1. INTRODUCTION

The subsequent discovery of superconductivity (SC) at T c ∼ 5 K in Na0.3CoO2·1.3H2O has caused great excitement [1]. Although its T c is too low for practical applications, the structural and chemical similarities between Na0.3CoO2·1.3H2O compound and Cu-based high T c superconductors provided hope of an additional insight into the physics of SC in layered transition-metal oxides. The crystal structures of the Na0.3CoO2·1.3H2O family are built up of hexagonal layers composed of nonmagnetic Co3+ in a background of low-spin Co4+ (\(S={\frac{1}{2}}\)) ions (similar to Cu2+ in the cuprates) that are separated by a “charge reservoir” of Na x (H2O) y . The role of this “charge reservoir” is not at all clear and further chemical and physical modifications are required to probe the stability field of this superconducting family.

Structurally, the anhydrous “parent” Na0.7CoO2 compound consists of alternate layers of CoO2 and Na. The crystal structure is hexagonal (P63/mmc) with a \(\sim 2.83\) Å and c ∼10.9 Å (c/a ∼ 3.8). The absence of superconductivity for the anhydrous compound Na0.7CoO2 is intriguing. When exposed to saturated water vapor or liquid water, anhydrous Na0.7CoO2 intercalates water between CoO2 layers to form the superconducting bilayer hydrate Na0.3CoO2·1.3H2O. The water forms two additional layers between the Na and CoO2 increasing the c-axis lattice parameter of the hexagonal structure. This induces an expansion of the c-axis from c ∼ 10.9 Å to c ∼ 19.7 Å (c/a ∼ 6.9). Thus the c/a ratio is a reliable parameter to determine whether the material is a superconductor or not [2]. The Na ions are found to occupy a different configuration from the parent compound, while water forms a structure that replicates the structure of ice. The large separation enhances the two-dimensionality, which may induce the superconductivity, because high two-dimensionality is the characteristic of high T c copper-oxide.

The copper-based high T c superconductors (HTSC) are perovskites. The prototype perovskite is BaTiO3, which is the “standard” ferroelectric. The cuprates indeed possess a high dielectric constant (\(\varepsilon \approx 30\)) at far IR frequencies (up to about 150–250 cm−1) [3]. This feature is not included in current theories of HTSC. A large ɛ is also observed in organic superconductors, of the TMTSF-X series, as well as in the two-dimensional BEDT-X series [4]. The relationship of a very high dielectric constant to an abnormally high T c was first pointed out by Cohen, predicting the superconductivity of semiconducting doped SrTiO3 [5]. A theory accounting for a very large enhancement of T c, due to a large ɛ, was proposed by Gersten and Weger [6]. It requires a very inhomogeneous ionic polarizability, which causes a screening of the electron–electron interaction, with much less screening of the electron–ion interaction, for ions located in parts of the unit cell (such as the planar oxygen ions in the cuprates) where the ionic polarizability is small. In this case, the McMillan [7] theory of “medium” T c, predicting a maximum T c of about 30–40 K, does not apply, because it is based on the properties of a nearly-homogeneous electron gas.

The main goal of the present paper is to find out, whether a very large ionic dielectric constant is a general property of materials with an abnormally large T c. In this regard Broad Band Dielectric Spectroscopy (BDS) covering the extremely wide frequency range (10−6–1011 Hz) is especially sensitive to intermolecular interactions, and cooperative processes may be monitored. It provides a link between the properties of the individual constituents of a complex material and the characterization of its bulk properties. We investigated the dielectric properties of the parent Na0.7CoO2 and the Na0.3CoO2·1.3H2O materials. We attempt at this stage to obtain an empirical indication about the value of ɛ, both in the unhydrated and hydrated materials. In Na0.3CoO2·1.3H2O the water may contribute to an abnormally large ionic ɛ, although this is by no means certain for isolated water molecules.

