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Calorimetric and electrical studies on the positional disorder of lithium ions in lithium lanthanum titanate
Solid State Communications, Vol. 91, No. 8. pp. 627-630. 1994 Elsevier Science Ltd Printed in Great Britain 0038- 1098194 S7.00 + .OO
Pergamon
O&38-1098(94)00356-4
CALORIMETRIC
AND ELECTRICAL STUDIES ON THE POSITIONAL DISORDER IONS IN LITHIUM LANTHANUM TITANATE
OF LITHIUM
Masaharu Oguni Department
of Chemistry, Faculty of Science, Tokyo Institute of Technology, Tokyo 152, Japan
0-okayama,
Meguro-ku,
and Yoshiyuki Inaguma, Mitsuru Itoh and Tetsuro Nakamura Research Laboratory
of Engineering Materials, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan (Received
2 1 April 1994 by C. N.R. Rao)
Heat capacities and electrical moduli of high lithium ion conductor Lio.3sLao.slTi02.94 were measured below 300 K. A glass transition was observed at Tg = (102 f 2) K as due to the freezing-in of positional disorder of lithium ions. The associated heat capacity jump was found to be (O.O3$$)JK-’ mol-’ at 125 K. The energy of the excited state as referred to the ground state was evaluated from the jump to be cu. 9 kJmol_‘. The calorimetric and electrical relaxation times for the rearrangement of lithium ions were well fitted by a straight line on an Arrhenius plot, and the activation energy of the process was derived to be (32.0 f 0.1) kJmol_‘. A potential close relation was suggested to exist in general between the high ionic conductivity and the positional disorder of mobile ions. Keywords: C: point defects, D: dielectric response, heat capacity, order-disorder effects and thermodynamic properties. 1. INTRODUCTION LITHIUM ION conducting solid electrolytes have been the subject of considerable attention in recent years because of their potential high energy densities and lightweights in the use [l], and exploitation of materials with high ionic conductivity at room temperature has been attempted. The highest conductivities so far attained at room temperature are around 10e3 S cm-’ in Li3N, Li-P-A1203 and so on [l]. The lithium conductivities in perovskite-type compounds have been first investigated by Latie et al. for Li,Ln,,sNb, _.Ti,03 (Ln = La, Nd and x < 0.1) [2], and we previously found that polycrystalline Lio,34Lao,s,Ti02.94 showed conductivity as high as 1 x 10e3 Scm-’ at room temperature as well [3]. Elucidation of the microscopic reasoning for such a high conductivity is valuable for further exploitation of high lithium conduction materials in the future. In this respect, it is attractive to see if there exists an
appreciable positional disorder of lithium ions in the crystal. This is because most of crystalline superionic conductors have been clarified to be in the disordered phase concerning the arrangement of mobile ions [4], and further because we have found the existence of positional disorder even in amorphous superionic conductors as observation of the glass transition due to freezing-in of the positional disorder of silver ions in AgI-AgPOs systems [5]. In this paper, the existence of positional disorder of lithium ions in lithium lanthanum titanate was examined through calorimetric observation of a glass transition, temperature dependence of electrical properties, and the interrelation in the relaxation times between the two properties.
627
2. EXPERIMENTAL Sample was prepared and chemically analyzed as
POSITIONAL
628
DISORDER
OF LITHIUM
Vol. 91, No. 8
IONS
described previously [3], and composition of the sample was determined to be Lio.~s(,~Lao.sl(l~TiO*,~~~*~. ZHeat capacities of the polycrystalline sample were m measured with an adiabatic calorimeter reported previously [6]. The imprecision and inaccuracy of the measurements were confirmed previously to be within f0.06% and f0.3%, respectively [6]. Mass of the sample used was weighed to be 18.604g . I I (corresponding to 0.1106 mol). Electrical properties were studied with an LCZ 80 100 120 140 meter 2340 (NF Electronic Instruments Co.) in the T/K frequency range of 10Hz to 1 MHz and in the temperature range below 250K. Inaccuracies of Fig. 2. Spontaneous temperature drift rates observed the frequency and temperature were estimated to be of a calorimeter cell in the region of 70- 140 K. 0 and fO.l% and fO.1 K, respectively. Details of the l represent results of the samples cooled rapidly at 5 Kmin-’ and slowly at 15 mK min-’ , respectively. cryostat and dielectric cell used for the measurements will be described elsewhere [7]. Both opposite 120K. Such dependences of the drift rates on the faces of the polycrystalline pellet were pasted with precooling rates are characteristic of a glass transition gold as the electrodes. due to a freezing-in of some configurational disorder [8]. The relaxation times as a function of temperature 3. RESULTS AND DISCUSSION of this configurational degree of freedom could not be Figure 1 shows molar heat capacities of determined from the drift rates because the relaxation Lio.ssLao.5iTi02.94. The temperature dependence is effects were too small for their evaluation. Thus, only rather smooth, but anomalous spontaneous tem- the glass transition temperature at which the perature drifts of a calorimeter cell were observed relaxation time became 1 ks was determined to be around lOOK. The sample was cooled at two Tg = (102 f 2) K according to the