Journal of Materials Science

, Volume 47, Issue 19, pp 6992–7002

The comparative influences of structural ordering, grain size, Li-content, and bulk density on the Li+-conductivity of Li0.29La0.57TiO3


    • U.S. Army Research LaboratoryRDRL WMM E
  • Matthew D. Green
    • U.S. Army Research LaboratoryRDRL WMM E
  • Christopher Cooper
    • U.S. Army Research LaboratoryRDRL WMM E
  • Jeffrey Wolfenstine
    • U.S. Army Research LaboratoryRDRL SED C
  • Gary Gilde
    • U.S. Army Research LaboratoryRDRL WMM E

DOI: 10.1007/s10853-012-6650-5

Cite this article as:
Sutorik, A.C., Green, M.D., Cooper, C. et al. J Mater Sci (2012) 47: 6992. doi:10.1007/s10853-012-6650-5


The lattice and total Li+-ionic conductivity of Li0.29La0.57TiO3 ceramic (LLTO) sintered at 1200 °C were determined as functions of powder calcination temperature and sintering duration, and these results were correlated with the relative degrees of Li+-ordering, Li-content, grain size, and bulk density to assess the relative impact of these parameters on material performance. Under all conditions, LLTO formed with a high degree of tetragonal superstructure to its perovskite related framework, and the lattice conductivity closely followed the relative amounts of the superstructure, as evaluated via determination of the sample ordering parameter from X-ray diffraction data. LLTO powders that were calcined at 900 °C for 1 h and sintered at 1200 °C for 6 h gave lattice conductivity values (~1.14 × 10−3 S cm−1) comparable within the highest ranges reported in the literature. This coincided with the lowest degree of tetragonal superstructure formation, and it was also found to be largely independent of the values of Li-content measured on sintered ceramic despite significant Li2O volatilization at longer sintering times (up to 23 % after 12 h at 1200 °C). Samples of LLTO powder that were calcined at 1100 °C and sintered at 1200 °C for 12 h resulted in the highest total Li-ion conductivity value ~6.30 × 10−5 S cm−1. The total conductivity of LLTO varied inversely with grain size when the grains were <20 μm but was insensitive to that parameter above that size threshold. The strongest influence on total conductivity was primarily the bulk ceramic density. It was estimated from measured values that as the bulk ceramic density approached the full theoretical value for LLTO the total conductivity could near the lattice conductivity of ~1.2 × 10−3 S cm−1.


Aqueous lithium-air batteries offer the potential for higher energy density compared to the current battery technologies [1, 2]. However, many technical challenges remain until their full potential can be realized. One of the most significant issues is that aqueous Li-air battery technology requires a solid electrolytic membrane that possesses fast lithium ion transport, low electronic conductivity, high mechanical strength, and excellent chemical stability [2]. Ceramic electrolytes offer several of the needed characteristics, and lithium lanthanum titanate (LLTO) (stoichiometry Li3xLa(2/3)−xTiO3) is currently one of the materials under consideration for this application.

One reason for the interest in LLTO is that among Li+ conducting ceramics it has some of the highest reported values for room temperature lattice conductivities at ~1 × 10−3 S cm−1 (R.T.) [3, 4]. However, the total conductivity of polycrystalline LLTO is a function of both the lattice and grain boundary contributions. Li-ion conduction through the grain boundaries still limits the total conductivity of LLTO to the typical range of 1 × 10−5–1 × 10−4 S cm−1 [4, 5]. A primary requirement for optimized conductivity of the phase pure ceramic is that the final product needs to be near full density to maximize grain-to-grain contact and, ideally, remove porosity [4, 5].

Previous studies have examined the correlation between LLTO synthesis, sintering, and ionic conductivity. Ceramics of LLTO are most commonly sintered in the temperature ranges of 1100–1350 °C from powder which has been previously prepared from direct combination, solid-state reaction between Li2CO3, La2O3, and TiO3 [5, 6]. There is general agreement in the open literature that the maximum lattice conductivity (σL) of ~1 × 10−3 S cm−1 occurs for Li3xLa(2/3)−xTiO3 with x close to 0.1 [5]. Some groups have reported a range of high conductivity for x = 0.11–0.13 [5, 6, 8] but a maximum value at compositions as high as x = 0.21 has also been reported [12]. In most of the literature, it is also believed that decreased Li-content in LLTO ceramics, resulting from Li2O volatilization on prolonged thermal exposure, leads to a decrease in lattice conductivity [2, 58]. Due to possible Li2O volatility at sintering temperatures, precautions are typically taken to retard Li-loss during powder synthesis and sintering. These include over batching of the Li-content in the starting materials, minimizing the temperature of powder reaction (i.e., the calcination temperature), packing of the green ceramic parts in loose LLTO powder to provide a Li2O-vapor-rich local atmosphere around the parts, and minimizing the time and temperature of final sintering [2, 69]. Once LLTO is fully sintered, the Li-content appears stable as the material can undergo repeated annealing cycles in the temperature range 600–1350 °C and yet still recover its original conductivity [8, 9].

