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27Al NMR study of mixed alkali effects in β-alumina
Solid State Ionics 34 (1989) 207-210 North-Holland, Amsterdam
27A1 N M R S T U D Y O F M I X E D A L K A L I E F F E C T S I N I I - A L U M I N A D.E. H I N T E N L A N G * ,
E.J. H O L U P K A * * , P.J. B R A Y
Department of Physics, Brown University, Providence, RI 02912, USA and S.G. G R E E N B A U M
Department of Physics and Astronomy, Hunter Collegeof CUNY, New York, NY 10021, USA Received 17 August 1988; accepted for publication 22 December 1988
Nuclear spin-lattice relaxation measurements are reported for 27AI in Na-, K-, and Na^~3~Rai~.K" ~ h ~ mixed-aluminacationin the temperatUreand range 5-670K. shallow Tl-minimum is observed at compound is attributed to A substantlally altered population of two-level system (TLS) tunneling modes. The high temperature T1-minimum in the alloy crystal occurs at a significantly higher temprature than in either the Na- or K S-alumina. Both phenomena are discussed in terms of mixed ion pair distributions and are consistent with other manifestations of the mixed alkali effect in ~-alumina reported in the literature.
INTRODUCTION The crystalline fast ion conductor Na #-alumina has been the subject of many studies [1] which have led to a better understanding of fast ion transport processe in solids. Materials in the #-alumina family are quasi-two dimensional conductors in which the conducting species is usually an alkali or silver ion, but need not be restricted to these. High conductivities are obtained by incorporating an excess of the mobile species into the conducting plane, usually 20-30% in the form of alkali-oxide. The excess oxygen enters the conduction plane interstitially, incorporating a degree of disorder in the conduction plane. Several investigators have shown that #-alumina containing more than one conducting species of ion can exhibit behavior similar to the mixed-alkali effect that is observed in glasses [4-7]. The disordered conduction plane produces some glass-like properties in #-alumina [1,8]. Some of these properties are attributable to the presence of disorder modes, or two level systems (TLS), that are observable at low temperatures [1]. Previous investigations have shown that the NMR spin-lattice relaxation time (T1) in #-alumina exhibits a temperature dependence at low temperatures similar to that obtained in glasses [9, 10]. The relaxation process responsible for this behavior is attributed to the presense of TLS. A nearest-neighbor tunneling defect can modulate the electric field gradient (efg) present at the site of a nucleus being studied by NMR, * Present address: Department of Nuclear Engineering, University of Florida, Gainesville, FL 32611, USA. Present address: Department of Physical Chemistry, University of Geneva, CH 1211 Geneva 4, Switzerland. 0 1 6 7 - 2 7 3 8 / 8 9 / $ 0 3 . 5 0 © E l s e v i e r S c i e n c e P u b l i s h e r s B.V. (North-Holland Physics Publishing Division)
thus enhancing quadrupolar relaxation [9-1 I]. This usually produces a temperature dependence of T 1 of the form T -a with 1
D.E. Hintenlang et al. / 27Al NMR study of mixed alkali effects
208
RESULTS Spin-lattice relaxation times were measured on Na, Nap ~-Ko 5 and K B-alumina as a function of temperature. At hlghel: temperatures (>200K), the 27A1 T 1 was measured only for Nao 5-Ko s and K B-alumina since Na #-alumina has been extensive'ly investigated in this temperature region [12, 13]. Although the magnetization recovery profile for the central transition of ~TAi (spin 5/2) is generally nonexponential, previous studies of B-alumina have shown that a single effective relaxation time can be employed as a reliable monitor of ionic or lattice motion [12, 14]. In particular the recovery profile is observed to be nearly