La_1–yBa_yF_3–y Solid Solution Crystals as an Effective Solid Electrolyte: Growth and Properties

Abstract

A series of nonstoichiometric La_1–yBa_yF_3–y (0 ≤ y ≤ 0.12) single crystals with a tysonite-type structure (sp. gr. P-3c1) was grown from the melt by the directional crystallization method in a fluorinating atmosphere, and some physical properties were characterized. The concentration dependence of electrical conductivity σ_dc(y) La_1–yBa_yF_3–y crystals was studied. The composition of the ionic conductivity maximum for this solid electrolyte was refined. It was confirmed that the maximum conductivity σ_max = 8.5 × 10^–5 S/cm (295 K) was observed at the composition y_max = 0.05 ± 0.01. Analysis of the electrophysical data for the group of tysonite-type solid electrolytes R_1–yM_yF_3–y (M = Ca, Sr, Ba, Eu²⁺ and R = La, Ce, Pr, Nd) showed that the compositions of the maxima of their conductivity were close and amount to y = 0.03−0.05. This fact indicates a weak influence of the size effect (ionic radii R³⁺ and M²⁺) on the value of y_max for R_1–yM_yF_3–y solid electrolytes.

1. Introduction

One of the paths in the search for new materials with specified properties in modern materials science is the complication of chemical composition, i.e., transition from one-component to multicomponent crystals. Nonstoichiometric phases M_1–xR_xF_2+x with a fluorite-type structure and R_1–yM_yF_3–y with tysonite-type one are formed in all binary systems MF₂–RF₃ (M are alkaline-earth elements; R are rare-earth elements). With a change in the component concentration of such phases, the physical properties of crystals vary in wide ranges due to heterovalent isomorphic substitutions. The ability to smoothly change the chemical composition of crystals allows effectively controlling the physical properties and determining compositions with an optimal combination of parameters.

Wide areas of solid solutions with a fluorite-type (sp. gr. Fm-3m) structure Ba_1–xLa_xF_2+x (0 ≤ x ≤ 0.52) and with a tysonite-type (sp. gr. P-3c1) structure La_1–yBa_yF_3–y (0 ≤ y ≤ 0.14) are formed in a condensed system BaF₂–LaF₃ (Figure 1) [1]. These solid solutions demonstrate high stability to degradation; therefore, there is a possibility of growing both fluorite and tysonite single crystals from a melt in a wide concentration range. Heterovalent solid solutions Ba_1–xLa_xF_2+x [2] and La_1–yBa_yF_3–y are promising optical materials with variable properties due to the changeable composition. Their high fluorine-ionic conductivity σ_dc is especially attractive. [3,4,5,6,7]. They have very low electronic conductivity [8,9] and therefore are effective fluorine-conducting solid electrolytes. The method of growing fluorite-type crystals Ba_1–xLa_xF_2+x is well developed, and their electrophysical properties have been studied in detail [3,4,5,6,7,10,11]. Tysonite La_1–yBa_yF_3–y crystals have higher conductometric characteristics than Ba_1–xLa_xF_2+x, but the conditions for their preparation and properties have been studied much less. At the present time, the solid electrolyte La_1–yBa_yF_3–y in terms of the set of performance characteristics has been proposed for use in the designs of the prototypes of fluorine-ion current sources of a new generation [12,13,14,15,16].

Bulk R_1–yM_yF_3–y (R = La–Lu, Y, and M = Ca, Sr, Ba) crystals are usually grown by melt crystallization methods, predominantly the Bridgman–Stockbarger method [17,18] or Czochralski method. [19,20]. The Bridgman–Stockbarger method is technologically simple and allows, due to the use of multi-cell crucibles, a concentration series of solid solution crystals to grow under identical preparative and thermal conditions.

The ionic conductivity σ_dc of La_1–yBa_yF_3–y solid electrolyte was studied on polycrystalline samples [21,22,23,24], single crystals [5], nanoceramics [24,25,26,27,28,29], and films [30,31]. It was found that the concentration dependence σ_dc(y) has a nonmonotonic character and passes through a maximum σ_max at the composition y = y_max. The conductivity values significantly depend on the technological form (crystals, ceramics, films, etc.) of the material and are maximum for single crystals.

