Growth Peculiarities and Properties of KR3F10 (R = Y, Tb) Single Crystals

Cubic KR3F10 (R = Y, Tb) single crystals have been successfully grown using the Bridgman technique. Growth of crystals of this type is complicated due to the hygroscopicity of potassium fluoride and melt overheating. The solution to the problem of oxygen-incorporated impurities has been demonstrated through the utilization of potassium hydrofluoride as a precursor. In this study, the crystal quality, structure features, and optical, thermal and electrophysical properties of KR3F10 were examined. Data on the temperature dependences of conductivity properties of KTb3F10 crystals were obtained for the first time. These crystals indicated thermal conductivity equal to 1.54 ± 0.05 Wm−1K−1 at room temperature caused by strong phonon scattering in the Tb-based crystal lattice. Ionic conductivities of KY3F10 and KTb3F10 single crystals were 4.9 × 10−8 and 1.2 × 10−10 S/cm at 500 K, respectively, and the observed difference was determined by the activation enthalpy of F− ion migration. Comparison of the physical properties of the grown KR3F10 crystals with the closest crystalline analog from the family of Na0.5−xR0.5+xF2+2x (R = Tb, Y) cubic solid solutions is reported.


Introduction
Crystalline materials are the basis of any optical and optoelectronic device. The possibility to grow bulk crystals with unique fundamental properties determines the functionality of the instrumentation, practical technological applications, and common progress in science and industry. Among complex inorganic fluorides based on rare-earth ions, KR 3 F 10 (where R = Y, Tb-Lu) single crystals with a cubic structure attract special attention as promising materials for optics and photonics [1][2][3][4]. KY 3 F 10 (KYF) single crystals, as the best studied representatives of this large KR 3 F 10 family, have acquired practical importance as a construction optical material and a laser matrix for various rare-earth ion doping [4][5][6][7][8][9][10][11][12][13][14][15]. Another prospective representative, KTb 3 F 10 (KTF) crystal, is the next generation magneto-optical material for the visible and near infrared optical Faraday isolators [16][17][18][19]. In contrast to Tb-based fluoride crystals such as TbF 3 and LiTbF 4 , this material is optically isotropic and has serious advantages over the traditionally used magneto-optical terbium-gallium garnet crystals due to their excellent thermo-optical performance. In addition, KTb 3 F 10 crystals are of interest as a high power converter phosphor for LEDs and a potential candidate for X-ray slow scintillating applications [20].
At present, large-size fluoride single crystals are grown from the melt using the Czochralski and Bridgman (Stockbarger) methods [31][32][33][34], and less often using the Kyropoulos and vertical gradient freeze (VGF) methods. The micro-pulling-down (µ-PD) method for obtaining single-crystal fibers has also been presented [35,36]. The Czochralski method allows high quality single crystals to be obtained. However this technology is expensive and complicated in comparison with the Bridgman technique.
In this work, the Bridgman-Stockbarger method for growing KR 3 F 10 single crystals was used. The use of a heating unit in the single-heater configuration to provide a sharp temperature gradient at the crystal-melt interface and in the cooling zone allows the growth of crystals of the simple fluorides and multicomponent congruently melting compositions. In most cases such thermal conditions lead to significant mechanical stresses and block the crystal structure. The growth of perfect crystals (especially incongruently melting and with pronounced cleavage) without plastic deformation traces requires a presence of the special zone with a relatively small temperature gradient at the cooling and annealing stages. Thus, complex multi-zone temperature conditions are required for the crystal growth. The best results can be obtained by using a configuration of multi-zone heating units (with two or more heaters) and a water-cooled diaphragm between them. Modeling of the crystallization conditions for our objects (transparent dielectrics) is complicated by the fact that the dominant thermal radiation in the process of heat transfer in the melt and crystal introduces nonlinearity. Complex numerical and experimental studies of thermal fields during crystallization of partially transparent materials have demonstrated that to maintain optimal crystallization conditions (uniform axial temperature gradient and preservation of the linear solidification rate), programmed variation of the heaters electric power is required [31,37].
The heating furnace split into two independent sections by means of Mo or a graphite diaphragm was employed in this work. (Figure 1a,b). This equipment allows crystals to be grown using various methods of vertical directional crystallization of the melt (Bridgman-Stockbarger, gradient freezing, Kyropoulos methods) under a minor reconstruction of the heating unit. Thus, it is possible to grow crystals of high-temperature hydrolysable fluoride with diameter up to 80 mm and length up to 140 mm, both in vacuum and in a fluorinating atmosphere [38][39][40][41]. The upper temperature limit is 2250 K. The growth chamber provides deep evacuation to a residual pressure of 10 −3 Pa using a turbomolecular pump system. be grown using various methods of vertical directional crystallization of the melt (Bridgman-Stockbarger, gradient freezing, Kyropoulos methods) under a minor reconstruction of the heating unit. Thus, it is possible to grow crystals of high-temperature hydrolysable fluoride with diameter up to 80 mm and length up to 140 mm, both in vacuum and in a fluorinating atmosphere [38][39][40][41]. The upper temperature limit is 2250 K. The growth chamber provides deep evacuation to a residual pressure of 10 −3 Pa using a turbomolecular pump system. Figure 1. The external view of the two-section growth facility (a); a simplified design of the furnace heating unit: 1-watercooled chamber shell; 2-independent blocks of the radiation thermal screens (graphite/ carbon felt); 3-upper and lower resistance heaters; 4-graphite crucible; 5-graphite (molybdenum) diaphragm; 6-pulling rod with crucible supporting holder and inner W/Re thermocouple (b) and axial temperature distribution along the growth chamber length at the different electric power ratios of the upper (W1) and lower (W2) resistance heaters (c).
The axial temperature gradient at the crystallization front is varied through the double-zone configuration of the heating unit (Figure 1c). Such a configuration provides fine tuning of the crystallization process thermal parameters for a specific type of crystal, both in the growth zone and in the cooling zones, and ultimately improves the quality of the grown crystals. By varying the electric power ratio (W1/W2) of the heaters, it is possible to change the temperature gradient in the range of 15-100 K/cm in the growth zone and create practically gradient-free conditions in the cooling zone under optimally selected parameters of the crystallization process.