temperature-independent for all three samples in this work, and it is therefore reasonable that variations in effective 27A1 T i reflect true dynamical differences between the samples. Ti is here defined as the time at which the magnetization recovers (1 - e -i) of its initial value. The spin-lattice relaxation times can be divided into roughly two temperature regions, a high temperture region where the relaxation rate is determined by ionic diffusion, and a low temperature region where diffusive motion is frozen out. The results of the ~TAI spin-lattice relaxation time measurement for Na, K and Nao s - K o s B-aluminas are presented in Fig. 1 for temperatui:es below 200K. Up to about 100K, T 1 appears to follow a power law, TlctT "a with a=l.ht0.03 and ~=0.87+0.07 for Na B-alumina and K Balumina, respectively. These two materials behave similarly except that the K #-alumina has relaxation times about an order of magnitude larger than those of Na B-alumina. The Nao.5-Ko. s B-alumina exhibits markedly different behavior [9]. At temperatures below ~I5K the relaxation time behavior for the mixed-alkali sample approximates that of
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Na B-alumina. As the temperature is further incre~ed, the relaxation time becomes longer until the onset of ionic motion where it decreases again. This produces a shallow minimum at about 30K. In the high temperature regime where the spin-lattice relaxation process is dominated by ionic motion, both K Balumina and Na, s-Ko 5 #-alumina exhibit behavior that is typical of the ZrAI relaxation times in Na #-alumina with some minor differences. The logarithm of the relaxation times for these samples are plotted as a function of reciprocal temperature in Fig. 2. Both curves exhibit a clear minimum and are asymmetric. The. K B-alumina curve is only slightly asymmetric while that of Nap 5-Ko 5 B-alumina is more asymmetric. These asymmetrl~s ar~ frequently observed in NMR but there is currently no universally accepted analysis of such minima. Additional room temperature measurements were performed at 16, 19, and 21 MHz, yielding the results that Tla~o1"19 and to1"25 for K and Nao.sKo. s B-alumina, respectively. A single'21 MHz measurement at 620K (significantly above the T 1 minimum) yielded no apparent frequency dependence of T 1 in this high temperature region. These findings are quite similar to those obtained in Na Balumina by other investigators [15, 16], where Tl,~OJ1"2s was observed on the low temperature side of the minimum and little or no frequency dependence was observed on the high temperature side of the minimum. Spin-lattice relaxation in #-alumina and disordered or anisotropic materials, in general, is not adequately described by the Bloembergen, Pound and Purcell (BPP) formalism [17] which predicts a symmetric temperature dependence on both sides of the minimum, and a quadratic frequency dependence of T) on the low temperature side. Previous studies have treatea the data in a variety of ways. One method is to ignore the experimentally observed frequency dependence of T 1 and apply the high and low temperature limits of the BPP results to the high and low temperature sides of the T 1 minimum independently. The activation energy determined from the high temperature region often agrees with results obtained by conductivity measurement. The T l results may also be described by invoking a distribution of activation energies as shown by several investigators [16, 18]. These theories adequately describe
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Effective spin-lattice relaxation time for 9"7A1 in Na, Nao.sKo.s, and K B-alumina at low temperatures.
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High temperature spin-lattice relaxation time for 27A1 in the Nao.sKo.5 and K #-alumina.
