Nanostructured Fluorite-Type Fluorides As Electrolytes for Fluoride Ion

Article pubs.acs.org/JPCC

Nanostructured Fluorite-Type Fluorides As Electrolytes for Fluoride Ion Batteries Carine Rongeat,*,† M. Anji Reddy,† Raiker Witter,†,‡ and Maximilian Fichtner†,§ †

Karlsruhe Institute of Technology (KIT), Institute of Nanotechnology (INT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ‡ Technomedicum, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia § Helmholtz Institute Ulm (HIU), Electrochemical Energy Storage, Albert-Einstein-Allee 11, 89081 Ulm, Germany S Supporting Information *

ABSTRACT: Fluoride ion batteries (FIB) provide an interesting alternative to lithium ion batteries, in particular because of their larger theoretical energy densities. These batteries are based on a F anion shuttle between a metal fluoride cathode and a metal anode. One critical component is the electrolyte that should provide fast anion conduction. So far, this is only possible in solid so-called superionic conductors, at elevated temperatures. Herein, we analyze in detail the ionic conductivity in barium fluoride salts doped with lanthanum (Ba1−xLaxF2+x). Doping by trivalent cations leads to an increase of the quantity of point defects in the BaF2 crystal. These defects participate in the ionic motion and therefore improve the ionic conductivity. We demonstrate that further improvement of the conductivity is possible by using a nanostructured material providing additional conduction paths through the grain boundaries. Using electrochemical impedance spectroscopy and AC conductivity analysis, we show that the ionic conduction in this material is controlled by the motion of vacancies through the grain boundaries. The mobility of the vacancies is influenced by the quantity of dopant but decrease for too large dopant concentrations. The optimum compositions having the highest conductivities are Ba0.6La0.4F2.4 and Ba0.7La0.3F2.3. The compound Ba0.6La0.4F2.4 was successfully used as an electrolyte in a FIB.

1. INTRODUCTION The demand for more efficient and powerful secondary batteries is increasing owing to the development of portable devices and electric vehicles or the need to store the electricity produced by renewable energies. A large research effort is done toward Li-ion battery technologies in particular to improve the storage capacities of the electrodes.1−3 An alternative technology could be a battery using a fluoride (F) anion shuttle.4 Such a battery possesses a much higher theoretical energy density than current Li-ion batteries. With certain materials combinations, up to more than 5000 Wh·L−1 are possible, which is 50% above the theoretical capacity of the Liair cell. In an initial work, the reversible storage of electricity on the basis of the F− shuttle has been demonstrated according to the following reactions at the electrodes: at cathode: x e− + MFx → M + x F−

BaF2, known as a superionic F anion conductor. Optimization of all components (cathode, anode, and electrolyte) is then necessary to develop practical applications for this new type of battery. The present work is mainly dedicated to the improvement of the electrolyte. F anion conductors working at room temperature would be of great benefit for practical applications. To the best of our knowledge, no liquid F anion conductor with a good performance is known, but a variety of fluorides salts can be used as solid electrolytes:5 alkaline-earth fluorides (fluorite-type structure), rare-earth fluorides (tysonite-type structure), or lead-based fluorides (e.g., PbF2 or PbSnF4). The latter have very high conductivities but unfortunately are not compatible for a battery application due to their limited electrochemical stability. The first type of solid electrolyte used, La0.9Ba0.1F2.9, was selected for its good conductivity and its stability in the potential window used for cycling. Nanocrystalline La0.9Ba0.1F2.9 was prepared by ball milling and displayed an ionic conductivity of 2.8·10−4 S·cm−1 at 160 °C, which is lower than reported for single crystals.6 However, a powder produced by ball milling is a more scalable and flexible synthesis technique for battery applications than single crystal growth. Moreover, the electrolyte needs to be part of the electrode nanocomposite which

(1)

at anode: x F− + M′ → M′Fx + x e−

(2)

The performances were not satisfactory at this early stage of development. For example, the capacity of the battery reached only 60% of the theoretical value in the first cycle and was decreasing during cycling. The cathode was composed of various metal fluorides (MFx), the anode of a metal (M′ = Ce), and the (solid) electrolyte was a fluoride salt, LaF3 doped by © XXXX American Chemical Society

