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Colossal dielectric constant in K 2 Ti 2 O 5
Rashmi Rani, Sofia de Sousa Coutinho, Stephane Holé, Brigitte Leridon
To cite this version:
Rashmi Rani, Sofia de Sousa Coutinho, Stephane Holé, Brigitte Leridon. Colossal dielectric constant in K 2 Ti 2 O 5. Materials Letters, Elsevier, 2020, 258, �10.1016/j.matlet.2019.126784�. �hal-02401154�
Colossal dielectric constant in K
2Ti
2O
5Rashmi Rani, Sofia De Sousa Coutinho, Stephane Hol´e, Brigitte Leridon
LPEM – ESPCI-Paris – PSL Universit´e – Sorbonne Universit´e – CNRS 10 rue Vauquelin – 75005 Paris – France
Abstract
Potassium dititanate (K2Ti2O5) ceramics are shown to exhibit solid electrolyte proper- ties with a colossal dielectric constant (up to 107) together with a high ionic conductivity (up to 10−5 S cm−1) at room temperature. Compared to Rb2Ti2O5crystals and ceramics, this is 2 orders of magnitude below but uses more abundant and eco-friendly compounds.
For both materials, the dielectric constant and the ionic conductivity as a function of tem- perature and frequency seem to be linked together. The 2-order-of-magnitude difference can be attributed to a c-axis variation in the structure. K2Ti2O5material can be interesting for electronic applications as a supercapacitor compound.
Keywords: Colossal dielectric constant, Potassium dititanate, Ionic conductivity, Electrical properties, Ceramics.
1. Introduction
Since the discovery of potassium dititanate K2Ti2O5 by Andersson in 1960, number of studies were focused on formation and growth of K2Ti2O5 using methods from con- ventional solid state, flux or hydrothermal [1, 2, 3, 4]. Later on,attention has been given toion-exchange syntheses of K2−xHxTi2O5and K2Ti2O5.xH2O from K2Ti2O5[2, 5]. Sys- tematic research were dedicated to modulations of morphologies, sizes, water contents,
Email address:[email protected](Brigitte Leridon)
Preprint submitted to Materials Letters August 29, 2019
and crystallinity of K2Ti2O5and corresponding reaction conditions[6, 7].
The crystal structure of K2Ti2O5 possesses (Ti2O5)2− layers separated by potassium ions in which titanium atoms are five-fold coordinated and at the center of oxygen pyra- mids.These pyramids are partly edge-shared and partly corner shared and the structure is lamellar with C2/m space group [8]. It has been used in various applications such as an ion-exchanger, highly active photocatalyst and photoluminescence [3, 9, 10, 11].
In the present paper we aim at investigating the electrical properties of K2Ti2O5 in comparison with the exceptional properties of the parent compound Rb2Ti2O5 such as 109 dielectric constant and 0.1-C cm−1 electrical polarization [12, 13] . The fact that K is more abundant and eco-friendly than Rb makes it an ideal candidate for supercapacitors.
2. Material and methods
K2Ti2O5 crystals were prepared by conventional solid state route method. Starting materials are high purity metal oxide or nitrate powder, KNO3 (> 99.9%) and TiO2 (> 99.8%). Powders were weighed according to the stoichiometric proportion for the required compositions and mixed for 30 min using acetone. They were then calcined at 930◦C for 3 h in a platinum crucible and finally crystals were obtained after a slow cool- ing down process at 0.3◦C/min. In order to obtain sample pellets suitable for electrical measurements, as-grown crystals were ground and then pressed in a 13-mm-diameter die under 7 tons/cm2 at room temperature. Gold electrodes were evaporated on both sides of the sample pellets.
The crystal structure was controlled by X-ray diffraction using a PhilipsX’pert-MPD, employing CuKαradiation under 50 kV and 40 mA. Samples were scanned at 0.03◦/min for 2θfrom 10◦to 60◦. Fig. S1 [15] shows a typical diffraction pattern of K2Ti2O5 which is consistent with previously reported diffractograms [8].
Dielectric constant measurements were performed with Solartron 1296 Dielectric in- terface and 1260 impedance/gain-phase analyser both automated by SMART software.
The sample temperature was varied using a Quantum Design Physical Properties Mea- surement System (PPMS). Real and imaginary parts of equivalent capacitance were mea- sured as a function of temperature and frequency from 10−1Hz to 106Hz under 100-mV ac voltage and the equivalent dielectric constant was inferred from the capacitance con- sidering area and thickness of sample pellets.
3. Results
Maps of real (r0) and imaginary (r00) parts of complex permittivityr are displayed in logarithmic scale in Fig.1a and 1b respectively. Above 200 K, the dielectric permittivity increases to colossal values, as high as 107at 300 K and 10−1 Hz.
Fig.1c shows real and imaginary parts ofras a function of frequency at three different temperatures. At 400 K and 300 K,r0andr00follow similar behaviour and are decreasing with frequency, while at 170 K they are much smaller and around the system detection level. The black solid lines represent respectively the slope corresponding to the Warburg effect, when bothr0 andr00 vary asω−1/2, and to the conduction effect whenr00 varies as ω−1see [13] and references therein. It appears that the system is dominated by Warburg behaviour at low frequency and ion conduction at high frequency.