D.E. Hintenlang et al. /27Al NMR study of mixed alkali effects most data for glasses where a distribution of ionic sites might be expected. It is doubtful, however, that these models should be applied to ~-alumina since there is little physical evidence to suggest such a distribution of sites. Other treatments include a two-dimensinal continuum diffusion model developed by Bjorkstam and Villa [15, 19] which employs non-exponential correlation functions, and the universal dissipation-fluctuation formalism (as applied to T 1 measurements) elaborated by Ngai [20]. However both theories predict T 1- activation energies on the high T side of the minimum that are too large by almost a factor of three for both samples, based on the observed low T activation energy (0.145eV for both samples) and frequency dependence as input parameters• The high T activation energies from Fig. 2 are 0.155 and 0•22 eV for K and Nao.sKo.s 0-alumina, respectively. It is apparent that no single theoretical description of nuclear spin-lattice relaxation adequately explains all aspects of the data. Therefore it is reasoned that a simple BPP-like theory, applied to each side of the T t minimum as described above, is at least as meaningful as an analysis by any of the other currently proposed theories. This has the advantage that the resulting activation energies are easily compared to those obtained by the vast majority of other NMR studies. In addition, the same approach applied consistently to three similar materials (Na, K, and the mixed p-alumina) is expected to yield a valid reflection of systematic differences between samples. We therefore treat our data as approximately fitting the relation given by Cohen and Reif [19] for quadrupolar relaxation by diffusing charges: T1-1
c~
1
+
f (5/2) ~ o =
where We is the Larmor frequency and r = r o exp (E=/kT), by fitting the data with a different activation energy on each side of the minimum• This expression predicts a minimum when the condition wgr = (2/5) /2 is obtained. This result is not significantly different from the predictions of the other theories discussed above, which yield t~or',l at the T 1 minimum• From Fig. 2 it is clear that the T x minimum occurs at significantly higher temperature for the mixed alkali ~-alumina (490K) than for K /~-alumina (340K). the attempt frequency vo ro "1, where rQ = r exp (-E=/kT), is calculated from the temperature of the T z minimum and the high T activation energy. The results are vo = 1.35x101°s "1 and 7.7x109s "1 for K and Nao.sKo.s ~-alumina, respectively. Previous measurements on Na /~-alumina found the T 1 minimum occurring at 190K at a frequency of 21 MHz [12]. This data, interpreted for consistency according to the model employed for the other two materials above yields an attempt frequency of approximately 5xl01°s "1. DISCUSSION The Tlc~T"= dependence observed at low temperatures is characteristic of the relaxation by TLS in disordered solids. The significance of small differences in a has, however, not been determined. The qualitative behavior of Na o 5-K0 s B" alumina is markedly different than that of the other samples indicating that the observed TLS are somehow related to the distribution of alkali ions. There appears to he a decrease in the density of TLS that provide relaxation in the 25-35K region, resulting in the observed shallow minimum. A possible mechanism is the creation of Na-K pairs at the expense of Na-Na pairs as K replaces Na. At low temperatures alkali ions will be located in Beevers-Ross (BR) sites and mid-Oxygen (toO) sites near interstitial oxygen ions
209
[2]. Dobbs et al. [22] have determined that the density of TLS in Na ~-alumina is independent of excess Na at temperatures below 2K. Since the number of m e sites varies with excess stoichiometry while the number of BR sites is independent of stoichiometry, it seems reasonable to hypothesize that the TLS associated with BR sites are primarily responsible for the relaxation at the lowest temperatures. A possible identification of a low-temperature single particle tunneling mode involves the triangular region near BR sites, in which two of the three positions around the triangle may be occupied with nearly equal probability, as suggested by Strom [1]. Consequently, the potential wells associated with this configuration would exhibit very little asymmetry. At higher temperatures other possible configurational tunneling processes may involve pairs of ions distributed among the three m e sites or even larger groups of ions moving cooperatively within oxygen-cation pair clusters [1]. The TLS associated with the latter are likely to be more asymmetric and responsible for relaxation at slightly higher temperatures. As K is substituted for Na, mixed alkali (Na-K) pairs are formed at the m e sites. The TLS at these sites are now so asymmetric that the frequency of tunneling transitions is drastically reduced, and these systems