Received: November 30, 2012 Revised: January 30, 2013

A

dx.doi.org/10.1021/jp3117825 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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R and with various compositions. For all rare-earth elements, the conductivity increased with x, but sometimes it saturated at high concentration (probably above the percolation threshold), which was explained by the decrease (and saturation) of the activation energy. The highest conductivities (and lowest activation energies) have been obtained for lanthanum doped BaF2 with for example σ200°C = 1.9 × 10−4 S·cm−1 for Ba0.6La0.4F2.4. Similar results have been reported by Sorokin and Breiter.26 In this work, we report on the study of doped BaF2 compounds prepared by ball milling. To the best of our knowledge, all studies published so far on Ba1−xRxF2+x have been done on single crystals.19,26 This is the first time that both homogeneous (addition of LaF3) and heterogeneous (preparation of a nanocrystalline material) is described for BaF2 ion conductor. We discuss a potential conduction mechanism and demonstrate that the nanocrystalline doped-BaF2 can have conductivity high enough for electrolyte applications.

rules out the use of single crystals. In this work, we concentrate on fluorides having a fluorite-type structure (CaF2 type) as they are also known as excellent ionic conductors.7−9 Of particular interest are the alkaline-earth fluorides of Ca, Ba, and Sr for electrolyte applications. The ionic conductivity in solids is provided by point defects which are able to migrate in the lattice, mostly by a hopping mechanism. The intrinsic defects present in crystals with a fluorite-type structure are anti-Frenkel pairs (one anion vacancy combined with one interstitial anion). While the pure fluoritetype compounds show rather low conductivity, it can be improved dramatically by generating additional mobile defects, that is, by homogeneous and/or heterogeneous doping. Heterogeneous doping can be achieved by creating interfaces containing defects and/or providing fast diffusion paths.10 Different types of interfaces are possible: (i) between an ionic conductor and an insulator,11 (ii) between two different conductors,12,13 and (iii) within a polycrystalline ionic conductor (grain boundaries).14 In the case of fluorides, an increase of the anionic conductivity has been reported for nanocrystalline CaF215 or for CaF2/BaF2 nanolayers.13 The preparation of nanocrystalline materials by ball milling has also led to an improvement of the ionic conductivity of BaF2,14 CaF 2 , 14,16 or SnF 2 :PbF 2 mixtures. 17 In all cases, the conductivity increased when the crystallite size decreased pointing at a conduction mechanism along the grain boundaries. The improvement of the conductivity of CaF2 has also been demonstrated by activating the grain boundaries using Lewis acids.18 The adsorbed SbF5 or BF3 species at the boundaries attract F atoms and create vacancies that facilitate the F anion mobility. The conductivity of CaF2 and BaF2 could also be improved by mixing them with an insulator, for example, Al2O3.11 Homogeneous doping consists of adding an aliovalent cation/anion to an ionic conductor. The presence of these ions leads to the creation of point defects to compensate the additional charge and maintain the electroneutrality of the crystal. The doping of alkaline-earth fluorides by monovalent cations (Na, K) creating vacancies and trivalent cations (rare earth) creating interstitials is widely reported.5,18−21 The fluorite structure is rather open and can accommodate a relatively large amount of dopant.22 Particularly high ionic conductivities have been reported for doped BaF2 compounds. For example, an increase of the conductivity has been observed by adding small quantities of KF or NaF.23,24 More complete studies have been performed for BaF2 doped with rare-earth fluorides (Ba1−xRxF2+x) with a description of the different conductivity mechanisms obtained as a function of the quantity of dopant x.19 For a small quantity of dopant, the conductivity increases drastically with x and is related to a decrease of the activation energy. Increasing x means increasing the number of interstitial F anions and so the number of anions participating in the conduction. The maximum is obtained at the percolation threshold corresponding to a continuous interstitial site conduction path. For a higher concentration of dopant, the conductivity still increases with x but less rapidly, and the activation energy decreases linearly with x. Above the percolation threshold, some defects aggregate in clusters and do not contribute anymore to the conduction. Only free defects are mobile; however the presence of clusters induces a large distribution of energy barriers for anion jump and may favor anion mobility, too. Ivanov-Shits and co-workers25 have prepared Ba1−xRxF2+x crystals with different rare-earth elements