Bulk single crystals are of particular interest for studying the fundamental characteristics of ionic transfer since only the single-crystal form gives fundamental conductivity values that are not distorted by the influence of the grain boundaries and pores. Investigating single crystals can accurately identify the composition La_1–yBa_yF_3–y solid solution, which corresponds to the maximum conductivity level. It is known that electrophysical studies of La_1–yBa_yF_3–y single crystals were carried out in [5] only. The authors used samples with a large step in composition y, which made it impossible to determine the coordinate of the σ_max exactly. A large scatter in the experimental data on the value y_max = 0.04–0.06 [21,24,28], 0.07–0.09 [5,22], 0.10 [25,27,30], and 0.15 [26] was observed for La_1–yBa_yF_3–y solid solution crystals.

Until now, there are few studies on growing concentrated tysonite-type fluoride solid solutions. Only the possibility of growing crystals of R_1–ySr_yF_3–y (R = La–Nd (0 ≤ y ≤ 0.16)) tysonite solid solutions, which are isostructural to La_1–yBa_yF_3–y crystals, have been studied [17,32]. These SrF₂-containing solid solutions have an important advantage for crystallization from a melt–congruent compositions corresponding to a singular point (temperature maximum) on the liquidus curve. The crystals with a homogeneous axial and radial distribution of the components can be grown in the vicinity of this chemical composition. Unfortunately, La_1–yBa_yF_3–y solid solution does not have compositions with congruent melting; a large difference in the liquidus and solidus temperatures leads to a significant inhomogeneous distribution of the components along the length of the crystals during directional crystallization from the melt.

The aims of the present work are:

—Growing from the melt of concentration series of La_1–yBa_yF_3–y single crystals under identical conditions and its some physical properties characterization;

—Measurement of their ionic conductivity to refine y_max on the dependence σ_dc(y);

—Comparative analysis of conductometric data for tysonite-type solid electrolytes in systems MF₂–RF₃ with M = Ca, Sr, Ba, Pb, Eu²⁺ and R = La, Ce, Pr, Nd.

2. Materials and Methods

2.1. The Peculiarities of the Growth Process

On the one hand, the proximity of the melting temperatures of LaF₃ (T_fus = 1773 ± 10 K) and BaF₂ (T_fus = 1627 ± 5 K) and their low volatility contribute to the production of La_1–yBa_yF_3–y single crystals from the melt by the direction crystallization method; on the other hand, this is hindered by the incongruent melting of the solid solution, as mentioned earlier. For tysonite-type structure, solid solutions, in comparison with fluorite-type structure solutions, a tendency to melt supercooling and spontaneous nucleation are characteristic [11], which prevents the growth of the high-quality bulk crystals. These problems are solved by increasing the temperature gradient at the growth interface and reducing the crucible pulling rate [10].

The La_1–yBa_yF_3–y solid solution compositions were chosen in the range 0 ≤ y ≤ 0.12 for the investigation. The crystals were grown by the vertical directional crystallization method in a two-section growth facility with resistive heating in graphite crucibles using non-oriented seeds. BaF₂ (purity 99.99%, Sigma-Aldrich, Darmstadt, Germany) and LaF₃ (99.99%, Lanhit Ltd., Moscow, Russia) powders were used as starting reagents. The initial powders were preliminarily calcined in a vacuum (~10^–2 Pa) at a temperature of 450 K and remelted to remove oxygen-containing impurities. The temperature gradient in the growth zone was ~100 K/cm and the crucible pulling rate was 3 mm/h. It should be noted that 5 wt.% PbF₂ was added to the charge as an oxygen scavenger in [32,33]. This is not the best choice because PbF₂ is not completely removed from the RF₃ and MF₂ melts and obviously modifies the physical properties of the crystals. Probably, at low concentrations of PbF₂ in some systems, azeotropic mixtures are formed [33,34]. Therefore, in our work, a mixture of high-purity He + CF₄ was used to create a fluorinating atmosphere in growth experiments. The evaporation loss during crystallization was no more than 2 wt. %. The La_1–yBa_yF_3–y tysonite-type crystals with a diameter of 12–14 mm and a length of up to 30 mm with the compositions y = 0; 0.005; 0.025; 0.035; 0.050; 0.060; 0.080; 0.090; 0.100; 0.120 (by charge) were successfully grown. The Ba_1–xLa_xF_2+x fluorite-type crystals in the range 0 ≤ x ≤ 0.50 and eutectic composite (BaF₂/LaF₃ = 0.68/0.32 by charge) were obtained by the above method for comparative analysis of properties.