can no longer provide an efficient relaxation mechanism. In addition, the presence of an attractive interaction between K + and Na + ions on m e sites inferred from X-ray scattering results. [6] would reduce further the tunneling probability. The relaxation time is correspondingly increased. There are still some Na-Na pairs present to provide relaxation, but their number is considerably reduced• A simple statistical argument shows that with replacement of 50% of the Na + ions by K +, the number of Na + ions in BR sites is reduced by 5096, but the number of Na-Na m e pairs is reduced by 75%. Recent evidence from X-ray diffraction measurements indicate that the cations do not populate the allowed sites randomly but, in fact, exhibit a marked site preference (with K + occupying BR sites preferentially) [6, 7]. It is postulated, nevertheless, that in the 50% Na material there are enough single-ion BR-associated TLS modes to provide an efficient relaxation mechanism, and that the observed increase in T t above 30K corresponds to a decrease in TLS modes associated with Na-Na pairs which presumably provide the dominant relaxation process in that temperature region. At temperatures above 100K, thermally activated motion of the alkali ions occurs• The motion of these ions couples to the 27AI via the quadrupole interaction to produce relaxation of the 27A1 nuclei. T h e 27AI spin-lattice relaxation time, therefore, reflects the motion of both alkali species• The activation energies that are obtained from the high temperature side of the T z vs T minimum are generally a s s u m e d to represent directly long-range diffusional processes. The high temperature activation energies obtained for K ~-alumina and Na o.5 - K 0.5 p-alumina (0 155 and 0 22 eV. respecUvely) are both somewhat lower than those obtained from conductivity [4]. This is characteristic of NMR experiments, and may be attributed to the fact that these measurements are more sensitive to local motion than some other techniques. The activation energy, even on the high temperature side of the minimum, will be more heavily weighted by the activation energies of local motions. Although the absolute magnitudes of the activation energies are lower than those obtained from conductivity measurements, the percentage change from K B-alumina to Na o s-Ko ~-alumina agrees well with the change observed by conductivity measurements [4]. The most dramatic change in the mixed-alkali ~-alumina •
"
"
210
D.E. Hintenlang et al. /2ZAl NMR study of mixed alkali effects
occurs in the temperature at which the T,-minimum occurs (Fig. 2). The minimum shifts from 340K in the case of K B-alumina, and ~I90K for Na B-aluminas [12], to 490K for Nao -Ko .~ 5 B-alumina." This result is similar to the shifts observed m other m,xed catmn B-alumina [13], and also implies that the attempt frequencies increase in the order Na, K, and mixed B-alumina as previously mentioned. Since the cooperative motion of cation pairs is required for the conduction process it is assumed that such motion is primarily responsible for the ~TAI relaxation at higher temperatures. It is therefore reasonable that the high temperature attempt frequency may be identified with some vibrational mode of the paired ions. .s
.
.
CONCLUSIONS Measurement of the 27A1 nuclear spin-lattice relaxation time over the temperature range 5-670K indicate both low and high temperature manifestations of the mixed alkali effect in Nao.s-Kos B-alumina. It is suggested that both phenomena result f'rom the presence of Na+K + cation pairs. The mixed cation pairs result in TLS modes with anomalously low transition rates leading to a shallow T~ minimum at ~30K, and in a higher activation energy aria reduced attempt frequency (as compared to Na and K Balumina) associated with diffusive motion. ACKNOWLEDGEMENT The authors acknowledge Dr. U. Strom of the Naval Research Laboratory for many illuminating discussions.
7.
J . A . Bruce, R. A. Howie, and M. D. Ingram, Solid State Ionics 18 & 19, 1129 (1986.)
8.
K . L . Ngai and U. Strom, Phys. Rev. B 27, 6031 (1983).
9.
S . G . Greenbaum and U. Strom, Sol. State Comm. 46, 437 (1983).
10. S.G. Greenbaum, U. Strom, and M. Rubinstein, Phys. Rev. B 26, 5226 (1982). 11. J. Szeftel and H. Alloul, J. Non-Cryst. Sol. 29,253 (1978). 12. J. L. Bjorkstam, S. Manzini, and M. Villa, Fast I0n TransnorL Vashishta, Mundy, Shenoy eds., Elsevier North Holland Inc. (1979) , p . 2 9 3 . 13. J. L. Bjorkstam, M. Villa, S. AIdrovani and M. Cortl, Nuclear and Electron Soectroscovies Avvlied to Materials Science, Kaufman and Shenoy, eds., Elsevier North Holland Inc. 289 (1981). 14. R. E. Walstedt, R. S. Berg, J. P. Remeika and R. Dupree, Sol. State Comm. 37, 209 (1981). 15. M. Villa and J. L. Bjorkstam, Phy. Rev. B 22, (1980).
5033
16. R.E. Walstedt, R. Dupree, J. P. Remeika, and A. Rodriguez, Phys. Rev. B 15~ 3442 (1977). U. Strom, Sol. State Ionics 8, 255 references therein.