2. EXPERIMENTAL AND BASICS ON AC AND DC CONDUCTIVITY MEASUREMENTS 2.1. Material Preparation and Characterization. Sample Preparation. Ba1−xLaxF2+x samples (0 ≤ x ≤ 0.55) were prepared by ball milling under Ar atmosphere of a mixture of appropriate amounts of BaF2 and LaF3 for 24 h. A planetary type mill (Fritsch Pulverisette 6) was employed at 600 rpm with silicon nitride vials and balls (ball-to-powder ratio 12:1). Characterization. The as-milled samples were analyzed by X-ray diffraction (XRD) using a Bruker D8 Advance instrument with Cu Kα radiation. Nuclear Magnetic Resonance (NMR) Investigations. The ball-milled powders were filled into 1.8 mm rotors for magic angle spinning (MAS). The experiments were performed at a Bruker Avance NMR spectrometer with 19F resonance frequency of 338 MHz. For the experimental setup, a homebuilt 1.8 mm MAS NMR probe was adjusted to fluorine frequency. At 180 W 90°/180° pulses of 1.2/2.4 μs were achieved. Hahn-echo was applied at 40 kHz MAS spinning speed with a repetition time of 4 s. The air temperature was set to 300, 310, 320, 330, 340, and 350 K which resulted at the samples in 318, 327, 336, 345, 354, and 363 K at the given spinning speed. Spectra were referenced to NaF (aqueous solution). Impedance Spectroscopy. The impedance spectra were measured at different temperatures using a Zahner IM6 device. The frequency range was 1 Hz to 8 MHz, and the voltage amplitude was 10 mV. The measurements were done on pellets (ca. 1 mm thick and 13 mm diameter) pressed at 105 N and covered by gold which was sputtered on both faces as ionblocking electrodes. The impedance spectra were fitted using the EIS Spectrum Analyzer software.27 Battery Testing. Three-layer pellets were prepared by pressing together the cathode, the electrolyte, and the anode. The cathode material BiF3 was mixed with the electrolyte and carbon to ensure both electronic and ionic conductivity.4 The anode was pure Li metal foil. The pellet was introduced in a modified Swagelok-type cell designed to work at elevated temperature. We set a working temperature of 150 °C. Discharge was performed at ca. −4 mA·g−1 until 1.5 V cutoff potential and charge at +4 mA·g−1 until 3.5 V. 2.2. AC and DC Conductivity Measurements Using Impedance Spectroscopy. Impedance spectroscopy is commonly used to measure the ionic conductivity of a B



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The DC ionic conductivity of most ionic conductors can be described as a hopping mechanism of point defects from one site to another and may be written as follows:32,33

compound by measuring the complex impedance using a blocking electrode setup.25,28,29 The electrolyte material is inserted between two equivalent electrodes showing no ionic conductivity. The resistance of the electrolyte R is determined from the impedance spectrum and the conductivity (also called DC conductivity) is given by:

σDC

l 1 = × A R

σDC =

(3)

Z′(ω) Z′(ω) l l × = × A A |Z(ω)|2 Z′(ω)2 + Z″(ω)2

(8)

fh = f0 exp( −ΔHm/kT )

(9)

σDC =

a 2q2N0f0 6kT

⎛ ΔH0 + ΔHm ⎞ ⎛ E ⎞ σ ⎟ = 0 exp⎜ − a ⎟ exp⎜ − ⎝ kT ⎠ ⎝ ⎠ kT T (10)

where is σ0 the pre-exponential factor and Ea the activation energy. Studies about DC ionic conductivity typically show plots with log(σDC·T) versus 1/T and give the activation energy Ea (slope) and the pre-exponential factor σ0 (intercept). The concentration of charge carrier is often temperature-independent (ΔH0→0), in particular in the extrinsic region (lower temperatures) of doped ionic conductors where the number of defects created by doping largely exceeds the number of intrinsic defects. In this case the activation energy Ea is similar to the migration enthalpy. The fitting of the AC conductivity at different temperatures using eq 6 gives the additional possibility to determine the hopping frequency f h. Thus, f 0, the migration enthalpy (ΔHm), and the concentration of mobile defects (Nc, N0, ΔH0) can be calculated using eqs 8 and 9. Note that f h can also be directly obtained graphically from the AC conductivity spectrum since according to eq 6, we have ω = ωp = 2πf h for σAC = 2σDC. Hence, reliable values of f h can only be obtained from the fit of σAC(ω) curves when the maximum σAC value measured is superior to 2σDC.