following different rates of 5 K min-’ and 15 mK min-’ empirical relation between the temperature depenthrough the anomalous temperature range, and the dences of the relaxation times and of the drift rates drifts were repeatedly followed under adiabatic [6, 9, lo]; when the sample is precooled at the rate conditions for 10min after each intermittent heating about 10 mK min-’ and heat capacities are measured by about 2K. Figure 2 shows temperature depenby the intermittent heating method with energy input dences of the drift rates observed on heating. When of l-2 K and temperature rating for cu. lOmin, the the sample was cooled rapidly, exothermic drift endothermic drift rates observed in the rating periods started to appear at 80K, reached maximum rate become maximum at around Tg with T = 1 ks. around 95 K, and returned to more or less the normal The heat capacity jump of the glass transition was behavior around 110 K. When it was cooled slowly, very small in association with the smallness in the on the other hand, rather endothermic drift started to 0. IO, appear around 85 K, reached maximum rate around 1 3 102 K, and returned to the normal drift around
-11
I
100 7 i
E” 7
Y 4
50
7E
I 110
0”
/ 120
I
130
I 140
T/K 0
100
T/
Fig. 1. Molar heat Lio.34Lao.51TiO2.94.
300
200
K
capacities
of
crystalline
Fig. 3. Excess heat capacities due to the positional rearrangement of lithium ions in the glass transition region. A broken line represents the probable temperature dependence of the contribution in equilibrium.
POSITIONAL
Vol. 91, No. 8
DISORDER
above-stated spontaneous drifts, and was estimated after subtracting a smooth baseline from the observed heat capacities. The baseline was so drawn by extrapolating smoothly the heat capacities below 120K as to expose the jump as clearly as possible. Figure 3 shows the excess heat capacities derived by the subtraction, and the broken line represents the expected contribution due to the relevant configurational degree of freedom. The heat capacity jump was estimated from the broken line to be (0.03?~$) JK-’ mol-’ at 125 K. Supposed that all the lithium ions of 0.35mol are located in the same energetic circumstance with respect to the positional disorder and that the freezing-in of the disorder is attributed to the glass transition, the energy difference between the ground and excited state, AC, and the equilibrium fraction of lithium ions in the excited states at 125 K, p(Ae), are roughly evaluated using the following expressions for a Schottky anomaly and Boltzmann’s equation to be 9 kJ mol-* and only 0.01% or so, respectively; exp (Ae/RT) [1 + exp (Ac/RT)]*
’
and P(A~) =
exp (-Af/RT) 1 + exp (-Ac/RT)
’
Figure 4 shows the frequency dependences of the imaginary part of complex electrical modulus (M’ = l/e* where E* denotes complex dielectric constant) at some different temperatures. A reason 0.002
‘,
-%
0.001
0
log
(f/Hz)
Fig. 4. Frequency dependences of the imaginary component of complex electrical modulus M* (= l/e*) at 8 different temperatures. E* denotes complex dielectric constant. o, 145.0K; l , 154.0K; IJ, 164.9K; W, 176.lK; 0, 189.2K; +, 207.2K; A, 226.4K; A, 249.4K.
OF LITHIUM
IONS
629
Fig. 5. Arrhenius plot of the relaxation times for the positional rearrangement of mobile lithium ions. 0 and l represent the results by electrical and calorimetric measurements, respectively. for selecting M * for describing electrical properties is that electrode effects which may interfere with the bulk behavior of the sample are suppressed in this representation [1 11. The M” peak is interpreted as ascribed to the diffusional motion of lithium ions in view of the mobilities of each ionic species in the present crystal. The relaxation times r of the motions were evaluated from the peak frequencies fnl to be 1/(27rf$,), and are plotted in Fig. 5 as an Arrhenius expression together with the point r = 1 ks at Tg obtained above by the calorimetry. All the relaxation time data are well fitted by a following straight line; where r. = 10-‘3.5 s. The r. r = 70exp [&/(RT)], value is in the reasonable range from the expected frequency of translational vibration of lithium ions. The activation energy AC, was calculated from the slope of the line to be (32.0 f 0.1) kJ mol-‘. This value almost corresponds with the activation energy calculated from ionic conductivities in the range between 240 and 294K [3]. The fact that the relaxation times derived by both the calorimetry and electrical measurements are well fitted by a straight line indicates that the high conductivity of lithium ions in crystalline Lio.3sLao.s,Ti02.94 is due to the presence of positional disorder of lithium ions though the disordering would not take place between symmetrically equivalent sites. This is quite suggestive of the potential close interrelation between the high ionic conductivity and the positional disorder of mobile ions in the entropic sense. If this relation really holds in general, the way how one can introduce the positional disorders into any system of amorphous or crystalline materials should be indispensably developed for
630
POSITIONAL
DISORDER
designing high ionic conductors. In the present case, some defect sites accessible to lithium ions would have been formed during calcination at high temperatures of crystalline Li0,5La0,sTiOs though they are located at considerably high energy levels.
