Growth from the Melt and Properties Investigation of ScF₃ Single Crystals

Abstract

ScF₃ optical quality bulk crystals of the ReO₃ structure type (space group $Pm\overline{3}m$, a = 4.01401(3) Å) have been grown from the melt by Bridgman technique, in fluorinating atmosphere for the first time. Aiming to substantially reduce vaporization losses during the growth process graphite crucibles were designed. The crystal quality, optical, mechanical, thermal and electrophysical properties were studied. Novel ScF₃ crystals refer to the low-refractive-index (n_D = 1.400(1)) optical materials with high transparency in the visible and IR spectral region up to 8.7 µm. The Vickers hardness of ScF₃ (H_V ~ 2.6 GPa) is substantially higher than that of CaF₂ and LaF₃ crystals. ScF₃ crystals possess unique high thermal conductivity (k = 9.6 Wm⁻¹К⁻¹ at 300 K) and low ionic conductivity (σ = 4 × 10⁻⁸ Scm⁻¹ at 673 К) cause to the structural defects in the fluorine sublattice.

1. Introduction

Crystalline materials based on the rare-earth fluorides RF₃ (where R = La – Lu, Y, Sc) play a significant role in the photonics and optoelectronic instrument engineering for many years [1]. ScF₃ is one of the most unusual and insufficiently explored fluoride. It is a thermomiotic, i.e., it features a negative thermal expansion (NTE) coefficient over a wide temperature range from 10 to 1100K [2]. The stability of the RF₃ structural type under standard conditions changes in the rare-earth row as R³⁺ ionic radius decreases [1]:

LaF₃-type (tysonite) → β-YF₃ (Fe₃C-cementite) → ReO₃.

In this case coordination number (CN) of the rare-earth cations changes, respectively, from CN = 11 (LaF₃-type) to CN = 8–9 (β-YF₃-type), and then up to CN = 6 (ReO₃-type). According to the crystal-chemical characteristics, ScF₃ differs drastically from other RF₃, and is close to InF₃, but its compounds have high chemical stability. In the RF₃ row, it is the only one that has structural ReO₃ type and it belongs to the perovskite-like compounds family with the common formula АВХ₃, in which the position of one of the cations (at the unit cell center) is vacant. Sc atoms are located in the centers of the octahedra composed of F atoms (Figure 1). In the ScF₃ structure, Sc³⁺ cations are located at the vertices of the primitive cubic cell. ScF₆ octahedra join with their vertices to form a three-dimensional framework. Volume voids in the structure give place to its looseness.

ScF₃ exhibit a large band gap (E_g~10.5 eV [3]) and a high chemical resistance. Among all inorganic fluorides MF_m (m = 1–4) ScF₃ has the highest melting temperature T_m = 1822 ± 3 К [4]. Under normal pressure, ScF₃ has no solid state polymorphic transitions up to melting, but under hydrostatic pressure it transforms from ReO₃-type to β-YF₃- and LaF₃-types structure forms [5,6,7,8].

Structural type ReO₃ is very sensitive to the impurities. Cubooctahedron voids between ScF₆ octahedra can be filled with rather large impurity ions. Hence, physical properties determined experimentally are often distorted. Insignificant oxygen contamination in ScF₃ crystals leads to the structure rhombohedral distortion (sp.gr. R32) [8,9,10], and phase transition at T = 1623 ± 20 К [7,8] and 1748 ± 20 К [10]. However, the authors [4,11] have not found any phase transformations in ScF₃.

ScF₃ exhibit a great isomorphous capacity with respect to the transition and rare-earth metals ions. Isomorphous doping enables varying of materials properties over a wide range. Solid solutions Sc_1–xM_xF₃, where M = Y [12,13], Al [14], Ga and Fe [15], Ti [16] were obtained with solid-phase synthesis and then investigated. Cubic phase of Sc_1–xAl_xF₃ exists up to х = 0.5 at T = 1340 К, and with Al content increasing the thermal expansion coefficient of the material changes from negative to positive [14]. Phases in Sc_1–xM_xF₃ with M = Ga, Fe exhibit a practically zero thermal expansion material over a wide temperature range 300−900 K [15]. The NTE of ScF₃ induce by the fluorine transverse oscillations normal to the Sc-F-Sc bonds and result in decreasing distance between Sc³⁺ ions [17,18]. Wide-range solid solutions Sc_1–xR_xF₃ with R = Yb [19,20] and Lu [21] were discovered by differential thermal analysis technique. Thus, ScF₃-based materials are interesting for the fundamental physical investigations of the NTE and phase-transition mechanisms.