In addition to the Li-content, another key parameter impacting the lattice conductivity of LLTO is the crystal structure polytype which is stabilized on sintering. These are all variations on a perovskite (ABO3) framework. At its most idealized is the cubic structure (PDF# 46–465; Space Group: Pm-3m) in which Li+- and La3+-cations are randomly distributed among the A sites. This structure can be promoted by values of x close to 0.11, but regardless of its composition, it is a high temperature phase and must be stabilized by quenching from ≥1150 °C [8, 9]. With slow cooling or low temperature annealing, a tetragonal superstructure forms as the Li+- and La3+-cations partially order into alternate A-site layers in the lattice (PDF# 53–109; Space Group: P4/mmm). This is accompanied by a slight shrinking of the ao lattice parameter, which distorts the [TiO6] octahedron positions and forms “bottlenecks” around the A-site cations [10]. Li+-mobility is consequently lowered, as evidenced by both a reduction in ionic conductivity and an increase in its activation energy [8, 10]. The extent of tetragonal superstructure ordering can vary with processing conditions, and so to maximize Li+-conductivity procedures which retard its formation are favored. Attempts to increase the stability of the cubic phase and, concomitantly, the Li+-conductivity, through doping of different sized cations have not proven successful [5]. The kinetic equilibrium between the cubic and tetragonal superstructures is actually one of the simplest models for LLTO structure. Not only do other polymorphs form for other values of x [5], but also the existence of two different orthorhombic superstructures has been reported using either synchrotron X-ray diffraction [11] or neutron diffraction [12]. Because of the rapid diffusion of cations through a network of A-site vacancies, a precise structural model of LLTO is difficult to attain, and it is clearly high-influenced by synthetic conditions. Nevertheless, a general distinction between an A-site cation-disordered structure (i.e., more cubic character) and an A-site cation ordered structure (i.e., more tetragonal) can readily be distinguished by X-ray diffraction and so can serve as a valuable guiding principle toward the synthesis of LLTO with optimized Li+-lattice conductivity.

While lattice conductivity is tied to the atomic scale properties of composition and crystal structure, representing, in effect, a sample’s maximum Li+-conductivity, the total conductivity is how the sample actually performs macroscopically as this value includes resistance from the grain boundaries. This is tied to characteristic of the ceramic part such as residual porosity and grain size [13]. To maximize total conductivity, near full density should be attained for the ceramic but care should be made that the determination of sample density with the Archimedes method include evaluation of the sample open porosity, without which a ceramic’s apparent density (i.e., the density of the contiguously connected ceramic) may be confused with the bulk density (the density of the ceramic piece which includes both open and closed porosity).

The synthesis and sintering of LLTO ceramics thus present an interesting challenge because processing conditions which promote one aspect of the materials conductivity can simultaneously degrade conductivity by a different mechanism. For example, sintering temperatures >1150 °C would work to achieve high density and the more conductive cation disordered, cubic superstructure, but such temperatures also could cause Li+-loss thru Li2O volatilization, which can lower ionic conductivity. The interpretation of experimental results in the open literature is further complicated when incomplete characterization is presented, thereby introducing doubt as to the actual cause of variation in both lattice and total conductivity. To elucidate some of these issues, experiments have been performed in which ceramics of LLTO have been prepared and extensively characterized for ionic conductivity (lattice and total), electronic conductivity, phase content, bulk and apparent density, Li-content remaining after sintering, and grain size. By this approach the relative impacts of the competing factor which could influence Li+-conductivity can be compared and prioritized so as to guide the consistent optimization of the material’s performance. Since the experimental range of such an undertaking would be considerable, the current report is limited in scope to LLTO with x = 0.097 (that is, Li0.29La0.57TiO3) and to sintering at 1200 °C for 1, 6, and 12 h. Future reports will detail studies on other compositions and processing conditions with the eventual goal of preparing LLTO with optimized and consistent properties suitable for evaluation in Li-air battery test cells.


Starting materials

The following powders were used in the synthesis of LLTO: Li2CO3 (Alfa Aesar, 99.0 %), La2O3 (99.99 %; Alpha Aesar), and TiO2 (99.8 % Alfa Aesar). Materials were used as received. The amount of moisture and other volatile impurities for each powder was determined by a loss on ignition (LOI) procedure in which 1–2 g of sample were loaded into alumina crucibles, and sample masses were determined before and after firing under a ramp rate of 5 °C min−1–900 °C with a 1 h hold. These correction factors were then used in the stoichiometric calculations.