2.
D. Wolf, J. Phy. Chem. Sol. 48,757
3.
J.C. Wang, J. B. Bates, T. Kaneda, H. Engstrom, D. F. Pickett, Jr., and Sang-il Chou, in: Fast ion transport in solids, eds. P. Vashishta, J. N. Mundy, and G. H. Shenoy (North-Holland, Amsterdam, 1979), 0.379.
20. K. L. Ngai, Comments Solid State Physics 9, (1980).
4.
G. V. Chandrashekar and L. M.Forster, Sol. State Comm. 27, 269 ( 1 9 7 8 ) .
21. M. H. Cohen and F. Reif, Solid State Physics 5, Seitz and Turnbull, eds., Academic Press (1957).
5.
C.C. Hunter, M.D. Ingrain and A. R. West, Sol. State
22. J . N . Dobbs, A. C. Anderson and W. Hayes, Phys. Rev. B 28, 3559 ( 1 9 8 3 ) .
lonics 8, 55 6.
(1983),
and
17. N. Bloembergen, E. M. Purcell and R. V. Pound, Phys. Rev. 7.3, 679 (1948).
I.
(1979).
(1983).
T. Tsurumi, G. Singh, and P. S. Nichoison, Solid State Ionics 23, 81 (1987).
18. E. Gobel, W. Miiller-Warmuth, H. Olyschlager, and H. Dutz, J. Mag. Res. 3_6, 371 (1979). 19. J.L. Bjorkstam and M. Villa, Phys. Rev. B 22, (1980).
5025 141
27A1 N M R S T U D Y O F M I X E D A L K A L I E F F E C T S I N I I - A L U M I N A D.E. H I N T E N L A N G * ,
E.J. H O L U P K A * * , P.J. B R A Y
Department of Physics, Brown University, Providence, RI 02912, USA and S.G. G R E E N B A U M
Department of Physics and Astronomy, Hunter Collegeof CUNY, New York, NY 10021, USA Received 17 August 1988; accepted for publication 22 December 1988
Nuclear spin-lattice relaxation measurements are reported for 27AI in Na-, K-, and Na^~3~Rai~.K" ~ h ~ mixed-aluminacationin the temperatUreand range 5-670K. shallow Tl-minimum is observed at compound is attributed to A substantlally altered population of two-level system (TLS) tunneling modes. The high temperature T1-minimum in the alloy crystal occurs at a significantly higher temprature than in either the Na- or K S-alumina. Both phenomena are discussed in terms of mixed ion pair distributions and are consistent with other manifestations of the mixed alkali effect in ~-alumina reported in the literature.
INTRODUCTION The crystalline fast ion conductor Na #-alumina has been the subject of many studies [1] which have led to a better understanding of fast ion transport processe in solids. Materials in the #-alumina family are quasi-two dimensional conductors in which the conducting species is usually an alkali or silver ion, but need not be restricted to these. High conductivities are obtained by incorporating an excess of the mobile species into the conducting plane, usually 20-30% in the form of alkali-oxide. The excess oxygen enters the conduction plane interstitially, incorporating a degree of disorder in the conduction plane. Several investigators have shown that #-alumina containing more than one conducting species of ion can exhibit behavior similar to the mixed-alkali effect that is observed in glasses [4-7]. The disordered conduction plane produces some glass-like properties in #-alumina [1,8]. Some of these properties are attributable to the presence of disorder modes, or two level systems (TLS), that are observable at low temperatures [1]. Previous investigations have shown that the NMR spin-lattice relaxation time (T1) in #-alumina exhibits a temperature dependence at low temperatures similar to that obtained in glasses [9, 10]. The relaxation process responsible for this behavior is attributed to the presense of TLS. A nearest-neighbor tunneling defect can modulate the electric field gradient (efg) present at the site of a nucleus being studied by NMR, * Present address: Department of Nuclear Engineering, University of Florida, Gainesville, FL 32611, USA. Present address: Department of Physical Chemistry, University of Geneva, CH 1211 Geneva 4, Switzerland. 0 1 6 7 - 2 7 3 8 / 8 9 / $ 0 3 . 5 0 © E l s e v i e r S c i e n c e P u b l i s h e r s B.V. (North-Holland Physics Publishing Division)
thus enhancing quadrupolar relaxation [9-1 I]. This usually produces a temperature dependence of T 1 of the form T -a with 1
D.E. Hintenlang et al. / 27Al NMR study of mixed alkali effects
208
