Materials Research Bulletin 53 (2014) 32–37

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Materials Research Bulletin

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Lithium stoichiometry of solid electrolytes based on tetragonal

Li7La3Zr2O12

E.A. Il’ina a, A.A. Raskovalov a,*, P.Y. Shevelin a, V.I. Voronin b, I.F. Berger b, N.A. Zhyravlev c

a Institute of High-Temperature Electrochemistry, Ural Branch of RAS, Ekaterinburg, Russiab Institute of Metal Physics, Ural Branch of RAS, Ekaterinburg, Russiac Institute of Solid State Chemistry, Ural Branch of RAS, Ekaterinburg, Russia

A R T I C L E I N F O

Article history:

Received 11 July 2013

Received in revised form 26 September 2013

Accepted 29 January 2014

Available online 10 February 2014

Keywords:

A. Ceramics

B. Sol–gel chemistry

C. Impedance spectroscopy

C. Neutron scattering

D. Ionic conductivity

A B S T R A C T

Samples of LixLa3Zr2O8.5+0.5x (x = 6, 7, 8, 9, 10) were synthesized with the citrate–nitrate method. Neutron

diffraction studies have shown the presence of lithium carbonate impurities in the synthesized

compounds. We propose a simple and effective method to determine the carbonate impurity content in

the solid electrolytes. The technique is based on the measurement of the carbon dioxide volume

produced from the interaction of the investigated material with acid. Determined in this way, the

content of Li2CO3 in the synthesized electrolytes Li7La3Zr2O12, Li8La3Zr2O12.5 and Li9La3Zr2O13 are

1.32 � 0.04, 1.95 � 0.06 and 3.49 � 0.10 wt.%, respectively. From the obtained data, the actual lithium

content per formula unit of complex oxide was calculated for the synthesized compounds. The composition

with x = 9 had the highest total conductivity, s = 7.5 � 10�6 S cm�1, at room temperature. All the

investigated electrolytes have an activation energy of approximately 50 kJ mol�1.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Ceramic lithium electrolytes are being considered as one of thealternatives to replace the liquid electrolyte in lithium powersources; this replacement will create safer all-solid-state lithium-ion batteries. The synthesis and study of new lithium ceramics ofvarious compositions with different crystalline structures and highconductivity are of great interest [1,2]. Thangadurai and Weppnerwere the first to explore novel garnets with the nominal chemicalcomposition Li5La3M2O12 (M = Nb, Ta) for fast lithium ionconduction [3]. In later years, work was performed to expandthis family of compounds and improve the properties of thesecompounds. Analyzing a huge number of data, Ramzy andThangadurai [4] noted that the ionic conductivity of the cubicgarnets LixA3M2O12 linearly increases as the amount of lithium performula unit increases.

For use as a solid electrolyte, the most interesting representa-tive of this family of garnets is the complex oxide Li7La3Zr2O12

(LLZ). This compound has two structural forms: cubic andtetragonal. The cubic phase of LLZ has higher conductivity atroom temperature than the tetragonal form [5]. However, the

* Corresponding author. Tel.: +7 343 362 31 81/+79222961441;

fax: +7 343 374 59 92.

E-mail address: other@e1.ru (A.A. Raskovalov).

0025-5408/$ – see front matter � 2014 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.materresbull.2014.01.041

synthesis of the cubic LLZ is performed at high temperatures for along time [6].

In superionic compounds with structural disorder, the chargecarriers are the ions themselves rather than vacancies [7]. BecauseLLZ is a superionic conductor, the electrical conductivity of LLZ willincrease as the concentration of lithium ions increase. It is knownthat the stoichiometry of alkali cations in garnet-type compoundscan vary without changing the structure [8]. Most likely, theconductivity of tetragonal LLZ can be increased through theintroduction of additional carriers to the structure. However, it isunknown to what extent it is possible to vary the lithium content inthe structure of LLZ and how this change in lithium content willaffect the properties of the system. The objective of the presentwork was to synthesize solid electrolytes based on LLZ withdifferent stoichiometric amounts of lithium and to study thestructure and transport properties of these electrolytes.