(4)

3. RESULTS Doped BaF2 compounds (Ba1−xLaxF2+x) were prepared with several compositions up to x = 0.55. The XRD patterns of the samples after 24 h milling are given in Figure 1. For all LaF3 concentrations, only a single phase with a fluorite-type structure is obtained. Compared to pure BaF2, the peaks are shifting to higher angles when increasing x, indicating a reduction of the lattice parameter. The lattice parameter decreases linearly with x as described for single crystals,22,34 confirming the formation of a solid solution Ba1−xLaxF2+x. This is related to the insertion of the smaller La atoms in the fluorite-type structure. In addition, the peaks are much broadened because of the formation of very small crystalline domains (crystallites) during milling. Using Rietveld refinement, we found crystallite sizes in the range 20−30 nm for all samples. No influence of the concentration on the crystallite size was found. The crystallite size was slightly larger for the pure BaF2 (40 nm).

(5)

The AC conductivity is found to follow a universal Jonscher law31 and can be written following the Almond−West formalism:32 ⎛ ⎛ ω ⎞n ⎞ σAC(ω) = σDC⎜⎜1 + ⎜⎜ ⎟⎟ ⎟⎟ ⎝ ωp ⎠ ⎠ ⎝

Nc = N0 exp( −ΔH0/kT )

where N0 is the carrier concentration at infinite temperature, ΔH0 the enthalpy for the creation of mobile charge carriers, f 0 the fundamental vibrational frequency, and ΔHm the migration enthalpy. Combining these equations, we obtain:

In addition, a straight line at the lowest frequencies can be observed which corresponds to the contribution of the blocking electrodes (polarization effects at the interface electrode/ electrolyte). This part is represented experimentally by a CPE element introduced in the equivalent circuit25 as the straight line is tilted in the complex plane. Going a step further in the understanding of the conductivity mechanism, it is possible to obtain more information from the impedance measurements by studying the AC conductivity (real part of the complex conductivity) as a function of the angular frequency ω (ω = 2πf). The AC conductivity can be calculated at different frequencies using the impedance measurements: σAC(ω) =

(7)

6kT

where a is the hopping distance, q the electronic charge, k the Boltzmann constant, T the absolute temperature, and Nc the charge carrier concentration. Nc and f h are temperature dependent and follow Arrhenius laws:

where l is the thickness of the electrolyte and A the area of the contact electrode/electrolyte. Note, the DC conductivity represents the conductivity measured under constant current/ voltage. Here, using a blocking electrode setup, only the electrolyte resistance is measured, and so the electrolyte conductivity can be equaled to the DC conductivity. In the complex plane, the impedance plot obtained for a polycrystalline conductor is expected to be composed of two semicircles.29 The impedance spectrum can be fitted using an equivalent circuit as presented by Puin et al.15 At high frequencies, it refers to the bulk having a low capacitance (ca. 10−12 F) and also to effects parallel to the grain boundary. The bulk resistance is usually short-circuited by the lower resistance of the grain boundary (in parallel direction). At lower frequencies, it refers to effects in the grain boundaries, in series and in the perpendicular direction, for which the capacitance is higher (10−11 to 10−8 F).15 Experimentally, the semicircles are often depressed because of some diffusion phenomena occurring at the electrodes, and the capacitance can be replaced by a constant phase element (CPE). The CPE element is characterized by two parameters Q and n with Z*(CPE) = 1/Q(jω)n. A CPE represents a distribution of relaxation times that could originate from surface roughness or nonuniform reaction rates. The effective capacitance corresponding to a R-CPE circuit can be calculated from eq 4.30 C = (R1 − nQ )1/ n

a 2q2Ncfh

(6)

where n is a number between 0 and 1 and ωp is the hopping rate (ωp = 2πf h with f h as the hopping frequency). C



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tion times for the samples are given in Figure 2b. Short relaxation times, that is, high volume ionic mobility (conductivity), are observed for doped samples with x = 0.3, 0.4, 0.5, and 0.55 showing a minimum at x = 0.5. The ionic conductivity was measured from impedance measurements at different temperatures. Figure 3a and b

Figure 1. XRD patterns of Ba1−xLaxF2+x samples after 24 h milling.

