Sodium ion diffusion in layered Na_xMnO₂ (0.49 ≤ x ≤ 0.75): Comparison with Na_xCoO₂

P2-type Na_xMO₂ (M: transition metal element) with a layered structure is not only a fascinating electronic material that exhibits large thermoelectricity¹⁾ and superconductivity,²⁾ but also a possible candidate for the cathode material in sodium-ion secondary batteries (SIBs).^3–8) In particular, Na_0.6MnO₂ exhibits a large capacity of 140 mAh/g and an average operating voltage V_av of ∼2.5 V.⁷⁾ Na_0.74CoO₂ also exhibits a good capacity of 120 mAh/g (V_av ∼ 3.0 V) and good cyclability, with a loss of less than 4% after 40 cycles.⁸⁾ P2-type Na_xMO₂ exhibits alternately stacked MO₂ layers and Na sheets with an ABBA oxygen stacking sequence.⁹⁾ The MO₂ layer consists of edge-sharing MO₆ octahedra. The sodium atom is surrounded by six oxygens, and they form a NaO₆ prismatic structure in the P2-type structure, whereas Li and six oxygens form a LiO₆ octahedron in Li_xCoO₂.

The sodium ion diffusion coefficient D is an important parameter that governs the critical discharge rate ν_c according to the relationship ν_c = 4D/L², where L is the diffusion length, in a one-dimensional (1D) diffusion model.¹⁰⁾ In the Na⁺-diffusion process, thermally activated Na⁺ jumps to a nearest-neighbor site beyond a potential barrier. Recently, Shibata et al. experimentally determined the D value of a Na_xCoO₂ thin film using electrochemical impedance spectroscopy (EIS).¹¹⁾ The magnitude of D was found to be (0.7–1.9) × 11⁻¹¹ cm²/s at 0.54 ≤ x ≤ 0.85 at 303 K. They also reported that the activation energy decreases significantly from 0.51 eV at x = 0.85 to 0.32 eV at x = 0.54. These features were interpreted as an increase in the interlayer distance (d ≡ c/2, where c is the c-axis lattice constant) with a decrease in x.¹¹⁾ P2-type Na_xMnO₂ is an alternative candidate for the cathode material in SIBs because it exhibits a high capacity, comparable to that of Na_xCoO₂. In addition, the material does not contain costly Co.

In this paper, we evaluate the magnitudes of D and the charge-transfer resistance R_CT in a well-characterized Na_xMnO₂ thin film prepared by pulsed laser deposition (PLD). The magnitude of D (R_CT) is (1.0–1.4) × 10⁻¹⁰ cm²/s (45.0–55.7 Ω cm²) for 0.49 ≤ x ≤ 0.75 at 329 K. This value is significantly larger (smaller) than that for Na_xCoO₂ at 328 K.¹¹⁾ We interpret the improved Na⁺ diffusion properties in terms of the larger interlayer distance (d = 5.54 Å) between the neighboring Mn sheets.

A thin film of Na_0.58MnO₂ was grown on a Au-deposited MgO(100) substrate at 800 °C and an oxygen partial pressure of 100 Pa for 30 min by PLD. The Na concentration (x = 0.58) of the as-grown film was evaluated in terms of the spontaneous potential (= 2.70 V) versus that of Na metal and is close to the value of the target, x = 0.59. The target, whose thickness and diameter were 2 and 10 mm, respectively, was prepared by sintering Na_0.59MnO₂ powder. The synthesis condition and characterization of the Na_0.59MnO₂ powder are described elsewhere.¹²⁾ The distance between the target and substrate was kept at 35 mm. A yttrium aluminum garnet (YAG) laser with a wavelength of 532 nm was used in the deposition. The laser intensity and repetition frequency were ∼1.7 J/cm² and 10 Hz, respectively. The film thickness was evaluated to be 220 nm using a cross-sectional scanning electron microscope (SEM) image, and the film area was 0.45 cm². The crystal structure and surface morphology were characterized by the X-ray diffraction (XRD) patterns obtained with Cu Kα radiation (Rigaku RINT2000PC) and SEM (TECHNEX Mighty-8).