2. Experiment

Samples of LixLa3Zr2O8.5+0.5x with x = 6, 7, 8, 9, and 10 weresynthesized. Li2CO3, La2O3 and an aqueous solution of ZrO(NO3)2

were used as the precursors for the citrate–nitrate synthesis. Thestarting materials were taken in a stoichiometric ratio. Thesecomponents were dissolved in a mixture of dilute nitric and citricacids. The resulting solution was evaporated at 80 8C to form atransparent gel. The gel was then dried and was pyrolyzed at�200 8C; this pyrolysis resulted in the formation of black powder.

1250

1500

#

x=10

#

E.A. Il’ina et al. / Materials Research Bulletin 53 (2014) 32–37 33

The synthesis was performed by increasing the temperaturestepwise from 700 8C to 900 8C for 5 h and with calcination at thefinal temperature for 1 h. After each stage of the synthesis, themixture of reagents was thoroughly ground in an agate mortar.

X-ray diffraction analysis (XRD) was performed with a RigakuD-MAX-2200V diffractometer with a vertical goniometer, Cu Ka-radiation and 2u = 10–708. The XRD patterns of the compoundswere compared with those in the PDF-2 database.

Neutron diffraction measurements of LixLa3Zr2O8.5+0.5x (x = 7, 8,9) at room temperature were performed on the high-resolutionpowder diffractometer D7a at the research reactor IVV-2M of theInstitute of Metal Physics, Ural Branch of the Russian Academy ofSciences. The powdered samples were sealed in cylindricalvanadium containers with diameters of 8 mm. The D7a diffrac-tometer used a double graphite (0 0 2)–Ge (5 1 1) monochromator;the neutron wavelength was 1.5321 A. The neutron diffractionpatterns were recorded over a scattering angle range of 10–1258with a step of 0.058. The profiles of the diffraction patterns wererefined by Rietveld analysis with the FULLPROF program.

The investigated material was treated with aqueous solutionsof hydrochloric (HCl) or acetic (CH3COOH) acids to determine thecarbonate impurity content in the solid electrolytes. The volume ofcarbon dioxide liberated is directly proportional to the amount ofcarbonate in the sample. This volume of gas was determined with aliquid volumeter (Fig. 1). A saturated aqueous solution ofpotassium chloride (KCl) was used as the volumetric liquid toprevent the dissolution of CO2 in the water.

To determine the amount of gas based on Avogadro’s law it isnecessary to relate the volume of gas liberated during theexperiment to the volume at normal conditions:

V0 ¼VT T0ðP �D� PV Þ

P0T; (1)

where V0 is the volume of the gas at normal conditions (T0 = 273 K,P0 = 760 Torr), VT is the volume of the gas liberated during theexperiment, T is the temperature of the experiment (K), P is thebarometric pressure (Torr), D is the correction to the reading ofthe barometer (Torr), and PV is the vapor pressure (Torr) above thevolumetric liquid at the temperature T [9]. The proposed techniquewas verified with different pure carbonates (Li2CO3, Na2CO3, andK2CO3) and with mixtures of these carbonates with an inertmaterial (SiO2). The relative error of the determination of CO2

volume did not exceed 3%.7Li NMR spectra for Li7La3Zr2O12 and Li9La3Zr2O13 were

recorded in the temperature range from �150 to 150 8C with abroad-line NMR spectrometer with a working frequency of34 MHz.

The conductivity measurements were performed with pellets ofLLZ powder; to form the pellets, LLZ was pressed under 100 MPaand was annealed at 1130 8C for 1 h. Both sides of the pellets werepainted with gallium-silver electrode paste. The impedance

[(Fig._1)TD$FIG]

Fig. 1. The scheme of the cell to determine the amount of carbon dioxide liberated

from the interaction of the investigated electrolyte with acid.

measurements were performed in air at temperatures from 20to 230 8C with an LCR-meter 819 (Goodwill Instruments) in the0.012–100 kHz frequency range and with a two-probe cell withsilver electrodes. The results were fitted with mathematicalmodeling. All of the conductivity measurements were performedon two sets of identical samples to assess the reproducibility ofthe results.