Initial Chemical Reagents and Growth Parameters of Growth Process
As mentioned above, KYF crystals have a distinctly congruent melting character, whereas KTF crystals melts incongruently, and this greatly complicates the growth of this Tb-based compound ( Figure 2). The initial melt composition for growing KYF is determined by its stoichiometry, although the optimal composition of the melt for KTF growth by the Bridgman-Stockbarger technique corresponds to a content of 27.5 ± 0.5 mol. % KF [25]. The external view of the two-section growth facility (a); a simplified design of the furnace heating unit: 1-watercooled chamber shell; 2-independent blocks of the radiation thermal screens (graphite/ carbon felt); 3-upper and lower resistance heaters; 4-graphite crucible; 5-graphite (molybdenum) diaphragm; 6-pulling rod with crucible supporting holder and inner W/Re thermocouple (b) and axial temperature distribution along the growth chamber length at the different electric power ratios of the upper (W 1 ) and lower (W 2 ) resistance heaters (c).
The axial temperature gradient at the crystallization front is varied through the doublezone configuration of the heating unit (Figure 1c). Such a configuration provides fine tuning of the crystallization process thermal parameters for a specific type of crystal, both in the growth zone and in the cooling zones, and ultimately improves the quality of the grown crystals. By varying the electric power ratio (W 1 /W 2 ) of the heaters, it is possible to change the temperature gradient in the range of 15-100 K/cm in the growth zone and create practically gradient-free conditions in the cooling zone under optimally selected parameters of the crystallization process.

Initial Chemical Reagents and Growth Parameters of Growth Process
As mentioned above, KYF crystals have a distinctly congruent melting character, whereas KTF crystals melts incongruently, and this greatly complicates the growth of this Tb-based compound ( Figure 2). The initial melt composition for growing KYF is determined by its stoichiometry, although the optimal composition of the melt for KTF growth by the Bridgman-Stockbarger technique corresponds to a content of 27.5 ± 0.5 mol. % KF [25]. The following technological parameters of the growth process were applied: preliminary homogenization of the melt for 3 h, melt overheating of about 100 K, the temperature was controlled by the W/Re thermocouple and by the reference substance melting (TbF3, Tm = 1455 ± 8 K); the temperature gradient in the growth zone was ~80 K/cm. After starting the growth, the pulling rate was set to 2-3 mm/h; the cooling rate of the crystals was 50-100 K/h. The evaporation losses during the crystallization process did not exceed 1 wt. %. Thus, 30-50 mm long KR3F10 crystals with 10-30 mm in diameter were successfully grown. Cubic Na0.4R0.6F2.2 (R = Y, Tb) single crystals were grown additionally according to previously described methods [42][43][44] for comparative analysis of the properties.

X-ray Diffraction (XRD) Analysis
The XRD analysis of the crystal was carried out using an X-ray powder diffractometer Rigaku MiniFlex 600 (CuKα radiation). The diffraction peaks were recorded within the angle range 2θ from 10 to 140°. Crystal phases were identified using the ICDD PDF-2 (2017). The unit-cell parameters were calculated using the Le Bail full-profile fitting (the Jana2006 software). The high purity anhydrous powder YF 3 , TbF 3 (99.99%, LANHIT, Moscow, Russia), KF (≥99.9% Sigma-Aldrich, Louis, MO, USA), and laboratory-made hydrofluoride KHF 2 , which was obtained by the interaction of carbonate K 2 CO 3 (99.995%, Sigma-Aldrich) with a concentrated HF solution, were utilized as raw materials. The rare-earth trifluoride powders were preliminarily annealed in vacuum (~10 −2 Pa) for 3-5 h at 450 K, then melted in a fluorinating (He+CF 4 +HF) atmosphere for deep purification from oxygen-containing impurities. Directional crystallization of KYF and KTF was carried out in a He+CF 4 atmosphere in a multicellular graphite crucible. Fused YF 3 or TbF 3 were separately placed in the crucible channels as seeds. The melt composition was stoichiometric (25/75 mol. %) for KYF and enriched in KF (28/72 mol. %) for KTF.

