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NMR study of one-dimensional ionic conductor, sodium titano-gallates (I)
SOLID STATE IONICS
Solid State Ionics 79 (1995) 45-50
EUEVIER
NMR study of one-dimensional ionic conductor, sodium titano-gallates (I) Y. Onoda a, Y. Michiue a, M. Watanabe a, S. Yoshikado
b, T. Ohachi b
aNational Institute for Research in Inorganic Materials, Ibaraki 305, Japan ’ Faculty of Engineering, Doshisha University, Kyoto 602, Japan
Abstract Temperature dependence of spin-lattice relaxation time T,* of mobile 23Na and immobile ‘lGa in the framework of Na,Ti,_,Ga 4+x010 was measured in the temperature range of 4.2-900 K. The dependence is divided into four temperature regions, corresponding to different activation-type ionic motions. T,* above about 700 K is probably dominated by the interchannel hopping of Na+. Activation energy E,,, in the middle temperature range below 600 K, obtained using 23Na as the probe to observe NaC ionic motion, is 0.069 eV and is about 1.8 times as large as the value obtained using “Ga as the probe. The discrepancy commonly observed in sodium titano-gallates is discussed.
Keywords: One-dimensional ionic conductor; NMR, Sodium titan0 gallates
1. Introduction Because of the nature of the one-dimensional (1-D) system dictating that a mobile ion cannot jump over another mobile ion ahead of it, nor can it avoid impurity barriers in the conduction path, conduction properties in the 1-D system have been a target of intensive study from a mainly fundamental point of view [l-4]. Priderite A.(B, Ti)8_x016(A = K+, Rb+, Cs+ B = A13+, Mg*+, etc.) with the hollandite-type strulture and alkaline gallo-titano-gallate A,Ga,Ga s+xTi 16_xO56, (A = K+, Rb+, Cs+, abbreviation: AGGTO) were the typical materials, on which researches were focused. Mobile ions which keep the structures stable are alkali ions with larger ionic radius than Na’. 0167-2738/95/$09.50
As 1-D Na+ ion conductors, Na,_.Ti,+&,_,(NTAO12) and Na,_,+3yTixGaS_x_yOs 012 (NTG08) are already known [5], and their conduction properties have been reported [6,7]. Recently, a titano-gallate, Na, _xTi2+xGa5_x012 (NTG0121, isostructural with NTA012, and a new type of titano-gallate, NaxTi2_xGa4+x01,, (NTGOlO) have been synthesized in our institute [8,9]. Hereafter, we name generically these materials, including NTA012, as sodium titano-gallate (NTGOX). NTGOlO and NTG012 have similar 1-D channels of distorted 8-oxygen ring, and main difference between them is the arrangement of the channel in the plane perpendicular to the channel direction [8,9]. The tunnel shape and the arrangement of NTGOX is anisotropic, and is different from those of priderite
0 1995 Elsevier Science B.V. All rights reserved
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Y. Onoda ei at. /Solid
and AGGTO. Conductivity measurement, done on NTA012 and K1_,Ti2+x Al_xO12 showed similar frequency-dependent conductivity to that of the priderites [6]. It is easy to vary temperature extensively in an NMR experiment. Thus, it is possible to observe mostly the ionic motions which would occur in the 1-D channel in the temperature range that can be achieved. One purpose of this work is to observe, without omission, the ionic motion in these materials over a wide temperature range and to investigate the difference in the conduction properties with other 1-D materials, if it exists. The advantage of these materials in NMR measurement is that we can use two nuclei as the probe to observe the ionic motion: the direct observation using movable nucleus 23Na, and the indirect observation using immovable nucleus such as ‘r Ga or 27Al in the framework. The spin-lattice relaxation (SLR) of these nuclei is caused by the fluctuation of the electric field gradient (efg) around the observing nucleus via nuclear quadrupole coupling. If the fluctuation is predominantly caused by the motion of the mobile ion, the indirect observation gives fundamentally the same temperature dependence of Tr with the direct observation, as long as the correlation function (CF) of the fluctuation is not affected by some unknown effects. In fact the indirect observation using “Ga gave fundamentally the same temperature dependence with the direct observation using ‘33Cs or “Rb in AGGTO [lo]. However, as reported in some ionic conductors [11,12], NTGOX shows different temperature dependence between the direct and the indirect observation. A further purpose of this work is to gather experimental data in the simple 1-D system and to investigate the reason for the difference. This is the first paper in a series of studies on NTGOX. Here, we present the experimental data of the temperature dependence of T,* of 23Na and 71Ga in NTGOlO. Next, the discrepancy between the direct and indirect observation is described and the reason is discussed. After that, the cause of the decrease in T,’ observed above 700 K is commented on. Finally, the cause of temperature dependence of T,* below 20 K is discussed, and the dependence is also attributed to some activation-type ionic motion. The model of the ionic motion which is responsible
State him
79 (1995) 45-50
for the SLR in the temperature region I, II and III will be described in the next paper [13].
