Arrhenius Behavior of the Bulk Na-Ion Conductivity in Na3Sc2(PO4)3 Single Crystals Observed by Microcontact Impedance Spectroscopy.

NASICON-based solid electrolytes with exceptionally high Na-ion conductivities are considered to enable future all solid-state Na-ion battery technologies. Despite 40 years of research the interrelation between crystal structure and Na-ion conduction is still controversially discussed and far from being fully understood. In this study, microcontact impedance spectroscopy combined with single crystal X-ray diffraction, and differential scanning calorimetry is applied to tackle the question how bulk Na-ion conductivity σbulk of sub-mm-sized flux grown Na3Sc2(PO4)3 (NSP) single crystals is influenced by supposed phase changes (α, β, and γ phase) discussed in literature. Although we found a smooth structural change at around 140 °C, which we assign to the β → γ phase transition, our conductivity data follow a single Arrhenius law from room temperature (RT) up to 220 °C. Obviously, the structural change, being mainly related to decreasing Na-ion ordering with increasing temperature, does not cause any jumps in Na-ion conductivity or any discontinuities in activation energies Ea. Bulk ion dynamics in NSP have so far rarely been documented; here, under ambient conditions, σbulk turned out to be as high as 3 × 10-4 S cm-1 at RT (Ea, bulk = 0.39 eV) when directly measured with microcontacts for individual small single crystals.

Introduction

Li-ion conducting solid electrolytes are highly desired for new battery concepts overcoming serious safety issues of state-of-the-art battery technologies using liquid-based electrolytes. Moreover, the use of solid electrolytes enables very high energy densities as well as chemical and electrochemical stability, which is needed for any automotive and grid storage applications. Concerns regarding the availability of mineral resources of Li, however, increase the interest in other cations such as Na. Among Na-ion conducting solid electrolytes, NASICON-based materials, with the formula NaM2(XO4)3 (M = Sc, Zr, etc.; X = Si4+, P5+, etc.), are considered as one of the most promising candidates for future all solid-state Na-ion battery (ASSNIB) technologies. These solid electrolytes were discovered by Hong et al. about 40 years ago described with the rhombohedral space group (SG) R3̅c, known as the NASICON structure.[1,2]

The structural situation in this class of material is, however, rather complicated and still not fully understood. As an example, in the case of Na3V2(PO4)3 (NVP) a phase transition sequence from an ordered monoclinic α form (space group (SG) C2/c, a = 15.1244(6) Å, b = 8.7287(3) Å, c = 21.6143(8) Å, β = 90.163(2)) to the classical disordered rhombohedral cell (SG R3̅c, a = 8.73382(4) Å, c = 21.91438(17) Å) with two intermediate incommensurate modulated structures β and β′ was described.[3] A further complication arises due to the different and conflicting behavior of powders and single crystals of NASICON-materials.[4] For polycrystalline samples of Na3Sc2(PO4)3 (NSP), fabricated at high temperatures, two phase transitions are reported[5−7] with the room temperature (RT) structure often being described using a monoclinic cell with space group symmetry C2/c.[8−11] In contrast, flux grown single crystals are reported to show only a single phase transition at around 160 °C from the high temperature structure with SG R3̅c to a more complicated trigonal structure with a 2a, c supercell.[4,12,13]

It has been reported that these structural changes in NASICON materials are associated with changes of the thermal activation of Na-ion conductivity. While for NSP in some papers only a single change in activation energy (Ea) associated with the α → β or β → γ phase transition is detected, in other papers, however, two changes in Na-ion conductivity were reported and assigned to the two structural changes. Some of these discrepancies in structure–property relationships published in literature seem to be related to the use of total Na-ion conductivities instead of bulk Na-ion conductivities. The total conductivity comprises both grain boundary and bulk contributions. Of course, only the latter contains intrinsic transport properties which, to our opinion, will be mostly affected by the crystal chemical changes. Hence, with the data available until now, the apparently observed jumps in the thermal activation of the conductivity cannot be unequivocally assigned to the phase transitions reported.

