ELECTRICAL PROPERTIES OF LLTO THICK FILMS

1. Introduction

Lithium-ion conducting solid materials may be applied in various electrochemical devices such as all solid state lithium batteries  [1], CO₂, SO₂ or NO₂ gas sensors  [2] and pH sensors  [3]. Li_3xLa_2/3–xTiO₃ (LLTO) is one of the most promising Li⁺-ion solid electrolyte because of its high grain conductivity, which for x = 0.11 (Li_0.33La_0.56TiO₃) reaches the value of 0.1 S m⁻¹ at room temperature [4]. LLTO crystallizes in a perovskite structure, which consists of TiO₆ octahedra and A-cages with either La³⁺ ions, Li⁺ ions or vacancies surrounded by 12 oxygen ions [5, 6]. La³⁺ ions are unequally distributed in the structure forming La-rich and La-poor layers [6]. This unique superstructure leads to 2D conductivity up to 200 K [7, 8]. Such structural feature makes LLTO compound a  very interesting material both for fundamental studies and for applications. However, even the high density LLTO ceramic materials have major drawback, namely the low grain boundary conductivity, which lowers the overall conductivity [9]. The LLTO ceramics are studied well and recent results are summarized in the review paper [10]. There were some attempts to prepare LLTO thin films by pulsed laser deposition [11–13], electron-beam evaporation [14] and radiofrequency magnetron sputtering [15]. Thick LLTO films were also prepared by using the tape casting method, but the conductivity value was found to be low (σ_bulk = 1.7 · 10⁻⁵ S m⁻¹ @ 300 K) due to high film porosity [16]. Explicit investigation of technological tape casting conditions was performed [17] and the films with high relative density (about 98%) were prepared. The latter paper was showing electrical properties of the films at room temperature only. The  conductivity values for the  films were found slightly lower compared to the  conductivity of ceramic samples [17]. In our present work, we have prepared free-standing LLTO films by tape casting. Our aim was a detailed investigation of electrical properties of these films. Ultrabroadband (from 10 Hz up to 10 GHz) impedance spectroscopy was used and the results were analyzed by choosing a meaningful equivalent circuit. The conductivity results of thick films were compared to the ones of bulk ceramics.

2. Experiment

The aqueous sol–gel synthesis method was used for the LLTO ceramics powder preparation. The synthesis and sintering conditions were reported previously [18]. The Li loss during the sintering is known to be a common issue [9, 11], so the lithium excess was added to provide Li_0.4La_0.56TiO₃ instead of Li_0.33La_0.56TiO₃ (the abbreviation LLTO persists through the article). The bulk ceramic samples were ground to a cylindrical shape with dimensions of l = 1.5 mm length and A = 1.0 mm² electrode surface area. The thick films were prepared according to the already tested tape casting methodology [16]. The 40% volume slurry was gained by mixing the  powder with acetylacetone, polymethyl-methacrylate and Triton X-100 in a centrifugal mixer (Thinky ARE-250). The slurry was casted on alumina substrate with MTI AFA-III coater to yield the  thickness of 0.2  mm after drying. Part of the  film was removed from the  substrate to stay free-standing. The films were measured in the  ‘in-plane’ geometry by applying electrodes to the  opposite fracture surfaces (the l and A of the film’s samples are known). The Pt paste was used to prepare electrodes for impedance investigations and in both cases the paste was annealed at 1170 K for 15  min. A  coaxial line with the  sample was measured [19] and the impedances of the samples Z̃(ω) = Z'(ω) + iZ''(ω) were obtained in the frequency range (f = ω/2π) from 10 to 10¹⁰ Hz and temperature range from 300 to 1000 K.

3. Results and discussion

The XRD result in relative units (Fig.  1) shows that the  obtained LLTO powder has a  cubic perovskite-type superstructure and is consistent with the structure No. 155633 from the ICSD database. No impurities have been observed.

The SEM micrographs of bulk ceramic sample, free standing film and alumina substrate supported film are presented in Fig. 2. All the images show well crystallized microstructures with average grain size of 2 μm and relativity high uniformity of grain size. There are no significant microstructure differences among all three samples, which allows us to compare their electrical properties.

Figure 3 shows impedance and complex capacitance spectra measured at temperatures 300, 500 and 700  K of the  LLTO ceramic sample, free standing thick film and substrate supported thick film. Three dispersion regions can be seen for all the  investigated samples. A dispersion region can be identified as Z' decrease with increasing frequency and the onset of the dispersion is observed as a maximum of Z''(f), located at relaxation frequency. The maxima of Z'' and the dispersion region in the Z'(f) representation shift towards higher frequencies when the temperature of the sample is increased. It is well known for ceramic LLTO that the impedance at the highest frequencies correspond to Li⁺-ion migration in grains (Fig. 3, the maxima of Z''(f) indicated as G), the midrange frequency dispersion is caused by ionic transport in grain boundaries (Fig. 3, the maxima of Z''(f) indicated as GB), and the lowest frequency range dispersion is due to processes taking place at the  interface of LLTO and Pt electrode (Fig.  3, the region of Z''(f) indicated as E). The DC resistances of grain and grain boundary mediums (R_g and R_gb , respectively) can be estimated from characteristic plato regions in the spectra of Z'(f) (Fig. 3, the regions of Z'(f) indicated as G and GB, respectively). We have found that the impedance spectra are similar for the ceramic sample and free standing LLTO thick film, while the Z' platos and corresponding relaxation frequencies for the substrate supported thick film were shifted due to the influence of alumina substrate. The moderate shifts are also observed in the  cpectra of complex capacitance C̃(f) = C'(f) + iC''(f) = 1/(i2πf Z̃(f)) due to capacitance of the substrate (Fig. 3).