2. Experimental The sample was prepared by a direct synthesis method from a mixture of Na,CO,, TiO, and Ga,O, [9]. The powder X-ray pattern showed weak impurity peaks mainly from NTGO8, but the amount was estimated to be within few percent, which is not an obstacle to NMR measurement. Fig. 1 shows the crystal structure of NTGOlO (space group: C2/m, j3 = 92.29”). Ga, (tetrahedral) and Ga, (octahedral) sites are occupied by Ga3+ only. M, (octahedral) site is partially occupied by Ti4’ with the occupancy factor of 0.59. So, the x value of the composition is estimated to be 0.81 191. The shape of the 1-D channel is very similar to that of NTGO12 [8], but g-oxygen ring of NTGOlO is a little more distorted than NTG012. The main difference between the two structures is the arrangement of the channel in the b-plane. The SLR time of 71Ga and 23Na was measured by means of the saturation method, and in the case of 71Ga the solid echo method was incorporated. Be-
NTGOlO
CB = 92.3’)
1.209 nrn Fig. 1. Projection of the crystal structure of NTGOlO along the b-axis. Large light gray circles indicate oxygen ions, dark gray circles indicate Na+, and small black circles indicate Ga3+ or Ti4+.
Y. Onoda et al. /Solid
State Ionics 79 (1995) 45-50
41
part, respectively. The dependence is divided into four temperature regions I, II, III and IV as shown in the figures. 3.1. Temperature region III
0.01
50.0
0.0
100.0
150.0
200.0
250.0
KJOO/T (UK) Fig. 2. Temperature dependence of TT of 23Na (open circle) and “Ga (filled circle) in the low temperature range.
cause of the randomness of the efg, mainly due to random substitution of Ti4+ for the Ga3+ site, the recovery curves of the nuclear magnetization of ‘lGa and 23Na are non-exponential, as those of other 1-D materials. Consequently, the time T,* when [Mm M(t)]/W reaches l/e of the initial value was measured.
3.2. Difference in ENMRand T,*,,,inbetween ‘jNa and
3. Result and discussions
71Ga
Fig. 2 and 3 show the temperature dependence of T,* of 23Na (open circle) and “Ga (filled circle) in
the low temperature part and the high temperature
. .
l
.
. .
.
‘;; 0.1 8 1 F
0.01
5.0
Id.0
Ii.0
lOOUT (l/K) Fig. 3. High temperature
1
Based on the coupling model, Ngai et al. [14,15] attributed such discrepancy, often observed in ionic conductors, to the difference in the CF. That is, the correlation of the indirect observation is essentially the site-occupancy correlation, while that of the direct observation is the particle-particle correlation. So, the n parameter in the stretched exponential CF, C(t) a exp(- t/T * )lpn, in the case of the direct observation, becomes larger than the value in the indirect observation, because of a stronger correlation effect on the particle-particle correlation. However, AGGTO shows almost the same temperature dependence, in spite of the fact that the correlation of ionic motion in a channel is thought to be much stronger than that in NTGOlO. Therefore, we think it is not appropriate to adapt Ngai’s theory to our 1-D materials. As noted in the introduction, one of the differences in the structure between AGGTO and NTGOX
_-I NTGOlO
010
The region III has a clear V-shaped temperature dependence, and the region II also shows a shallow but clear V-shaped dependence. Therefore, it is evident that T,* of 23Na and ‘lGa in these regions is dominated by two different activation-type ionic motions. Remarkable features seen in the region III are that the temperature at Tl*minof the direct observation is located at much higher temperature ( = 450 IQ than that (= 330 K) of the indirect observation, and that the slope E,,, (= 0.069 eV) below T;min of the direct observation is about 1.8 times of the value ( = 0.038 eV> of the indirect observation. In the case of CGGTO and RGGTO, the indirect observation using ‘lGa gave almost the same result with the direct observation using mobile 133Cs or *‘Rb [lo]. On the contrary, NTGOX generally shows large discrepancies of E,,, and the temperature at T,‘min D31.
part of Fig. 2.