Extremely high bulk conductivities in the mS cm–1 range are equivalent to electrical relaxation processes with very short relaxation times. At ambient or slightly elevated temperature, the relaxation frequencies of these low resistive bulk processes with capacitances in the pF range are only seen in the MHz to GHz regime. If powder samples are examined, the presence of grain boundaries often complicates the evaluation of impedance data in Nyquist plots and may hinder an unambiguous analysis of the bulk conductivity. Moreover, chemical and structural inhomogeneities in polycrystalline samples may limit the accurate study of electrochemical properties as only mean values are accessible. The use of microelectrodes on top of single crystals, however, enables a very precise study of conductivity properties since the obtained electrochemical data usually only depend on electrical bulk properties and morphology. Therefore, they can directly be correlated with information from single crystal diffraction. Very recently, we used the same setup with microelectrodes to successfully investigate electrical bulk properties of Li1+AlTi2–(PO4)3 (LATP) single crystals.[14]

Here, microcontact impedance spectroscopy (MC IS) is combined with single crystal X-ray diffraction (SC XRD) to study possible interrelationships between intragrain Na-ion conductivity and phase transitions of flux grown NSP single crystals. Surprisingly, contrary to the various reports in literature, we do not observe any discontinuities in Na-ion conductivity as a function of temperature.

Experimental Section

Synthesis of Single Crystals

Single crystals of Na3Sc2(PO4)3 were grown using the flux method as described by Sotofte and Fu.[15] First, ScPO4 was prepared via solid state reaction from a stoichiometric amount of Sc2O3 (Projector GmbH, 99.5%) and NH4H2PO4 (Merck KGaA, 99%). The homogenized mixture was heated up with 300 K/h to 900 °C for 3 h. After grinding, the powder was annealed at 1200 °C for 20 h. A ratio 1:6 of ScPO4 and Na4P2O7 (Sigma-Aldrich, 95%) was heated in a Pt crucible at 1100 °C for 5 h in air, then cooled down to 900 °C at 3 K/h, before the furnace was free cooled to RT. The single crystals of several hundreds of μm in size were extracted from the molten mass with hot water.

Single Crystal X-ray Diffraction

SC XRD data at RT were collected on several crystals on a Bruker SMART APEX CCD-diffractometer. Intensity data were collected with graphite-monochromatized Mo Kα X-ray radiation (50 kV, 30 mA). The crystal-to-detector distance was 30 mm and the detector positioned at −28° 2Θ using an ω-scan mode strategy at four different ϕ positions (0°, 90°, 180°, and 270°). 630 frames with Δω = 0.3° were acquired for each run. Three-dimensional data were integrated and corrected for Lorentz-, polarization, and background effects using the APEX3 software.[16] To study the evolution of the crystal structure with temperature, three data sets (at 298, 403, and 503 K) were also collected at an STOE IPDS II single-crystal diffractometer system equipped with an image plate detector at the University of Innsbruck. Elongated exposure time of 120 s per frame and significantly finer increments of 0.1° were chosen. Intensity integration was performed with X-Area software.[17]

Differential Scanning Calorimetry

The heat capacity between 0 and 300 °C was measured using a power compensated PerkinElmer Diamond Differential scanning calorimetry (DSC) on samples weighing ∼38 mg. The DSC measurements were performed under a flow of Ar gas, with the calorimeter block kept at −20 °C using a PerkinElmer Intracooler. Each measurement consisted of a blank run with empty calorimeter chambers, a calibration, and a sample run, where the samples were placed into the sample chamber of the calorimeter. The heat flow data (difference in heating power between the sample and the reference chamber) were collected at 100 °C temperature intervals consisting of a temperature scan (heating rate of 10 °C/min) and isothermal periods of 3 min before and after the temperature scan. The heat flow versus temperature data from the sample runs were shifted and rotated until the data of the isothermal periods agreed with those of the blank run. A sample-saving method for heat capacity measurements on powders using relaxation calorimetry. The data from the blank run were then subtracted from those of the sample run to give the net heat flow of the sample. For calculating the heat capacity, the net heat flow data were finally divided by the heating rate and the mass of the sample. Each sample run was corrected against a calibration run using a synthetic single crystal of corundum (31.764 mg), whose heat capacities were taken from the National Bureau of Standards Certificate.[18] The accuracy of the DSC heat capacity data was determined to be better than 0.6%.

Application of Microelectrodes on Single Crystals

For electrochemical characterization, single crystals were embedded in epoxy resin. Pt thin films were sputter deposited with a thickness of 200 nm on top of approximately 10 nm Ti (used to improve the adhesion between the sample and the electrode). Afterward a negative photoresist was coated on top of the embedded and polished single crystals. After applying the mask with the appropriate microelectrode pattern, in our case circular electrodes with a diameter of 30 μm, the samples were exposed to UV light. Areas that were covered during exposure were removed using a developer solution (Microresist Technologies, Germany). In a subsequent step the microstructure was obtained by ion beam etching.