3. Results and discussion

3.1. The phase composition

The XRD patterns of LixLa3Zr2O8.5+0.5x (x = 6–10) are shown inFig. 2. The indexing of the XRD patterns shows that the major peakscorrespond to the tetragonal structure of LLZ; this structure hasbeen described by many researchers, for example, [5]. According toXRD, Li6La3Zr2O11.5 also contains an impurity phase of lanthanumzirconate (La2Zr2O7). It is likely that to maintain the tetragonalstructure of LLZ, more alkali cations are needed relative to thezirconate anions; otherwise, the excess anions are released aslanthanum zirconate. The XRD patterns of Li10La3Zr2O13.5 showsmall peaks with an unidentified phase. Thus, the compoundLixLa3Zr2O8.5+0.5x with lithium concentrations of x = 7–9 preservesthe structure of tetragonal LLZ and does not decompose intoseveral phases.

However, XRD analysis is not well suited for accurate determina-tion of the phase composition of lithium compounds because the X-ray scattering from lithium atoms has low amplitude, especiallyagainst a background of heavy atoms, such as lanthanum. Neutrondiffraction measurements are more suitable for such studies. Thus, formany lithium-containing garnets, the impurity of lithium carbonatewas only detected by neutron diffraction studies. The lithiumcarbonate content in these systems ranged from 0.7 to 6 wt.%[12,13], although XRD analysis did not detect this impurity. Therefore,in the present study, we additionally used neutron diffraction toclarify the phase composition and the structural parameters of thesynthesized solid electrolytes LixLa3Zr2O8.5+0.5x in the homogeneousregion (x = 7, 8, 9).

Peaks from Li2CO3 are clearly observed in the neutron patterns(Fig. 3). The intensity of these peaks increases as the lithiumcontent (x) increases. Based on neutronography, the concentra-tions of Li2CO3 in the samples LixLa3Zr2O8.5+0.5x are 0.5 (for x = 7),2.9 (x = 8) and 4.2 (x = 9) wt. %, respectively. Thus, even within the‘‘region of homogeneity’’ determined by XRD, the synthesizedelectrolytes do not have a single phase. Most likely, the synthesized[(Fig._2)TD$FIG]

10 20 30 40 50 60 700

250

500

750

1000

***

x=9

x=8

x=7

I

2 deg.

x=6

*

Fig. 2. XRD patterns of LixLa3Zr2O8.5+0.5x (x = 6–10). The peaks of impurities are

marked as: * (La2Zr2O7), # (unidentified).

[(Fig._3)TD$FIG]

10 20 30 40 50 60 70 80 90 120110100

0

2000

4000

6000

8000

10000

12000

Inte

nsity

2 , deg.

10 20 30 40 50 60 70 80 90 120110100

0

2000

4000

6000

8000

10000

12000

Inte

nsity

2 , deg.

10 20 30 40 50 60 70 80 90 120110100

0

3000

6000

9000

Inte

nsity

2 , deg.

a

b

c

Fig. 3. Fitted powder neutron diffraction profile for Li7La3Zr2O12 (a), Li8La3Zr2O12.5

(b), Li9La3Zr2O13 (c) at room temperature with observed (dots), calculated (solid

line) and difference plots. The markers indicate the reflections from the garnet (top)

and the lithium carbonate (bottom).

E.A. Il’ina et al. / Materials Research Bulletin 53 (2014) 32–3734

material interacts with carbon dioxide when the samples areannealed in air:

LixLa3Zr2O8:5þ0:5xþ yCO2 ! Lix�2yLa3Zr2O8:5þ0:5x�y þ yLi2CO3 (2)

Indeed, the formation of lithium carbonate can go through theintermediate stage of a reaction with water:

LixLa3Zr2O8:5þ0:5xþ yH2O ! Lix�2yLa3Zr2O8:5þ0:5x�yþ2yLiOH (2a)

LiOH þ CO2 ! Li2CO3þH2O (2b)

In any case, the final reaction product will be always Li2CO3 (inpresence of CO2), of which quantity we define. Unfortunately, atthis stage it is impossible to establish how the lithium carbonatewas formed (directly or through the ‘water’ stage). However, it isnot affected to determination of the amount of lithium thatescaped from the synthesized system.

The unavoidable presence of CO2 in air affects the phasecomposition of the synthesized LLZ and leads to some differencesin the conductivity of LLZ in various reports (for example,1.20 � 10�7 S cm�1 [10] and 4.16 � 10�7 S cm�1 [5] at roomtemperature). The existence of Li2CO3 in the LLZ samples can alsoexplain why Kotobuki and co-workers [11] obtained worseconductivity after sintering LLZ in Ar than after sintering LLZ inair. Through sintering in air, the samples contain some amountof lithium carbonate. This amount is much smaller with thesintering in Ar. Mostly likely, the presence of Li2CO3 results in moreeffective liquid-phase sintering (the melting point is approximately732 8C [9]).