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Y. Onoda ei al. /Solid
is whether the arrangement of the channel is isotropic or not. The efg of ‘lGa on M, site in NTGOlO is strongly fluctuated by the ionic motion in the two nearest neighbor (nn) channels, and that on M, or Ga, is affected by the ionic motion in one nn channel strongly and by motions in three or four second nn channels. On the other hand, the fluctuation of the efg of 23Na is caused mainly by its own motion in a channel, and the effect of the interchannel correlation is thought to be not so strong. Thus, the temperature dependence of the CF of the efg fluctuation of 71Ga may differ from that of 23Na. Until now, in the calculation of the SLR driven by the activation-type ionic motions, q dependence has not been considered because of the lack of a simple system of highly correlated ionic motion, where q vector is well defined, and because of the difficulty of the treatment, though q dependence was suggested to play an important role in the CF in some ionic conductors [11,12]. q sum was first included in the kink hopping model developed on the FrenkelKontorova model by Ishii [16,17], to explain the frequency dependence of the SLR of the type T,* a w3/*,observed in priderites [18], and the frequency dependence was successfully explained to appear in the low temperature limit when the diffusion length is less than the correlation length. However, the interchannel correlation of the ionic motion was not considered in the calculation, that is, only 1-D q dependence was treated because the inclusion of 3-D q sum was unnecessary. The discrepancy observed in NTGOX is thought to be related with the anisotropy of the tunnel structure via stronger interchannel correlation of ionic motion, and to consider 3-D q dependence especially in the treatment of the CF of 7*Ga is considered necessary for the explanation of the discrepancy. 3.3. High temperature
region
Above about 700 K, T,* of 71Ga begins to decrease. On comparison with data of other 1-D samples we measured, we can say that this decrease is not due to the Raman term of the lattice vibration, but due to the beginning of another activation-type ionic motion. Fig. 4 compares the temperature dependence of NTGOlO and those of CG-GTO and RGGTO in the high temperature region [lo]. As the
State Ionics 79 (I 995) 45-M
1 : ” Ga in RGGTO 0.0
5.0
10.0
15.0 1000/T
20.0
25.0
30.0
(l/K)
Fig. 4. Comparison of the temperature dependence tween NTGOIO and AGGTO in the high temperature
of TV’ beregion.
data of 71Ga in RGGTO typically shows, T,’ decreases above about 500 K and it appears like to have a Tl*min at about 1000 K. This indicates that this decrease is caused by the appearance of a slow fluctuation in efg due to the beginning of another activation-type ionic motion, which was attributed to the “going in and out” motion of an impurity Ga3+ ion between the pseudo-tetrahedaral site in the channel and the original tetrahedral site in the framework [19,20]. The decrease in T,* in NTGOlO is thought also to be caused by an activation-type ionic motion. Two types of ionic motion are thought possible in this case. One is a motion over impurity barriers in the channel caused, for example, by an oxygen defect as was considered in priderites [l], or by the motion like “going in and out” motion of Ga3+ if there is the impurity Ga3+ in the channel as in AGGTO. Preliminary data on ac conductivity show the similar frequency dependence (a = w”> to those of priderites. This means that impurity barriers, which played important role in priderites [l], also determine ac conductivity at low frequencies. However, the temperature of 700 K at which the redecrease in T,* begins, seems too high compared to the result of priderites, for a possible exponential-form distribution of impurity barrier height, whose form was presumed in the 1-D random barrier model [l]. The effect of the cut-off barrier originated from the impurity Ga3+ ion in the channel, which played the main role in AGGTO [20], does not appear
Y. Onoda et al. /Solid
explicitly in the ac conductivity. Thus, it is doubtful that such impurity Ga3’ exists in the channel so much as the “going in and out” motion dominates the SLR at high temperatures. The other is the interchannel hopping motion of a Na+ ion. The channel of NTGOlO is not as separated as that of AGGTO, and it seems not difficult for the Naf ion to move to an adjacent channel via the space surrounded by Ga, tetrahedron and Gaz and M, octahedra, since the ionic radius of Na+ ion is smaller than that of K+ or Rbf. Furthermore, about 40% of cation at M, site is Ga3+ and the weaker Coulomb repulsion at this site will make easier for Na+ to pass through near this site. So, we think that the interchannel hopping is the most probable reason for the decrease in T,’ in the temperature region IV.
State tonics 79 (1995) 45-50
49
As indicated by an arrow, there are slight troughs at about 11 K in the T,’ data of 23Na and 71Ga. These troughs are thought to be the T;min of Vshaped temperature dependence for another activation-type ionic motion. Thus, we think that the SLR in the region I is dominated mainly by some hopping motion of Na+ in the channel, and the contribution of the phonon or phonon-like modes to the SLR is probably more than one order less. A curve fitting result indicates that it is necessary to include phonon-like mode of T,* a T-” to obtain better fit in the low temperature region below 5 K. However, the value n must be 1.0 or less, and the contribution of the mode is about one order small [13].