Crystal samples were cut perpendicular to the growth axis from the ingots in the form of plane–parallel disks and were optically polished.

2.2. Density Measurement

The density ρ(y) of the samples was measured by the hydrostatic method in distilled water at room temperature. The density measurement error was Δρ = ±5 × 10^–3 g/cm³.

2.3. Refractive Indices

Refractive indices n_D for La_1–yBa_yF_3–y single crystals were measured using the refractometric technique with an accuracy of ±5 × 10^–4. The light source was Na-lamp (λ = 0.589 µm).

2.4. X-ray Diffraction (XRD) Analysis

The XRD analysis of the crystals was carried out by X-ray powder diffractometer Rigaku MiniFlex 600 (CuKα radiation). The diffraction peaks were recorded within the angle range 2θ from 10 to 140°. The calculation of the unit cell parameters a(y) and c(y) for sp. gr. P-3c1 was carried out by full-profile Rietveld analysis using the HighScore Plus software (PANanalytical, Almelo, The Netherlands).

Since a concentration gradient of the components along the crystals’ length was observed, the chemical composition of each sample was refined in terms of the unit cell parameters according to the equations for the concentration dependence of the unit cell parameters [11] and density [35] for the La_1–yBa_yF_3–y solid solution.

2.5. The Electrical Conductivity Measurements

The static electrical conductivity σ_dc at a direct current of the La_1–yBa_yF_3–y crystals was determined by impedance spectroscopy [36]. The impedance measurements were carried out in the frequency range of 5 to 5 × 10⁵ Hz using a Tesla B-507 impedance tester at temperatures of 294–800 K in a vacuum ~1 Pa. The relative measurement error did not exceed 5%.

3. Results and Discussion

3.1. Crystal Characterization

The grown La_1–yBa_yF_3–y crystalline boules were transparent and did not have cracks and light-scattering inclusions. The La_0.93Ba_0.07F_2.93 crystal is shown in Figure 1 as a typical sample.

According to XRD analysis, the La_1–yBa_yF_3–y samples were a single-phase solid solution and belonged to the tysonite (sp. gr. P-3c1) structural type (Figure 2a). The presence of impurity phases was not detected.

The unit cell parameters of this solid solution increase linearly with increasing of the fraction from y = 0 (a = 7.1832(1), c = 7.3493(1) Å) to limiting composition y = 0.14 (a = 7.2430(4), c = 7.4255(4) Å). An antibate dependence a(x) was observed for the Ba_1–xLa_xF_2+x solid solution, the lattice parameter decreased from a = 6.1992(1) Å for x = 0 (pure BaF₂) to a = 6.0378(2) Å for the limiting composition x = 0.50. The observed concentration dependences (Figure 2a, insert) coincided with the data of [1,11]. Eutectic composite contained both the saturated solid solution (F + T) which crystallized from the melt simultaneously.

The low-temperature tysonite modification is described in sp. gr. P-3c1 [37]. Purely anionic and cation-anionic layers alternated in the trigonal motif along the c axis (Figure 2b). The F^– anions were located in three non-equivalent structure positions. Substitution of La³⁺ cations on heterovalent M²⁺ ones led to the formation of vacancies in the fluorine sublattice (to maintain electroneutrality) and significantly affected the magnitude of the ionic conductivity of such tysonite solid solutions (see Section 3.2).

The La_1–yBa_yF_3–y crystals studied were uniaxial, optically negative, and were characterized by two refractive indices. The ordinary refractive index n_o was measured for La_1–yBa_yF_3–y crystals. The refractive index n_o (λ = 0.589 µm) of La_1–yBa_yF_3–y crystals decreased in a weakly square dependence from 1.5982(5) to 1.5841(5) with an increase in the fraction of y from 0 to 0.12 (Figure 3a). These crystals were highly refractive, exceeding the refractive indices of Ba_1–xLa_xF_2+x and other crystals with a fluorite-type structure. The known data for some other tysonite-type R_1–yM_yF_3–y crystals are shown for comparison. The La_1–yBa_yF_3–y crystals were similar in refractive properties to other isostructural La_1–yM_yF_3–y crystals (M = Ca, Sr, Ba) [17].

