Partial electronic conductivity of nanocrystalline Na2O2

Understanding charge carrier transport in Na2O2, being one of the possible storage materials in the non-aqueous Na–O2 battery, is key to the development of this type of energy storage system. The electronic and dynamic properties of Na2O2 are expected to greatly influence the overall performance and reversibility of the discharge process. Thus far experimental studies on this topic are rare. To measure the extremely low conductivities setups with sufficiently high sensitivity are needed. Here we studied the partial electronic conductivity σeon of nanocrystalline Na2O2 by potentiostatic polarization measurements which we carried out at room temperature. σeon turned out to be in the order of 8.8  ×  10−14 S cm−1; with a very poor total conductivity of σtotal  =  17  ×  10−14 S cm−1 we obtained σtotal/σeon  ≈  2 clearly showing that ionic transport of Na ions is strongly coupled to electronic dynamics.


M Philipp et al
We used a ZrO 2 beaker equipped with 180 balls; the milling time was set to 1 h. For the conductivity measurements pellets, 10 mm in diameter, ca. 1 mm in thickness, were prepared by cold-pressing the powders with a uniaxial force of 15 kN. Au electrodes, 100 nm in thickness) were applied by means of evaporation (MBraun MB-EVAP). All preparation steps were done in an inert Ar or N 2 atmosphere with O 2 and H 2 O contents below 1 ppm. The samples were characterized by x-ray powder diffraction (Bruker D8 Advance), scanning electron microscopy (Tescan VEGA3) as well as 23 Na magic angle spinning (MAS) NMR (Bruker Avance III, 11 Tesla (132 MHz), 30 kHz spinning frequency, 2.5 mm rotors). Polarization measurements were performed with a Parstat MC potentiostat (Princeton Applied Research) equipped with a low current interface. A Faraday cage was employed to suppress any electromagnetic influences.

Results and discussion
3.1. Characterization via x-ray powder diffraction and 23 Na MAS NMR Na 2 O 2 crystallizes with the hexagonal space group P m 62 (see figure 1(a)). The peroxide anions occupy the positions 2e and 4h; they are arranged along the c-axis; Na ions reside on 3f (Na 1 ) and 3g (Na 2 ). The cations are surrounded in a distorted trigonal prism by the oxygen ions. The closest Na 1 -Na 2 distance is given by 3.06 Å.
X-ray powder diffraction revealed that the starting material is of high purity, the pattern recorded as well as the lattice constants extracted (a = 6.207(1), b = 4.471(1)) fully agree with literature data (see figure 1(b)). The tiny reflection at ca. 47° most likely stems from Na 2 O; the reflection at ca. 38° represents a still unknown marginal impurity; it might be sodium bicarbonate, see below. After mechanical treatment for 60 min nanocrystalline Na 2 O 2 is obtained in high purity. X-ray diffraction neither indicates any decomposition processes having taken place nor a mechanically induced formation of new phases; according to Rietveld analysis the mean lattice parameters remain essentially the untouched (a = 6.207(1), b = 4.472(1)). Significant broadening of the reflections is attributed to the generation of nm-sized crystallites and strain introduced. Taking instrumental broadening into account, see figure 1(b), with the relation introduced by Scherrer we estimated the average crystallite size to be ca. 20 nm. This result agrees well with sizes usually obtained through ball milling of oxide ceramics [19]. The SEM image in figure 2(a) shows that the nanocrystallites agglomerate and form µm-sized clusters. Na 2 O 2 is extremely air sensitive and hygroscopic. The bright layer on top of the agglomerates represents NaOH. Sodium hydroxide was formed as a result of contact of the powder sample with ambient air atmosphere before placing it into the SEM vacuum chamber.
The 23 Na MAS NMR spectrum is clearly composed of two well-resolved lines showing up at 7.0 ppm and 11.6 ppm when referenced to an 1 M aqueous solution of NaCl. The lines represent the Na 1 and Na 2 sites in Na 2 O 2 and are in very good agreement with a recent study by Goward and co-workers [12]. The spectrum of non-milled, microcrystalline Na 2 O 2 is shown for comparison. The line at 55.6 ppm has to be assigned to Na 2 O [12] as also noticed through x-ray diffraction. Interestingly, this signal almost vanishes after ball milling. Most likely, residual Na 2 O of the starting material reacts with traces of oxygen to eventually form the thermodynamic more stable Na 2 O 2 . The signal at −4.7 ppm seems to reflect a tiny amount of sodium bicarbonate [12]. Fortunately, the contaminations are small enough not to influence the electronic and overall conductivity of our sample.