ScF₃-based crystalline materials are promising for the practical applications as low-refraction thin-film coatings, matrices for doping by transition and rare-earth metals ions with small ion radius, as well as a component of materials with high fluorine-ion conductivity [22]. Study of the growth techniques and the properties of ScF₃ crystals can provide the possibilities to obtain thermomiotics with programmable thermal behavior, e.g., optical elements, which preserve their fixed overall dimensions over a wide temperature range.

Flux-melt method for growing ScF₃ with several mm dimensions, pure and doped with transition metal ions, has been described in [5,8,23,24,25]. LiF or NaF were used as a solvent, and the melts with content of 20–40 (mol.) % ScF₃ in platinum ampoules were cooled at a rate of up to 3 K/h. Synthesis ScF₃ nano- and microcrystals (up to 200–500 nm) from various precursors by hydrothermal synthesis was described in [26,27,28]. Gas–solution interface technique (GSIT) was used to obtain ScF₃ in the form of nano-dimensional needles and tubes [29,30]. The above techniques enable to grow, as a rule, small single crystals.

For the first time, ScF₃ bulk crystals were obtained from a melt over 50 years ago by X.S. Bagdasarov with co-workers in Shubnikov Crystallography Institute of RAS using a direct crystallization technique [31,32]. The growth was carried out in the graphite crucibles in vacuum at the pulling rate up to 1 mm/h. The crucible was heated by means of an interaction with a non-focused electron beam, which is quite a tedious procedure. No details of the growth experiments were provided. Since then, no attempts were made to obtain ScF₃ crystals from the own melt. Growth of ScF₃ bulk crystals directly from its own melt is complicated by the high melting temperature, and NTE and high vapor pressure. Therefore, the low-temperature synthesis techniques for ScF₃-based crystals growth were utilized until now. Our group attempted to obtained ScF₃ crystal from own melt using a crucible patented by us for growing volatile substances [33]. Evaporation losses in such constriction crucible were high (more than 30 wt.%) and crystals demonstrated low optical quality. Nevertheless, we managed to fabricate a ScF₃ crystal elements of 0.5 cm³ in size and even to measure its ionic conductivity [33].

The purpose of this paper is the development of a method for ScF₃ bulk crystals growth from the own melt, crystal characterization, and investigation of its some physical properties.

2. Materials and Methods

2.1. Growth Problems and Crucible Design

High melting temperature T_m of ScF₃ and its reactivity strongly restrict the choice of the growth container materials, NTE and the high vapors pressure present almost impossible requirements to the crucible design.

Data on the ScF₃ saturated vapors pressure are fitted [34,35], and the vapors pressure (P, atm) for a wide temperature range (T = 1172–1528 K) can be calculated using the following equation:

lgP = (10.092 ± 0.253) − (2.0141 ± 0.0339)∙10⁴/T.

These P values obtained are higher than those observed during growth of СaF₂ or LaF₃ crystals by a factor of 10². Extrapolation of the P(T) relationship to the value P = 1 atm yields the boiling temperature value T_b ~ 2095 K. However, the standard accepted boiling temperature for ScF₃ is considered to be T_b = 1880 К, i.e., only ~60 K higher than its melting temperature [36,37]. This is in contradiction with the observed practical results of the growth experiments, when the ScF₃ melt was strongly overheated. Hence, the boiling temperature issue is subject to a separate investigation.