Additional information about the sample structure and property is obtained by magic angle spinning solid state NMR, the 19F spectra are given in Figure 2a. For the pure ball

Figure 3. (a) Complex impedance plots for the sample Ba0.6La0.4F2.4 with the values measured at different temperatures (symbols) and the corresponding fit (lines) calculated using the equivalent circuit given in inset. (b) Enlargement of the complex plane plot for the area close to zero (same legend).

shows the impedance spectra in the complex plane obtained at various temperatures for Ba0.6La0.4F2.4. The spectra are composed of one depressed semicircle and, mostly for higher temperatures, of a straight line at low frequencies. Similar behavior was obtained for all compositions. To fit the measured spectra, we used the equivalent circuit25 given in Figure 3a (inset). The calculated fits are displayed as solid lines in Figure 3 and correspond well with the measured data (symbols). The resistances given by the fits were used to calculate the DC conductivity. As expected, the resistance decreased with temperature, and thus the conductivity increased, following an Arrhenius-type law for σDC·T (Figure 4). The conductivity at a given temperature increased with x up to 0.4 and then decreased for higher concentrations. In Figure 4, the data published for single crystals of equivalent compositions are also plotted for comparison. The values measured for the milled samples are clearly higher than the conductivity reported for single crystals for x ≤ 0.4.

Figure 2. (a) 19F NMR spectra of Ba1−xLaxF2+x samples after 24 h milling measured at room temperature. Intensity was normalized to 1. (b) 19F NMR temperature dependent relaxation times of the Ba1−xLaxF2+x samples.

milled BaF2 sample, a main resonance peak is obtained at −14 ppm, and two small contributions are detected at −63 and +9 ppm. These last two resonances are likely corresponding to the orthorhombic BaF2 phase which has already been observed after ball milling.14 For the doped samples, these two lines disappear, and new resonances lines grow beside the main −14 ppm resonance of BaF2. Their intensities increase gradually with the dopant content x. These lines are related to the F anion located in different interstitial positions available in the crystal structure.35 For high dopant content (x ≥ 0.5), all resonances are overlapping, and only a very broad signal is measured. Averaged temperature-dependent NMR T1 relaxaD



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frequency, and three zones can be distinguished in the curve. At lower frequency (for high temperature only), σAC increases steeply with ω, and this part represents the polarization effects at the electrodes.36,37 This part was not considered for the analysis of the conductivity mechanism. At medium frequencies, a plateau is observed corresponding to the DC conductivity, and at higher frequencies, σAC increases again corresponding to the dispersive region38 and following a linear trend when plot in a log−log scale. These last two parts can be described by eq 6, and f h was obtained by the fitting of the different curves (solid lines in Figure 5a). The variation of f h and σDC·T as a function of the inverse of the temperature are compared in Figure 5b for Ba0.6La0.4F2.4. Note, the hopping frequency f h cannot be calculated for temperatures above 140 °C because σAC values are not high enough above the σDC plateau (see Experimental Section) for the frequency range used. From the plot ln f h vs 1/T, we determined f 0 and ΔHm the migration enthalpy and from the plot ln σDC·T vs 1/T, σ0, and the activation energy Ea (and ΔH0). The values obtained for all samples are given in Table 1. The values of Ea are only slightly higher than ΔHm indicating that the ionic motion is almost temperature-independent in the range considered. Table 1 also gives the values of Nc obtained from eqs 8 and 10. For fluorite-type compounds, the hopping distance a can be taken as aL/2 (aL = lattice parameter).33,39

Figure 4. Arrhenius plot of the ionic conductivity for Ba1−xLaxF2+x compounds (0 ≤ x ≤ 0.55). Symbols: values measured from impedance measurements for the ball milled samples and lines: values given for single crystals in literature.19,25,26 The color of symbols and lines are the same for a specific composition.

The AC conductivity calculated from the impedance measurements is plotted in Figure 5a for Ba0.6La0.4F2.4. The behavior observed is the same for all compositions. At a given temperature, the AC conductivity increases with the angular