4. Summary
3.4. Low temperature region Below 20 K, T,* is weakly dependent on temperature and can be described by the functional form of T,* = c X T-” (n = 1.3-2.0) as shown by two curves in Fig. 2, where the coefficient c is chosen arbitrarily. The TW2 form is a characteristic dependence when the SLR is dominated by the Raman two phonon process of the lattice vibration in the region, T EC-O,, where 0, is the Debye temperature [21]. The 0, of this material is supposed to be larger than 20 K, but 1-D materials are strongly anisotropic and the very slow vibrational mode of Na+ along the channel is expected to exist. If so, it is thought possible that the TV2 dependence extends to sufficiently low temperatures. On the other hand, the T-” (n = 1.3) or the TP(l+a) (a = 0.3) dependence was often observed in glassy materials, and was attributed to the existence of phonon-like disorder modes caused by low energy excitation in the twolevel-system (TLS) [22] or asymmetric double well potentials (ADW) 1141. However, these contributions to the SLR are thought to persist at high temperatures above 20 K as long as there is no mechanism through which these contributions cease at high temperatures. Experimental data show that there are some temperature regions where T,* becomes longer than the two curves, and this fact indicates that the Raman or the TLS process is not the main cause of the SLR in the region I.
The temperature dependence of spin-lattice relaxation time T,’ of mobile 23Na and immobile 71Ga has been shown to be divided into four temperature regions, corresponding to different activation-type ionic motions. NTGOlO shows a large discrepancy and temperature at T~*min between the in E,,, direct and the indirect observation in the temperature region III below 700 K. These features are different from CGGTO or RGGTO. The anisotropy of the channel shape and arrangement, and the stronger interchannel correlation than AGGTO are thought to be the cause of this discrepancy. 3-D q dependence is though to be important especially on the CF of “Ga, The decrease in T,* of 7’Ga above 700 K is presumed to be caused by the beginning of the interchannel hopping of Na+ ion.
References [l] I. Bernasconi, H.U. Beyeler, S. Sh%ssler and S. Alexander, Phys. Rev. J.&t. 42 (1979) 819. [21 H.U. Beyeler, L. Pietronero, and S. StrIssler, Phys. Rev. B22 (1980) 2988. [31 S. Yoshikado, T. Ohachi, I. Taniguchi, Y. Onoda, M. Watanabe and Y. Fujiki, Solid State Ionics 7 (1982) 335. [4] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Fujiki and Y. Onoda, Solid State Ionics 28-30 (1988) 173. [5] W.G. Mumme and A.D. Wadsley, Acta. Cryst. 23 (1967) 754.
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[6] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Fujiki and Y. Onoda, Solid State Ionics 35 (1989) 377. [7] G.V. Chandrashekhar, A. Bednowitz and S.J. La Placa, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North-Holland, Amsterdam, 1979) p. 447. [S] Y. Michiue, T. Sasaki, M. Watanabe and Y. Fujiki, Mater. Res. Bull. 28 (1993) 173. [9] Y. Michiue and M. Watanabe, Solid State Ionics 70/71 (1994) 186. [lo] Y. Onoda, M. Watanabe, Y. Fujiki, S. Yoshikado, T. Ohachi and I. Taniguchi, Solid State Ionics 40/41 (1990) 147. [11) M. Villa and J.L. Bjorkstam, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North-Holland, Amsterdam, 1979) p. 447. [12] M. Trunnel, D.R. Torgeson, S.W. Martin, and F. Borsa, J. Non-Cryst. Solids 139 (1992) 257.
State Ionics 79 (1995) 45-50 [13] Y. Onoda, Y. Michiue, M. Watanabe, S. Yoshikado and T. Ohachi, in preparation. [14] K.L. Ngai, J. Non-Cryst. Solids 162 (1993) 268. [15] K.L. Ngai, Solid State Ionics 61 (1993) 345. [16] T. Ishii, J. Phys. Sot. Japan 60 (1991) 4203. [17] T. Ishii, Solid State Ionics 53-56 (1992) 928. [18] Y. Onoda, Y. Fujiki, M. Takigawa, H. Yasuoka, S. Yoshikado, T. Ohachi and I. Taniguchi, Solid State Ionics 17 (1985) 127. [19] M. Watanabe, Y. Fujiki, S. Yoshikado and T. Ohachi, and Y. Kudo, Solid State Ionics 40/41 (1990) 139. [20] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Onoda and Y. Fujiki, Solid State Ionics 40/41 (1990) 142. [21] J. Van Kranendonk, Physica 20 (1954) 781. [22] J. Szeftel and H. AIlouI, J. Non-Cryst. Solids 29 (1978) 253.