Polarization measurements
The total conductivity σ total of nanocrystalline Na 2 O 2 , i.e. the conductivity comprising both the ionic and electronic contribution, has previously been reported. For a sample which was ball-milled for 60 min σ total amounts to 1.7 × 10 −13 S cm −1 at 293 K (see figure 3(a)), which shows σ total T in an Arrhenius representation). So far and in contrast to the practical measurement of the total conductivity at room temperature, the corresponding electronic conductivity σ eon was only calculated; Yang et al [20] reported on a value of 10 −20 S cm −1 (hole polarons, 0.47-0.62 eV) while Araujo et al [21] presented a value of 10 −19 S cm −1 (hole polarons, 0.32-0.38 eV). To compare these conductivity values with practical ones the gold sputtered sodium peroxide pellets were assembled into air-tight Swagelok-cells and measured at room temperature on the Parstat MC potentiostat, see above. For this purpose, a constant voltage U of 0.5 V was applied across the symmetrical Au|Na 2 O 2 |Au pellet and the change of the current I over time (t) was recorded, see also [9]. In figure 3 When a material with mixed electronic and ionic conductivity is electrically polarized, at the beginning, both ions and electrons will contribute to the total conductivity of the sample. By using ion-blocking electrodes, e.g. Au, the mobile ion species will either accumulate or be depleted in the vicinity of the electrode. Hence, a concentration gradient will develop. As the ion concentration gradient builds up, the contribution of the ionic transport to the total conductivity will continuously decrease. The overall current also decreases until eventually a constant current plateau is reached that corresponds to conduction by electrons only. From this constant current value the electronic conductivity can easily be calculated according to σ eon = I/U · d/(r 2 π), whereby d corresponds to the thickness of the tablet, and r denotes its radius. Note that the absolute values of the currents are below 1 pA and that any disturbances may result in noticeable effects that may easily explain the noise observed. We have to keep in mind that also electric contacts do not behave in their usual manner at such low currents. Nevertheless, even at such extremely low values of I it can be clearly seen that a plateau I(t → ∞) was reached at the end of the measurement. The lowest current value (3.6 × 10 −13 A, tablet A) was taken for the calculation of the electronic conductivity which results in a value of 1 × 10 −13 S cm −1 . For pellet B we obtain 2.9 × 10 −13 A which yields σ eon = 7.6 × 10 −14 S cm −1 . The average value is given by 8.8 × 10 −14 S cm −1 . σ eon exceeds the theoretical values [21,22] by 6 to 8 orders of magnitude. Since the theoretical values refer to an ordered single crystalline state it is evident that the much higher values probed experimentally are chiefly affected by defect sites. Importantly, the electronic conductivity turned out to be very similar to the ionic one determined by AC impedance measurements. At ambient temperature the ratio σ total /σ eon is given by σ total /σ eon ≈ 2. This ratio is also obtained when we look at the initial current I(t = 0) ≈ 8 × 10 −13 A; it is indeed twice the final one and hence in good agreement with our earlier AC impedance data. With I(t = 0) = 0.8 pA (pellet A) we end up with σ total = 2.2 × 10 −13 S cm −1 at 293 K, see also [10]. For pellet B the same ratio I(t = 0)/I(t → ∞) ≈ 0.6/0.29 ≈ 2 can be estimated.
Similarly to our study Gerbig [13] has investigated ionic and electronic conductivities of microcrystalline Na 2 O 2 and a ball-milled sample (60 min, Pulverisette 5) but at higher temperatures than ambient. Some of the results are shown in the inset of figure 3. Keep in mind that σ eon will depend on the measuring conditions (Ar atmosphere (this work) versus oxygen atmosphere [13]); thus, they are not directly comparable to each other. Furthermore, the samples are expected to differ in morphology as well as the number and type of ionic and electronic defects, e.g. (isolated) superoxide defects as suggested in [13]. Despite of these differences our value is not in contradiction with the high-T data; quite the contrary, it supports the results presented recently. By analyzing measurements carried out as a function of oxygen partial pressure Gerbig concluded that sodium interstitials, Na i , are involved in ionic transport; for electronic conduction p-type behavior was found [13]. The calculations mentioned above discussed the transport behavior of several ionic and electronic charge carriers; for electronic conduction hole polarons have been identified as the most important charge carriers in crystalline Na 2 O 2 . Note, however, that the activation energies probed experimentally (ca. 1 eV) significantly differ from calculated values, most of them are well below 1 eV, see [20,21].

Conclusion
We investigated the poor electronic conductivity in nanocrystalline, defect-rich Na 2 O 2 that was prepared by highenergy ball milling. The sample turned out to be a mixed conductor with the ionic and electronic conduction contributing in equal shares when measured under O 2 -free atmosphere. While the partial electronic conductivity was in the order of only 8.8 × 10 −14 S cm −1 , the total one is given by ca. 22 × 10 −14 S cm −1 . The results indicate a strong coupling of the ion movements with electronic dynamics. Modifying the electric properties of the discharge products might be a not unreasonable strategy to overcome the current limitations in reversibility.  The time periods refer to the milling times. Data taken from [10]. After milling the starting material for 60 min an overall conductivity in the order of 1.7 × 10 −13 S cm −1 is expected at room temperature; see the corresponding dashed line used to extrapolate measured data. σ total corresponds to a solid-state diffusion coefficient D in the order of 3.2 × 10 −23 S cm −1 , see right axis. (Inset) Comparison of σ eon (this work, 293 K) with values, for a milled sample, taken from literature, see Gerbig [13]; the latter were measured at much higher T and at 1 bar O 2 [13]. (b) Potentiostatic polarization curves for two Na 2 O 2 samples measured at 293 K with a symmetrical cell configuration. Values in the pA range point to very poor electric conductivity at room temperature, see inset in (a). The lines represent exponential functions to guide the eye.