Scanning Electron Microscopy (SEM)
The following technological parameters of the growth process were applied: preliminary homogenization of the melt for 3 h, melt overheating of about 100 K, the temperature was controlled by the W/Re thermocouple and by the reference substance melting (TbF 3 , T m = 1455 ± 8 K); the temperature gradient in the growth zone was~80 K/cm. After starting the growth, the pulling rate was set to 2-3 mm/h; the cooling rate of the crystals was 50-100 K/h. The evaporation losses during the crystallization process did not exceed 1 wt. %. Thus, 30-50 mm long KR 3 F 10 crystals with 10-30 mm in diameter were successfully grown.
Cubic Na 0.4 R 0.6 F 2.2 (R = Y, Tb) single crystals were grown additionally according to previously described methods [42][43][44] for comparative analysis of the properties.

X-ray Diffraction (XRD) Analysis
The XRD analysis of the crystal was carried out using an X-ray powder diffractometer Rigaku MiniFlex 600 (CuKα radiation). The diffraction peaks were recorded within the angle range 2θ from 10 to 140 • . Crystal phases were identified using the ICDD PDF-2 (2017). The unit-cell parameters were calculated using the Le Bail full-profile fitting (the Jana2006 software).

Scanning Electron Microscopy (SEM)
The SEM and mapping/elemental area analysis of the grown crystals were performed on Quanta 200 3D scanning electron microscope (FEI, Hillsboro, IL, USA) equipped with EDX (EDAX, Hillsboro, IL, USA).

Single-Crystal X-ray Diffraction Study of KR 3 F 10
For both compounds, KTb 3 F 10 and KY 3 F 10 suitable crystals were selected and mounted on the Rigaku XtaLAB Synergy-DW diffractometer equipped with HyPix-Arc 150 detector. Single-crystal X-ray diffraction data were collected at room temperature using monochromatized MoKα-radiation for KTb 3 F 10 and AgKα-radiation for KY 3 F 10 . The intensities were corrected for numerical absorption based on Gaussian integration over a multifaceted crystal model using the CrysAlisPro software [45]. The crystal structures of KR 3 F 10 (R = Y, Tb) were solved by the intrinsic phasing method using ShelXT [46] structure solution program with Olex2 [47] and refined with the anisotropic displacement parameters for all sites using ShelxL [48] by the full-matrix least-squares method.

Optical Properties
Transmission spectra of the crystals were recorded under room temperature using a Varian Cary 5000 spectrophotometer (Agilent Technologies, Santa Clara, CA, USA) in the spectral region λ = 0.19-3.30 µm. Samples for investigation were taken from the middle part of the crystal ingots.

The Thermal Conductivity Measurements
The temperature dependence of crystal thermal conductivity k(T) was measured by an absolute steady-state axial heat flow technique in the temperature range of 50-300 K. The measurement procedure was described in detail in [49]. The samples represented non-oriented parallelepipeds with an approximate size of 6 × 6 × 20 mm 3 . The error in determining the absolute k value did not exceed ±5%.

The Electrical Conductivity Measurements
The electrical conductivity σ dc of the KR 3 F 10 crystals was determined by impedance spectroscopy. The impedance measurements were carried out in the frequency range of 5-5 × 10 5 Hz and the resistance range of 1-10 7 Ohm using a Tesla B-507 impedance tester at temperatures of 550-825 K in the vacuum~1 Pa. KR 3 F 10 single crystals have a perfect cleavage along the crystallographic (111) plane. Taking this into account, samples oriented along the crystallographic [111] direction were prepared. The thickness of the samples was about 1.5 mm and the silver electrode areas were about 20-30 mm 2 . Silver paste (Leitsilber) was used as a current-conducting electrode. The relative measurement error did not exceed 5%. The presence in the impedance spectra of the blocking effect from inert (silver) electrodes at low frequencies indicates the ionic nature of the electrical transfer.