Solid State Ionics 79 (1995) 45-50
EUEVIER
NMR study of one-dimensional ionic conductor, sodium titano-gallates (I) Y. Onoda a, Y. Michiue a, M. Watanabe a, S. Yoshikado
b, T. Ohachi b
aNational Institute for Research in Inorganic Materials, Ibaraki 305, Japan ’ Faculty of Engineering, Doshisha University, Kyoto 602, Japan
Abstract Temperature dependence of spin-lattice relaxation time T,* of mobile 23Na and immobile ‘lGa in the framework of Na,Ti,_,Ga 4+x010 was measured in the temperature range of 4.2-900 K. The dependence is divided into four temperature regions, corresponding to different activation-type ionic motions. T,* above about 700 K is probably dominated by the interchannel hopping of Na+. Activation energy E,,, in the middle temperature range below 600 K, obtained using 23Na as the probe to observe NaC ionic motion, is 0.069 eV and is about 1.8 times as large as the value obtained using “Ga as the probe. The discrepancy commonly observed in sodium titano-gallates is discussed.
Keywords: One-dimensional ionic conductor; NMR, Sodium titan0 gallates
1. Introduction Because of the nature of the one-dimensional (1-D) system dictating that a mobile ion cannot jump over another mobile ion ahead of it, nor can it avoid impurity barriers in the conduction path, conduction properties in the 1-D system have been a target of intensive study from a mainly fundamental point of view [l-4]. Priderite A.(B, Ti)8_x016(A = K+, Rb+, Cs+ B = A13+, Mg*+, etc.) with the hollandite-type strulture and alkaline gallo-titano-gallate A,Ga,Ga s+xTi 16_xO56, (A = K+, Rb+, Cs+, abbreviation: AGGTO) were the typical materials, on which researches were focused. Mobile ions which keep the structures stable are alkali ions with larger ionic radius than Na’. 0167-2738/95/$09.50
As 1-D Na+ ion conductors, Na,_.Ti,+&,_,(NTAO12) and Na,_,+3yTixGaS_x_yOs 012 (NTG08) are already known [5], and their conduction properties have been reported [6,7]. Recently, a titano-gallate, Na, _xTi2+xGa5_x012 (NTG0121, isostructural with NTA012, and a new type of titano-gallate, NaxTi2_xGa4+x01,, (NTGOlO) have been synthesized in our institute [8,9]. Hereafter, we name generically these materials, including NTA012, as sodium titano-gallate (NTGOX). NTGOlO and NTG012 have similar 1-D channels of distorted 8-oxygen ring, and main difference between them is the arrangement of the channel in the plane perpendicular to the channel direction [8,9]. The tunnel shape and the arrangement of NTGOX is anisotropic, and is different from those of priderite
0 1995 Elsevier Science B.V. All rights reserved
SSDI 0167-2738(95)00028-3
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Y. Onoda ei at. /Solid
and AGGTO. Conductivity measurement, done on NTA012 and K1_,Ti2+x Al_xO12 showed similar frequency-dependent conductivity to that of the priderites [6]. It is easy to vary temperature extensively in an NMR experiment. Thus, it is possible to observe mostly the ionic motions which would occur in the 1-D channel in the temperature range that can be achieved. One purpose of this work is to observe, without omission, the ionic motion in these materials over a wide temperature range and to investigate the difference in the conduction properties with other 1-D materials, if it exists. The advantage of these materials in NMR measurement is that we can use two nuclei as the probe to observe the ionic motion: the direct observation using movable nucleus 23Na, and the indirect observation using immovable nucleus such as ‘r Ga or 27Al in the framework. The spin-lattice relaxation (SLR) of these nuclei is caused by the fluctuation of the electric field gradient (efg) around the observing nucleus via nuclear quadrupole coupling. If the fluctuation is predominantly caused by the motion of the mobile ion, the indirect observation gives fundamentally the same temperature dependence of Tr with the direct observation, as long as the correlation function (CF) of the fluctuation is not affected by some unknown effects. In fact the indirect observation using “Ga gave fundamentally the same temperature dependence with the direct observation using ‘33Cs or “Rb in AGGTO [lo]. However, as reported in some ionic conductors [11,12], NTGOX shows different temperature dependence between the direct and the indirect observation. A further purpose of this work is to gather experimental data in the simple 1-D system and to investigate the reason for the difference. This is the first paper in a series of studies on NTGOX. Here, we present the experimental data of the temperature dependence of T,* of 23Na and 71Ga in NTGOlO. Next, the discrepancy between the direct and indirect observation is described and the reason is discussed. After that, the cause of the decrease in T,’ observed above 700 K is commented on. Finally, the cause of temperature dependence of T,* below 20 K is discussed, and the dependence is also attributed to some activation-type ionic motion. The model of the ionic motion which is responsible
State him
79 (1995) 45-50
for the SLR in the temperature region I, II and III will be described in the next paper [13].