Synthesis and sintering

Starting powders of Li2CO3, La2O3, and TiO2, were mixed via magnetic stirring in ethanol in amounts necessary to form Li0.29La0.57TiO3. In a typical procedure for a target yield of 100 g of LLTO, 6.051 g Li2CO3, 52.439 g La2O3, and 45.112 g TiO2 were added to stirring ethanol. No other dispersants or additives were used. The slurry was stirred for approximately 1 h. After mixing, the slurry was poured into a Labrota 4000 rotary evaporator where the bulk of the ethanol was volatilized under 23 kPa of pressure and 60 rpm rotation in a 60 °C oil bath. Once the ethanol was visibly removed, the remaining powder was coarsely broken and transferred to a clean, loosely covered, watch-glass. The powder was left to stand, loosely covered for a period of 1–2 days to allow for complete solvent volatilization. After drying, the powder was calcined in a high-alumina crucible under ambient atmosphere in a closed box furnace. Samples were heated with a ramp rate of 5 °C min−1 to either 900 or 1100 °C (hereafter denoted C900 or C1100), held isothermally for 1 h, and cooled back to room temperature at 5 °C min−1.

Powders were pressed into pellets in a 13 mm diameter stainless steel die with a uni-axial hydraulic press. Each sample was pressed under 68 MPa for approximately 10 s. Samples were also subjected to further consolidation in the green state using a cold isostatic press under 207 MPa pressure. Duplicate samples for each calcination condition were sintered in ambient atmosphere in a closed box furnace to 1200 °C at 5 °C min−1. Isothermal hold durations were varied from 1, 6, and 12 h, and all samples were cooled at a rate of 5 °C min−1.

Characterization methods

Dynamic light scattering

Particle size distributions for synthesized powders were measured using a Horiba LA-910 Light Scattering Particle Size Distribution Analyzer. Samples were prepared by pre-dispersion of 0.1 g powder into 10 g of deionized water with the container immersed in an ultrasonic bath (Li2CO3 was dispersed in ethanol). Samples were added drop wise to a blanked sample holder containing the necessary medium under magnetic stirring until instrument response fell into the optimum measurement range. Values of D50 and D90 are reported on a volume distribution basis.

Surface area analysis

The surface area of starting and synthesized powders was measured using a computer controlled Micromeritics ASAP 2010 using an 11-point BET analysis protocol. One gram of sample was loaded into a dry sample tube and stored open in a dynamic vacuum furnace at 75 °C overnight to insure physisorbed species were removed from the samples surface. Nitrogen gas was used for the adsorbing agent.

Powder X-ray diffraction (XRD)

Powder X-ray diffraction analysis was employed to determine the crystalline phases in the starting powders, calcined LLTO, and sintered LLTO ceramics. Powders of sintered pellets were prepared by grinding fragments in a high-alumina mortar and pestle. Measurements were taken using a computer controlled Rigaku minflex operating at 30 kV and 15 mA with a step size of 0.03° 2θ and scan rate of 2° 2θ/min, scanning over 5–60°. Powder samples were loaded directly into low-background Si sample holders.

The degree of tetragonal superstructure ordering can be described by the ordering parameter, S, which is defined as
$$ S = \frac{{R_{\text{La - rich}} - R_{\text{dis}} }}{{1 - R_{\text{dis}} }} $$
where RLa-rich and Rdis are the occupancies of the A-sites by La3+ in the La-rich layers of the cation ordered tetragonal form and in the (001) planes of the cation-disordered cubic form, respectively. The method of Harada et al. [9] was used to determine values of S directly from powder diffraction data. The authors used Reitvelt refinement to calculate theoretical intensities of (001) and (110) reflections based on varied occupancies of La3+ for different values of S. They then plotted the calculated ratio of I(001)/I(110) against S to use as a calibration curve for experimental values of I(001)/I(110) taken from powder diffraction data [9].

Field emission scanning electron microscopy (FESEM)

A Hitachi 4700 Scanning Electron Microscope was used to observe powder morphology of starting powders, synthesized LLTO powders, and sintered ceramic grain structure. An accelerating voltage of 2 kV and beam current of ~10 mA were used throughout this procedure to minimize charging. Samples were applied to double sided carbon tape and attached to an aluminum sample holder.

Grain size measurements

The grain size of the sintered LLTO samples was determined from FESEM photomicrographs using the linear intercept method of Mendelson [14]
$$ D = 1.56\frac{C}{MN} $$
where D is the average grain size, C is the length of a test line overlaying the micrograph, N is the number of grain boundaries intercepting the line, and M is the magnification. Samples were prepared by polishing with successively finer diamond slurry (9, 3, 1, and 0.25 μm) until the final polish which used 0.06 μm silica slurry. Ceramic parts were cleaned in an ultrasonic bath and then thermally etched at 1000 °C in air for 2 h with cooling at 50 °C min−1 to room temperature.