Graphite is the most commonly used crucible material for a fluoride crystals growth from melt. However, ScF₃ melting at T ~ 1822–1875 К in the open crucible results in material evaporation losses exceeding 50 wt.% already after 1.5–2 h of the melt exposure. Generally, obtaining a pressure-tight connection in graphite details is quite a problem. There are several models of graphite crucibles [38,39,40] suitable for growth of crystal with high saturated vapor pressure. Sealing of the growth cell volume is achieved by using a thread connection between several graphite elements. When operating such crucibles, the melt flows into the thread connection, the result being that the crucible gets broken during its disassembly. The design suggested in [38] is essentially axially arranged and inserted into each other graphite cartridges sealed on their side surface with the condensate of the initial material during growth experiment. This model was taken as a crucible prototype used to obtaining ScF₃ crystals in our previous work [33]. But evaporation losses were still very high for it. For the purpose of this work, a special design graphite crucible, which enabled maintaining some excessive vapor pressure inside it, was developed [41]. Earlier, a graphite container based on this principle was successfully used by the authors to grow crystals of highly volatile fluoride compounds [42,43]. A crucible image is shown in Figure 2a.

The design is essentially an upturned graphite crucible with a conical bottom which is pressed up against the base by tightening up the thread connection. The charge material placed inside provides additional sealing of the crucible bottom after melting. Utilization of such a crucible results in substantially lower material losses compared to the designed models from [38,39]. It was expected that gap availability between crucible parts will also compensate for the crystal thermal expansion during their cooling.

2.2. Impurity Composition

Impurity composition of crystals was determined by a spark source mass spectrometry technique based on JMS-01-BM2 mass-spectrometer (JEOL, Tokyo, Japan). The analysis results random inaccuracy was characterized by the standard deviation value 0.15–0.30. The content of inert gases and transuranic elements is below their detection limit (0.1 ppm). ScF₃ crystal analysis for the oxygen content was carried out with vacuum induction fusion in graphite capsules. The sensitivity of this analysis was 200 ppm.

2.3. Thermal Stability

Thermal stability of the ScF₃ crystals was investigated by heating the samples in air (under low-humidity conditions), in Pt-crucibles in a muffle furnace, in the temperature range of 500–900 K for 20–24 h. The temperature was maintained constant with an error of ±2 K.

2.4. X-ray Diffraction (XRD) Analysis

XRD patterns of the crystal samples, both before and after thermal treatment, were carried out on an X-ray powder diffractometer MiniFlex 600 (Rigaku, Tokyo, Japan) with CuK_α radiation. The diffraction peaks were recorded within the angle range 2θ from 10° to 140°. Phases were identified using the ICDD PDF-2 (2014) and Crystallography Open Databases. The unit-cell parameters were calculated by the Le Bail full-profile fitting (the Jana2006 software). A high resolution X-ray diffractometer (Rigaku SmartLab diffractometer (Tokyo, Japan) equipped with 9kW rotating anode and double-crystal Ge (220) monochromator, MoK_α1 radiation) was employed to collect the X-ray rocking curve.

The samples for investigation were essentially polished plates, 0.5–5 mm thick, cut out perpendicular to the crystal growth axis.

2.5. Crystal Chemical Etching

Chemical etching was carried out by concentrated hydrofluoric acid as etching solution; the crystal samples were etched for 100 h at about 300 K. The surface morphology of ScF₃ crystals was investigated using optical microscopy and scanning electron microscopy techniques (Quanta 200 3D, FEI, Hillsboro, OR, USA).

2.6. Refractive Index

Refractive index n and its dispersion n(λ) for ScF₃ in the visible spectrum were measured using refractometric technique with the accuracy ±10^–3. Light sources were Hg– (λ = 0.436 and 0.546 µm) and Na– (λ = 0.589 µm) lamps.

2.7. Transmission Spectra

Transmission spectra of the crystals were recorded under room temperature (RT) using Varian Cary 5000 spectrophotometer (Agilent Technologies, Santa Clara, CA, USA) in the spectral region λ = 0.19–2.50 µm, and AF-1 analytical Fourier-transform spectrometer (Moscow, Russia) in the region λ = 2–16 µm.

2.8. Hardness of Crystal

Crystal hardness was investigated under room temperature (RT) by the microhardness indentation technique using Wilson 2100 Tukon Vickers/Knoop hardness tester (Aachen, Germany) operating in automatic mode.

The Vickers hardness (H_V) values at different loads were calculated using the following equation:

H_V = 1.854P/d² [kgf/mm²],

where P is the applied load and d is the diagonal length of the indentation imprint (1 kgf = 9.807 N). Measurement error was not in excess of 3%.