2. EXPERIMENTAL DETAILS

The parent Na0.7CoO2 compound was synthesized by solid-state reaction of Na2CO3 (99.5%) and Co3O4 (99.7%) heated for 24 h in flowing oxygen at 800°C. Hydration and deintercalation of Na to obtain Na0.3CoO2·1.3H2O was then performed using equimolar ratio of Na2S2O8 in aqueous solution with Na0.7CoO2 and stirring for 22 h in a covered beaker. Applying 4–5 drops of 1N NH4OH in 20 ml deionized water gave us a pH 10.5, which is optimal to obtain reproducibly Na0.3CoO2·1.3H2O [1–2]. All samples were placed in humidified containers and characterized by X-ray powder diffraction.

In the frequency band 10−2–106 Hz the dielectric properties were measured using an Alpha analyzer from Novocontrol GMBH. The hydrated samples were mixed with KBr in order to preserve the water content. The samples were first compacted into pellets with dimensions of 1.25 mm × 1.8 mm × 11.2 mm, and the faces were polished and gold electrodes were evaporated on to them. Dielectric measurements were carried out at room temperature, T=295 K. For the higher frequency band of 106–1010 Hz Time Domain Dielectric Spectrometry (TDDS) was used with an open-ended coaxial probe configuration [8,9]. The samples were densely compacted and the faces polished. The coaxial probe was terminated by a flange matched to the sample surface. The measurements were carried out at room temperature, T=295 K in the frequency range 106–\(1.2\times 10^{10}\) Hz directly after sample preparation. Two samples were measured; the dry Na0.7CoO2 and the hydrated Na0.3CoO2·1.3H2O/KBr at a ratio of 1:1.

3. RESULTS AND DISCUSSION

Powder X-ray patterns of the hydrated and anhydrous Na\(_x{\rm CoO}_2\) materials are shown in Fig. 1. The typical (001) reflections for the hydrated sample are shifted to lower angles indicating an increase in the c lattice parameter. Notably, there is a new reflection (002) for d=5.12Å (at 2\(\theta=8.13\it{}^\circ\)) for the bilayer-hydrate sample as shown in Fig. 1. Both samples are hexagonal and have the same a = 2.82(1) Å lattice parameter, whereas c=10.81(2) Å for the anhydrous Na0.3CoO2 material and c=20.5(4) Å for the hydrated one, values which are consistent with the published data [1,10]. The c/a ratio for the hydrated material is related to a SC material with T c near 4.2 K. The temperature dependence of the dc magnetic curves are in good agreement with the published data [11].

Fig. 1.
figure 1

XRD patterns of the anhydrous and hydrated (dash line) Na\(_x{\rm CoO}_2\) samples.

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4. THE DIELECTRIC MEASUREMENTS

The complex dielectric permittivity of anhydrous Na0.7CoO2 for frequencies between 10−2 and 106 Hz is presented in Figs. 2 and 3. The data demonstrates the existence of strong dielectric relaxations in the considered frequency band with a weak contribution from dc conductivity. The main process is characterized by a power low dependence, implying that its characteristic peak frequency is in fact at a far lower range than the measurement window. There is a further relaxation centered around \(10^4\) Hz. The data was fitted using the Havrilak–Negami phemenological description of relaxation processes [12], a Jonscher power [13] law term, and a dc conductivity term using the special Matfit routine [14].

$$\varepsilon^\ast(\omega)=\varepsilon_\infty +\frac{\Delta \varepsilon}{(1+(i\omega \tau)^\alpha)^\beta}+A(i\omega)^{n-1}+\frac{\sigma}{i\omega\varepsilon_0}$$
(1)

Here \(\varepsilon_\infty\) is the high frequency limit of the dielectric permittivity, τ is the characteristic relaxation time of the process, α and β are the shape parameters, \(\Delta \varepsilon\) is the dielectric strength, A is a real coefficient, σ is the dc conductivity, and \(\varepsilon_0\) is the permittivity of free space. The fitting parameters are outlined in Table I.