3.2. Volumetric measurements

Because quantitative analysis by diffraction methods containssome assumptions and is not obvious, we propose a simple andphysically valid method. This method is based on the mea-surement of the volume of carbon dioxide produced by theinteraction of the investigated material with acid. In the volumetricexperiments, the solid electrolytes Li7La3Zr2O12, Li8La3Zr2O12.5 andLi9La3Zr2O13 were determined to contain 1.32 � 0.04, 1.95 � 0.06and 3.49 � 0.10 wt.% Li2CO3, respectively. Liberated amount of carbondioxide is reproduced for a series of measurements. Samples keepingin air for several months contained a larger volume of carbon dioxide(for LixLa3Zr2O8.5+0.5x (x = 7–9) from 4.5 to 6 wt.% Li2CO3), thusreacting with air is obvious. The obtained values follow the sametrend as those determined from neutron diffraction; i.e., the amountof Li2CO3 increases as the lithium content increases. After determin-ing the mass fraction of lithium carbonate in the samples, wecalculated the lithium content in the solid electrolyte using a numberof assumptions: 1) the two-phase samples consist of lithiumcarbonate and a phase with the structure of LLZ; 2) lithium oxidedoes not evaporate from the sample during synthesis; 3) oxygencompensates for the charge from the lithium. Then, the mass of theinitial mixture can be defined by:

min ¼ mLLZ þmLi2O; (3)

where min – mass of the initial mixture; mLLZ – mass of the solidelectrolyte with structure of LLZ; and mLi2O – mass of lithium oxide,which absorbs carbon dioxide from the atmosphere and trans-forms into Li2CO3. Given the mass fraction of lithium carbonate inthe sample, formula (3) can be rewritten as:

min ¼ m 1�vLi2CO3

� �þmvLi2CO3

MLi2O

MLi2CO3

; (4)

where m – mass of the sample; vLi2CO3– mass fraction of lithium

carbonate in the sample; MLi2O – molar mass of Li2O; and MLi2CO3–

molar mass of Li2CO3. The amount of the initial material (nLLZ) canbe calculated with:

nLLZ ¼min

Min; (5)

where Min – molar mass from the initial formula LixLa3Zr2O8.5+0.5x.Because a certain amount of lithium oxide from the complex oxideturned into carbonate, the quantity of lithium can be recalculatedwith the formula:

nLi ¼ xnLLZ � 2�mvLi2O3

MLi2CO3

; (6)

Table 2The distance between the atoms Li–O.

x (Li)

6.7 7.5 8.2

<Li1–O>, A 1.909(1) 1.912(2) 1.911(2)

<Li2–O>, A 2.265(1) 2.261(1) 2.256(2)

<Li3–O>, A 3. 313(2) 3.311(2) 3.305(2)

[(Fig._5)TD$FIG]

150

200

250

300

350

35 kHz0.015 kHz

x = 6

x = 7

x = 8

x = 9

x = 10

-Z'',

kO

hm

E.A. Il’ina et al. / Materials Research Bulletin 53 (2014) 32–37 35

where nLi – quantity of lithium that remains in the phase withstructure of LLZ and x – lithium index from the formulaLixLa3Zr2O8.5+0.5x. Thus,

x fact ¼nLi

nLLZ; (7)

where xfact – actual lithium content per formula unit of the syn-thesized compound with the structure of LLZ. Based on thecalculations, the compositions with x = 7, 8, and 9 actuallyrepresent Li6.7La3Zr2O11.85, Li7.5La3Zr2O12.25 and Li8.2La3Zr2O12.6,respectively. From the formulas, we can see that all of the excesslithium (x > 7) does not transform into lithium carbonate, some ofthe excess lithium remains in the LLZ structure.