2. Experimental The sample was prepared by a direct synthesis method from a mixture of Na,CO,, TiO, and Ga,O, [9]. The powder X-ray pattern showed weak impurity peaks mainly from NTGO8, but the amount was estimated to be within few percent, which is not an obstacle to NMR measurement. Fig. 1 shows the crystal structure of NTGOlO (space group: C2/m, j3 = 92.29”). Ga, (tetrahedral) and Ga, (octahedral) sites are occupied by Ga3+ only. M, (octahedral) site is partially occupied by Ti4’ with the occupancy factor of 0.59. So, the x value of the composition is estimated to be 0.81 191. The shape of the 1-D channel is very similar to that of NTGO12 [8], but g-oxygen ring of NTGOlO is a little more distorted than NTG012. The main difference between the two structures is the arrangement of the channel in the b-plane. The SLR time of 71Ga and 23Na was measured by means of the saturation method, and in the case of 71Ga the solid echo method was incorporated. Be-
NTGOlO
CB = 92.3’)
1.209 nrn Fig. 1. Projection of the crystal structure of NTGOlO along the b-axis. Large light gray circles indicate oxygen ions, dark gray circles indicate Na+, and small black circles indicate Ga3+ or Ti4+.
Y. Onoda et al. /Solid
State Ionics 79 (1995) 45-50
41
part, respectively. The dependence is divided into four temperature regions I, II, III and IV as shown in the figures. 3.1. Temperature region III
0.01
50.0
0.0
100.0
150.0
200.0
250.0
KJOO/T (UK) Fig. 2. Temperature dependence of TT of 23Na (open circle) and “Ga (filled circle) in the low temperature range.
cause of the randomness of the efg, mainly due to random substitution of Ti4+ for the Ga3+ site, the recovery curves of the nuclear magnetization of ‘lGa and 23Na are non-exponential, as those of other 1-D materials. Consequently, the time T,* when [Mm M(t)]/W reaches l/e of the initial value was measured.
3.2. Difference in ENMRand T,*,,,inbetween ‘jNa and
3. Result and discussions
71Ga
Fig. 2 and 3 show the temperature dependence of T,* of 23Na (open circle) and “Ga (filled circle) in
the low temperature part and the high temperature
. .
l
.
. .
.
‘;; 0.1 8 1 F
0.01
5.0
Id.0
Ii.0
lOOUT (l/K) Fig. 3. High temperature
1
Based on the coupling model, Ngai et al. [14,15] attributed such discrepancy, often observed in ionic conductors, to the difference in the CF. That is, the correlation of the indirect observation is essentially the site-occupancy correlation, while that of the direct observation is the particle-particle correlation. So, the n parameter in the stretched exponential CF, C(t) a exp(- t/T * )lpn, in the case of the direct observation, becomes larger than the value in the indirect observation, because of a stronger correlation effect on the particle-particle correlation. However, AGGTO shows almost the same temperature dependence, in spite of the fact that the correlation of ionic motion in a channel is thought to be much stronger than that in NTGOlO. Therefore, we think it is not appropriate to adapt Ngai’s theory to our 1-D materials. As noted in the introduction, one of the differences in the structure between AGGTO and NTGOX
_-I NTGOlO
010
The region III has a clear V-shaped temperature dependence, and the region II also shows a shallow but clear V-shaped dependence. Therefore, it is evident that T,* of 23Na and ‘lGa in these regions is dominated by two different activation-type ionic motions. Remarkable features seen in the region III are that the temperature at Tl*minof the direct observation is located at much higher temperature ( = 450 IQ than that (= 330 K) of the indirect observation, and that the slope E,,, (= 0.069 eV) below T;min of the direct observation is about 1.8 times of the value ( = 0.038 eV> of the indirect observation. In the case of CGGTO and RGGTO, the indirect observation using ‘lGa gave almost the same result with the direct observation using mobile 133Cs or *‘Rb [lo]. On the contrary, NTGOX generally shows large discrepancies of E,,, and the temperature at T,‘min D31.
part of Fig. 2.