Growth Process Results and Crystals Characterization
The utilization of KF as a precursor is absolutely unsuitable for the production of oxygen-free KR 3 F 10 crystals (see Figure 3a) as shown by our growth experiments. These crystals appeared cloudy and opalescent or contained cloudy inclusions in the bulk. The use of a hard fluorinating growth atmosphere (fully consisting of CF 4 ) did not lead to positive results. The use of potassium hydrofluoride in the synthesis of KR3F10 single crystals has shown significant advantages. Hydrofluoride KHF2 decomposes according to the scheme: KHF2 = KF + HF in the temperature range from 430 to 450 K with the evolution of anhydrous hydrogen fluoride [50], which has an additional fluorinating effect on the melt during growth process. KR3F10 crystals grown using potassium hydrofluoride were colorless and transparent in ambient light, and did not contain scattering inclusions (Figure 3b,с). In some cases, crystals had cracks due to perfect cleavage along the (111) planes if high cooling rates (over 75 K/h) were applied.
The assignment of grown crystals to the СaF2 structure type (space group 3 , Z = 8) was confirmed by XRD. The diffraction patterns of the KR3F10 crystals are shown in Figure 4. Transparent crystal parts are single phase. The cubic lattice parameter of the KYF crystal is a = 11.5468(1) Å at room temperature, which is confirmed by the published data (coincides with the standard patterns PDF #75-3059). The composition of the transparent part of KTF crystal is not constant and represents a partial solid solution; a change in the lattice parameter a from 11.679 (1) to 11.663 (1) Å is observed along the length of the ingot, respectively. The structural aspects of the formation of such a solid solution and the mechanism of its nonstoichiometry require detailed study in the future. Crystal density ρ = 4.262(5) g/cm 3 for KYF (measured by hydrostatic weighing in distilled water) is insignificantly lower than the theoretical density data for KYF. For the terbium analogue, ρ = 5.806(5) g/cm 3 . The use of potassium hydrofluoride in the synthesis of KR 3 F 10 single crystals has shown significant advantages. Hydrofluoride KHF 2 decomposes according to the scheme: KHF 2 = KF + HF in the temperature range from 430 to 450 K with the evolution of anhydrous hydrogen fluoride [50], which has an additional fluorinating effect on the melt during growth process. KR 3 F 10 crystals grown using potassium hydrofluoride were colorless and transparent in ambient light, and did not contain scattering inclusions (Figure 3b,c). In some cases, crystals had cracks due to perfect cleavage along the (111) planes if high cooling rates (over 75 K/h) were applied.
The assignment of grown crystals to the CaF 2 structure type (space group Fm3m, Z = 8) was confirmed by XRD. The diffraction patterns of the KR 3 F 10 crystals are shown in Figure 4. Transparent crystal parts are single phase. The cubic lattice parameter of the KYF crystal is a = 11.5468(1) Å at room temperature, which is confirmed by the published data (coincides with the standard patterns PDF #75-3059). The composition of the transparent part of KTF crystal is not constant and represents a partial solid solution; a change in the lattice parameter a from 11.679(1) to 11.663(1) Å is observed along the length of the ingot, respectively. The structural aspects of the formation of such a solid solution and the mechanism of its nonstoichiometry require detailed study in the future. Crystal density ρ = 4.262(5) g/cm 3 for KYF (measured by hydrostatic weighing in distilled water) is insignificantly lower than the theoretical density data for KYF. For the terbium analogue, ρ = 5.806(5) g/cm 3 .
Losses during growth (up to 1 wt. %) are mainly due to the evaporation of more volatile KF. Therefore, a shift of the composition to the RF 3 -enriched region occurs. As a result of incongruent melting, additional impurity phases were detected in the parts of the KR 3 F 10 crystalline boules, which crystallized last. SEM and XRD revealed the presence of additional impurity of YF 3 in the opaque part of the KYF crystal. The eutectic (KYF + YF 3 ) mixture and the precipitated YF 3 rod-like phase in the bulk KYF matrix were clearly observed ( Figure 5).  