The spectra differences are even more pronounced in the  linear impedance spectra representation, which is shown as Nyquist plot in Fig. 4. In the  Nyquist plot the  diameter of the  high frequency semicircle (inset of Fig. 4) corresponds to the  resistance of ceramics or film grains R_g and the diameter of the semicircle in the intermediate frequency range corresponds to grain boundary resistance R_gb.

In order to extract sample resistances R_g and R_gb from the  impedance spectra, the  corresponding equivalent circuits have been composed. Figure  5(a) shows the  equivalent circuit used to describe impedance spectra of LLTO bulk ceramics and free standing film. It is common to use a so-called ZARC circuit to describe an impedance of ionic conductors [20–22]. It consists of resistance R and constant phase element CPE [20, 23] in parallel. The impedance of the ZARC can be expressed by Eq. (1). The Q and n in Eq. (1) are parameters of CPE, the n may assume values 0  ⩽ n  ⩽ 1.

The Z̃(ω) of the  grains were satisfactorily fitted to ZARC (indicated as ’grains’ in Fig. 5(a), and describes the  region G in Fig.  3) and the  values of R_g were extracted. The ZARC function did not work for the impedance of grain boundaries due to strong overlap with responses E and G on both sides (Fig. 3). To get the better quality of the fit, the more generalized version of ZARC impedance, known as empirical function of Havriliak–Negami  [24–27], was used (eq. (2)).

The exponents in Eq. (2) may assume values such that 0 ⩽  n × m  ⩽ 1. The representation of Havriliak–Negami function is shown as H-N element in Fig. 5(a). It describes the region GB in Fig. 3 and yields the values of R_gb. The common combination of CPE and Warburg [28] elements in parallel was used to fit the impedance of the electrode interface (region E in Fig. 3, Warburg element is indicated as W in Fig.  5). The  equivalent circuit shown in Fig. 5(b) takes into account the alumina substrate (capacitance connected in parallel) and it was used to fit the experimental impedance spectra of substrate supported LLTO film.

Figure  6 shows the  temperature dependences of grain conductivity in Arrhenius representation. The  conductivity was calculated from R_g considering the sample size, i.e. σ_g = l/(AR_g). At high temperatures the  deviation from Arrhenius law (σT = σ₀ exp(∆E/k_BT)) is observed. Such behaviour of LLTO bulk conductivity has already been explained by correlated Li⁺-ion motion [18]. Our present results show that a similar deviation from Arrhenius activation is observed in thick LLTO films, both free standing and alumina supported. Besides, the grain conductivity of free standing films was almost identical with the grain conductivity of ceramics. The grain conductivity of the supported film was found to be lower: we relate this with alteration of the composition of the film due to interaction with the substrate during the sintering.

The grain boundary conductivity σ_gb (Fig. 7) followed Arrhenius law in the whole investigated temperature range. It is important to note that the highest value of grain boundary conductivity was found for the free standing LLTO film and its activation energy was the lowest. This suggests that the grains of the powder accommodate slightly better in the slurry than during the pressing of the dry powder.

4. Conclusions

Relatively dense LLTO thick films have been successfully tape-casted. Free standing and alumina supported films were analyzed by impedance spectroscopy in the  frequency range from 10  Hz up to 10  GHz and temperatures up to 1000  K. The  meaningful equivalent circuits are proposed for the  analysis of impedance spectra of thick films, both free standing and supported by dielectric substrate. These equivalent circuits allowed us to extract grain and grain boundary conductivity values of the  films and to compare them with the ones of bulk ceramics. In this work, we show that by using the tape-casting methodology it is possible to make free standing LLTO thick films, which show grain conductivity values identical to the  bulk ceramics and even higher grain boundary conductivity values. Thus LLTO is a  strong candidate for the  applications where Li⁺-ion solid conductors are required.

References

LLTO STORŲJŲ SLUOKSNIŲ ELEKTRINĖS SAVYBĖS

^a  Vilniaus universiteto Fizikos fakultetas, Vilnius, Lietuva

^b  Vilniaus universiteto Chemijos ir geomokslų fakultetas, Vilnius, Lietuva

Santrauka

Li_0,4La_0,56TiO₃ (LLTO) ličio jonų laidininkai buvo sintezuoti zolių-gelių metodu. Rentgeno spindulių difrakcijos analizė parodė, kad šis junginys kristalizuodamasis sudaro perovskito struktūrą, o kitų priemaišinių fazių stebėta nebuvo. Iš gautų superjoninių miltelių sluoksnių liejimo metodu buvo pagaminti stori sluoksniai: vienas ant aliuminio oksido padėklo, kitas – be padėklo. LLTO keramika ir storieji sluoksniai buvo ištirti pilnutinės varžos spektroskopijos metodu dažnių srityje tarp 10 Hz ir 10 GHz. Rezultatams nagrinėti buvo pasitelkta ekvivalentinių grandinių analizė. Nustatyta, kad LLTO sluoksnio be padėklo kristalinis laidumas yra identiškas keramikos kristaliniam laidumui, o tarpkristalinis šio sluoksnio laidumas gautas kiek didesnis, palyginti su to paties junginio keramika.