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Y. Onoda ei al. /Solid
is whether the arrangement of the channel is isotropic or not. The efg of ‘lGa on M, site in NTGOlO is strongly fluctuated by the ionic motion in the two nearest neighbor (nn) channels, and that on M, or Ga, is affected by the ionic motion in one nn channel strongly and by motions in three or four second nn channels. On the other hand, the fluctuation of the efg of 23Na is caused mainly by its own motion in a channel, and the effect of the interchannel correlation is thought to be not so strong. Thus, the temperature dependence of the CF of the efg fluctuation of 71Ga may differ from that of 23Na. Until now, in the calculation of the SLR driven by the activation-type ionic motions, q dependence has not been considered because of the lack of a simple system of highly correlated ionic motion, where q vector is well defined, and because of the difficulty of the treatment, though q dependence was suggested to play an important role in the CF in some ionic conductors [11,12]. q sum was first included in the kink hopping model developed on the FrenkelKontorova model by Ishii [16,17], to explain the frequency dependence of the SLR of the type T,* a w3/*,observed in priderites [18], and the frequency dependence was successfully explained to appear in the low temperature limit when the diffusion length is less than the correlation length. However, the interchannel correlation of the ionic motion was not considered in the calculation, that is, only 1-D q dependence was treated because the inclusion of 3-D q sum was unnecessary. The discrepancy observed in NTGOX is thought to be related with the anisotropy of the tunnel structure via stronger interchannel correlation of ionic motion, and to consider 3-D q dependence especially in the treatment of the CF of 7*Ga is considered necessary for the explanation of the discrepancy. 3.3. High temperature
region
Above about 700 K, T,* of 71Ga begins to decrease. On comparison with data of other 1-D samples we measured, we can say that this decrease is not due to the Raman term of the lattice vibration, but due to the beginning of another activation-type ionic motion. Fig. 4 compares the temperature dependence of NTGOlO and those of CG-GTO and RGGTO in the high temperature region [lo]. As the
State Ionics 79 (I 995) 45-M
1 : ” Ga in RGGTO 0.0
5.0
10.0
15.0 1000/T
20.0
25.0
30.0
(l/K)
Fig. 4. Comparison of the temperature dependence tween NTGOIO and AGGTO in the high temperature
of TV’ beregion.
data of 71Ga in RGGTO typically shows, T,’ decreases above about 500 K and it appears like to have a Tl*min at about 1000 K. This indicates that this decrease is caused by the appearance of a slow fluctuation in efg due to the beginning of another activation-type ionic motion, which was attributed to the “going in and out” motion of an impurity Ga3+ ion between the pseudo-tetrahedaral site in the channel and the original tetrahedral site in the framework [19,20]. The decrease in T,* in NTGOlO is thought also to be caused by an activation-type ionic motion. Two types of ionic motion are thought possible in this case. One is a motion over impurity barriers in the channel caused, for example, by an oxygen defect as was considered in priderites [l], or by the motion like “going in and out” motion of Ga3+ if there is the impurity Ga3+ in the channel as in AGGTO. Preliminary data on ac conductivity show the similar frequency dependence (a = w”> to those of priderites. This means that impurity barriers, which played important role in priderites [l], also determine ac conductivity at low frequencies. However, the temperature of 700 K at which the redecrease in T,* begins, seems too high compared to the result of priderites, for a possible exponential-form distribution of impurity barrier height, whose form was presumed in the 1-D random barrier model [l]. The effect of the cut-off barrier originated from the impurity Ga3+ ion in the channel, which played the main role in AGGTO [20], does not appear
Y. Onoda et al. /Solid
explicitly in the ac conductivity. Thus, it is doubtful that such impurity Ga3’ exists in the channel so much as the “going in and out” motion dominates the SLR at high temperatures. The other is the interchannel hopping motion of a Na+ ion. The channel of NTGOlO is not as separated as that of AGGTO, and it seems not difficult for the Naf ion to move to an adjacent channel via the space surrounded by Ga, tetrahedron and Gaz and M, octahedra, since the ionic radius of Na+ ion is smaller than that of K+ or Rbf. Furthermore, about 40% of cation at M, site is Ga3+ and the weaker Coulomb repulsion at this site will make easier for Na+ to pass through near this site. So, we think that the interchannel hopping is the most probable reason for the decrease in T,’ in the temperature region IV.
State tonics 79 (1995) 45-50
49
As indicated by an arrow, there are slight troughs at about 11 K in the T,’ data of 23Na and 71Ga. These troughs are thought to be the T;min of Vshaped temperature dependence for another activation-type ionic motion. Thus, we think that the SLR in the region I is dominated mainly by some hopping motion of Na+ in the channel, and the contribution of the phonon or phonon-like modes to the SLR is probably more than one order less. A curve fitting result indicates that it is necessary to include phonon-like mode of T,* a T-” to obtain better fit in the low temperature region below 5 K. However, the value n must be 1.0 or less, and the contribution of the mode is about one order small [13].