Table I. The Fitting Parameters Derived in the Frequency Band 10−1 to 106 Hz
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Fig. 2.
figure 2

The real part of the complex dielectric permittivity measured in the frequency band 1–106 Hz for anhydrous Na0.7CoO2. The solid line is the experimental data, (▵) Eq. (1), (○) the Jonscher term. The (square) is the Havrilak–Negami function.

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Fig. 3.
figure 3

The imaginary part of the dielectric permittivity for anhydrous Na0.3CoO2.

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The exponent of the power law, \(n=0.188\), is consistent with a very low frequency Maxwell–Wagner process [15]. The correspondence of \(\varepsilon_\infty\), in Table I, to the value of the dielectric constant derived in the high frequency measurements (Table II) negated the possibility that the power law was due to surface contact effects. Given the layered structure of the crystal lattice this would suggest strong interfacial polarization at the layer interfaces. The process centered around 104 Hz requires further investigation. High-frequency measurements were carried out using Time Domain Spectrometry. The time domain response function to a step input is related to the dielectric permittivity by the Laplace transform

$$\frac{\varepsilon^\ast(\omega)-\varepsilon_\infty}{\Delta \varepsilon}=-i\omega \int_0^\infty\phi(t)\,{\rm exp}(-i\omega t)\,dt$$
(2)

Fitting of the data was carried out in the time domain using the stretched exponential [16]

$$\phi (t)=\varepsilon_{\rm s}\left[1-\exp \left(-\left(\frac{t}{\tau}\right)^v\right)\right]$$
(3)
Table II. The Fitting Parameters of Na\(_x{\rm CoO}_2\) Samples Derived From TDDS Measurements
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Then, the data was transformed to the frequency domain using Eq. (2). The time domain results are presented in Table II.

For the hydrated sample, the following mixing formula was used to extract the response due to the hydrated Na\(_{0.3}{\rm CoO}_2\cdot\)1.3H2O from the influence of KBr

$$\varepsilon_{\rm measured}^\ast(\omega)=p\varepsilon_{{\rm Na}_{0.3}{\rm CoO}_2}^\ast(\omega)+(1-p)\varepsilon_{{\rm KBr}}^\ast(\omega)$$
(4)

where p is the fraction of Na0.3CoO2. Due to the low permittivity of KBr (\(\varepsilon \approx 4\)) this translates to

$$\varepsilon_{{\rm NCO2}}^\ast(\omega)=2\varepsilon_{\rm measured}^\ast(\omega)$$
(5)

The complex dielectric permittivity results are presented in Fig. 4. The stretched exponential model of dielectric response has been linked to the transport of charge carriers in the medium [17,18]. To understand the transport mechanism fully, temperature measurements are required. However, from the value of the exponent we can derive the fractal dimension of the matrix and its resulting porosity [19]. The fractal dimension D is governed by

$${D}=3\nu$$
(6)
Fig. 4.
figure 4

The dielectric permittivity of anhydrous and hydrated Na\(_x{\rm CoO}_2\) in the frequency band 1 MHz to 10 GHz.

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The value then for the anhydrous sample \(D=1.59\), is indicative of transport in a plane. In the hydrated sample \(D=3\) and the transport would then be throughout the sample. The porosity φ is given by

$$\varphi=(4-D)^{-1}$$
(7)

For the anhydrous sample, we have a porosity of \(\varphi=0.414\) —the sample is very porous and the transport is likely to be some form of percolation via the pores. For the hydrated sample the porosity is 1—the pores are most likely filled with water and the transport is ionic inside bulk water, or the presence of KBr radically changes the structure of the ceramic.

5. CONCLUSIONS

Na0.3CoO2 demonstrates a rich and varied dielectric landscape. The origin of exceptionally high static permittivity probably lies in the layered structure of the crystal lattice. Interfacial polarization of internal charge carriers trapped at the layer boundary would lead to the sort of relation noted in Fig. 4. Intriguingly, the results of the high-frequency measurements reflect charge carriers that are mobile, their transport being heavily influenced by the state of the background matrix. The resolution of such a dilemma would be the existence of two separate systems of charge carriers inside the lattice. Temperature-based measurements would be required to investigate the true nature of these relaxations.