Density measurements

The Archimedes method was used to determine the bulk density and apparent density of the sintered pellets. Each pellet was first weighed to obtain the dry mass. They were then placed under vacuum in a closed vessel for 1 h. The vessel was backfilled with de-ionized water, and samples were left submerged for a few minutes to allow absorption of water into any available open porosity. The pellets were removed and wiped with a damp cloth to remove residual surface water. The wet pellets were then weighed immediately (before significant water evaporation could occur) in air (wet mass) and in a water submerged basket (submerged mass) using a Mettler Toledo AX205 balance. Using these values, the bulk and apparent densities (ρBulk and ρApparent, respectively) of the pellets were calculated as follows:
$$ \rho_{\text{Bulk}} = \left( {\frac{{m_{\text{dry}} }}{{m_{\text{wet}} - m_{\text{submerged}} }}} \right)\rho_{{{\text{H}}_{2} {\text{O}}}} $$
$$ \rho_{\text{Apparent}} = \left( {\frac{{m_{\text{dry}} }}{{m_{\text{dry}} - m_{\text{submerged}} }}} \right)\rho_{{{\text{H}}_{2} {\text{O}}}} $$
where m is the mass of the dry, wet, and submerged pellet (as noted in subscript) and \( \rho_{{{\text{H}}_{2} {\text{O}}}} \) is the density of water.

Inductively coupled plasma mass spectroscopy measurements (ICP-MS)

ICP-MS was conducted to determine the Li-, Ti-, and La-content of the uncalcined, calcined, and sintered LLTO. Analysis was performed by NSL Analytical (Cleveland, OH).

Electrochemical characterization

Samples were prepared for electrochemical characterization by applying a gold coating of ~50 nm to the electrode contact surfaces with a Denton Desk IV vacuum cold-sputtering/etch unit. Dimensions of the samples were measured using a Vernier caliper. Averages of five diameter and five width measurements from opposing points around the pellets were used in subsequent calculations.

A Solatron SI 1287 Electrochemical Interface was used to measure the AC impedance of the LLTO samples. All samples were measured under a 100 mV AC potential, from an initial frequency of 1.0 × 10Hz to a final frequency of 1.0 Hz using a logarithmic scale in a Teflon sample holder. All measurements were conducted in a dry-room with negligible humidity at room temperature. Electronic resistance of each of the samples was measured using a Keithly 6517A High Resistance Electrometer with 8009 Resistivity Test Fixture. All samples were left overnight in the test fixture and final electronic resistivity was reported from the equilibrated value.

Results and discussion

Powder characterization

Because of the possible impacts on reaction and sintering, the particle size distribution and phase purity of the starting materials were determined as a matter of quality control. The surface areas and size distributions of the starting powders are given in Table 1. The measured D50 and D90 for Li2CO3 and La2O3 represent a fairly course grained powder for both solid-state reaction and sintering, although the surface areas are larger than would be expected for hard spheres 10’s of microns in diameter, suggesting a modest amount of porosity or agglomeration of smaller particulates. TiO2 clearly has the smallest size distribution and highest surface area which suggests that it is likely to disperse and mix at a smaller length scale than the other reagents.
Table 1

Starting powder surface areas and particle diameters


D-50 (μm)

D-90 (μm)

Surface area (m2 g−1)


28.66 ± 0.02

50.47 ± 0.02

1.03 ± 0.04


14.07 ± 1.27

37.88 ± 10.18

3.95 ± 1.50


1.13 ± 1.59

2.37 ± 2.61

4.63 ± 0.80

The starting powders were also investigated with powder X-ray diffraction. No crystalline impurities were found in Li2CO3. In addition to being free from impurities, the TiO2 proved to be 100 % in the rutile structure type; the relative amounts of anatase and rutile structure types in TiO2 starting powders is not typically reported in papers on LLTO synthesis, so the potential impact on reactivity and ceramic properties is not known. The La2O3 starting material proved to be a mixture of the oxide and La(OH)3; LOI analysis confirmed the presence of 0.7 wt % volatile species, on average. Note that if the hydroxide content is not taken into account, the intended composition of LLTO would be in error.

