnates with the pyrochlore structure from nanophase precursors was clarified using thermal analysis, IR spectroscopy and Raman spectroscopy.
It is absolutely clear that, in syntheses via both co-precipitation and mechanical activation, reaction intermediates react with CO 2 and atmospheric moisture during milling or hydroxide co-precipitation. In connection with this, an important feature is the formation of basic RE carbonates (Ln 2 O 3 •2CO 2 •2H 2 O and LnOHCO 3 •nH 2 O) and hydroxycarbonates (Ln 2 (CO 3 ) 2 (OH) 2(3−x) • n H 2 O) in intermediate synthesis steps [56,57]. Their decomposition in air is reversible up to 800-900 • C, so residual amounts of these compounds typically prevent one from obtaining dense ceramics [58][59][60].
If mixed oxides are prepared by solid-state reaction, which uses crystalline oxides, carbonates are even more difficult to decompose. Unlike solid-state reaction, synthesis methods utilizing nanophase precursors (co-precipitation, hydrothermal synthesis and mechanical activation in high-energy mills) produce a medium for active mass transport and allow one to minimize the amount of unreacted components. At the same time, thulium titanates prepared by different methods [20,23] differ in oxygen-ion conductivity by three orders of magnitude, so the above explanation is open to question.
In our opinion, studies of single crystals with the pyrochlore structure are important for understanding the origin of differences in conductivity between ceramics having identical or similar compositions. Single crystals were mainly grown for furthering the understanding of geometrically frustrated magnetism in Ln 2 Ti 2 O 7 (Ln = Sm -Yb) [18,[61][62][63][64][65][66]. The synthesis of large single crystals of many compounds in this series was carried out by the optical floating zone (OFZ) method [26,64]. Yb 2 Ti 2 O 7 single crystals grown by the same method but at different process parameters differed drastically in magnetic properties (specific heat anomaly). According to neutron diffraction results, one crystal had the stoichiometric composition (T = 1050 • C; slow growth speed (1.5 mm/h); air atmosphere) [65], whereas another Yb 2 Ti 2 O 7 single crystal (T = 1200 • C; slow growth speed (6 mm/h); 4 atm O 2 ) had a small deviation from stoichiometry: Yb 2 (Ti 2−x Yb x )O 7−x/2 (x = 0.046) [26].
Recall that a flux-grown Tm 2 Ti 2 O 7 single crystal had a predominantly electronic conductivity at elevated temperatures [24], unlike the ceramics prepared in this work and having the same nominal composition. In addition to pyrochlores, Gd 3 Ga 5 O 12 garnet (GGG) single crystals can be referred to as "stuffed" because they were found to contain 1-2% excess Gd on the Ga sites. Gd accommodation on the Ga site occurs in a natural way during crystal growth [67].
Analysis of the above data for single crystals makes it possible to understand the origin of the considerable differences in oxygen-ion conductivity between ceramics having identical compositions but prepared by different methods. We believe that high firing temperatures ensure insignificant deviations from stoichiometry in materials synthesized from nanophase precursors. As a result, their composition approaches that of lightly doped "stuffed" pyrochlores, which typically have high oxygen-ion conductivity. It seems likely that the deviation from stoichiometry can be so small that it cannot always be detected by diffraction techniques. According to Ross et al. [26], possible XRD evidence of such a lightly doped lattice is an increased intensity of the pyrochlore 222, 440 and 622 lines. In this study, an increased intensity of these lines was observed in the case of the Tm 2 Ti 2 O 7 ceramic.

Conclusions
Precursors for the synthesis of "stuffed" Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1, 0.18, 0.28, 0.74) pyrochlores have been prepared via co-precipitation, using aqueous ammonia as a precipitant. Optimization of precursor decomposition conditions has been shown to play an important role in the synthesis of dense ceramics at 1600 • C.
Relaxation processes related to oxygen transport activity are characterized by a maximum in the temperature dependence of permittivity and are more pronounced at a low frequency of 0.5 Hz for the Tm 2 (Ti 2−x Tm x )O 7−x/2 (x = 0, 0.1) "stuffed" pyrochlores.
We have discussed the cause of the three orders of magnitude difference in conductivity between Tm 2 (Ti 2−x Tm x )O 7−x/2 ceramics prepared using co-precipitation and solid-state reaction and assumed that the use of high firing temperatures (1600-1670 • C) and nanophase precursors leads to the formation of lightly doped "stuffed" pyrochlores having high oxygen-ion conductivity.
Slow cooling initiates growth of fluorite nanodomains in a pyrochlore matrix and favors the formation of nanostructured dense "composites," which have great potential for use in SOFCs.

Conflicts of Interest:
The authors declare no conflict of interest.