OF LITHIUM 4. 5. 6. 7.
REFERENCES 1.
2. 3.
M.Z.A. Munshi & B.B. Owens, Superionic Solids and Solid Electrolytes (Edited by A.L. Laskar & S. Chandra), p. 631. Academic Press, San Diego (1989). L. Latie, G. Villeneuve, D. Conte & G.L. Flem, J. Solid State Chem. 51, 293 (1984). Y. Inaguma, C. Liquan, M. Itoh, T. Nakamura, T. Uchida, H. Ikuta & M. Wakihara, Solid State Commun. 86, 689 (1993).
8. 9. 10. 11.
IONS
Vol. 91, No. 8
S. Chandra, Superionic Solids, North Holland, Amsterdam (1981). M. Nakayama, M. Hanaya & M. Oguni, Solid State Commun. 89, 403 (1994). H. Fujimori & M. Oguni, J. Phys. Chem. Solids 54, 271 (1993). A. Hatate, M. Hanaya & M. Oguni (to be published). H. Suga & S. Seki, J. Non-Cryst. Solids 16, 171 (1974). T. Matsuo, M. Oguni, H. Suga, S. Seki & J.F. Nagle, Bull. Chem. Sot. Jpn. 47, 57 (1974). M. Oguni, T. Matsuo, H. Suga & S. Seki, Bull. Chem. Sot. Jpn. 50, 825 (1977). P.B. Macedo, CT. Moynihan & R. Bose, Phys. Chem. Glasses 13, 171 (1972).
Pergamon
O&38-1098(94)00356-4
CALORIMETRIC
AND ELECTRICAL STUDIES ON THE POSITIONAL DISORDER IONS IN LITHIUM LANTHANUM TITANATE
OF LITHIUM
Masaharu Oguni Department
of Chemistry, Faculty of Science, Tokyo Institute of Technology, Tokyo 152, Japan
0-okayama,
Meguro-ku,
and Yoshiyuki Inaguma, Mitsuru Itoh and Tetsuro Nakamura Research Laboratory
of Engineering Materials, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan (Received
2 1 April 1994 by C. N.R. Rao)
Heat capacities and electrical moduli of high lithium ion conductor Lio.3sLao.slTi02.94 were measured below 300 K. A glass transition was observed at Tg = (102 f 2) K as due to the freezing-in of positional disorder of lithium ions. The associated heat capacity jump was found to be (O.O3$$)JK-’ mol-’ at 125 K. The energy of the excited state as referred to the ground state was evaluated from the jump to be cu. 9 kJmol_‘. The calorimetric and electrical relaxation times for the rearrangement of lithium ions were well fitted by a straight line on an Arrhenius plot, and the activation energy of the process was derived to be (32.0 f 0.1) kJmol_‘. A potential close relation was suggested to exist in general between the high ionic conductivity and the positional disorder of mobile ions. Keywords: C: point defects, D: dielectric response, heat capacity, order-disorder effects and thermodynamic properties. 1. INTRODUCTION LITHIUM ION conducting solid electrolytes have been the subject of considerable attention in recent years because of their potential high energy densities and lightweights in the use [l], and exploitation of materials with high ionic conductivity at room temperature has been attempted. The highest conductivities so far attained at room temperature are around 10e3 S cm-’ in Li3N, Li-P-A1203 and so on [l]. The lithium conductivities in perovskite-type compounds have been first investigated by Latie et al. for Li,Ln,,sNb, _.Ti,03 (Ln = La, Nd and x < 0.1) [2], and we previously found that polycrystalline Lio,34Lao,s,Ti02.94 showed conductivity as high as 1 x 10e3 Scm-’ at room temperature as well [3]. Elucidation of the microscopic reasoning for such a high conductivity is valuable for further exploitation of high lithium conduction materials in the future. In this respect, it is attractive to see if there exists an
appreciable positional disorder of lithium ions in the crystal. This is because most of crystalline superionic conductors have been clarified to be in the disordered phase concerning the arrangement of mobile ions [4], and further because we have found the existence of positional disorder even in amorphous superionic conductors as observation of the glass transition due to freezing-in of the positional disorder of silver ions in AgI-AgPOs systems [5]. In this paper, the existence of positional disorder of lithium ions in lithium lanthanum titanate was examined through calorimetric observation of a glass transition, temperature dependence of electrical properties, and the interrelation in the relaxation times between the two properties.