Microcontact Solid-State Impedance Spectroscopy

The electrochemical characterization of NSP was carried out by electrical impedance spectroscopy according to ref (14). All impedance measurements were performed between RT and 200 °C in a tube furnace using an Alpha-A High Resolution dielectric analyzer with a ZG-2 interface (Novocontrol, Germany) in the frequency range from 3 × 106 Hz to 102 Hz with a voltage amplitude of 100 mV. The temperature were measured using a thermocouple placed close to the single crystals. In Figure the microcontact setup and a schematic picture of the performed experiment are shown.

Figure 1

(left) Sketch of the microcontact setup. (right) Enlarged view of an embedded and polished single crystal with patterned electrodes. White areas represent the lithographically prepared Ti/Pt microelectrodes having a diameter of 30 μm. The black triangles are WC needles used to contact the electrodes.

Results

Structural Behavior of NSP Single Crystals as Function of Temperature

In agreement with suggestions presented in literature so far, the RT SC XRD data reveal distinct superstructure reflections and cannot be indexed with a rhombohedral nor with a monoclinic cell.[4,13] This structural complexity was in the very same manner observed for dozens of single crystals, which were tested in the initial phase of our investigation. Figure a shows calculations of the precession images from the SC XRD data at different layers at 25 °C, the peaks belonging to the R3̅c cell are marked to highlight the superstructure peaks. The pattern cannot be indexed with the monoclinic cell, frequently encountered in literature for NSP, for example, see Collin et al. (SG C2/c, a = 15.404(4) Å, b = 9.103(3), c = 8.919(2), β = 123.53).[13] Also with the enlarged monoclinic cell, recently suggested by Chotard et al. for NVP, it is not possible to index all observed Bragg peaks.[3] The comparison of their reconstructed reciprocal space layer 0kl with those of this study reveals substantial differences with the superstructure peaks appearing along the c* direction; for NVP, they appeared along the b* direction. The only possibility to index all Bragg peaks for NSP fit with a 2a, 2b, c trigonal cell. The space group is P3̅cl, which is a natural subgroup of R3̅c and which is in line with findings of Collin et al. and Tran Qui et al.[12,13]

Figure 2

(a) Calculated precession images of the hk1 and 0kl layers in Na3Sc2(PO4)3; the green circles represent the reciprocal lattice point positions of the R3̅c lattice. (b) Calculated precession images of the hk1 layer in Na3Sc2(PO4)3 at different temperatures as extracted from single crystal the X-ray diffraction data using the STOE IPDS-II system. (c) Unit cell (space group R3̅c) of Na3Sc2(PO4)3. Dark and bright brownish ellipsoids indicate sodium ions in octahedral sides (Wyckoff position (WP) 6b and 18e, respectively). Purple octahedral denotes scandium atoms coordinated by oxygen atoms (WP 12c). Blue tetrahedral denotes phosphorus atoms coordinated to oxygen atoms (WP 18e). Oxygen atoms are located at the corner of the polyhedral (reddish spheres; WP 36f).

To monitor possible changes of the crystal structure with temperature, we collected two data sets at elevated temperatures. The data set collected at 130 °C, that is, between the two phase transition temperatures proposed for polycrystalline samples, still shows trigonal symmetry with the only difference of somewhat weaker superstructure reflections.

Importantly, at 230 °C the superstructure has completely vanished and the data can be indexed and refined with the commonly observed R3̅c NASICON structure. Figure b shows the reconstructed reciprocal space layer hk1 at different temperatures, which clearly shows that the superstructure reflections disappear. The results of the refinements of the high-temperature structure are illustrated in Figure c and presented in Table .

Table 1

Atomic Coordinates and Equivalent Isotropic Displacement Parameters for NSP Single Crystals at 230 °Ca

	site	x	y	z	Occ	Ueq
Sc1	12c	0	0	1493(1)	1	13(1)
P1	18e	2936(1)	0	2500	1	15(1)
O1	36f	306(3)	2122(2)	1954(1)	1	39(1)
O2	36f	1943(2)	1737(2)	905(1)	1	26(1)
Na1	6b	0	0	0	0.53(1)	161(11)
Na2	18e	6364(3)	0	2500	0.71(1)	81(2)

Atomic coordinates (Å × 104); equivalent isotropic displacement parameters (Å2 × 103); Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

At 503 K, the Na(1) site is occupied by ∼50%, the Na(2) by ∼70%; these estimations give rise to a total Na content of ∼2.66 per formula unit (pfu). The structure is characterized by distinct anisotropic motion of the Na atoms. The observation of the β (most probably P3̅cl, see above) to γ (R3̅c) phase transition in single crystalline NSP material is further supported by DSC measurements (see Figure a), which show a weak and broad peak centered around 140 °C. In strong contrast to the situation reported for powder samples, we found no measurable indications for the α to β phase transition for single crystals.[5] This clear difference might be caused by different synthesis conditions.