Permittivity of K2Ti2O5 ceramics was also measured at various bias voltage ranging from−10 V to+10 V. The corresponding results measured at 100 Hz for 100-mV ampli- tude are shown in Fig. 2. Permittivity exhibits strongly nonlinear behavior and depends on the bias voltage sweeping direction. Two symmetrical broad peaks in the graph are rem- iniscent of the strong remanent polarization, evocative of a ferroelectric-like behaviour.
However, the material is not ferroelectric, due to the lack of spontaneous symmetry break- 3
ing inside the unit cell. Due tomacroscopicalinversion symmetry breaking of the system due to the accumulation of ions at the blocking interface, the overall response of the sam- ple is ferroelectric. Such behaviour was already reported in single crystals of the parent compound Rb2Ti2O5 [14].
Ionic conductivity of K2Ti2O5ceramic taken at 1 kHz wherer00slope is−1 is plotted in Fig. 3 as a function of temperature. It can be seen that the conductivity reaches its highest value, 10−5S cm−1, at around 300 K. The conductivity increases by 5 orders of magnitude from 150 to 300 K and decreases by 2 orders of magnitude from 300 K to 400 K. It is worth noting that K2Ti2O5 ceramics and Rb2Ti2O5crystals behave qualitatively the same however the value of conductivity is two orders of magnitude lower in K2Ti2O5 and the maximum is found at around 270 K in Rb2Ti2O5crystals [13].
4. Discussion
Previous work [13] reported colossal dielectric permittivity up to 109in Rb2Ti2O5sin- gle crystals due to ionic diffusion processes. This mechanism was attested by the presence of a Warburg element in the dielectric permittivity at low frequency, wherer0andr00vary asω−1/2. In the present case, curves at 300 K exhibit a low frequency dependence consis- tent with Warburg diffusion and a high frequency behaviour consistent with conduction.
But while the qualitative behaviour of permittivity is the same, the highest value is two orders of magnitude below the one of Rb2Ti2O5 single crystals and the maximum value is still attained at 300 K rather than at 270 K. In order to understand the difference, we measured Rb2Ti2O5 ceramics and the results are displayed in[15]. The maximum value is still attained at 270 K and permittivity is around 109at 0.1 Hz which indicates that the observed difference is due to K2Ti2O5 material itself and not to sample ceramic nature.
The behaviour of ionic conductivity is also qualitatively similar to the one reported in
Rb2Ti2O5 crystals, though the maximum value is obtained at 300 K and is two orders of magnitude lower than in Rb2Ti2O5. While we do not have a definite explanation for the decreasing in conductivity above 300 K, we suspect that it is related to thermally activated phonons slowing down the mobile ions.
While the work reported in [13] had enabled to clearly establish the ionic origin for the permittivity, more recent work has provided an additional mechanism which explains its colossal value [14]. Indeed, at odds with previous assumptions, only negative charges are found to accumulate at the anode in Rb2Ti2O5 while the cathode is virtually shifted into the material, due to the presence of an insulator/metal transition [14]. Such mech- anism could lead to the existence of an ultrathin insulating layer of ionic charges at the anode, yielding colossal equivalent permittivity. The present results seem to indicate that mechanisms at play in K2Ti2O5are similar, but that two-order-of-magnitude-smaller ionic conductivity produces a two-order-of-magntitude-smaller equivalent permittivity, further sustaining the assumption that ionic conductivity is responsible for colossal polarization.
Finally, the highest ionic conductivity is shifted from 270 K in Rb2Ti2O5to 300 K in K2Ti2O5. In any case this points to the effect of the structure itself on the ionic diffusion processes. Indeed, though (Ti2O5)2−planes are quite similar in the case of Rb2Ti2O5and K2Ti2O5, the distance between the planes in c-axis as inferred from X-ray diffractionis decreased by∼5.3% in K2Ti2O5[15].
5. Conclusion
We have evidenced colossal permittivity (up to 107) in potassium dititanate at low frequency, and ionic conductivity of the order of 10−5 S cm−1 at 300 K. The overall fre- quency behaviour of permittivity and conductivity is consistent with previous measure- ments in the Rb2Ti2O5 parent compound and points out to the same mechanism which is
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an accumulation of negative ions at the anode with the creation of a virtual cathode inside the material. However permittivity and ionic conductivity are two orders of magnitude smaller in K2Ti2O5. In addition the maximum for both ionic conductivity and permittivity is shifted to 300 K.
6. Acknowledgement
We gratefully acknowledge support from Fondation Jean Langlois. This work has received support under the program ”Investissement d’Avenir” launched by the French Government and implemented by ANR with the reference ANR-10-IDEX-0001-02 PSL.
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[15] See Supporting Information.
(a)
(b)
(c)
Figure 1: Dielectric constant of K2Ti2O5 (a) Re(r) and (b) Im(r) as a function of temperature and fre- quency with Vac=100 mV. (c) Re(r) red dots and Im(r) (blue dots) curves vs frequency at three different temperatures: 170 K, 300 K, 400 K. Black solid lines indicate respectfully a−1/2 slope (Warburg regime) and a−1 slope (conduction regime)
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Figure 2: Dependence of K2Ti2O5 dielectric constant on bias voltage at 300 K with 0.1-V/min sweep rate and 100-mV ac voltage at 100 Hz.
Figure 3: Ionic conductivity extracted from the value of Im (r) at 1 kHz and plotted as a function of temperature.