627
2. EXPERIMENTAL Sample was prepared and chemically analyzed as
POSITIONAL
628
DISORDER
OF LITHIUM
Vol. 91, No. 8
IONS
described previously [3], and composition of the sample was determined to be Lio.~s(,~Lao.sl(l~TiO*,~~~*~. ZHeat capacities of the polycrystalline sample were m measured with an adiabatic calorimeter reported previously [6]. The imprecision and inaccuracy of the measurements were confirmed previously to be within f0.06% and f0.3%, respectively [6]. Mass of the sample used was weighed to be 18.604g . I I (corresponding to 0.1106 mol). Electrical properties were studied with an LCZ 80 100 120 140 meter 2340 (NF Electronic Instruments Co.) in the T/K frequency range of 10Hz to 1 MHz and in the temperature range below 250K. Inaccuracies of Fig. 2. Spontaneous temperature drift rates observed the frequency and temperature were estimated to be of a calorimeter cell in the region of 70- 140 K. 0 and fO.l% and fO.1 K, respectively. Details of the l represent results of the samples cooled rapidly at 5 Kmin-’ and slowly at 15 mK min-’ , respectively. cryostat and dielectric cell used for the measurements will be described elsewhere [7]. Both opposite 120K. Such dependences of the drift rates on the faces of the polycrystalline pellet were pasted with precooling rates are characteristic of a glass transition gold as the electrodes. due to a freezing-in of some configurational disorder [8]. The relaxation times as a function of temperature 3. RESULTS AND DISCUSSION of this configurational degree of freedom could not be Figure 1 shows molar heat capacities of determined from the drift rates because the relaxation Lio.ssLao.5iTi02.94. The temperature dependence is effects were too small for their evaluation. Thus, only rather smooth, but anomalous spontaneous tem- the glass transition temperature at which the perature drifts of a calorimeter cell were observed relaxation time became 1 ks was determined to be around lOOK. The sample was cooled at two Tg = (102 f 2) K according to the following different rates of 5 K min-’ and 15 mK min-’ empirical relation between the temperature depenthrough the anomalous temperature range, and the dences of the relaxation times and of the drift rates drifts were repeatedly followed under adiabatic [6, 9, lo]; when the sample is precooled at the rate conditions for 10min after each intermittent heating about 10 mK min-’ and heat capacities are measured by about 2K. Figure 2 shows temperature depenby the intermittent heating method with energy input dences of the drift rates observed on heating. When of l-2 K and temperature rating for cu. lOmin, the the sample was cooled rapidly, exothermic drift endothermic drift rates observed in the rating periods started to appear at 80K, reached maximum rate become maximum at around Tg with T = 1 ks. around 95 K, and returned to more or less the normal The heat capacity jump of the glass transition was behavior around 110 K. When it was cooled slowly, very small in association with the smallness in the on the other hand, rather endothermic drift started to 0. IO, appear around 85 K, reached maximum rate around 1 3 102 K, and returned to the normal drift around
-11
I
100 7 i
E” 7
Y 4
50
7E
I 110
0”
/ 120
I
130
I 140
T/K 0
100
T/
Fig. 1. Molar heat Lio.34Lao.51TiO2.94.
300
200
K
capacities
of
crystalline
Fig. 3. Excess heat capacities due to the positional rearrangement of lithium ions in the glass transition region. A broken line represents the probable temperature dependence of the contribution in equilibrium.