3.3. Structural parameters

The calculations of the structural parameters of LixLa3Z-r2O8.5+0.5x (x = 7, 8, 9) from the neutronographic data were perfor-med with the two-phase model and the structure of Li7La3Zr2O12

from reference [5]. The final R-values were Rwp = 2.68, 2.21, 2.49%,Rp = 2.03, 1.69, 1.93%, with a fit indicator of S = Rwp/Re = 1.82, 1.75,1.75 for Li7La3Zr2O12, Li8La3Zr2O12.5 and Li9La3Zr2O13, respectively.This procedure gave us the next result: the reduction of the cellvolume and lattice parameters (Table 1) as the lithium content (x)increased. Simultaneously, relation of c/a decreased as x increased(Fig. 4) and this value moved away from 1 (i.e. the degree oflattice tetragonality increased). This behavior indirectly confirmedthe change in the lithium stoichiometry in LLZ. Otherwise, theadditional lithium would transform into another phase and thelattice parameters of LLZ would remain the same. The decrease inthe cell volume and the Li–O distance (Table 2) can be because ofthe stronger Coulombic interactions of additional lithium cationswith the oxygen anions. Unfortunately, our data do not allow us todetermine with sufficient precision what positions the additionallithium ions fill.

Table 1The parameters a and c as functions of the Li content in LixLa3Zr2O8.5+0.5x.

x (Li) a, A c, A

6.7 13.11734�0.00077 12.67150� 0.00082

7.5 13.11239�0.00062 12.66356� 0.00072

8.2 13.11169�0.00041 12.65779� 0.00052

[(Fig._4)TD$FIG]

6.5 7.0 7.5 8.0 8.5

0.9652

0.9654

0.9656

0.9658

0.9660

0.9662

c/a

x (Li)

Fig. 4. Relation c/a as a function of the Li content in LixLa3Zr2O8.5+0.5x.

3.4. Transport properties

The typical impedance plots obtained at room temperature areshown in Fig. 5. The impedance spectrum at room temperaturemay be separated into two semicircles. The high-frequencysemicircle can be attributed to the bulk resistance of the sampleswhereas the semicircle in the low-frequency range correlates withthe grain-boundary resistance [2]. The contribution of the grain-boundary resistance decreases as the temperature increases. Attemperatures higher than 100 8C, it is difficult to separate the bulkand grain-boundary contributions to resistance. Thus, we will onlydiscuss the values of the total resistance and the total conductivity.

Fig. 6 displays the temperature dependences of the totalconductivity of LixLa3Zr2O8.5+0.5x in Arrhenius coordinates. In the

0 50 500450400350300250200150100

0

50

100

Rb+gb

Rb

-Z', kOhm

Fig. 5. Impedance plots for LixLa3Zr2O8.5+0.5x (x = 6–10) at room temperature.

[(Fig._6)TD$FIG]

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

-10

-8

-6

-4

-2

0

2 x = 6

x = 8

x = 7

x = 9

x = 10

ln(

T),

S c

m-1 K

1000/T, K-1

Fig. 6. Arrhenius plots for the total conductivity of LixLa3Zr2O8.5+0.5x (x = 6–10).

Table 3Total conductivity at room temperature (s) and its activation energy (Ea) of solid

electrolytes LixLa3Zr2O8.5+0.5x (x = 6–10).

System s, S cm�1 Ea, kJ mol�1

Li6La3Zr2O11.5 2.4�10�7 49.2�2.8

Li7La3Zr2O12 3.2�10�7 50.0�1.5

Li8La3Zr2O12.5 7.2�10�7 55.7�2.4

Li9La3Zr2O13 7.5�10�6 46.9�1.8

Li10La3Zr2O13.5 1.1�10�6 49.8�1.2

[(Fig._8)TD$FIG]

6.5 7.0 7.5 8.0 8.5

-6

-5

-4

-3

-2

-1

log

[S c

m-1]

x (Li)

25oC

100oC

200oC

Fig. 8. The concentration dependence of the total conductivity of LixLa3Zr2O8.5+0.5x

for the refined values of x.

[(Fig._9)TD$FIG]

-200-150-100 -50 0 50 100 150 200

2

3

4

5

6

7

8

9

10

100 150 200 250 300 350 400 450

H, kHz

T, K

t, °

E.A. Il’ina et al. / Materials Research Bulletin 53 (2014) 32–3736

examined temperature range, the total conductivity varies linearlywith temperature. For all the studied compositions, ion transporthas an activation mechanism. The activation energies for eachsystem are close to each other in the error range; i.e., these systemshave a similar mechanism for lithium ion transfer. Table 3summarizes the total conductivity for all the compositions at roomtemperature and the activation energies for all the compositions.As shown, the composition with x = 9 has the highest totalconductivity at room temperature.