2.9. The Thermal Conductivity

The thermal conductivity k(T) of the crystal 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 elsewhere [44]. The sample was a non-oriented parallelepiped 6 × 6 × 20 mm³ in size. The error in determining the absolute k value did not exceed ±5%.

2.10. The Electrical Conductivity

The electrical conductivity σ of the crystals was determined by impedance spectroscopy. The measurements were carried out in the frequency range of 10⁻²–10⁷ Hz in the temperature range of 350–830 К using a Novoterm-HT 1200 system with Alpha-A+ZG4 (Novocontrol Technologies GmbH & Co KG, Montabaur, Germany) impedance tester. Silver paste (Leitsilber) as current-conducting electrodes was used. The relative measurement error was less than 1%.

3. Results and Discussion

3.1. Crystal Growth

Growth of ScF₃ crystals was carried out by the Bridgman technique in a double-zone growth chamber with resistive heating in the high pure He atmosphere, in the graphite heat unit.

ScF₃ charge material was obtained in a laboratory from Sc₂O₃ oxide (99.95%, Novosibirsk rare metals plant) by transferring it into chloride solution. Then it was deposited with concentrated HF acid followed by drying, vacuum calcination and melting in the atmosphere of polytetrafluoroethylene pyrolysis products. The growth chamber was evacuated to provide residual pressure ~10⁻³ Pa using a turbomolecular pump system. Mixture of NH₄HF₂ (97.5% Sigma-Aldrich) and СF₄ (99.999%) were used as fluorinating agents during growth. Temperature gradient in the growth zone was ~80 K/cm, crucible pulling rate - 5 mm/h, cooling rate of grown crystals ~100 К/h.

ScF₃ single crystals of optical quality have been grown in the self-sealing graphite crucibles described above. The crystals were colorless, transparent; losses of the substance during crystallization process were 4 wt.% only, no cracks and light-scattering centers were observed. Crystal ScF₃ boules 25 mm in diameter and 50 mm long were obtained. One of the as-grown ScF₃ crystals is shown in Figure 2b. With the spontaneous crystal seeding, the ScF₃ growth axis was close to [111] crystallographic direction.

Impurities content is provided in

Table 1. Results of chemical analysis of ScF₃ crystals.

Element	Content, ppm	Element	Content, ppm	Element	Content, ppm
Li	0.08	Ga	<0.02	Pr	20
Be	<0.01	Ge	<0.02	Nd	40
B	0.04	As	<0.02	Sm	8
O	300	Se	<0.02	Eu	1
F	Basis	Br	0.6	Gd	8
Na	0.2	Rb	<0.02	Tb	1
Mg	6	Sr	4	Dy	15
Al	0.2	Y	260	Ho	4
Si	1	Zr	<0.05	Er	15
P	<0.02	Mo	<0.05	Tm	3
S	2	Ru	<0.05	Yb	40
Cl	5	Rh	<0.05	Lu	6
K	0.5	Pd	<0.05	Hf	<0.1
Ca	580	Ag	<0.05	W	<0.1
Sc	Basis	Cd	<0.05	Re	<0.1
Ti	<0.01	In	<0.05	Os	<0.2
V	<0.01	Sn	<0.05	Ir	<0.1
Cr	<0.01	Sb	<0.05	Pt	<0.2
Mn	<0.01	Te	<0.05	Au	<0.2
Fe	2	I	0.4	Hg	<0.2
Co	<0.02	Cs	<0.1	Tl	<0.1
Ni	<0.02	Ba	9	Pb	<0.2
Cu	<0.02	La	40	Bi	<0.2
Zn	<0.02	Ce	4	U	<0.2

showing that the major contribution to the chemical composition is made by cations of alkali-earth and rare-earth metals resulting from the original Sc₂O₃, trace impurity of chlorine resulting from the ScF₃ reagent synthesis, and oxygen.

3.2. Crystal Structure and Quality

The assignment of crystals to the structure type ReO₃ ($Pm\overline{3}m$ space group) has been confirmed by XRD. XDR diffraction patterns of the as-grown and heat-treated ScF₃ crystals are shown in Figure 3a. The cubic lattice parameter of the as-grown ScF₃ crystal is a = 4.01401(3) Å at 295 K, which confirms well with the published data (coincides with the standard patterns PDF #79-8099, COD ID 4127282). Crystal density ρ = 2.601(3) g/cm³ (measured by hydrostatic weighing in distilled water) is insignificant lower than the theoretical density value.