4. DISCUSSION A more detailed analysis of the XRD patterns obtained for the different Ba1−xLaxF2+x compounds indicates that not only the cell parameter is changing with x but also the relative intensities of the different peaks. This is related to the presence of interstitial F anions as reported for CaF2.35,40 Four different interstitial positions (F1 to F4) are identified in the fluorite structure and are filled depending on the dopant content. At low concentrations, the excess F anions fill the empty (1/2,1/2, 1/2) position (F4) of the fluorite structure close to the dopant cations. As the number of excess anions increases, clusters are forming, and the interstitial ions occupy displaced positions along the ⟨111⟩ (F2) and the ⟨110⟩ (F1) directions. The presence of F1 and F2 also leads to a slight relaxation of the F anions in the normal positions to the F3 positions. Introduction of interstitials in these positions in the BaF2 structure improves the fit of the XRD pattern by Rietveld refinement. A comparison of the measured peak intensities to those calculated with or without integrating F atoms in interstitial positions is given in the Supporting Information for the sample Ba0.6La0.4F2.4 (Table S1). It can be seen that a better agreement is obtain by integrating F interstitials in the crystal structure. Unfortunately, because of the broadening of the peaks, it is not possible here to give more information about the quantity of F anions in each position from the XRD data. These four interstitial positions can be identified in the NMR spectra. It is possible to deconvolute the resonance peaks in 5 different signals corresponding to the F anions in the normal F position (−14 ppm) and in the interstitial positions roughly at −25, −11, +1, and +22 ppm (±2 ppm). The different line shapes observed for the Ba1−xLaxF2+x samples with different dopant concentration x suggest a progressive filling of the different interstitial positions when increasing x. Nevertheless, more systematic investigations would be necessary to attribute the different resonances to an interstitial position. Here, all positions are already filled for x = 0.1, and the different contributions cannot be separated. The line shape of the sample

Figure 5. (a) AC conductivity plots at different temperatures for the sample Ba0.6La0.4F2.4. Symbols: AC conductivities calculated from impedance measurements and solid lines: corresponding fits using eq 6. (b) Arrhenius plots of the hopping frequency f h and σDC·T for the sample Ba0.6La0.4F2.4. E



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Table 1. Summary of the Ionic Conductivity Parameters for the Ball Milled Samples Ba1−xLaxF2+xa compound

Ba1−xLaxF2+x

x

0 −1

σDC at 160 °C (S·cm ) Ea (eV) σ0 (S·K·cm−1) ΔHm (eV) ΔH0 (eV) f 0 (Hz) Nc (cm−3) at 25 °C capacitanceb at 25 °C (F) Ea (eV) single crystal a

2.7 × 0.65 4.8 × 0.59 0.06 2.2 × 4.5 × 9.2 × 0.83

0.1 −7

10

103

1011 1021 10−11

1.7 × 0.61 8.6 × 0.59 0.02 3.0 × 4.4 × 1.0 × 0.67

0.2 −5

10

104

1013 1021 10−10

7.5 × 0.60 2.7 × 0.57 0.03 7.6 × 3.8 × 9.4 × 0.64

0.3 −5

1.8 × 0.57 3.5 × 0.52 0.05 3.3 × 5.3 × 1.0 × 0.62

10

105

1013 1021 10−11

10

0.4 −4

105

1013 1021 10−10

1.9 × 0.58 4.9 × 0.54 0.04 7.0 × 5.1 × 9.1 × 0.58

10

0.5 −4

105

1013 1021 10−11

9.6 × 0.59 3.4 × 0.58 0.01 9.9 × 8.2 × 1.1 × 0.56

0.55 −5

10

105

1013 1021 10−10

5.5 × 0.61 3.2 × 0.59 0.02 1.0 × 5.1 × 9.8 ×

La0.9Ba0.1F2.9 −5

10

105

1014 1021 10−11

2.8 × 0.55 3.5 × 0.52 0.03 3.3 × 8.3 × 1.3 × 0.37

10−4 105

1013 1021 10−10

Data obtained for La0.9Ba0.1F2.94 are given for comparison. bEffective capacitance for the semicircle calculated from eq 4.