Figure 3

(a) DCS measurement of Na3Sc2(PO4)3 single crystals from 0 to 300 °C. The heat capacity versus temperature data do not show a smooth behavior, but show a peak centered at 140 °C. Although the peak is broad and not very pronounced, it is unmistakably an endothermic peak and can be associated with the β → γ phase transition. (b) Nyquist plot of a representative impedance measurements on Na3Sc2(PO4)3 single crystal measured at 23.5 °C. The equivalent circuit used to approximate the location curve is also shown. While the continuous line represents the total response, the dashed line shows the contributions of the bulk and the electrode. (c) Arrhenius plot of σbulkT of Na3Sc2(PO4)3 single crystals as obtained from micocontact impedance spectroscopy. For comparison, conductivity values extracted from literature are also shown. The β → γ phase transition as observed by DSC is indicated by the vertically drawn line. (d) Arrhenius plot of Na3Sc2(PO4)3 single crystals and value extracted from refs (5 and 19−22). The α → β and β → γ phase transitions are highlighted in gray.

To clarify this difference is beyond the scope of the present paper, which focuses on the impact of phase transformations on (bulk) ionic conductivities of NSP single crystals. As the RT structure is yet not complete resolved, no information can be extracted on Na disorder and its influence as a driving force for phase transitions. Symmetry and structural phase transitions of NSP between 100 and 500 K, as well as the role of synthesis conditions, will be presented in a follow-up paper.[19]

Na-Ion Conductivity and Arrhenius Behavior of NSP Single Crystals

As an example of the impedance measurements, a Nyquist plot obtained at 23.5 °C is shown in Figure b; in Figure c, the temperature dependence of σbulk is presented. The Nyquist plot recorded at RT is composed by parts of a semicircle at high frequencies, followed by a sharp increase at low frequencies. This low frequency impedance can be attributed to the strongly ion blocking electrode and described by a resistance in parallel to a constant phase element (CPEel) with the impedance given by ZCPE = 1/(iω)Q, where ω is the angular frequency and the exponent n is a fit parameter accounting for nonideal behavior of the capacitance. It does not imply any mechanistic information, however, it is needed to analyze the sample-specific high frequency arc at higher temperatures. The high frequency part represents the bulk resistivity of the individual single crystals. The resistive part of the arc is approximated by a resistance element (Rbulk) and can be attributed to the volumetric Na-ion conduction σbulk, see below. The bulk capacitance (Cbulk) of the NSP samples cannot be obtained as we have to deal with an unavoidable and high stray capacitance Cstray in the order of 100 fF. The whole equivalent circuit used to analyze the impedance spectra is depicted in Figure b. The bulk (spreading) resistance between two circular microelectrodes with an electrode diameter d and bulk conductivity σbulk is given by Rbulk = (dσbulk)−1.[20] Here we obtain σbulk = 3.04 × 10–4 S cm–1 at RT; this value shows almost no variation within 20 measured single crystals, the error turned out to be less than 1%.

σbulk, lit. (at 49 °C) is in almost perfect agreement with σbulk = 1.70 × 10–3 S cm–1 obtained in this study. Unfortunately, in ref (5), only activation energies Ea for the total conductivity are present from which we cannot access Ea, bulk. As can be seen in Figure c, the temperature dependence of σbulk of three randomly selected single crystals follows an almost perfect Arrhenius behavior according to σbulkT = A exp(−Ea, bulk/kBT), where A is the pre-exponential factor of the ionic conductivity, and kB denotes Boltzmann’s constant. Up to 200 °C, no change in slope of σbulkT versus 1000/T can be observed, for Ea, bulk we obtain 0.39 eV. This analysis does not take into account that true temperatures at the sample surface are slightly lower than the set temperature due to asymmetric heating.

Hence, the true activation energy might be slightly larger that 0.39 eV. Our observation that no jumps of σbulk or changes in Ea occurred contrasts with earlier studies reporting up to two changes in the thermal activation of Na-ion conduction, see Figure d.