The same characterization procedures were also performed on the formulated LLTO powder mixtures. D50 and D90 values of the uncalcined (UC) powder mixture represent an approximate weighted average of their starting size characteristics (Table 2). The UC surface area is close to the value of TiO2 starting material, suggesting that this component is dominating the measurement. Upon calcining at 900 °C for 1 h (C900), surface area decreases significantly and D50 nearly doubles, which indicates a significant amount of reaction has begun to take place. Interestingly, increasing the calcining temperature to 1100 °C (C1100, Table 2) does not significantly change the powder size characteristics from those of C900.
Table 2

Formulated powder surface areas and particle diameters for uncalcined (UC), C900, and C1100 powders


D-50 (μm)

D-90 (μm)

Surface area (m2 g−1)


4.35 ± 0.20

9.33 ± 0.32

5.31 ± 0.52


10.52 ± 0.25

26.62 ± 8.05

1.10 ± 0.87


10.25 ± 0.86

22.53 ± 4.64

1.47 ± 0.25

The XRD patterns of the formulated LLTO powders are shown in Fig 1. The observed peaks in the UC pattern correspond to a mixture of TiO2 (rutile) and La(OH)3. The absence of La2O3 peaks indicates that the oxide can more readily absorb moisture from the environment than was previously appreciated. Li2CO3 is also not detected in the uncalcined mixture, indicating that the component has lost crystallinity as a consequence of partial solubility in our slurry mixing procedure. The formulated powder mixture undergoes reaction on calcining at 900 °C but only a modest amount of LLTO as the tetragonal superstructure forms at this temperature (Fig. 1). The major crystalline component is La2Ti2O7 (PDF# 28–517), and a smaller amount of Li2Ti3O7 (PDF# 34–393) can also be identified. These are often observed as intermediate phases in solid-state reactions intended to form LLTO [15]. The diffraction pattern of the C1100 (Fig. 1) identifies the same phases which are observed for C900, but the amount of the tetragonal LLTO component has modestly increased, as indicated by the increase in its relative peak intensity.
Fig. 1

Powder XRD patterns of UC, C900, and C1100. [LH La(OH)3; R rutile TiO2; ‡La2Ti2O7; †Li2Ti3O7; *tetragonal LLTO]

Sintered ceramic characterization

As described in the experimental section, LLTO ceramics were sintered using C900 and C1100 powders at 1200 °C for hold times of 1, 6, and 12 h. The bulk density and apparent density of LLTO ceramics are shown in Fig. 2. The apparent density is based on the combined volume of ceramic and closed porosity; that is, pores which are fully enclosed in the interior of the ceramic body. However, if there is significant porosity which is open to the surface, this volume will quickly fill with water once submerged and not be accounted for in the Archimedes volume displacement. The bulk density measurement corrects for this by impregnating any surface porosity with water so as to account for its volume when the part is submerged. If the bulk density equals the apparent density then there is no open porosity, and any remaining deviation from full theoretical density is due to closed porosity. Depending on the relative amounts of tetragonal and cubic superstructure in the sample, theoretical density for the composition of LLTO used in this study would vary only modestly from 5.05 g cm−3 for a completely tetragonal cell, to 5.00 g cm−3 for the completely cubic. As such a density of 4.56 g cm−3 represents ~90 % of theoretical.
Fig. 2

Bulk (dashed lines) and apparent (solid lines) density of Li0.29La0.57TiO3 as a function of isothermal hold time: triangle (C900), diamond (C1100)

The density of LLTO ceramics relied more on the temperature of powder calcination than the duration of sintering at 1200 °C. The C900 powder sintered to a high apparent density of 4.856 ± 0.0168 g cm−3 after 1 h at 1200 °C. This sample, however, has a much lower bulk density of only 4.369 ± 0.571 g cm−3, indicating that significant open porosity remains in the sample. Note that if the bulk density had not been determined, then the Archimedes density measurement, using only the ceramic dry mass, would have erroneously indicated a much higher level of ceramic density. At a 6 h isotherm, the apparent and bulk density of C900 converge to similar values, which indicates that the ceramic is approaching a closed porosity stage. Sintering for 12 h brings the two density values even closer. The situation is very different for the C1100 samples which exhibit near identical values for the bulk and apparent densities for all sintering times. Closed porosity is achieved very readily with this formulation, and the remaining residual porosity is thus trapped within the ceramic. As noted in Table 2, the size distribution characteristics of C900 and C1100 are very similar, whereas the XRD analysis indicates that C1100 has a greater degree of conversion to LLTO. This modest difference may be enough to allow for a more active and uniform densification during sintering.