Losses during growth (up to 1 wt. %) are mainly due to the evaporation of more volatile KF. Therefore, a shift of the composition to the RF3-enriched region occurs. As a result of incongruent melting, additional impurity phases were detected in the parts of the KR3F10 crystalline boules, which crystallized last. SEM and XRD revealed the presence of additional impurity of YF3 in the opaque part of the KYF crystal. The eutectic (KYF + YF3) mixture and the precipitated YF3 rod-like phase in the bulk KYF matrix were clearly observed ( Figure 5).   Losses during growth (up to 1 wt. %) are mainly due to the evaporation of more volatile KF. Therefore, a shift of the composition to the RF3-enriched region occurs. As a result of incongruent melting, additional impurity phases were detected in the parts of the KR3F10 crystalline boules, which crystallized last. SEM and XRD revealed the presence of additional impurity of YF3 in the opaque part of the KYF crystal. The eutectic (KYF + YF3) mixture and the precipitated YF3 rod-like phase in the bulk KYF matrix were clearly observed ( Figure 5).  A decrease in the degree of melt overheating during growth results in an increase in the length of the useful transparent part of the KYF crystals. Two polymorphic modifications, KTb 2 F 7 and the compound KTbF 4 , were detected in addition to the main cubic phase in the top parts of the grown KTF crystals, which crystallized last, as shown in [25].
Taking into account the shortest distances between the R 3+ cations, one can consider the [R 6 F 32 ] cluster, in which the 24 external F(1) fluorine atoms form a truncated octahedron, and eight internal F(2) atoms form a cubic central cavity (Figure 6, left). The alternative means of describing the crystal structure is based on the polyanionic cluster [R 6 F 36 ] in which 12 internal F(1) atoms form a central cuboctahedral cavity and 24 outer F(2) atoms form a rhombicuboctahedron (Figure 7, left). In both cases, the clusters and K+ ions are arranged as Ca 2+ and Fions in the fluorite structure (Figures 6 and 7). The clusters [R 6 F 36 ] or [R 6 F 32 ] adopt a face-cubic centered arrangement, occupying the vertices and face centers of the cubic unit cell, and are connected through F-F edges to form a three-dimensional framework. The K + ions occupy the tetrahedral interstitial sites in fluorite-like structure and are coordinated with four nearest fluorine ions F(2) at distances of 2.786 Å in KTb 3 F 10 or 2.766 Å in KY 3 F 10 , and to twelve fluorine atoms F(1) at a distance of 3.226 Å in KTb 3 F 10 or 3.195 Å in KY 3 F 10 (Figure 7, right).
Crystals 2021, 11, x FOR PEER REVIEW 9 of 17 in which 12 internal F(1) atoms form a central cuboctahedral cavity and 24 outer F(2) atoms form a rhombicuboctahedron (Figure 7, left). In both cases, the clusters and K+ ions are arranged as Ca 2+ and Fions in the fluorite structure (Figures 6 and 7). The clusters [R6F36] or [R6F32] adopt a face-cubic centered arrangement, occupying the vertices and face centers of the cubic unit cell, and are connected through F-F edges to form a three-dimensional framework. The K + ions occupy the tetrahedral interstitial sites in fluorite-like structure and are coordinated with four nearest fluorine ions F(2) at distances of 2.786 Å in KTb3F10 or 2.766 Å in KY3F10, and to twelve fluorine atoms F(1) at a distance of 3.226 Å in KTb3F10 or 3.195 Å in KY3F10 (Figure 7, right).    in which 12 internal F(1) atoms form a central cuboctahedral cavity and 24 outer F(2) atoms form a rhombicuboctahedron (Figure 7, left). In both cases, the clusters and K+ ions are arranged as Ca 2+ and Fions in the fluorite structure (Figures 6 and 7). The clusters [R6F36] or [R6F32] adopt a face-cubic centered arrangement, occupying the vertices and face centers of the cubic unit cell, and are connected through F-F edges to form a three-dimensional framework. The K + ions occupy the tetrahedral interstitial sites in fluorite-like structure and are coordinated with four nearest fluorine ions F(2) at distances of 2.786 Å in KTb3F10 or 2.766 Å in KY3F10, and to twelve fluorine atoms F(1) at a distance of 3.226 Å in KTb3F10 or 3.195 Å in KY3F10 (Figure 7, right).   The composition of the polyanionic [R 6 F 36 ] cluster is similar to that of the rare-earth cluster in the ordered phases of the MF 2 -RF 3 systems (where M-alkaline earth, R-rare-earth cations). This reveals the affinity of the KR 3 F 10 structural type with other fluoritelike ordered phases containing anionic [R 6 F 36 ] cuboctahedra. This approach makes it possible to consider KR 3 F 10 crystals as representatives of fluorite-like phases MF 2 -RF 3 and to describe their structurally dependent properties from the point of view of general structural nature [56].