RESULTS Spin-lattice relaxation times were measured on Na, Nap ~-Ko 5 and K B-alumina as a function of temperature. At hlghel: temperatures (>200K), the 27A1 T 1 was measured only for Nao 5-Ko s and K B-alumina since Na #-alumina has been extensive'ly investigated in this temperature region [12, 13]. Although the magnetization recovery profile for the central transition of ~TAi (spin 5/2) is generally nonexponential, previous studies of B-alumina have shown that a single effective relaxation time can be employed as a reliable monitor of ionic or lattice motion [12, 14]. In particular the recovery profile is observed to be nearly temperature-independent for all three samples in this work, and it is therefore reasonable that variations in effective 27A1 T i reflect true dynamical differences between the samples. Ti is here defined as the time at which the magnetization recovers (1 - e -i) of its initial value. The spin-lattice relaxation times can be divided into roughly two temperature regions, a high temperture region where the relaxation rate is determined by ionic diffusion, and a low temperature region where diffusive motion is frozen out. The results of the ~TAI spin-lattice relaxation time measurement for Na, K and Nao s - K o s B-aluminas are presented in Fig. 1 for temperatui:es below 200K. Up to about 100K, T 1 appears to follow a power law, TlctT "a with a=l.ht0.03 and ~=0.87+0.07 for Na B-alumina and K Balumina, respectively. These two materials behave similarly except that the K #-alumina has relaxation times about an order of magnitude larger than those of Na B-alumina. The Nao.5-Ko. s B-alumina exhibits markedly different behavior [9]. At temperatures below ~I5K the relaxation time behavior for the mixed-alkali sample approximates that of
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Na B-alumina. As the temperature is further incre~ed, the relaxation time becomes longer until the onset of ionic motion where it decreases again. This produces a shallow minimum at about 30K. In the high temperature regime where the spin-lattice relaxation process is dominated by ionic motion, both K Balumina and Na, s-Ko 5 #-alumina exhibit behavior that is typical of the ZrAI relaxation times in Na #-alumina with some minor differences. The logarithm of the relaxation times for these samples are plotted as a function of reciprocal temperature in Fig. 2. Both curves exhibit a clear minimum and are asymmetric. The. K B-alumina curve is only slightly asymmetric while that of Nap 5-Ko 5 B-alumina is more asymmetric. These asymmetrl~s ar~ frequently observed in NMR but there is currently no universally accepted analysis of such minima. Additional room temperature measurements were performed at 16, 19, and 21 MHz, yielding the results that Tla~o1"19 and to1"25 for K and Nao.sKo. s B-alumina, respectively. A single'21 MHz measurement at 620K (significantly above the T 1 minimum) yielded no apparent frequency dependence of T 1 in this high temperature region. These findings are quite similar to those obtained in Na Balumina by other investigators [15, 16], where Tl,~OJ1"2s was observed on the low temperature side of the minimum and little or no frequency dependence was observed on the high temperature side of the minimum. Spin-lattice relaxation in #-alumina and disordered or anisotropic materials, in general, is not adequately described by the Bloembergen, Pound and Purcell (BPP) formalism [17] which predicts a symmetric temperature dependence on both sides of the minimum, and a quadratic frequency dependence of T) on the low temperature side. Previous studies have treatea the data in a variety of ways. One method is to ignore the experimentally observed frequency dependence of T 1 and apply the high and low temperature limits of the BPP results to the high and low temperature sides of the T 1 minimum independently. The activation energy determined from the high temperature region often agrees with results obtained by conductivity measurement. The T l results may also be described by invoking a distribution of activation energies as shown by several investigators [16, 18]. These theories adequately describe
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Effective spin-lattice relaxation time for 9"7A1 in Na, Nao.sKo.s, and K B-alumina at low temperatures.