Thermal treatment of crystals in the air showed that ScF₃ exhibit stability and do not loose transparency when heated up to T = 773 K. With increasing the temperature, the crystals surface was covered by additional phase Sc₂O₃ ($Ia\overline{3}$ space group, standard patterns PDF #84-1880, COD ID 4326666) with the lattice parameter a = 9.8420(3) Å (see Figure 3a), the phase being due to pyrohydrolysis of ScF₃. According to [1,37], the reaction of ScF₃ pyrohydrolysis follows the equation:

2ScF₃ + 3H₂O = Sc₂O₃ + 6HF,

without formation of intermediate oxofluoride phases specific for other RF₃.

The X-ray double-crystal rocking curve of the 222 reflection is shown in Figure 3b. The full width at half maximum (FWHM) intensity is 23" (0.0064°). The profile of the rocking curve is fairly smooth, symmetric, without splitting due to twinning. From this point of view, the measured curve indicates a relatively high quality of the ScF₃ crystal. The peak broadening (the typical FWHM for perfect semiconductor single crystals is about 5-10") is most likely due to the presence of crystal lattice deformations (strains) in the samples.

Selective chemical etching is an effective and simple method for investigation of the crystal surface morphology and structure imperfections. High chemical stability of ScF₃ hinders the search for an effective selective etchant. In our work HF was choose as an etchant during the long period of interaction. Wide mosaic structure and grain boundaries aggregations appears in the noncentral crystal parts (Figure 4a) due to NTE and arising strong strain in places where the crystal is in contact with the crucible walls. The triangle shape of dislocation etching pits is show in Figure 4b. Etching pits size varied in the range of 0.1 –0.5 μm², and their density was ~1*10⁷ сm⁻² in the central part but it increased up to ~6*10⁷ сm⁻² in the peripheral crystal area. Therefore, for improving the ScF₃ crystals quality (removing lattice strains and decreasing density of dislocations) it is necessary to post-growth ScF₃ crystal annealing.

3.3. Optical Properties

The RT transmission spectrum of the ScF₃ crystal over the wide range is shown in Figure 5a. The observed absorption bands and low transparency in UV spectral regions are attributed with presents of uncontrollable impurities, primarily, oxygen-containing. Transmission cutoff in IR-region is located at 8.7 µm. Additional deep purification of initial charge can significantly improve the transmission of ScF₃ crystals in the short-wavelength part of the transparency window. The last one is being very sensitive to the crystal impurity contaminations. A wide band gap of ScF₃ crystals makes it a promising candidate as a new transparent matrix in vacuum UV spectral range comparable to such material as LaF₃ et al. [45].

For the crystalline ScF₃, the refractive index was measured n_D = 1.400(1) and its dispersion dependence was obtained in the visible region (see Figure 5b). Dependence n(λ) for some low-refractive fluoride crystals [46,47,48] are also provided in Figure 5b for the comparison purposes.

Mathematical processing of dispersion dependence n(λ) of ScF₃ crystals was carried out using one-term Sellmeier equation:

$$n^2(\lambda )=1+\frac{A{\lambda }^2}{{\lambda }^2-{\lambda }_0^2},$$

where A = 0.9435(1) is the multiple related to the oscillators number and strength, ${\lambda }_0$ = 0.794(1) μm is the characteristic wavelength.

ScF₃ crystals refer to the low-refractive and low-dispersion materials. These materials can be considered as a promising isotropic material for antireflection coatings, on a par with the isostructural fluoroperovskite KMgF₃ crystal. Such materials with lower refractive index as KF and LiF are hygroscopic, and MgF₂ and LiCaAlF₆ – birefringent. It is worth noting that the data on the refractive indices for ScF₃ thin-film [49] are substantially higher than those for bulk crystals and coincides with vitreous silica.