Optical Properties of KR 3 F 10 Crystals
The optical absorption spectra of the grown KR 3 F 10 crystals are shown in Figure 8a, b. Both transparent and opalescent KYF crystals exhibit high absorption in the ultraviolet spectral region (Figure 8a). Significant increase in the overall absorption level in the visible region due to strong light scattering was observed for the opalescent oxygen-content KYF samples. Their short-wavelength transmission limit was significantly shifted to the visible spectral region. The composition of the polyanionic [R6F36] cluster is similar to that of the rare-earth cluster in the ordered phases of the MF2-RF3 systems (where M-alkaline earth, R-rareearth cations). This reveals the affinity of the KR3F10 structural type with other fluoritelike ordered phases containing anionic [R6F36] cuboctahedra. This approach makes it possible to consider KR3F10 crystals as representatives of fluorite-like phases MF2-RF3 and to describe their structurally dependent properties from the point of view of general structural nature [56].

Optical Properties of KR3F10 Crystals
The optical absorption spectra of the grown KR3F10 crystals are shown in Figure 8a, b. Both transparent and opalescent KYF crystals exhibit high absorption in the ultraviolet spectral region (Figure 8a). Significant increase in the overall absorption level in the visible region due to strong light scattering was observed for the opalescent oxygen-content KYF samples. Their short-wavelength transmission limit was significantly shifted to the visible spectral region. A number of additional weak absorption bands were observed in the IR range for the opalescent KYF crystal (Figure 8a, inset). It is known that some oxygen impurities, namely OHgroups and HCOcomplexes, are responsible for the appearance of absorption bands in the range λ = 2.6-3.5 μm [57]. As seen from Figure 8a, the IR spectrum contains weakly intense narrow bands that can be attributed to these complexes. The OH − and HCO − complexes are due to carbon contamination caused by oxides, which is not totally eliminated in the synthesis process and indicates that there were water vapor traces during the crystal growth process. No IR absorption bands appeared in this spectral range for the transparent KYF samples. Additional deep purification of the initial charge and atmosphere during the growth process can significantly improve the spectral quality of these crystals in the short-wavelength part of the transparency window. The last is highly sensitive to the oxygen impurity contaminations. Note that oxygen-free KYF crystals are characterized by a wide transparency region up to 0.13 μm and are promising optical materials for the VUV spectral region [58,59].
The absorption spectrum of KTb3F10 crystal is represented in Figure 8b. This is typical for crystals containing Tb 3+ ions. The electro-dipole transitions within the 4f 8 configuration A number of additional weak absorption bands were observed in the IR range for the opalescent KYF crystal (Figure 8a, inset). It is known that some oxygen impurities, namely OHgroups and HCOcomplexes, are responsible for the appearance of absorption bands in the range λ = 2.6-3.5 µm [57]. As seen from Figure 8a, the IR spectrum contains weakly intense narrow bands that can be attributed to these complexes. The OH − and HCO − complexes are due to carbon contamination caused by oxides, which is not totally eliminated in the synthesis process and indicates that there were water vapor traces during the crystal growth process. No IR absorption bands appeared in this spectral range for the transparent KYF samples. Additional deep purification of the initial charge and atmosphere during the growth process can significantly improve the spectral quality of these crystals in the short-wavelength part of the transparency window. The last is highly sensitive to the oxygen impurity contaminations. Note that oxygen-free KYF crystals are characterized by a wide transparency region up to 0.13 µm and are promising optical materials for the VUV spectral region [58,59].
The absorption spectrum of KTb 3 F 10 crystal is represented in Figure 8b. This is typical for crystals containing Tb 3+ ions. The electro-dipole transitions within the 4f 8 configuration of this ion are clearly observed without additional impurity lines [18,20,21]. KTb 3 F 10 crystals demonstrate a transparency window in the range of 0.4-1.5 µm, with the exception of a narrow absorption line near λ =~485 nm (7F 6 -5D 4 transition of Tb 3+ ion).