The density of La_1–yBa_yF_3–y samples quadratically decreased in the range from 5.917(5) to 5.741(5) g/cm³ with an increase in the fraction of y from 0 to 0.08 (Figure 3b) and exceeded the density of fluorite-type Ba_1–xLa_xF_2+x single crystals.

3.2. Ionic Conductivity of La_1–yBa_yF_3–y Crystals

We analyzed the impedance spectra of the La_1–yBa_yF_3–y crystals with silver electrodes. The impedance spectra were characterized by a depressed semi-circular arc at high frequency and an oblique tail at low frequency. As an example, Figure 4 shows the hodograph of the impedance Z*(ω) for the La_0.994Ba_0.006F_2.994 crystal with Ag-electrodes. The impedance spectrum Z*(ω) contained a semicircle (the center of which was displaced from the abscissa axis) simulating the electrical response from the crystal bulk and an oblique straight line (at low frequencies) simulating the electrical response from the crystal/electrode interface. An equivalent electrical circuit was used to describe the impedance hodographs. The circuit contained the crystal bulk resistivity R_b, the geometric capacitance of the crystal C_g, and the capacitance of the double layer of the crystal/electrode interface C_dl.

The bulk resistance R_b was found from the intersection of the hodograph Z*(ω) with the abscissa axis. Specific static electrical conductivity σ_dc was calculated by the formula:

σ_dc = R_b⁻¹h/S,

where h—sample thickness and S—electrode area. The temperature dependences of the ionic conductivity for La_1–yBa_yF_3–y crystals with y = 0.036 and 0.050 are shown in Figure 5a.

The σ_dc(T) dependences for all studied samples were divided into two sections, which satisfy the Arrhenius-Frenkel equation:

σ_dcT = Aexp(−ΔH_σ/k_BT),

where A—preexponential conductivity factor, ΔH_σ—activation enthalpy of ion transport, k_B—Boltzmann’s constant, T—temperature. The Arrhenius—Frenkel equations parameters A and ΔH_σ are given in

Table 1. Unit cell parameters a and c, preexponential conductivity factor A and activation enthalpy of ionic conductivity ΔH_σ for single crystals of La_1–yBa_yF_3–y solid electrolyte.

y	a, Å	c, Å	ΔT, K	A, SK/cm	ΔHσ, eV
0.006 (1)	7.1882 (1)	7.3545 (1)	294–437 437–615	7.8 × 103 3.5 × 102	0.373 0.256
0.025 (1)	7.1947 (1)	7.3611 (1)	295–419 419–534	1.9 × 104 1.6 × 103	0.347 0.258
0.036 (2)	7.1985 (2)	7.3647 (1)	295–505 505–800	1.5 × 104 6.1 × 102	0.345 0.208
0.050 (2)	7.2010 (1)	7.3682 (2)	295–557 557–754	1.1 × 104 1.6 × 103	0.332 0.241
0.055 (1)	7.2052 (1)	7.3716 (1)	294–427 427–623	5.5 × 104 3.0 × 103	0.371 0.265
0.080 (1)	7.2132 (1)	7.3802 (1)	295–419 419–531	9.0 × 104 6.3 × 103	0.389 0.294
0.086 (2)	7.2142 (2)	7.3806 (1)	294–436 436–614	1.2 × 105 2.7 × 103	0.397 0.257

.

The dependence lg σ_dc(y) at room temperature for the solid electrolyte La_1–yBa_yF_3–y, plotted based on our results and data [5,38], is shown in Figure 5b. In the range of compositions y = 0.006–0.086, the ionic conductivity varied from 1 × 10^–5 to 8.5 × 10^–5 S/cm.

The coordinates of the conductivity maximum were σ_max = 8.5 × 10^–5 S/cm and y_max = 0.05 ± 0.01. The minimum activation enthalpy ΔH_σ = 0.33 eV (low-temperature segment σ_dc(T)) corresponded to the maximum conducting composition y_max.

Note that the nonstoichiometric R_1–yM_yF_3–y crystals with a tysonite-type structure have an advantage in conductivity value over crystals with a fluorite-type structure M_1−xR_xF_2+x [3]. Apparently, this is due to the features of defect formation in these two structures. The conductivity is equalized in value only when the fluorite-type crystals are heated to 150–200 ˚C, which significantly complicates their practical application.