POSITIONAL
Vol. 91, No. 8
DISORDER
above-stated spontaneous drifts, and was estimated after subtracting a smooth baseline from the observed heat capacities. The baseline was so drawn by extrapolating smoothly the heat capacities below 120K as to expose the jump as clearly as possible. Figure 3 shows the excess heat capacities derived by the subtraction, and the broken line represents the expected contribution due to the relevant configurational degree of freedom. The heat capacity jump was estimated from the broken line to be (0.03?~$) JK-’ mol-’ at 125 K. Supposed that all the lithium ions of 0.35mol are located in the same energetic circumstance with respect to the positional disorder and that the freezing-in of the disorder is attributed to the glass transition, the energy difference between the ground and excited state, AC, and the equilibrium fraction of lithium ions in the excited states at 125 K, p(Ae), are roughly evaluated using the following expressions for a Schottky anomaly and Boltzmann’s equation to be 9 kJ mol-* and only 0.01% or so, respectively; exp (Ae/RT) [1 + exp (Ac/RT)]*
’
and P(A~) =
exp (-Af/RT) 1 + exp (-Ac/RT)
’
Figure 4 shows the frequency dependences of the imaginary part of complex electrical modulus (M’ = l/e* where E* denotes complex dielectric constant) at some different temperatures. A reason 0.002
‘,
-%
0.001
0
log
(f/Hz)
Fig. 4. Frequency dependences of the imaginary component of complex electrical modulus M* (= l/e*) at 8 different temperatures. E* denotes complex dielectric constant. o, 145.0K; l , 154.0K; IJ, 164.9K; W, 176.lK; 0, 189.2K; +, 207.2K; A, 226.4K; A, 249.4K.
OF LITHIUM
IONS
629
Fig. 5. Arrhenius plot of the relaxation times for the positional rearrangement of mobile lithium ions. 0 and l represent the results by electrical and calorimetric measurements, respectively. for selecting M * for describing electrical properties is that electrode effects which may interfere with the bulk behavior of the sample are suppressed in this representation [1 11. The M” peak is interpreted as ascribed to the diffusional motion of lithium ions in view of the mobilities of each ionic species in the present crystal. The relaxation times r of the motions were evaluated from the peak frequencies fnl to be 1/(27rf$,), and are plotted in Fig. 5 as an Arrhenius expression together with the point r = 1 ks at Tg obtained above by the calorimetry. All the relaxation time data are well fitted by a following straight line; where r. = 10-‘3.5 s. The r. r = 70exp [&/(RT)], value is in the reasonable range from the expected frequency of translational vibration of lithium ions. The activation energy AC, was calculated from the slope of the line to be (32.0 f 0.1) kJ mol-‘. This value almost corresponds with the activation energy calculated from ionic conductivities in the range between 240 and 294K [3]. The fact that the relaxation times derived by both the calorimetry and electrical measurements are well fitted by a straight line indicates that the high conductivity of lithium ions in crystalline Lio.3sLao.s,Ti02.94 is due to the presence of positional disorder of lithium ions though the disordering would not take place between symmetrically equivalent sites. This is quite suggestive of the potential close interrelation between the high ionic conductivity and the positional disorder of mobile ions in the entropic sense. If this relation really holds in general, the way how one can introduce the positional disorders into any system of amorphous or crystalline materials should be indispensably developed for
630
POSITIONAL
DISORDER
designing high ionic conductors. In the present case, some defect sites accessible to lithium ions would have been formed during calcination at high temperatures of crystalline Li0,5La0,sTiOs though they are located at considerably high energy levels.
OF LITHIUM 4. 5. 6. 7.
REFERENCES 1.
2. 3.
M.Z.A. Munshi & B.B. Owens, Superionic Solids and Solid Electrolytes (Edited by A.L. Laskar & S. Chandra), p. 631. Academic Press, San Diego (1989). L. Latie, G. Villeneuve, D. Conte & G.L. Flem, J. Solid State Chem. 51, 293 (1984). Y. Inaguma, C. Liquan, M. Itoh, T. Nakamura, T. Uchida, H. Ikuta & M. Wakihara, Solid State Commun. 86, 689 (1993).
8. 9. 10. 11.
IONS
Vol. 91, No. 8
S. Chandra, Superionic Solids, North Holland, Amsterdam (1981). M. Nakayama, M. Hanaya & M. Oguni, Solid State Commun. 89, 403 (1994). H. Fujimori & M. Oguni, J. Phys. Chem. Solids 54, 271 (1993). A. Hatate, M. Hanaya & M. Oguni (to be published). H. Suga & S. Seki, J. Non-Cryst. Solids 16, 171 (1974). T. Matsuo, M. Oguni, H. Suga, S. Seki & J.F. Nagle, Bull. Chem. Sot. Jpn. 47, 57 (1974). M. Oguni, T. Matsuo, H. Suga & S. Seki, Bull. Chem. Sot. Jpn. 50, 825 (1977). P.B. Macedo, CT. Moynihan & R. Bose, Phys. Chem. Glasses 13, 171 (1972).