Electrochemical measurements were conducted using a potentiostat (Bio-Logic SP-150) in an Ar-filled glove box using a beaker-type cell. The cathode, anode, and electrolyte were the Na_0.58MnO₂ thin film, Na metal, and propylene carbonate (PC) containing 1 mol/L NaClO₄, respectively. The charge/discharge current density was 1 µA/cm² to 4 mA/cm² (0.13–520 C), and the cut-off voltages were 1.5 and 3.8 V. The EIS measurements were conducted in the frequency range from 5 mHz to 200 kHz with an amplitude of 30 mV at various temperatures (301 ≤ T ≤ 355 K).

Figure 1 shows the XRD pattern of the as-prepared Na_0.58MnO₂ thin film. The (002) and (004) peaks are clearly observed, indicating a c-axis orientation. A c-axis orientation was also observed in a Na_xCoO₂ film.⁶⁾ The c-axis lattice constant c was evaluated to be 11.13 Å, which is consistent with that of Na_xMnO₂ with x ∼ 0.58.¹²⁾ No impurity peaks were observed. The inset of Fig. 1 shows a surface SEM image of the thin film. The grain size was roughly evaluated to be ∼150 nm.

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Figure 2(a) shows the discharge curves of the thin-film electrode at various discharge rates ν. These curves were measured after the charge process at 0.2 C. The discharge curve at 0.2 C well reproduces the curve of Na_xMnO₂ powder.¹²⁾ The capacity Q at 0.13 C is Q ∼ 145 mAh/g, which corresponds to an x variation of 0.6. Figure 2(b) shows the discharge capacity Q_D as a function of ν for the Na_xMnO₂ thin film. Q_D decreases linearly with ν and then drops steeply at ν_c = 200 C. If we assume a 1D diffusion process, the Na⁺ diffusion constant is roughly estimated to be D (= ν_cL²/4) ∼ 6.7 × 10⁻¹² cm²/s.

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Figure 3(a) shows the discharge curve at 0.5 C of the thin-film electrode after the charge process at 0.5 C. The arrows in Fig. 3(a) indicate the EIS measurement points.

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Figure 3(b) shows the Nyquist plot for x = 0.60 at 301 K. In the high-frequency region, the impedance spectrum exhibits semicircles with a radius of ∼100 Ω. Then, the impedance spectrum shows a straight line at an angle of 45° with respect to the horizontal axis in the medium-frequency region. At low frequencies, it seems to diverge with decreasing frequency. This behavior is quantitatively explained by the Randle's equivalent circuit shown in the inset of Fig. 3(b).¹³⁾ This equivalent circuit consists of the uncompensated ohmic resistance R_O of the electrolyte and electrode, the charge-transfer resistance R_CT across the electrolyte–electrode interface, the double layer capacitance C_dl at the electrolyte–electrode interface, and the complex impedance (Warburg impedance) Z_W arising from ionic diffusion at low frequencies. The semicircle at high frequencies is due to the parallel combination of C_dl and R_CT. The left and right edges of the semicircle correspond to R_O and R_O + R_CT, respectively. At x = 0.60 at 301 K, R_O, R_O + R_CT, and C_dl are 103.1 Ω, 293.5 Ω, and 2.7 µF, respectively. In the medium-frequency region, the linear-like impedance spectrum corresponds to the ionic diffusion process. The straight line with an angle of 45° with respect to the horizontal axis is attributed to semi-infinite Na⁺ ion diffusion. The divergent impedance spectrum at low frequencies corresponds to finite Na⁺ ion diffusion. The intersection of the horizontal axis and the broken line corresponds to R_O + R_CT + R_L, the value of which is 440 Ω for x = 0.60. R_L is the limiting low-frequency resistance. By solving Fick's second law with proper initial and boundary conditions, Z_W is expressed as

$$\begin{equation} Z_{\text{W}} = R_{\text{L}}\left(1 - \frac{3D}{L_{0}^{2}}\frac{i}{2\pi f} \right), \end{equation} \tag{ 1 }$$

where i, L₀, and f are the imaginary unit, thickness of the thin film, and frequency, respectively. Thus, the diffusion coefficient was evaluated using the slope of the broken line. D is evaluated to be 4.4 × 10⁻¹¹ cm²/s for x = 0.60 at 301 K. With increasing T, the divergent spectrum at low frequencies shifts to the left side [Fig. 3(c)], and the semicircle at high frequencies becomes small. This indicates that R_CT decreases with T.