XRD of sintered ceramics reveals that the target perovskite phase formed with modestly varying degrees of tetragonal superstructure. A representative diffraction pattern is shown in Fig. 3. No peaks of any starting materials or intermediate phases are observed in any of the final sintered ceramics. The major peaks of the cubic polytype (Space Group Pm-3m; PDF# 46-465) are all shared with the tetragonal diffraction pattern (Space Group P4/mmm; PDF# 53-109;), and the presence of tetragonal superstructure is indicated by several peaks that are unique to that phase. Since the structure types share their 100 % intensity peak at 32.6° 2θ [which is (110) for the cubic and (102) for the tetragonal] an estimate of the relative amount of tetragonal character requires a comparison of the observed intensity of tetragonal peaks relative to theoretical values calculated for different degrees of Li+- and La3+-ordering in the perovskite lattice. As described in the experimental section, we have used the values calculated by Harada et al. to estimate ordering parameters, S, for our ceramics based on the measured intensity ratio of I(001)/I(110) [9]. Values of S are given in Table 3. The higher the ordering parameter, the greater is the degree of tetragonal superstructure in the ceramic. For the ceramic prepared from the C1100 powder, the average S is 0.44 after sintering 1 h at 1200 °C and 0.53 for both of the other hold times. In the case of the C900, the average S is 0.49 after sintering 1 h, 0.43 after sintering 6 h, and 0.57 after sintering 12 h at 1200 °C. Harada et al. [9] showed that the amount of tetragonal formation could be controlled by a post sinter anneal, and S values of ~0.25 and ~0.5 were achieved with less than an hour of annealing time at 1100 and 1000 °C, respectively. Our sintering temperature was 1200 °C, but the ceramics were cooled at the relatively modest rate of 5 °C min−1. As such, the LLTO ceramics spent 20 min while cooling through the range 1000–1100 °C. Although the cooling rate likely plays a role in the formation of the tetragonal superstructure, it cannot be the primary factor because there is noticeable variation in S with both calcining temperature and sintering duration. As with the density data, the varied degree of reaction on calcination is influencing the homogeneity and extent of final reaction on sintering.
Fig. 3

Powder X-ray diffraction pattern of C1100 powder sintered at 1200 °C for 6 h (c cubic phase PDF# 46-465; t tetragonal phase PDF# 53–109). The t (001) and c (110) peaks used for the estimation of the ceramics ordering parameters are indicated

Table 3

Average ordering parameters S, for sintered ceramics with varied calcination temperature and sintering times


1 h

6 h

12 h


0.49 ± 0.04

0.43 ± 0.06

0.57 ± 0.04


0.44 ± 0.04

0.53 ± 0.03

0.53 ± 0.03

Electrochemical results

AC impedance measurements

A representative example of the room temperature AC conductivity results for the C1100 LLTO samples using Li-ion blocking Au electrodes is shown in the full complex impedance plot in Fig. 4. For this case, since we have Li-blocking electrodes, the shape of the curve represents a material which is predominately a Li+-conductor with very low electronic conductivity [16, 17]. The low frequency intercept of the semicircle on the Z′ axis gives the total ionic resistance (RT), which includes the contribution of the lattice (RL) and the grain boundary components (RGB) [16, 17]. The high frequency intercept of this semicircle is given by it extrapolation to the the Z′ axis, from which is determined the Li+-lattice conductivity (RL) [16, 17]. The values of RL, RGB, and RT were determined using the equivalent circuit shown in Fig. 4. Using these resistances and sample dimensions the total ionic conductivity (σT) and lattice conductivity (σL) were determined using the equation
$$ \sigma = \left( \frac{L}{AR} \right) $$
Fig. 4

Example of room temperature AC impedance data for C1100 LLTO samples (only lower frequency semi-circle shown). Duration of isothermal hold at 1200 °C for each sample is indicated above their respective curve. The inset shows an equivalent circuit that used to model the impendence of such ceramic materials using Li-blocking Au electrodes

In Eq. 5, L is the thickness of the measured sample (cm), A is the area of the sample (cm2), and R is the measured real resistance (Z′ ohms) [6, 10, 18]. For the representative AC impedance data shown in Fig. 4, the curvature and diameter of the RGB semi-circle component decreases with increased isothermal hold duration. Table 4 gives the average contributions of the RL and RGB to that of the RT, and as isothermal hold time increases, the contribution of RGB decreases for all samples. The C1100 samples exhibit a larger decrease in RGB with increased sintering duration than do the C900 samples. Table 4 also shows that even with longer isothermal hold times and higher calcination temperatures, the largest contribution to RT was still that of RGB.
Table 4

Contributions of grain boundary and lattice resistance to total resistance as a function of calcining temperature and sintering isothermal hold time


1 h

6 h

12 h


 RGB/RT (%)




 RL/RT (%)





 RGB/RT (%)




 RL/RT (%)




Lattice ionic conductivity

Lattice conductivity (σL) is plotted as a function of sintering duration for C900 and C1100 samples in Fig. 5. The maximum σL occurred for the C900 samples sintered for 6 h with a value of 1.14 ± 0.11 × 10−3 S cm−1. This value is consistent with the highest range of reported room temperature σL measurements ~1–1.13 × 10−3 S cm−1 (for compositions x = 0.1–0.12) [5, 6]. The σL of LLTO sintered from C1100 powders shows only modest change with isothermal hold duration; within error, the conductivity of ~9.00 × 10−4 S cm−1 is essentially unchanged for 1, 6, and 12 h holds. This characteristic mirrors the trend in density noted earlier for the C1100 series (Fig. 2).
Fig. 5