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High temperature spin-lattice relaxation time for 27A1 in the Nao.sKo.5 and K #-alumina.
D.E. Hintenlang et al. /27Al NMR study of mixed alkali effects most data for glasses where a distribution of ionic sites might be expected. It is doubtful, however, that these models should be applied to ~-alumina since there is little physical evidence to suggest such a distribution of sites. Other treatments include a two-dimensinal continuum diffusion model developed by Bjorkstam and Villa [15, 19] which employs non-exponential correlation functions, and the universal dissipation-fluctuation formalism (as applied to T 1 measurements) elaborated by Ngai [20]. However both theories predict T 1- activation energies on the high T side of the minimum that are too large by almost a factor of three for both samples, based on the observed low T activation energy (0.145eV for both samples) and frequency dependence as input parameters• The high T activation energies from Fig. 2 are 0.155 and 0•22 eV for K and Nao.sKo.s 0-alumina, respectively. It is apparent that no single theoretical description of nuclear spin-lattice relaxation adequately explains all aspects of the data. Therefore it is reasoned that a simple BPP-like theory, applied to each side of the T t minimum as described above, is at least as meaningful as an analysis by any of the other currently proposed theories. This has the advantage that the resulting activation energies are easily compared to those obtained by the vast majority of other NMR studies. In addition, the same approach applied consistently to three similar materials (Na, K, and the mixed p-alumina) is expected to yield a valid reflection of systematic differences between samples. We therefore treat our data as approximately fitting the relation given by Cohen and Reif [19] for quadrupolar relaxation by diffusing charges: T1-1
c~
1
+
f (5/2) ~ o =
where We is the Larmor frequency and r = r o exp (E=/kT), by fitting the data with a different activation energy on each side of the minimum• This expression predicts a minimum when the condition wgr = (2/5) /2 is obtained. This result is not significantly different from the predictions of the other theories discussed above, which yield t~or',l at the T 1 minimum• From Fig. 2 it is clear that the T x minimum occurs at significantly higher temperature for the mixed alkali ~-alumina (490K) than for K /~-alumina (340K). the attempt frequency vo ro "1, where rQ = r exp (-E=/kT), is calculated from the temperature of the T z minimum and the high T activation energy. The results are vo = 1.35x101°s "1 and 7.7x109s "1 for K and Nao.sKo.s ~-alumina, respectively. Previous measurements on Na /~-alumina found the T 1 minimum occurring at 190K at a frequency of 21 MHz [12]. This data, interpreted for consistency according to the model employed for the other two materials above yields an attempt frequency of approximately 5xl01°s "1. DISCUSSION The Tlc~T"= dependence observed at low temperatures is characteristic of the relaxation by TLS in disordered solids. The significance of small differences in a has, however, not been determined. The qualitative behavior of Na o 5-K0 s B" alumina is markedly different than that of the other samples indicating that the observed TLS are somehow related to the distribution of alkali ions. There appears to he a decrease in the density of TLS that provide relaxation in the 25-35K region, resulting in the observed shallow minimum. A possible mechanism is the creation of Na-K pairs at the expense of Na-Na pairs as K replaces Na. At low temperatures alkali ions will be located in Beevers-Ross (BR) sites and mid-Oxygen (toO) sites near interstitial oxygen ions
209
[2]. Dobbs et al. [22] have determined that the density of TLS in Na ~-alumina is independent of excess Na at temperatures below 2K. Since the number of m e sites varies with excess stoichiometry while the number of BR sites is independent of stoichiometry, it seems reasonable to hypothesize that the TLS associated with BR sites are primarily responsible for the relaxation at the lowest temperatures. A possible identification of a low-temperature single particle tunneling mode involves the triangular region near BR sites, in which two of the three positions around the triangle may be occupied with nearly equal probability, as suggested by Strom [1]. Consequently, the potential wells associated with this configuration would exhibit very little asymmetry. At higher temperatures other