Figure 4 shows the temperature dependence of (a) D and (b) R_CT for various values of x. The data were plotted using a logarithmic scale on the vertical axis and the reciprocal of the temperature on the horizontal axis. Because ln D (ln R_CT) decreases (increases) linearly versus 1/T, the data were least-squares fitted with an activation-type function as

$$\begin{equation*} D\sim \exp \left(-\frac{E_{\text{a}}^{D}}{k_{\text{B}}T}\right) \left[R_{\text{CT}}\sim \exp\left(\frac{E_{\text{a}}^{R}}{k_{\text{B}}T}\right)\right], \end{equation*}$$

where $E_{\text{a}}^{D}$ ($E_{\text{a}}^{R}$) and k_B represent the activation energy of D (R_CT) and the Boltzmann constant, respectively. The broken lines represent the results of least-squares fittings.

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In Figs. 5(a) and 5(b), we compare D and R_CT for Na_xMnO₂ at 329 K with those for Na_xCoO₂¹¹⁾ at 328 K.¹⁴⁾ The magnitudes of D for Na_xMnO₂ are much larger than those for Na_xCoO₂, although the data are somewhat scattered. On the other hand, the magnitudes of R_CT for Na_xMnO₂ are significantly smaller than those for Na_xCoO₂. As discussed below, the larger (smaller) D (R_CT) is ascribed to the larger interlayer distance d in Na_xMnO₂.

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Figures 5(c) and 5(d) show $E_{\text{a}}^{D}$ and $E_{\text{a}}^{R}$ for Na_xMnO₂ versus x. The magnitudes of $E_{\text{a}}^{D}$ for Na_xMnO₂ are slightly smaller than those for Na_xCoO₂, although the data are somewhat scattered. The magnitudes of $E_{\text{a}}^{R}$ are also slightly smaller than those for Na_xCoO₂. We ascribed the smaller $E_{\text{a}}^{D}$ and $E_{\text{a}}^{R}$ for Na_xMnO₂ to the structural difference between Na_xMnO₂ and Na_xCoO₂; Shimono et al.¹²⁾ reported that the d value of Na_xMnO₂ (d = 5.54 Å at x = 0.71) is larger than that of Na_xCoO₂ (d = 5.44 Å at x = 0.71). When a Na⁺ ion hops to the next Na site for diffusion, it must run close to four oxygens on a lateral surface of a NaO₆ prism. The four oxygens produce a Lennard-Jones potential originating in the Pauli exclusion principle.¹⁵⁾ The potential has a minimum at the center of the four oxygens. Thus, the Na⁺ ion will pass at the center. The height of the potential energy at the center corresponds to a potential barrier ($E_{\text{a}}^{D}$) for diffusion. When d is elongated, the height of the potential decreases, leading to a small $E_{\text{a}}^{D}$. A similar scenario is applicable to $E_{\text{a}}^{R}$ because the Na⁺ ion would feel a weaker repulsive interaction from the surrounding oxygens when it intercalates between the MnO₂ sheets. This argument is consistent with the findings of Kang and Ceder,¹⁶⁾ who performed a first-principle calculation for LiCoO₂ and reported that the activation energy for the Li⁺ diffusion constant increases with decreasing d.

In summary, we experimentally determined D and R_CT versus x for Na_xMnO₂ and compared the values with those of Na_xCoO₂.¹¹⁾ The magnitude of D is (1.0–1.4) × 10⁻¹⁰ cm²/s (0.49 ≤ x ≤ 0.75) at 329 K, which is one order of magnitude larger than that of Na_xCoO₂ in the same x range at 328 K. The magnitude of R_CT is 45.0–55.7 Ω cm² (0.49 ≤ x ≤ 0.75) at 329 K, which is smaller than that of Na_xCoO₂ in the same x range at 328 K. The enhanced D (suppressed R_CT) was interpreted in terms of the wider interlayer distance d between neighboring Mn sheets, which resulted in a lower potential barrier between neighboring Na sites.

Acknowledgment