Lattice conductivity of Li0.29La0.57TiO3 as a function of sintering time: triangle (C900), diamond (C1100)

Both the C900 and C1100 samples’ σL appear to follow an inverse relationship to the ordering parameters S taken for these samples (Figs. 5, 6). These values are similar to what has been reported for other LLTO samples that have similar amounts of measured tetragonal/cubic superstructure [8, 9]. The maximum σL (C900, 6 h) had the lowest average value for S indicating that it had the highest cubic character. After 12 h of isothermal hold time, both the ordering parameter and σL of the C900 samples approach the values resembling the more tetragonal character of the C1100 samples.
Fig. 6

Ordering parameter of Li0.29La0.57TiO3 as a function of sintering duration: triangle (C900), diamond (C1100)

As described in the introduction, a decreasing Li-stoichiometry in LLTO can both decrease the number of charge carriers and promote the formation of the tetragonal superstructure, which in turn retards Li+-mobility by structural constriction of migration pathways. In light of this, the pre- and post- sintering Li-content of LLTO ceramics in this study was measured using inductively coupled plasma mass spectroscopy (ICP-MS). Analysis was performed on both loose powders and sintered ceramic. The results of ICP-MS analysis in Fig. 7 show the molar ratio Li/Ti as a function of isothermal hold duration. Data points at zero isothermal hold time represent the calcined powders not yet sintered. It was found that the uncalcined LLTO powders were prepared very close to the target stoichiometry of Li/Ti = 0.29. A modest decrease from the original Li-content was seen in the C900 (0.60 %) and C1100 (1.75 %) samples after calcination. Between sintering durations of 1 and 6 h, no change was observed in C900 composition while only modest change was found for C1100 samples. After 12 h of sintering, however, the Li-content decreased by as much as 23 % for both calcination batches.
Fig. 7

Molar ratio of Li/Ti in samples [triangle (C900), diamond (C1100)] as determined through ICP-MS analysis, and dependence on isothermal hold duration. Data points at zero isothermal hold duration signify unsintered samples. Powder that was both uncalcined and unsintered is denoted by data point (X)

The σL data in Fig. 5 does not appear to trend with the decreasing Li-content as opposed to the apparent inverse relationship between σL and S noted earlier. This implies that once the structure reaches a thermodynamically stable endpoint, as in the case of C1100, changes to the Li+-content have reduced impact on σL. In other words, crystal structure appears more important than Li+-content to σL. Because of its calcination at a lower temperature, C900 has not advanced as far to the thermodynamic endpoint, and so its sintering at 1200 °C for 6 h represents a kinetically stabilized outcome in which the greater structural disorder (i.e., lower degree of tetragonal superstructure ordering) combines with the Li+-content (which is the highest of the sintered ceramics) to result in the highest σL among the present samples. The outcome, however, is metastable in the case of C900, and longer sintering times drive the ceramic to a more thermodynamically stable outcome and closer to the properties of C1100 for the same sintering conditions. This is a logical scenario in that the earlier stages of a solid-state reaction are more likely to exhibit residual levels of structural disorder before coming to full thermodynamic equilibrium. In the case of LLTO, disorder represented by randomization of Li+ and La3+ in the A-sites promotes higher Li+-conductivity. Hence, what is reported as a high temperature structural model can exist at low temperatures under kinetic conditions.

Total conductivity

In ionic-conducting polycrystalline ceramics such as LLTO, σT depends on both the σL and σGB contribution. Provided that σL is optimized to the full theoretical value, σGB remains the limiting variable controlling σT. Figure 8 shows the measured σT values for the C900 and C1100 samples as a function of isothermal hold duration. The highest σT values measured for the C900 and C1100 samples were 3.15 × 10−5 and 6.30 × 10−5 S cm−1, respectively. These values are in agreement with those of similar composition that were reported to have conductivities in the ranges of 10−4–10−5 S cm−1 [5, 7].
Fig. 8

Total conductivity of Li0.29La0.57TiO3 as a function of sintering duration: triangle (C900), diamond (C1100)

Figure 8 highlights that there is only a small change in σT as a result of increased isothermal hold time. For the C1100 samples, no changes in σT were observed by increasing the sintering duration from 6 to 12 h (a plateau in conductivity is seen within measurement error). Reasons for the differences between the C900 and C1100 samples’ σT may be a result of grain size and/or density [4, 13], and so both have been examined.