organize themselves and finally form clusters.35,40 In these clusters, the defects are immobile and do not participate in ionic conductivity. In addition, following our previous conclusion that the conductivity is governed by grain boundaries phenomena, the calculated number of mobile defects should mainly correspond to the number of defects in these boundaries. It is then not surprising that the number of mobile defects is similar in all samples as they have a similar microstructure (e.g., similar average crystallite sizes). This last explanation is confirmed by the fairly high number of mobile defects present in the ball milled BaF2 which is not so different to what is calculated for the doped samples although no extrinsic defects were created by homogeneous doping here. The mobile defects in pure BaF2 are nonetheless of different nature than in the doped compounds as their hopping frequency is noticeably lower. The interstitial F anions present in the doped samples may have an influence on the defects present in the grain boundaries. Note also that the number of mobile defects is rather temperature-independent (ΔH0 is close to 0) as expected for extrinsic defects created by doping. Moreover, the hopping frequencies calculated for the differently doped samples are very similar confirming an analogous conduction mechanism. The main difference between the different compositions, which mainly explains the different conductivities measured, is the migration enthalpy that is lower for the samples with x = 0.3 and 0.4. In the grain boundaries, the main mobile carriers are vacancies,10 and this is confirmed here by values of migration enthalpy close to 0.5− 0.6 eV, typical for vacancy migration in BaF2.20 Note that, for single crystals of doped BaF2, the migration enthalpies are also decreasing to values in this range pointing to a mixed conduction mechanism based on interstitial and vacancy motion. The presence of vacancies in addition to interstitials has for example been reported for YF3-doped CaF2 crystals.40 As already pointed out above, if the defects present in the crystals do not contribute directly to the conduction, they probably influence the defects present in the grain boundaries. This is in agreement with the space charge effect model10,30 developed in particular for polycrystalline compounds. It has been proven for doped ceria that the Schottky barrier height, the potential of the grain boundary core relative to the bulk, decrease when the dopant concentration increases,30 therefore decreasing the blocking effect of the grain boundary. We assume that a similar effect takes place for the Ba1−xLaxF2+x compounds explaining the migration enthalpy decrease with x up to 0.3−0.4. For higher concentration (x ≥ 0.5), the enthalpy increases with x pointing to a competing mechanism. The presence of defect clusters in the crystal may also influence the

with x = 0.4 may look slightly different considering the progressive broadening of the interstitial contribution with increasing the quantity of dopant. For this sample, the resonance peak of BaF2 at −14 ppm seems to grow again before almost vanishing for x = 0.5. This effect might be exaggerated by the normalization of the peak intensities. Nevertheless, some modification of the F anion local mobility in the normal or interstitial positions may appear for this composition considering that no discontinuity in the structure is found by XRD. For example, the formation of defect clusters has been reported for doped-BaF2,25 and the mobility of F anion is likely modified in such local arrangements of defects. From the analysis and fitting of the impedance spectra, we found that the resistance values depend strongly on the sample composition in contrast to the capacitance values which are very similar for all samples and vary only slightly with the temperature. They are close to 10−10 F for the capacitances corresponding to the semicircles (CPE1) and 10−6−10−5 F for the straight lines (CPE2). These values are in agreement with grain boundaries (10−11−10−8 F) and sample−electrode interfaces phenomena (10−7−10−5 F), respectively.29 The shape of the impedance spectra is different to what is expected for polycrystalline samples with two semicircles corresponding to bulk phenomena at high frequencies and to grain boundaries at lower frequencies.10,41 In our samples, the bulk phenomena are completely overshadowed by the grain boundary contribution. The bulk resistance is short-circuited by the very low resistance parallel to the grain boundaries.15 The conductivity in the milled samples is then mainly controlled by diffusion along these boundaries explaining why the values measured are much different from the data given for single crystals. This is also in agreement with the NMR T1 relaxation data that suggest a high average conductivity for increasing dopant concentration with an optimum for x = 0.5 although the DC conductivity was the highest for x = 0.3−0.4. With the NMR technique applied here, we could not distinguish between bulk and grain boundary contributions but merely expect to see the NMR signal dominating bulk effect. In addition, conductivity measurements were performed for Ba0.6La0.4F2.4 having larger grains (>100 nm) and gave much lower conductivity values (see Figure S1 in the Supporting Information) probably because of a smaller fraction of grain boundaries in the sample. More information about the conductivity mechanism is obtained by the analysis of the AC conductivity. The results given in Table 1 show that the number of free mobile defects Nc is similar in all samples. The number of interstitial anions increases with the quantity of dopant x; however, it is known than, for a high number of defects, a part of these defects F



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La0.9Ba0.1F2.9 as electrolyte with ca. 110 mAh·g−1 obtained during discharge at ca. 120 mAh·g−1 for charge. This is consistent with the slightly lower conductivity measured for Ba0.6La0.4F2.4 compared to La0.9Ba0.1F2.9 (see Table 1). The theoretical capacity is not reached likely because of the still too low F motion and difficult charge transfer from the solid electrolyte to the electrodes. These limitations also explain the decrease of the capacity during the following cycle. Further work is in progress to enhance the cycling performances of this FIB.