4. Summary
3.4. Low temperature region Below 20 K, T,* is weakly dependent on temperature and can be described by the functional form of T,* = c X T-” (n = 1.3-2.0) as shown by two curves in Fig. 2, where the coefficient c is chosen arbitrarily. The TW2 form is a characteristic dependence when the SLR is dominated by the Raman two phonon process of the lattice vibration in the region, T EC-O,, where 0, is the Debye temperature [21]. The 0, of this material is supposed to be larger than 20 K, but 1-D materials are strongly anisotropic and the very slow vibrational mode of Na+ along the channel is expected to exist. If so, it is thought possible that the TV2 dependence extends to sufficiently low temperatures. On the other hand, the T-” (n = 1.3) or the TP(l+a) (a = 0.3) dependence was often observed in glassy materials, and was attributed to the existence of phonon-like disorder modes caused by low energy excitation in the twolevel-system (TLS) [22] or asymmetric double well potentials (ADW) 1141. However, these contributions to the SLR are thought to persist at high temperatures above 20 K as long as there is no mechanism through which these contributions cease at high temperatures. Experimental data show that there are some temperature regions where T,* becomes longer than the two curves, and this fact indicates that the Raman or the TLS process is not the main cause of the SLR in the region I.
The temperature dependence of spin-lattice relaxation time T,’ of mobile 23Na and immobile 71Ga has been shown to be divided into four temperature regions, corresponding to different activation-type ionic motions. NTGOlO shows a large discrepancy and temperature at T~*min between the in E,,, direct and the indirect observation in the temperature region III below 700 K. These features are different from CGGTO or RGGTO. The anisotropy of the channel shape and arrangement, and the stronger interchannel correlation than AGGTO are thought to be the cause of this discrepancy. 3-D q dependence is though to be important especially on the CF of “Ga, The decrease in T,* of 7’Ga above 700 K is presumed to be caused by the beginning of the interchannel hopping of Na+ ion.
References [l] I. Bernasconi, H.U. Beyeler, S. Sh%ssler and S. Alexander, Phys. Rev. J.&t. 42 (1979) 819. [21 H.U. Beyeler, L. Pietronero, and S. StrIssler, Phys. Rev. B22 (1980) 2988. [31 S. Yoshikado, T. Ohachi, I. Taniguchi, Y. Onoda, M. Watanabe and Y. Fujiki, Solid State Ionics 7 (1982) 335. [4] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Fujiki and Y. Onoda, Solid State Ionics 28-30 (1988) 173. [5] W.G. Mumme and A.D. Wadsley, Acta. Cryst. 23 (1967) 754.
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[6] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Fujiki and Y. Onoda, Solid State Ionics 35 (1989) 377. [7] G.V. Chandrashekhar, A. Bednowitz and S.J. La Placa, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North-Holland, Amsterdam, 1979) p. 447. [S] Y. Michiue, T. Sasaki, M. Watanabe and Y. Fujiki, Mater. Res. Bull. 28 (1993) 173. [9] Y. Michiue and M. Watanabe, Solid State Ionics 70/71 (1994) 186. [lo] Y. Onoda, M. Watanabe, Y. Fujiki, S. Yoshikado, T. Ohachi and I. Taniguchi, Solid State Ionics 40/41 (1990) 147. [11) M. Villa and J.L. Bjorkstam, in: Fast Ion Transport in Solids, eds. P. Vashishta, J.N. Mundy and G.K. Shenoy (North-Holland, Amsterdam, 1979) p. 447. [12] M. Trunnel, D.R. Torgeson, S.W. Martin, and F. Borsa, J. Non-Cryst. Solids 139 (1992) 257.
State Ionics 79 (1995) 45-50 [13] Y. Onoda, Y. Michiue, M. Watanabe, S. Yoshikado and T. Ohachi, in preparation. [14] K.L. Ngai, J. Non-Cryst. Solids 162 (1993) 268. [15] K.L. Ngai, Solid State Ionics 61 (1993) 345. [16] T. Ishii, J. Phys. Sot. Japan 60 (1991) 4203. [17] T. Ishii, Solid State Ionics 53-56 (1992) 928. [18] Y. Onoda, Y. Fujiki, M. Takigawa, H. Yasuoka, S. Yoshikado, T. Ohachi and I. Taniguchi, Solid State Ionics 17 (1985) 127. [19] M. Watanabe, Y. Fujiki, S. Yoshikado and T. Ohachi, and Y. Kudo, Solid State Ionics 40/41 (1990) 139. [20] S. Yoshikado, T. Ohachi, I. Taniguchi, M. Watanabe, Y. Onoda and Y. Fujiki, Solid State Ionics 40/41 (1990) 142. [21] J. Van Kranendonk, Physica 20 (1954) 781. [22] J. Szeftel and H. AIlouI, J. Non-Cryst. Solids 29 (1978) 253.