3.4. Thermal Conductivity Measurements

Measurement results for thermal conductivity k(T) of ScF₃ crystal are shown in the graphical form in Figure 6a. Experimental curves of CaF₂ (space group $Fm\overline{3}m$, Z = 4) [50] and LaF₃ (space group $P\overline{3}c1$, Z = 6) [51] with different from ScF₃ crystals structure are also shown for the comparison. As can be seen in Figure 6a, absolute values for ScF₃ thermal conductivity within the observed temperature range are intermediate between the relative values for CaF₂ and LaF₃. However, temperature dependence k(T) for ScF₃ is noted for its weakness. Within the temperature range, the value of k changes only by a factor of 2, i.e., from 20.5 Wm⁻¹К⁻¹ at Т = 50 К to 9.6 Wm⁻¹К⁻¹ at Т = 300 К. The nature of the temperature dependence is slightly different from that determined by logarithmic function of the following type:

k(T)= −6.171 × ln T+44.4 [Wm⁻¹К⁻¹]

The extrapolation of our experimental data into the high temperature range (T = 400–1500 К) provides a rather accurate coincidence with the calculated ab initio values k(T) obtained by authors [52].

The availability of experimental data on the ScF₃ heat capacity [13] makes it possible to calculate temperature dependence of the mean free path l(T) of the phonons in this crystal. For the calculation, use has been made of the known Debye expression:

$$k=C\mathsf{\nu }l/3,$$

where $C$ is the heat capacity of a crystal volume unit, $\mathsf{\nu }$ is the mean phonons velocity. Thermal phonons mean velocity $\mathsf{\nu }$ was estimated as follows. Using elastic constants $c_{11}$ = 233, $c_{12}$= 17 and $c_{44}$ = 18 GPа [53,54] and referring to the known relationships for the cubic crystal system, calculations were made for the longitudinal wave velocity ${\nu }_l$ = 7.48 km/s and velocities of two transverse waves – ${\nu }_{S_1}$ = 2.67 km/s and ${\nu }_{S_2}$ = 6.48 km/s. The averaging was made as per the known formula:

$$\frac{3}{{\nu }^3}=\frac{1}{{\nu }_1^3}+\frac{1}{{\nu }_{S_1}^3}+\frac{1}{{\nu }_{S_2}^3}.$$

As a result, $\mathsf{\nu }$ = 3.71 km/s for ScF₃ crystals. The results of calculation of the phonons mean free path as a function of temperature l(T) are shown in Figure 6b. The similar data for CaF₂ [50] and LaF₃ [51] crystals are also provided here for the comparison.

One can note the weak relative dependence l(T) obtained for ScF₃, even for lowest temperatures. Such temperature dependence is specific for materials with disturbances in the periodicity of their crystal field [55]. Such disturbances perhaps are related to the ScF₃ structure intrinsic imperfection.

Indeed, the investigation of ScF₃ crystals using the electron paramagnetic resonance technique [24] showed that there are lines in the spectrum that can be referred to as the local defects in the crystal structure. Sc³⁺ vacancies in the octahedral cation positions (Frenkel defect i.e., the vacancies being, perhaps, related to the fact that Sc³⁺ cations occupy other initially vacant positions with a large CN) were considered as the defects. The evident signs of local distortion in the cubic symmetry crystal field are also indicated. (see also [25]). The electrical conductivity of undoped ScF₃ crystals with application of the anti-Frenkel anion defects model (F^- ions transition into cubooctahedron void and vacancies formation in the main anion sublattice) and their associates was considered in Reference [56].

It does not seem possible to divide contributions of the above defects into the thermal resistance of the ScF₃ crystal. Taking account of the substantial role of Sc³⁺ cations in maintaining crystal structure stability one may assume a more substantial effect in thermal phonons dispersion on the cation defects (without referring to the number of these defects). Relationship between fluorine ion conductivity and the anion sublattice disorder in fluoride crystals, and observed correlation with thermal conductivity was reported in Reference [57].

Let us note the following distinction of the obtained results. Extrapolation of l(T) into the melting temperature value T_m (Figure 6b) provides the value l_min ≈ a for both CaF₂ crystal and other crystal with fluorite structure [58], whereas for LaF₃ l_min is close to the mean interstitial distance l₀. In case of ScF₃ crystals the value l_min is three-fold the parameter a of the unit cell. Perhaps, specifics in the behavior of l(T) and k(T) are related with the special type of individual modes anharmonicity of ScF₃ crystal thermal vibrations. Necessity of description of ScF₃ phonon spectrum with the application of a quantum quartic oscillator model was noted in Reference [17].