defect mobility in the grain boundaries as already reported for single crystals.19 The most remarkable property of conductivity in polycrystalline-doped BaF2 is the higher conductivity obtained compared to the similarly doped single crystals. The opposite trend has been observed for doped LaF3 prepared by ball milling.4 Hence, we also analyzed the AC conductivity for the La0.9Ba0.1F2.9 compound in more detail, and the calculated parameters are given in Table 1. A slightly faster ionic conductivity is obtained compared to Ba0.6La0.4F2.4, which is mainly explained by an even smaller migration enthalpy of mobile defects. The defects are nevertheless much less mobile than in the single crystal. The comparison of the conductivity parameters for the La0.9Ba0.1F2.9 and the Ba1−xLaxF2+x samples suggests different properties of the grain boundaries in both types of compounds. The difference observed could be related to the different nature of extrinsic defects created by doping LaF3 by Ba (vacancies) or BaF2 by La (interstitials). We assume that the vacancies created in La0.9Ba0.1F2.9 are very mobile in the crystal but are greatly affected by the grain boundary barrier and have less influence on the point defects created at the grain boundaries. The nature of the space charge layer is different to what is obtained in Ba1−xLaxF2+x compounds where the interstitials are slower but influence greatly the vacancies present in the grain boundary region. The negatively charged interstitials present at the surface of the grains could lead to an accumulation of vacancies in the grain boundary. The change from an interstitial to a vacancy ionic conduction for doped BaF2 (by increasing the dopant content or creating boundaries) could then explain the drastic decrease of the migration enthalpy to values close to those reported for pure vacancy motion in BaF2 (from 0.79 eV21 for interstitials to 0.56 eV20 for vacancies). In contrast, for LaF3, the migration enthalpy is only slightly influenced by the dopant content.6 Hence, there is only a blocking effect of the grain boundaries acting as barrier for the conduction. Note that the activation energy found here for polycrystalline La0.9Ba0.1F2.9 is close to the values reported for nanocrystalline42 LaF3, pointing to a value typical for a grain boundary mechanism. The highest conductivity for doped BaF2 is obtained for the sample Ba0.6La0.4F2.4 (ca. 1.9 × 10−4 S·cm−1 at 160 °C). This composition was then chosen as electrolyte to construct a cell using BiF3 as cathode material and Li metal as anode material. The discharge and charge behavior in the first two cycles is given in Figure 6. The capacities obtained for the first cycle are similar but slightly lower to the earlier report4 using

5. CONCLUSION The conductivity of Ba1−xLaxF2+x solid solution was studied for polycrystalline samples prepared by ball milling. Single crystals of such compounds are known to be good F anion conductors, but after ball milling the conductivity obtained was much higher. Here, the highest conductivity was measured for Ba0.6La0.4F2.4 and reached 1.9 × 10−4 S·cm−1 at 160 °C. This compound was used as electrolyte in a FIB, and it was possible to discharge and recharge such a cell. In doped BaF2 ball milled compounds, the ionic conductivity is thought to proceed through the migration of vacancies along the grain boundaries. After ball milling, very small crystallite sizes are obtained providing fast conduction paths along the boundaries. Such an improvement of the conductivity for polycrystalline fluoritetype fluorides could not be obtained for compounds with a tysonite-type structure, the conductivity of polycrystallinedoped LaF3 is much lower than for the single crystals. We assume that this is related to the nature of the grain boundaries themselves that have a higher blocking effect for tysonite-type fluorides. This is likely related to the type and migration properties of the defects created by doping. Further improvement of the ionic conductivity may come from the tuning of the grain boundaries properties as they control the ion migration in polycrystalline materials.

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ASSOCIATED CONTENT

* Supporting Information S

For sample Ba0.6La0.4F2.4, a table with the results of Rietveld refinement and a figure with the DC conductivity measured on samples having different grain sizes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49-721-608-28925. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the State of Baden-Wurttemberg, Project house e-drive (#PHed.L.0208.01) is gratefully acknowledged. We are also greatly thankful to European Social Fund, Estonian Research Council for projects MTT68, SF0690034s09 and for the assistance from KBFI especially to Ivo Heinmaa, Tiit Tuherm, and Jaan Past.

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REFERENCES

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Figure 6. Voltage−composition profiles obtained at 150 °C for a cell BiF3/Ba0.6La0.4F2.4/Li (current ±4 mA·g−1) during the two first cycles. G



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Nanostructured Fluorite-Type Fluorides As Electrolytes for Fluoride Ion

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