The concentration dependence of the total conductivity ofLixLa3Zr2O8.5+0.5x (x = 6–10) shows that the conductivity rises asthe Li content increases and has a maximum at x = 9 (Fig. 7). Theconductivity of the composition with x = 10 is lower than that ofx = 9; this decrease is because of the appearance of an appreciableamount of a second phase. Within the ‘‘region of homogeneity,’’the conductivity rises as the Li content increases; this increase isapparently because of the increase in the number of chargecarriers (lithium ions) in the structure of the compounds. Basedon the above determination of the lithium content in LixLa3Z-r2O8.5+0.5x (x = 7–9), the concentration dependence of the totalconductivity can be redrawn as shown in Fig. 8.

According to the phenomenological equation, the conductivity(s) of an unipolar electrolyte can be expressed by:

s ¼ cqm; (8)

where c, q and m are the concentration, charge and mobility ofthe charge carriers, respectively. From Eq. (8), we can see that theconductivity growth may be because of an increase in theconcentration of charge carriers or an increase in the mobility ofthe charge carriers (or may arise from both factors simultaneous-ly). NMR is one of the methods that allow us to estimate themobility of charge carriers in a solid electrolyte. The 7Li NMR signalfor the composition Li9La3Zr2O13 is wider than the signal forLi7La3Zr2O12 (Fig. 9). The broadening of the NMR signal indicates an

Fig. 9. Temperature-dependent full width at half maximum of the static 7Li NMR

spectra of Li7La3Zr2O12 (squares) and Li9La3Zr2O13 (triangles/rhombus).

[(Fig._7)TD$FIG]

6 7 8 9 10

-6

-5

-4

-3

-2

-1

log

S c

m-1

x (Li)

25oC

100oC

200oC

Fig. 7. The concentration dependence of the total conductivity of LixLa3Zr2O8.5+0.5x

(x = 6–10).

increase in the dipole-dipole interaction. This enhancement maybe because of the decrease in the interatomic distance; thisdecrease was established by neutron diffraction. In turn, strongerinterparticle interactions should reduce the mobility of the lithiumions in Li9La3Zr2O13. However, the total conductivity for thecomposition Li9La3Zr2O13 is significantly higher. This result ispossible if the increase in the concentration of charge carriers inEq. (8) has a greater effect on the conductivity than the reduction inmobility.

4. Conclusions

Solid electrolytes LixLa3Zr2O8.5+0.5x (x = 6, 7, 8, 9, 10) based onLLZ were synthesized. XRD analysis showed the presence ofimpurities for x = 6 and 10. The single-phase samples (based onXRD) were studied with neutron diffraction, which showed a

E.A. Il’ina et al. / Materials Research Bulletin 53 (2014) 32–37 37

decrease in the cell parameter as x increased and showed thepresence of a lithium carbonate impurity in all the samples.Volumetry was used to determine the exact content of lithiumcarbonate in the solid electrolytes. The volumetric experimentsdetermined that the solid electrolytes Li7La3Zr2O12, Li8La3Zr2O12.5

and Li9La3Zr2O13 contain 1.32 � 0.04, 1.95 � 0.06 and 3.49 �0.10 wt.% Li2CO3, respectively. Most likely, lithium carbonate formsthrough the interaction of the material with carbon dioxide. Thisinteraction is inevitable in air, and we should consider this interactionwhen working with such compounds.

Within the ‘‘region of homogeneity,’’ the compound withthe highest number of lithium ions per formula unit has thehighest conductivity. The total conductivity of Li9La3Zr2O13

(7.5 � 10�6 S cm�1 at room temperature) is higher than theconductivity of Li7La3Zr2O12 (3.2 � 10�7 S cm�1 at room temper-ature). All the investigated electrolytes have similar activationenergies; this similarity means that these systems have a similarmechanism for transfer of lithium ions. The combination ofthe neutron diffraction method, NMR, and impedance spectros-copy suggests that the growth of conductivity as x increases isbecause of the increase in the concentration of charge carriersrather than because of an increase in the mobility of the chargecarriers.

Acknowledgements

We are grateful to Antonov Boris Dmitrievich for performingthe XRD analysis.

This work was supported by the Program of the Presidium of theRAS ‘‘Chemical aspects of energy’’ (project No. 12-P-3-1012) andState contract No. 14.518.11.7020.

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