The coordinates of the conductivity maxima (y_max, σ_max) for a large family of tysonite-type solid electrolytes R_1–yM_yF_3–y with M = Ca, Sr, Ba, Pb, Eu²⁺ and R = La, Ce, Pr, Nd are presented in

Table 2. Coordinates of the maxima (y_max, σ_max) on the dependences σ_dc(y) at room temperature for R_1–yM_yF_3–y solid electrolytes.

Composition	Material Type *	ymax	σμαξ, Σ/Aμ	Reference
La1–yBayF3–y	S	0.05 ± 0.01	8.5 × 10–5	This work
	−«−	0.05	8 × 10–5	[39]
	−«−	0.07–0.09	8 × 10–5	[5]
	P	0.04	3 × 10–5	[21]
	−«−	0.05	2 × 10–5	[24]
	−«−	0.05	4 × 10–5	[40]
	−«−	0.06	6 × 10–5	[16]
	−«−	0.05−0.07	6 × 10–5	[22]
La1–ySryF3–y	S	0.05	2 × 10–4	[41]
	−«−	0.03	3 × 10–4	[42]
	P	0.05	5 × 10–5	[21]
La1–yCayF3–y	P	0.06	8 × 10–6	[21]
Ce1–yBayF3–y	P	0.05	1 × 10–4	[43]
	−«−	0.04–0.06	−	[44]
Ce1–ySryF3–y	S	0.03	5 × 10–4	[45]
	P	0.04	1 × 10–4	[44]
	−«−	0.07	3 × 10–5	[43]
	−«−	0.06	8 × 10–5	[16]
Ce1–yCayF3–y	P	0.05	2 × 10–4	[43]
	−«−	0.04–0.06	–	[44]
Pr1–ySryF3–y	S	0.03	5 × 10–4	[45]
Pr1–yPbyF3–y	S	0.04	7 × 10–5	[46]
Nd1–yBayF3–y	P	0.04–0.05	−	[47]
Nd1–ySryF3–y	S	0.03	3 × 10–4	[45]
	P	0.04–0.05	−	[47]
Nd1–yCayF3–y	S	0.05	1.5 × 10–4	[48]
	P	0.04–0.05	−	[47]
Nd1–yEuyF3–y	S	0.03	2 × 10–4	[49]
Nd1–yPbyF3–y	S	0.05	3 × 10–5	[46]

* S—single crystals, P—polycrystals.

. It can be seen that the maxima of ionic conductivity were realized in a narrow concentration range of y = 0.03–0.05. This fact indicates a weak effect of the R³⁺ and M²⁺cations sizes on the value of the coordinate y_max for this type of solid electrolytes with heterovalent isomorphic substitutions.

4. Conclusions

The series of La_1–yBa_yF_3–y solid electrolyte crystals with 0.00 ≤ y ≤ 0.12 was successfully grown from the melt by the Bridgman technique. Temperature measurements of the ionic conductivity of La_1–yBa_yF_3–y crystals by impedance spectroscopy were carried out in the range of 294 to 800 K. The composition of single-crystal samples was refined in terms of the unit cell parameters and density for the La_1–yBa_yF_3–y tysonite-type phase. The results of conductometric data for La_1–yBa_yF_3–y single crystals indicate that the σ_dc(y) dependence had a maximum σ_max = 8.5×10^–5 S/cm at y_max = 0.05 ± 0.01. Analysis of the published data on the compositions of the conductivity maxima for a large family of solid electrolytes R_1–yM_yF_3–y (M = Ca, Sr, Ba, Eu²⁺ and R = La, Ce, Pr, Nd) showed that they fall within the range of 0.03 ≤ y_max ≤ 0.05 regardless of the type of R³⁺ and M²⁺ cations. It is shown that the size of the cation forming a solid solution practically does not affect the value of y_max for R_1–yM_yF_3–y solid electrolytes.

Despite the high level of room temperature conductivity of the studied LaF₃-based materials, crystals of R_1–yM_yF_3–y (R = Ce, Pr, Nd; M = Ca, Sr) should be considered promising for practical implementation as a solid electrolyte with better electrophysical characteristics. It is these crystals that will become the next step in solid-state ionics as room temperature fluoride solid electrolytes and as promising polyfunctional crystalline materials of the future.