Thermal Conductivity Measurements
The thermal conductivity of KTb 3 F 10 crystals was measured for the first time in a wide temperature range (Figure 9a). The thermal conductivity temperature dependences k(T) of KYF [60], Na 0.4 Y 0.6 F 2.2 , and Na 0.37 Tb 0.63 F 2.26 [61] crystals are shown for comparison (Figure 9b). It is noticeable that the k(T) dependences of the KR 3 F 10 and Na 0.5-x R 0.5+x F 2+2x crystal families differ significantly. The presence of a large number of phonon scattering centers in Na 0.5-x R 0.5+x F 2+2x crystals determines the glass-like character of their k(T) dependences.
The thermal conductivity of the KTb3F10 crystal is also low; it varies within narrow limits, from 1.54 to 1.74 Wm −1 K −1 in the explored temperature range. Amorphous materials have similar values of the thermal conductivity coefficient. However, in the region of T = 74 K, a low-temperature maximum k(T) characteristic of crystalline media was observed for KTb3F10. These features indicate, on the one hand, the presence of a long-range order in the crystal structure of this material, and, on the other hand, a very significant phonon scattering manifestation in the investigated temperature range. The KTF crystal is significantly inferior to its yttrium isostructural KYF analogue in terms of thermal conductivity. For comparison, the composition of KTF contains K + and Tb 3+ cations, which differ greatly in mass, whereas the corresponding difference is less in KYF crystal. A significant difference in the masses of the oscillators predetermines the presence of optical modes in the phonon spectrum of a crystal, which usually make a small contribution to heat transfer compared to acoustic modes. So this factor makes the crystal a poor heat conductor. In addition, a higher density of the KTb3F10 crystal corresponds to a lower average propagation velocity of acoustic vibration modes.
Another possible factor determining the comparatively low thermal conductivity of KTb3F10 crystal should be indicated. In many cases, Tb 3+ ions exhibit splitting of the electron paramagnetic levels of the 4f shell. Oxide Tb-based crystals (differing from fluoride The thermal conductivity of the KTb 3 F 10 crystal is also low; it varies within narrow limits, from 1.54 to 1.74 Wm −1 K −1 in the explored temperature range. Amorphous materials have similar values of the thermal conductivity coefficient. However, in the region of T = 74 K, a low-temperature maximum k(T) characteristic of crystalline media was observed for KTb 3 F 10 . These features indicate, on the one hand, the presence of a long-range order in the crystal structure of this material, and, on the other hand, a very significant phonon scattering manifestation in the investigated temperature range.
The KTF crystal is significantly inferior to its yttrium isostructural KYF analogue in terms of thermal conductivity. For comparison, the composition of KTF contains K + and Tb 3+ cations, which differ greatly in mass, whereas the corresponding difference is less in KYF crystal. A significant difference in the masses of the oscillators predetermines the presence of optical modes in the phonon spectrum of a crystal, which usually make a small contribution to heat transfer compared to acoustic modes. So this factor makes the crystal a poor heat conductor. In addition, a higher density of the KTb 3 F 10 crystal corresponds to a lower average propagation velocity of acoustic vibration modes.
Another possible factor determining the comparatively low thermal conductivity of KTb 3 F 10 crystal should be indicated. In many cases, Tb 3+ ions exhibit splitting of the electron paramagnetic levels of the 4f shell. Oxide Tb-based crystals (differing from fluoride crystals due to a stronger crystal field) are characterized by a relatively low thermal conductivity [62]. If the magnitude of the splitting ∆E is in the range of 0-200 cm -1 , then it should be the cause of resonant phonon scattering and a corresponding decrease in thermal conductivity. Unfortunately, no data on this level splitting in the KTb 3 F 10 can be found in the literature.
Disorder in the crystal structure usually results in phonon scattering. The basic fluorite structure of KR 3 F 10 crystals is characterized by a divalent oxidation state of cations. The presence of trivalent rare-earth ions causes the appearance of large defect clusters, which are effective centers of phonon scattering. The consequence of this is a significant decrease in thermal conductivity and a weakening of its k(T) dependence. This phenomenon is well known (see, for example, [63][64][65]) for the heterovalent solid solution M 1-x R x F 2+x (M = Ca, Sr, Ba; R-rare-earth) crystals with a fluorite structure. The behavior of the thermal conductivity of M 1-x R x F 2+x crystals becomes characteristic of glasses due to percolation of clusters at high concentrations of trivalent ions. Apparently, the presence of [R 6 F 36 ] structural blocks and their ordering can determine the thermal conductivity in the case of KR 3 F 10 crystals. Therefore, the temperature dependence of the thermal conductivity of KR 3 F 10 crystals can be considered as transitional from k(T) of undoped MF 2 crystals to k(T) of concentrated heterovalent M 1-x R x F 2+x solid solutions.
The results of a comparison of the thermal conductivity of Na 0.4 Y 0.6 F 2.2 and Na 0.37 Tb 0.63 F 2.26 crystals were as expected (Figure 9b). The presence of Tb 3+ ions in the crystal composition in this case is also a negative factor and leads to its significant decrease, converting crystals of this type into low-temperature heat insulators.

Ionic Conductivity Measurements
The temperature dependences of ionic conductivity σ dc (T) for different crystal samples in the KF-YF 3 system are shown in Figure 10a. It can be seen that the transparent and opalescent KYF crystal fragments have the same σ dc values. The conductivity for the eutectic (KY 3 F 10 + YF 3 ) composite is higher than for the pure KYF compound. The extrapolated σ dc values at 500 K are 1.7 × 10 −9 and 1.2 × 10 −10 S/cm for the composite and KYF single crystal, respectively. The comparison σ dc (T) dependences for KR 3 F 10 crystals are shown in Figure 10b. Data for Na 0.5-x R 0.5+x F 2+2x solid solution crystals are shown additionally.
Crystals 2021, 11, x FOR PEER REVIEW 12 of 17 crystals due to a stronger crystal field) are characterized by a relatively low thermal conductivity [62]. If the magnitude of the splitting ΔE is in the range of 0-200 cm -1 , then it should be the cause of resonant phonon scattering and a corresponding decrease in thermal conductivity. Unfortunately, no data on this level splitting in the KTb3F10 can be found in the literature. Disorder in the crystal structure usually results in phonon scattering. The basic fluorite structure of KR3F10 crystals is characterized by a divalent oxidation state of cations. The presence of trivalent rare-earth ions causes the appearance of large defect clusters, which are effective centers of phonon scattering. The consequence of this is a significant decrease in thermal conductivity and a weakening of its k(T) dependence. This phenomenon is well known (see, for example, [63][64][65]) for the heterovalent solid solution M1-xRxF2+x (M = Ca, Sr, Ba; R-rare-earth) crystals with a fluorite structure. The behavior of the thermal conductivity of M1-xRxF2+x crystals becomes characteristic of glasses due to percolation of clusters at high concentrations of trivalent ions. Apparently, the presence of [R6F36] structural blocks and their ordering can determine the thermal conductivity in the case of KR3F10 crystals. Therefore, the temperature dependence of the thermal conductivity of KR3F10 crystals can be considered as transitional from k(T) of undoped MF2 crystals to k(T) of concentrated heterovalent M1-xRxF2+x solid solutions.
The results of a comparison of the thermal conductivity of Na0.4Y0.6F2.2 and Na0.37Tb0.63F2.26 crystals were as expected (Figure 9b). The presence of Tb 3+ ions in the crystal composition in this case is also a negative factor and leads to its significant decrease, converting crystals of this type into low-temperature heat insulators.