3.5. Mechanical Properties

Dependence of ScF₃ microhardness on indentation load is shown in Figure 7. Vickers microhardness, under the load P = 0.3 H, is H_V = 2.58(4) GPa which is higher than that of both alkali-earth (CaF₂, SrF₂ [59]) and rare-earth (LaF₃ [60]) fluoride crystals. When the load was P > 0.4 N the area around indentation exhibited cracks in the material. ScF₃ crystal refers to the group of solid materials with a high tendency to brittle failure.

3.6. Ionic Conductivity

Temperature dependences of the ionic conductivity of the ScF₃ and some rare earth fluoride crystals are shown in Figure 8. The anionic transport parameters for ScF₃ are well described by the Arrhenius-Frenkel equation:

σT = Aexp(−ΔH_σ/kT),

where A = 9.7 × 10³ SKcm⁻¹ is the pre-exponential factor for electrical conductivity, ΔH_σ = 1.13 ± 0.05 eV is the ion transport activation enthalpy, k is the Boltzmann’s constant, T is the temperature.

Electrical conductivity of ScF₃ crystals changes by the order of 8 within the presented temperature range 350–833 К. Ionic conductivity is σ = 2 × 10⁻⁹ Sm/cm at T = 573 К. These results coincide with data previously published in Reference [33] within experimental error. Such low conductivity of the ScF₃ single crystal confirms data for the polycrystalline ScF₃ solid [56]. The mobility of highly charged Sc³⁺ cations is unlikely; the ion transport in ScF₃ crystals is related to anti-Frenkel defects in the anion (fluorine) crystal sublattice that is created due to the F^- ions transition into interstitial positions and simultaneous formation of anion vacancies [33]. The same crystal-chemical specifics belong to CaF₂ crystals featuring low intrinsic conductivity [61,62]. As can clearly be seen in Figure 8, ScF₃ crystal is substantially inferior to another RF₃, such as HoF₃ [63], recently studied similar TbF₃ [64] (with β-YF₃-type) and tysonite LaF₃ crystals [61,65,66] in terms of the ionic conductivity.

Low conductivity of ScF₃ crystal (compared to other RF₃ crystals) is caused by the Sc³⁺ ions low coordinating ability (CN = 6), which is not typical for rare-earth cations in fluorides, their low electron polarizability (α_cat = 1.1 ų [56]), and by strong Sc−F couplings in crystal structure (ScF₃ has the highest melting temperature among all fluorides).

4. Summary

A novel bulk ScF₃ crystal growth procedure with a self-sealing graphite crucible was designed. Optical quality ScF₃ crystals were grown successfully from the own melt by the Bridgman technique. It was noted that the density of the etching pits is very high (more than 10⁷ сm⁻²), which will require further development of the post-growth annealing procedure to reduce it.

Grown cubic ScF₃ crystals are superior to such materials as LaF₃ and СaF₂ due to their unique mechanical and optical properties. Crystals are transparent in broad spectral range up to 8.7 µm and save optical transparency under heating on air up to T = 773 K; observed weak absorption bands are related to the oxygen contamination and a more chemically pure initial charge should be used to solve this problem. ScF₃ crystals shows the isotropy of optical properties and low refractive index n_D = 1.400(1), which is close to the data for other cubic LiF and KMgF₃ crystals.

The ScF₃ thermal conductivity examination demonstrate k = 9.6 Wm⁻¹К⁻¹ at room temperature, which coincides with CaF₂ crystals. The Vickers hardness of the ScF₃ crystals strongly depends on the applied load and average is H_V ~ 2.6 GPa, which is substantially more than similar data for LaF₃ and СaF₂ crystal. Among others studied RF₃, these crystals show a very low ionic conductivity (σ = 4 × 10⁻⁸ Scm⁻¹ at 673 К) cause to structural defects in the fluorine sublattice.

We believe that our data on crystalline ScF₃ are important for the rare earth materials science and demonstrate the competitive possibilities for its application in photonics and optical instrumentation.