As shown in Figure d, Boehm et al. and Susman et al. (idem) reported a temperature dependency of the Na-ion conductivity with two discontinuities in the Ea caused by the α → β (64 °C) and β → γ (166 °C) phase transition.[5,22] In contrast, Winand et al., Delmas et al., and Sorokin et al. observed an α → β or β → γ phase transition.[20,23,24] The Ea values from literature and this study are summarized in Table .

Table 2

Bulk Na-Ion Conductivities (σbulk) and Activation Energies (Ea) of Na3Sc2(PO4)3 Single Crystals Compared to Literature Values for Polycrystalline Samplesa

	Ea [eV]
phase	α	β	γ	σbulk @49 °C [S cm–1]
this study	0.39	0.39	1.70 × 10–3
Boehm[5]	0.56	0.45	0.15	1.25 × 10–3
Delmas[20]		1.10	0.42
Winand[22]	0.49	0.34
Sorokin[23]		0.55	0.42

Since no σbulk values are reported in literature, we used the only available Nyquist plot of ref (5) to extract σbulk, lit. = 1.25 × 10–3 S cm–1 at 49 °C (see Table ).

Unfortunately, in most of the previous experimental reports, only the final conductivity values are presented without providing details on the procedures how source data were analyzed. At least Boehm et al. and Sorokin et al. give some information about the inability to separate bulk and grain boundary contributions at temperatures above 50 °C. Their experimental setup was limited and only allowed impedance measurements up to 500 kHz, which seems to be too low to separate bulk electrical processes with fast relaxation rates. Consequently, they were restricted to use only total conductivities instead of bulk values to correlate Na-ion conductivity with structural changes.[5,24] Since the crystal chemistry of a material is usually correlated mainly to bulk properties, the use of overall conductivities could be misleading. In many cases, so far powders with μm-sized crystallites were considered and no nanostructured materials with disordered interfacial regions. Therefore, σbulk is then expected to exceed σg.b.; furthermore, we would anticipate Ea, bulk < Ea, g.b.. If σtotal represents a mixture of the two components with mutable contributions over the temperature range covered, slope changes in Arrhenius plots might be artificially generated. These changes might not show up if characteristic electric relaxation frequencies are used to evaluate conduction processes.

In our case, we did not find any convincing indications for a α → β transition of NSP single crystals grown by the flux method. Hence, we do not expect a change in σbulk at temperatures below 120 °C. Indeed, the measured bulk conductivities simply follow a straight Arrhenius line (see Figures c and 3d). Importantly, the β → γ phase transition, for which we in fact find indications from DSC, has no measurable impact on σbulk. Up to 200 °C the pre-exponential factor A and Ea, bulk remain unchanged. A point worth mentioning is that the space groups suggested for the β and γ phase, and even for the α form, are very similar. The structural changes only result from different Na-ion ordering.[4] Of course, order–disorder phenomena may easily influence configurational and vibrational entropy contributions of the pre-exponential factor. Also activation energies of local hopping processes can change and affect long-range ion transport. Here, as far as the bulk conductivity is concerned, we exclude any significant influence of the β → γ phase transition on σbulk of single-crystalline NSP. Finally, this finding agrees well with the singular result of Winand et al.,[23] see Figure d. Although they studied polycrystalline samples as others,[5,21−24] they analyzed impedance data[23] recorded up to 10 MHz instead of only 500 kHz (see above). In summary, on the basis of the microcontact impedance measurements σbulk is, if at all, only marginally influenced by the decreasing Na-ion ordering in NSP single crystals.

Conclusions

NSP single crystals were prepared by flux growth and investigated by SC XRD, MC IS, and DSC with respect to its crystal structure and Na-ion conduction as a function of temperature. SC XRD experiments in the suggested α (RT), β (130 °C), and γ phase (230 °C) regions identified at least two different modifications. The phases can be assigned to the β and γ modification, with SG P3̅cl and SG R3̅c, respectively. From our data, we do not find clear indications of the α phase although superlattice peaks become more intense with decreasing temperature. Instead, DSC measurements point to a single phase transition at about 140 °C, which we assign to the β → γ phase transition; a possible α → β transition remains invisible in our DSC and SC XRD measurements.

The β → γ transition does not lead to discontinuities of the Arrhenius behavior of σbulkT of NSP single crystals when investigated with microcontact impedance spectroscopy. As far as ionic bulk properties are considered, this behavior is characterized by σbulk = 3.04 × 10–4 S cm–1 at RT Ea, bulk = 0.39 eV.