possible configurational tunneling processes may involve pairs of ions distributed among the three m e sites or even larger groups of ions moving cooperatively within oxygen-cation pair clusters [1]. The TLS associated with the latter are likely to be more asymmetric and responsible for relaxation at slightly higher temperatures. As K is substituted for Na, mixed alkali (Na-K) pairs are formed at the m e sites. The TLS at these sites are now so asymmetric that the frequency of tunneling transitions is drastically reduced, and these systems can no longer provide an efficient relaxation mechanism. In addition, the presence of an attractive interaction between K + and Na + ions on m e sites inferred from X-ray scattering results. [6] would reduce further the tunneling probability. The relaxation time is correspondingly increased. There are still some Na-Na pairs present to provide relaxation, but their number is considerably reduced• A simple statistical argument shows that with replacement of 50% of the Na + ions by K +, the number of Na + ions in BR sites is reduced by 5096, but the number of Na-Na m e pairs is reduced by 75%. Recent evidence from X-ray diffraction measurements indicate that the cations do not populate the allowed sites randomly but, in fact, exhibit a marked site preference (with K + occupying BR sites preferentially) [6, 7]. It is postulated, nevertheless, that in the 50% Na material there are enough single-ion BR-associated TLS modes to provide an efficient relaxation mechanism, and that the observed increase in T t above 30K corresponds to a decrease in TLS modes associated with Na-Na pairs which presumably provide the dominant relaxation process in that temperature region. At temperatures above 100K, thermally activated motion of the alkali ions occurs• The motion of these ions couples to the 27AI via the quadrupole interaction to produce relaxation of the 27A1 nuclei. T h e 27AI spin-lattice relaxation time, therefore, reflects the motion of both alkali species• The activation energies that are obtained from the high temperature side of the T z vs T minimum are generally a s s u m e d to represent directly long-range diffusional processes. The high temperature activation energies obtained for K ~-alumina and Na o.5 - K 0.5 p-alumina (0 155 and 0 22 eV. respecUvely) are both somewhat lower than those obtained from conductivity [4]. This is characteristic of NMR experiments, and may be attributed to the fact that these measurements are more sensitive to local motion than some other techniques. The activation energy, even on the high temperature side of the minimum, will be more heavily weighted by the activation energies of local motions. Although the absolute magnitudes of the activation energies are lower than those obtained from conductivity measurements, the percentage change from K B-alumina to Na o s-Ko ~-alumina agrees well with the change observed by conductivity measurements [4]. The most dramatic change in the mixed-alkali ~-alumina •
"
"
210
D.E. Hintenlang et al. /2ZAl NMR study of mixed alkali effects
occurs in the temperature at which the T,-minimum occurs (Fig. 2). The minimum shifts from 340K in the case of K B-alumina, and ~I90K for Na B-aluminas [12], to 490K for Nao -Ko .~ 5 B-alumina." This result is similar to the shifts observed m other m,xed catmn B-alumina [13], and also implies that the attempt frequencies increase in the order Na, K, and mixed B-alumina as previously mentioned. Since the cooperative motion of cation pairs is required for the conduction process it is assumed that such motion is primarily responsible for the ~TAI relaxation at higher temperatures. It is therefore reasonable that the high temperature attempt frequency may be identified with some vibrational mode of the paired ions. .s
.
.
CONCLUSIONS Measurement of the 27A1 nuclear spin-lattice relaxation time over the temperature range 5-670K indicate both low and high temperature manifestations of the mixed alkali effect in Nao.s-Kos B-alumina. It is suggested that both phenomena result f'rom the presence of Na+K + cation pairs. The mixed cation pairs result in TLS modes with anomalously low transition rates leading to a shallow T~ minimum at ~30K, and in a higher activation energy aria reduced attempt frequency (as compared to Na and K Balumina) associated with diffusive motion. ACKNOWLEDGEMENT The authors acknowledge Dr. U. Strom of the Naval Research Laboratory for many illuminating discussions.
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