Average grain sizes are listed in Table 5, and Fig. 9 shows the samples’ σT plotted as a function of their average grain size. The largest increases in σT occur by increasing the sintering duration from 1 to 6 h, but this did not coincide with the largest increases in grain size. Indeed, a very significant increase in grain size for the C900 samples on increasing the sintering time from 6 to 12 h coincided with only a modest increase in σT. Presently, reasons for this particular example of rapid grain growth are not clear. It has been reported by Ban et al. [4] that increased σT is directly proportional to a sample’s average grain size in the ranges of 1–6 μm, and such a trend has also been observed for other ionic conductive ceramics such as Y2O3 [19]. Data in Fig. 9 show that there is a correlation between increased σT and increased grain size, but it occurs in a different size range for the two different calcination temperatures. This implies that another factor is exerting a greater influence on the changing σT, particularly in the early stages of sintering.
Table 5

Sintered LLTO average grain size (μm) as a function of the calcination temperature of the starting powder and the sintering hold time


1 h

6 h

12 h


6.87 ± 0.22

6.75 ± 1.26

45.28 ± 15.69


12.23 ± 1.21

19.53 ± 0.75

25.73 ± 2.25
Fig. 9

LLTO total conductivity as a function of average grain size: triangle (C900), diamond (C1100). Sintering durations are noted on the figure

The correlation between bulk density and σT is shown in Fig. 10. The C1100 samples achieved the highest bulk densities (which, in their cases also represent the highest apparent density) and also exhibit the highest σT. Data from both C900 and C1100 samples can be fit to a third-order polynomial. At lower bulk densities, there is little dependence of σT, whereas higher densities influence σT much more. These results suggest that σT is primarily a function of the samples’ bulk densities rather than grain size. When the data in Fig. 10 is extrapolated to the full theoretical density (~5 g cm−1), the curve predicts an expected theoretical σT of 1.2 × 10−3. This value is close to the value for lattice conductivity in the LLTO material. Therefore, if higher densities are reached in the LLTO material, it is possible that the fully sintered polycrystalline material can achieve the higher conductivities found in the lattice. This is a situation analogous to that of transparent ceramics, where the residual porosity of only a few hundred ppm (i.e., density >99.99 %) is sufficient to degrade visible light transmission through the sample [20].
Fig. 10

LLTO total conductivity as a function of bulk density: triangle (C900), diamond (C1100). Sintering durations are noted on the figure

Electronic conductivity

All sintered LLTO samples used in this study were found to have electronic conductivities (σe) averaging 4.92 × 10−9 ± 8.42 × 10−10 S cm−1. This value is about an order of magnitude higher than values reported for other ionic conductors [19]. This may be a result of differences in starting material impurities, heating temperatures, isothermal hold durations, and atmospheres. The ionic transference ratio, Tionic, can be determined using the total ionic conductivity and electronic conductivity.
$$ T_{\text{ionic}} = \left( {\frac{{\sigma_{\text{T}} }}{{\sigma_{\text{T}} + \sigma_{\text{e}} }}} \right) $$
Since σe values are several orders of magnitude lower than σT, Tionic is ~1 for all our samples, and thus they can be considered as purely ionic conductors.


Ceramic powders of LLTO with compositions of Li0.29La0.57TiO3 were prepared under varied calcination temperatures and sintering durations to assess the relative impacts of phase content, Li+-content, bulk density, and grain size on lattice and total conductivity. Samples of LLTO powder that were calcined at 900 °C for 1 h and sintered at 1200 °C for 6 h exhibited σL of 1.14 × 10−3 ± 0.11 × 10−3 S cm−1, a value comparable to the highest reported in the literature. This also coincided with the lowest amount of tetragonal superstructure ordering as represented by the sample ordering parameter, S, and the inverse relationship between S and σL is observed, consistent with the work of Harada et al. Structural disorder appears to exert a greater influence on σL than Li+-loss (which was significant after 12 h of sintering at 1200 °C), and the more ordered tetragonal superstructure appears to have preferred thermodynamic stability.

It was also observed that polycrystalline LLTO σT is more dependent on bulk sample density than on average grain sizes. LLTO samples with grain sizes >20 μm were found to influence σT to a significantly lesser degree than samples with grains smaller than 20 μm. Moreover, it was determined that σT is primarily a function of the samples’ bulk densities. At densities approaching the theoretical value for LLTO ceramics, σT’s dependence on density rapidly increased; it was estimated that a value of 1.2 × 10−3 S cm−1 for σT can be possible if density is optimized. If both A-site cation ordering (or the lack thereof) and density can be optimized for the LLTO material, rapid improvements can be made in its overall σT.


The authors of this paper would like to acknowledge and thank the Oak Ridge Institute for Science and Education (ORISE) and the United States Army Research Laboratory (ARL), for their unwavering support in this research effort.

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© Springer Science+Business Media, LLC (outside the USA) 2012