Ionic Conductivity Measurements
The temperature dependences of ionic conductivity σdc(T) for different crystal samples in the KF-YF3 system are shown in Figure 10a. It can be seen that the transparent and opalescent KYF crystal fragments have the same σdc values. The conductivity for the eutectic (KY3F10 + YF3) composite is higher than for the pure KYF compound. The extrapolated σdc values at 500 K are 1.7 × 10 −9 and 1.2 × 10 −10 S/cm for the composite and KYF single crystal, respectively. The comparison σdc(T) dependences for KR3F10 crystals are shown in Figure 10b. Data for Na0.5-xR0.5+xF2+2x solid solution crystals are shown additionally.  The σ dc (T) dependences for KR 3 F 10 (R = Tb, Y) single crystals were fitted according to the Arrhenius-Frenkel equation: where A-preexponential conductivity factor, H σ -activation enthalpy of ion transport, k B -Boltzmann's constant, T-temperature. The Arrhenius-Frenkel equations parameters and measured room temperature thermal conductivity data are given in Table 2. The ionic conductivity of KYF was much higher than that of KTF, because KYF has a lower potential barrier for the charge carrier migration (H σ ) than that of KTF. The σ dc value for KTb 3 F 10 is two orders of magnitude higher than for KY 3 F 10 crystals. Nevertheless, results obtained for KR 3 F 10 compounds and the electrophysical data for the Na 0.5-x R 0.5+x F 2+2x solid solutions show that the fluorine-ion transfer in the KF-based compounds is significantly lower than in the NaF-based ones (Figure 10b). This drop in ionic conductivity magnitude is primarily associated with a twofold increase in potential barriers to the migration of charge carriers: from 0.7-0.8 eV for Na 0.5-x R 0.5+x F 2+2x (R = Tb, Y) to 1.2-1.6 eV for KR 3 F 10 crystals. The σ dc (T) dependences for Na 0.5-x R 0.5+x F 2+2x solid solution crystals consist of two linear segments with the temperature of the transition between them of T =~750 K (Figure 10b). Each segment of conduction dependences satisfies the Arrhenius-Frenkel equation. A similar situation is valid for fluorite-type Ca 1-x R x F 2+x (R = La-Lu, Y) crystals [68]. A common feature of the conductivity of these crystals is the fulfillment of the following condition: activation enthalpy of ion transport in the high-temperature region is greater than in the low-temperature region. The hightemperature region of conductivity is probably connected with the process of dissociation of bonded fluorine ions from clusters.

Conclusions
Bulk KR 3 F 10 (R = Y, Tb) single crystals were successfully grown by the Bridgman technique. The synthesis, growth parameters, and investigation of properties are presented for crystals of this type in detail.
Thermal conductivity k(T) of KR 3 F 10 crystals experimentally determined for the first time in the temperature range of 50-300 K noticeably exceeds the thermal conductivity of isostructural Na 0.5-x R 0.5+x F 2+2x solid solution crystals (R = Tb, Y). It is shown that the Tb-based fluoride crystals are inferior in thermal conductivity to yttrium analogs due to significant phonon scattering manifestation. The temperature dependences of the ionic conductivity σ dc (T) of KR 3 F 10 (R = Y, Tb) crystals were investigated. σ dc (T) dependences satisfy the Frenkel-Arrhenius equation in the temperature range 550-820 K. Comparison of the electroconductive properties of KR 3 F 10 compounds and Na 0.5-x R 0.5+x F 2+2x solid solutions, the structure of which builds on the [R 6 F 37 ] clusters basis, is performed. The ordered KR 3 F 10 superstructure formed on the basis of these clusters leads to a twofold increase in potential barriers for the migration of charge carriers and a drop in ionic conductivity (at 500 K) by 2-4 orders of magnitude in KR 3 F 10 single crystals compared to Na 0.5-x R 0.5+x F 2+2x solid solutions with a disordered cluster formation.
These complex studies, from crystal growth to structure determination and study of properties, will be of great importance for photonic applications of complex fluorides KR 3 F 10 (R = Y, Tb) in the future.